.. _Exciter: ================================================================================ Exciter ================================================================================ Exciter group for synchronous generators. Common Parameters: u, name, syn Common Variables: vout, vi Available models: EXDC2_, IEEEX1_, ESDC1A_, ESDC2A_, EXST1_, ESST3A_, SEXS_, IEEET1_, EXAC1_, EXAC2_, EXAC4_, ESST4B_, AC8B_, IEEET3_, ESAC1A_, ESST1A_, ESAC5A_ .. _EXDC2: -------------------------------------------------------------------------------- EXDC2 -------------------------------------------------------------------------------- EXDC2 model. Parameters ---------- +--------+------------------+--------------------------------------+---------+--------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +========+==================+======================================+=========+========+============+ | idx | | unique device idx | | | | +--------+------------------+--------------------------------------+---------+--------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | name | | device name | | | | +--------+------------------+--------------------------------------+---------+--------+------------+ | syn | | Synchronous generator idx | | | mandatory | +--------+------------------+--------------------------------------+---------+--------+------------+ | TR | :math:`T_R` | Sensing time constant | 0.010 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | TA | :math:`T_A` | Lag time constant in anti-windup lag | 0.040 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | TC | :math:`T_C` | Lead time constant in lead-lag | 1 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | TB | :math:`T_B` | Lag time constant in lead-lag | 1 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | TE | :math:`T_E` | Exciter integrator time constant | 0.800 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | TF1 | :math:`T_{F1}` | Feedback washout time constant | 1 | *p.u.* | non_zero | +--------+------------------+--------------------------------------+---------+--------+------------+ | KF1 | :math:`K_{F1}` | Feedback washout gain | 0.030 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | KA | :math:`K_A` | Gain in anti-windup lag TF | 40 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | KE | :math:`K_E` | Gain added to saturation | 1 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | VRMAX | :math:`V_{RMAX}` | Maximum excitation limit | 7.300 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | VRMIN | :math:`V_{RMIN}` | Minimum excitation limit | -7.300 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | E1 | :math:`E_1` | First saturation point | 0 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | SE1 | :math:`S_{E1}` | Value at first saturation point | 0 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | E2 | :math:`E_2` | Second saturation point | 1 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | SE2 | :math:`S_{E2}` | Value at second saturation point | 1 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | ug | :math:`u_g` | Generator online status | 0 | *bool* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | Sn | :math:`S_m` | Rated power from generator | 0 | *MVA* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | Vn | :math:`V_m` | Rated voltage from generator | 0 | *kV* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | bus | :math:`bus` | Bus idx of the generators | 0 | | | +--------+------------------+--------------------------------------+---------+--------+------------+ Variables --------- +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +=========+========================+==========+======================================================+========+============+ | vp | :math:`V_{p}` | State | Voltage after saturation feedback, before speed term | *p.u.* | v_str | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | LS_y | :math:`y_{LS}` | State | State in lag transfer function | | v_str | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | LL_x | :math:`x'_{LL}` | State | State in lead-lag | | v_str | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | LA_y | :math:`y_{LA}` | State | State in lag TF | | v_str | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | W_x | :math:`x'_{W}` | State | State in washout filter | | v_str | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | v | :math:`E_{term}` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | vout | :math:`v_{out}` | Algeb | Exciter final output voltage | | v_str | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | vref | :math:`V_{ref}` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | Se | :math:`S_e(|V_{out}|)` | Algeb | saturation output | | v_str | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | vi | :math:`V_{i}` | Algeb | Total input voltages | *p.u.* | v_str | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | LL_y | :math:`y_{LL}` | Algeb | Output of lead-lag | | v_str | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | W_y | :math:`y_{W}` | Algeb | Output of washout filter | | v_str | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | vf | :math:`v_{f}` | ExtAlgeb | Excitation field voltage to generator | | | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | Armature excitation current | | | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | a | :math:`\theta` | ExtAlgeb | Bus voltage phase angle | | | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | vbus | :math:`V` | ExtAlgeb | Bus voltage magnitude | | | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ Initialization Equations ------------------------ +---------+------------------------+----------+---------------------------+ | Name | Symbol | Type | Initial Value | +=========+========================+==========+===========================+ | vp | :math:`V_{p}` | State | :math:`v_{f0}` | +---------+------------------------+----------+---------------------------+ | LS_y | :math:`y_{LS}` | State | :math:`1.0 E_{term}` | +---------+------------------------+----------+---------------------------+ | LL_x | :math:`x'_{LL}` | State | :math:`V_{i}` | +---------+------------------------+----------+---------------------------+ | LA_y | :math:`y_{LA}` | State | :math:`K_{A} y_{LL}` | +---------+------------------------+----------+---------------------------+ | W_x | :math:`x'_{W}` | State | :math:`V_{p}` | +---------+------------------------+----------+---------------------------+ | omega | :math:`\omega` | ExtState | | +---------+------------------------+----------+---------------------------+ | v | :math:`E_{term}` | Algeb | :math:`V` | +---------+------------------------+----------+---------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} v_{f0}` | +---------+------------------------+----------+---------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`E_{term} + V_{b0}` | +---------+------------------------+----------+---------------------------+ | Se | :math:`S_e(|V_{out}|)` | Algeb | :math:`S_{e0}` | +---------+------------------------+----------+---------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`V_{b0}` | +---------+------------------------+----------+---------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`V_{i}` | +---------+------------------------+----------+---------------------------+ | W_y | :math:`y_{W}` | Algeb | :math:`0` | +---------+------------------------+----------+---------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | | +---------+------------------------+----------+---------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | | +---------+------------------------+----------+---------------------------+ | a | :math:`\theta` | ExtAlgeb | | +---------+------------------------+----------+---------------------------+ | vbus | :math:`V` | ExtAlgeb | | +---------+------------------------+----------+---------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+--------------------------------------------------------------------------+----------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+==========================================================================+================+ | vp | :math:`V_{p}` | State | :math:`u_{e} \left(- K_{E} V_{p} - S_e(|V_{out}|) V_{p} + y_{LA}\right)` | :math:`T_E` | +--------+-----------------+----------+--------------------------------------------------------------------------+----------------+ | LS_y | :math:`y_{LS}` | State | :math:`1.0 E_{term} - y_{LS}` | :math:`T_R` | +--------+-----------------+----------+--------------------------------------------------------------------------+----------------+ | LL_x | :math:`x'_{LL}` | State | :math:`V_{i} - x'_{LL}` | :math:`T_B` | +--------+-----------------+----------+--------------------------------------------------------------------------+----------------+ | LA_y | :math:`y_{LA}` | State | :math:`K_{A} y_{LL} - y_{LA}` | :math:`T_A` | +--------+-----------------+----------+--------------------------------------------------------------------------+----------------+ | W_x | :math:`x'_{W}` | State | :math:`V_{p} - x'_{W}` | :math:`T_{F1}` | +--------+-----------------+----------+--------------------------------------------------------------------------+----------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+--------------------------------------------------------------------------+----------------+ Algebraic Equations ----------------------------- +---------+------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+========================+==========+=====================================================================================================================================+ | v | :math:`E_{term}` | Algeb | :math:`- E_{term} + V` | +---------+------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`V_{p} \omega u_{e} - v_{out}` | +---------+------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`V_{ref0} - V_{ref}` | +---------+------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`S_e(|V_{out}|)` | Algeb | :math:`B^q_{SAT} z_{0}^{SL} \left(- A^q_{SAT} + V_{p}\right)^{2} - S_e(|V_{out}|) V_{p}` | +---------+------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`- V_{i} + V_{ref} - y_{LS} - y_{W}` | +---------+------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- x'_{LL} + y_{LL}\right) + T_{B} x'_{LL} - T_{B} y_{LL} + T_{C} \left(V_{i} - x'_{LL}\right)` | +---------+------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | W_y | :math:`y_{W}` | Algeb | :math:`K_{F1} \left(V_{p} - x'_{W}\right) - T_{F1} y_{W}` | +---------+------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | :math:`u_{e} \left(- v_{f0} + v_{out}\right)` | +---------+------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | :math:`0` | +---------+------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | :math:`0` | +---------+------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | :math:`0` | +---------+------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +==========+=======================+=============================================================================================================================================================================================================================================+=================+ | ue | :math:`u_e` | :math:`u u_{g}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E1 | :math:`E^{1c}_{SAT}` | :math:`E_{1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E2 | :math:`E^{2c}_{SAT}` | :math:`E_{2} - 2 z^{SE2}_{SAT} + 2` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE1 | :math:`SE^{1c}_{SAT}` | :math:`S_{E1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE2 | :math:`SE^{2c}_{SAT}` | :math:`S_{E2} - 2 z^{SE2}_{SAT} + 2` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_a | :math:`a_{SAT}` | :math:`\sqrt{\frac{E^{1c}_{SAT} SE^{1c}_{SAT}}{E^{2c}_{SAT} SE^{2c}_{SAT}}} \left(\operatorname{Indicator}{\left(SE^{2c}_{SAT} > 0 \right)} + \operatorname{Indicator}{\left(SE^{2c}_{SAT} < 0 \right)}\right)` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_A | :math:`A^q_{SAT}` | :math:`E^{2c}_{SAT} - \frac{E^{1c}_{SAT} - E^{2c}_{SAT}}{a_{SAT} - 1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_B | :math:`B^q_{SAT}` | :math:`\frac{E^{2c}_{SAT} SE^{2c}_{SAT} \left(a_{SAT} - 1\right)^{2} \left(\operatorname{Indicator}{\left(a_{SAT} > 0 \right)} + \operatorname{Indicator}{\left(a_{SAT} < 0 \right)}\right)}{\left(E^{1c}_{SAT} - E^{2c}_{SAT}\right)^{2}}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Se0 | :math:`S_{e0}` | :math:`\frac{B^q_{SAT} \left(A^q_{SAT} - v_{f0}\right)^{2} \operatorname{Indicator}{\left(v_{f0} > A^q_{SAT} \right)}}{- u_{g} + v_{f0} + 1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vr0 | :math:`V_{r0}` | :math:`v_{f0} \left(K_{E} + S_{e0}\right)` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vb0 | :math:`V_{b0}` | :math:`\frac{V_{r0}}{K_{A}}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`V_{ref}` | PostInitService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ Discretes ----------- +---------+------------------+------------+----------------+ | Name | Symbol | Type | Info | +=========+==================+============+================+ | SL | :math:`SL` | LessThan | | +---------+------------------+------------+----------------+ | LL_LT1 | :math:`LT_{LL}` | LessThan | | +---------+------------------+------------+----------------+ | LL_LT2 | :math:`LT_{LL}` | LessThan | | +---------+------------------+------------+----------------+ | LA_lim | :math:`lim_{LA}` | AntiWindup | Limiter in Lag | +---------+------------------+------------+----------------+ Blocks ------- +------+-------------+---------------+------------------------------+ | Name | Symbol | Type | Info | +======+=============+===============+==============================+ | SAT | :math:`SAT` | ExcQuadSat | Field voltage saturation | +------+-------------+---------------+------------------------------+ | LS | :math:`LS` | Lag | Sensing lag TF | +------+-------------+---------------+------------------------------+ | LL | :math:`LL` | LeadLag | Lead-lag for internal delays | +------+-------------+---------------+------------------------------+ | LA | :math:`LA` | LagAntiWindup | Anti-windup lag | +------+-------------+---------------+------------------------------+ | W | :math:`W` | Washout | Signal conditioner | +------+-------------+---------------+------------------------------+ Config Fields in [EXDC2] +---------------+--------+-------+---------------------------------------+-----------------+ | Option | Symbol | Value | Info | Accepted values | +===============+========+=======+=======================================+=================+ | allow_adjust | | 1 | allow adjusting upper or lower limits | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_lower | | 0 | adjust lower limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_upper | | 1 | adjust upper limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _IEEEX1: -------------------------------------------------------------------------------- IEEEX1 -------------------------------------------------------------------------------- IEEEX1 Type 1 exciter (DC) Derived from EXDC2 by varying the limiter bounds. Parameters ---------- +--------+------------------+--------------------------------------+---------+--------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +========+==================+======================================+=========+========+============+ | idx | | unique device idx | | | | +--------+------------------+--------------------------------------+---------+--------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | name | | device name | | | | +--------+------------------+--------------------------------------+---------+--------+------------+ | syn | | Synchronous generator idx | | | mandatory | +--------+------------------+--------------------------------------+---------+--------+------------+ | TR | :math:`T_R` | Sensing time constant | 0.010 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | TA | :math:`T_A` | Lag time constant in anti-windup lag | 0.040 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | TC | :math:`T_C` | Lead time constant in lead-lag | 1 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | TB | :math:`T_B` | Lag time constant in lead-lag | 1 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | TE | :math:`T_E` | Exciter integrator time constant | 0.800 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | TF1 | :math:`T_{F1}` | Feedback washout time constant | 1 | *p.u.* | non_zero | +--------+------------------+--------------------------------------+---------+--------+------------+ | KF1 | :math:`K_{F1}` | Feedback washout gain | 0.030 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | KA | :math:`K_A` | Gain in anti-windup lag TF | 40 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | KE | :math:`K_E` | Gain added to saturation | 1 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | VRMAX | :math:`V_{RMAX}` | Maximum excitation limit | 7.300 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | VRMIN | :math:`V_{RMIN}` | Minimum excitation limit | -7.300 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | E1 | :math:`E_1` | First saturation point | 0 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | SE1 | :math:`S_{E1}` | Value at first saturation point | 0 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | E2 | :math:`E_2` | Second saturation point | 1 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | SE2 | :math:`S_{E2}` | Value at second saturation point | 1 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | ug | :math:`u_g` | Generator online status | 0 | *bool* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | Sn | :math:`S_m` | Rated power from generator | 0 | *MVA* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | Vn | :math:`V_m` | Rated voltage from generator | 0 | *kV* | | +--------+------------------+--------------------------------------+---------+--------+------------+ | bus | :math:`bus` | Bus idx of the generators | 0 | | | +--------+------------------+--------------------------------------+---------+--------+------------+ Variables --------- +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +=========+========================+==========+======================================================+========+============+ | vp | :math:`V_{p}` | State | Voltage after saturation feedback, before speed term | *p.u.* | v_str | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | LS_y | :math:`y_{LS}` | State | State in lag transfer function | | v_str | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | LL_x | :math:`x'_{LL}` | State | State in lead-lag | | v_str | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | LA_y | :math:`y_{LA}` | State | State in lag TF | | v_str | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | W_x | :math:`x'_{W}` | State | State in washout filter | | v_str | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | v | :math:`E_{term}` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | vout | :math:`v_{out}` | Algeb | Exciter final output voltage | | v_str | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | vref | :math:`V_{ref}` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | Se | :math:`S_e(|V_{out}|)` | Algeb | saturation output | | v_str | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | vi | :math:`V_{i}` | Algeb | Total input voltages | *p.u.* | v_str | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | LL_y | :math:`y_{LL}` | Algeb | Output of lead-lag | | v_str | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | W_y | :math:`y_{W}` | Algeb | Output of washout filter | | v_str | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | vf | :math:`v_{f}` | ExtAlgeb | Excitation field voltage to generator | | | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | Armature excitation current | | | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | a | :math:`\theta` | ExtAlgeb | Bus voltage phase angle | | | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ | vbus | :math:`V` | ExtAlgeb | Bus voltage magnitude | | | +---------+------------------------+----------+------------------------------------------------------+--------+------------+ Initialization Equations ------------------------ +---------+------------------------+----------+---------------------------+ | Name | Symbol | Type | Initial Value | +=========+========================+==========+===========================+ | vp | :math:`V_{p}` | State | :math:`v_{f0}` | +---------+------------------------+----------+---------------------------+ | LS_y | :math:`y_{LS}` | State | :math:`1.0 E_{term}` | +---------+------------------------+----------+---------------------------+ | LL_x | :math:`x'_{LL}` | State | :math:`V_{i}` | +---------+------------------------+----------+---------------------------+ | LA_y | :math:`y_{LA}` | State | :math:`K_{A} y_{LL}` | +---------+------------------------+----------+---------------------------+ | W_x | :math:`x'_{W}` | State | :math:`V_{p}` | +---------+------------------------+----------+---------------------------+ | omega | :math:`\omega` | ExtState | | +---------+------------------------+----------+---------------------------+ | v | :math:`E_{term}` | Algeb | :math:`V` | +---------+------------------------+----------+---------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} v_{f0}` | +---------+------------------------+----------+---------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`E_{term} + V_{b0}` | +---------+------------------------+----------+---------------------------+ | Se | :math:`S_e(|V_{out}|)` | Algeb | :math:`S_{e0}` | +---------+------------------------+----------+---------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`V_{b0}` | +---------+------------------------+----------+---------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`V_{i}` | +---------+------------------------+----------+---------------------------+ | W_y | :math:`y_{W}` | Algeb | :math:`0` | +---------+------------------------+----------+---------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | | +---------+------------------------+----------+---------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | | +---------+------------------------+----------+---------------------------+ | a | :math:`\theta` | ExtAlgeb | | +---------+------------------------+----------+---------------------------+ | vbus | :math:`V` | ExtAlgeb | | +---------+------------------------+----------+---------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+--------------------------------------------------------------------------+----------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+==========================================================================+================+ | vp | :math:`V_{p}` | State | :math:`u_{e} \left(- K_{E} V_{p} - S_e(|V_{out}|) V_{p} + y_{LA}\right)` | :math:`T_E` | +--------+-----------------+----------+--------------------------------------------------------------------------+----------------+ | LS_y | :math:`y_{LS}` | State | :math:`1.0 E_{term} - y_{LS}` | :math:`T_R` | +--------+-----------------+----------+--------------------------------------------------------------------------+----------------+ | LL_x | :math:`x'_{LL}` | State | :math:`V_{i} - x'_{LL}` | :math:`T_B` | +--------+-----------------+----------+--------------------------------------------------------------------------+----------------+ | LA_y | :math:`y_{LA}` | State | :math:`K_{A} y_{LL} - y_{LA}` | :math:`T_A` | +--------+-----------------+----------+--------------------------------------------------------------------------+----------------+ | W_x | :math:`x'_{W}` | State | :math:`V_{p} - x'_{W}` | :math:`T_{F1}` | +--------+-----------------+----------+--------------------------------------------------------------------------+----------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+--------------------------------------------------------------------------+----------------+ Algebraic Equations ----------------------------- +---------+------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+========================+==========+=====================================================================================================================================+ | v | :math:`E_{term}` | Algeb | :math:`- E_{term} + V` | +---------+------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`V_{p} u_{e} - v_{out}` | +---------+------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`V_{ref0} - V_{ref}` | +---------+------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`S_e(|V_{out}|)` | Algeb | :math:`B^q_{SAT} z_{0}^{SL} \left(- A^q_{SAT} + V_{p}\right)^{2} - S_e(|V_{out}|) V_{p}` | +---------+------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`- V_{i} + V_{ref} - y_{LS} - y_{W}` | +---------+------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- x'_{LL} + y_{LL}\right) + T_{B} x'_{LL} - T_{B} y_{LL} + T_{C} \left(V_{i} - x'_{LL}\right)` | +---------+------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | W_y | :math:`y_{W}` | Algeb | :math:`K_{F1} \left(V_{p} - x'_{W}\right) - T_{F1} y_{W}` | +---------+------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | :math:`u_{e} \left(- v_{f0} + v_{out}\right)` | +---------+------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | :math:`0` | +---------+------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | :math:`0` | +---------+------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | :math:`0` | +---------+------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +==========+=======================+=============================================================================================================================================================================================================================================+=================+ | ue | :math:`u_e` | :math:`u u_{g}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E1 | :math:`E^{1c}_{SAT}` | :math:`E_{1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E2 | :math:`E^{2c}_{SAT}` | :math:`E_{2} - 2 z^{SE2}_{SAT} + 2` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE1 | :math:`SE^{1c}_{SAT}` | :math:`S_{E1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE2 | :math:`SE^{2c}_{SAT}` | :math:`S_{E2} - 2 z^{SE2}_{SAT} + 2` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_a | :math:`a_{SAT}` | :math:`\sqrt{\frac{E^{1c}_{SAT} SE^{1c}_{SAT}}{E^{2c}_{SAT} SE^{2c}_{SAT}}} \left(\operatorname{Indicator}{\left(SE^{2c}_{SAT} > 0 \right)} + \operatorname{Indicator}{\left(SE^{2c}_{SAT} < 0 \right)}\right)` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_A | :math:`A^q_{SAT}` | :math:`E^{2c}_{SAT} - \frac{E^{1c}_{SAT} - E^{2c}_{SAT}}{a_{SAT} - 1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_B | :math:`B^q_{SAT}` | :math:`\frac{E^{2c}_{SAT} SE^{2c}_{SAT} \left(a_{SAT} - 1\right)^{2} \left(\operatorname{Indicator}{\left(a_{SAT} > 0 \right)} + \operatorname{Indicator}{\left(a_{SAT} < 0 \right)}\right)}{\left(E^{1c}_{SAT} - E^{2c}_{SAT}\right)^{2}}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Se0 | :math:`S_{e0}` | :math:`\frac{B^q_{SAT} \left(A^q_{SAT} - v_{f0}\right)^{2} \operatorname{Indicator}{\left(v_{f0} > A^q_{SAT} \right)}}{- u_{g} + v_{f0} + 1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vr0 | :math:`V_{r0}` | :math:`v_{f0} \left(K_{E} + S_{e0}\right)` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vb0 | :math:`V_{b0}` | :math:`\frac{V_{r0}}{K_{A}}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`V_{ref}` | PostInitService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VRTMAX | :math:`V_{RMAX}V_T` | :math:`E_{term} V_{RMAX}` | VarService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VRTMIN | :math:`V_{RMIN}V_T` | :math:`E_{term} V_{RMIN}` | VarService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ Discretes ----------- +---------+------------------+------------+----------------+ | Name | Symbol | Type | Info | +=========+==================+============+================+ | SL | :math:`SL` | LessThan | | +---------+------------------+------------+----------------+ | LL_LT1 | :math:`LT_{LL}` | LessThan | | +---------+------------------+------------+----------------+ | LL_LT2 | :math:`LT_{LL}` | LessThan | | +---------+------------------+------------+----------------+ | LA_lim | :math:`lim_{LA}` | AntiWindup | Limiter in Lag | +---------+------------------+------------+----------------+ Blocks ------- +------+-------------+---------------+------------------------------+ | Name | Symbol | Type | Info | +======+=============+===============+==============================+ | SAT | :math:`SAT` | ExcQuadSat | Field voltage saturation | +------+-------------+---------------+------------------------------+ | LS | :math:`LS` | Lag | Sensing lag TF | +------+-------------+---------------+------------------------------+ | LL | :math:`LL` | LeadLag | Lead-lag for internal delays | +------+-------------+---------------+------------------------------+ | LA | :math:`LA` | LagAntiWindup | Anti-windup lag | +------+-------------+---------------+------------------------------+ | W | :math:`W` | Washout | Signal conditioner | +------+-------------+---------------+------------------------------+ Config Fields in [IEEEX1] +---------------+--------+-------+---------------------------------------+-----------------+ | Option | Symbol | Value | Info | Accepted values | +===============+========+=======+=======================================+=================+ | allow_adjust | | 1 | allow adjusting upper or lower limits | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_lower | | 0 | adjust lower limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_upper | | 1 | adjust upper limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _ESDC1A: -------------------------------------------------------------------------------- ESDC1A -------------------------------------------------------------------------------- ESDC1A model. This model derives from ESDC2A and changes the regular limits to "VRMAX" and "VRMIN". Parameters ---------- +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | Name | Symbol | Description | Default | Unit | Properties | +=========+==================+=====================================+=========+========+=======================+ | idx | | unique device idx | | | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | u | :math:`u` | connection status | 1 | *bool* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | name | | device name | | | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | syn | | Synchronous generator idx | | | mandatory | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | TR | :math:`T_R` | Sensing time constant | 0.010 | *p.u.* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | KA | :math:`K_A` | Regulator gain | 80 | | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | TA | :math:`T_A` | Lag time constant in regulator | 0.040 | *p.u.* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | TB | :math:`T_B` | Lag time constant in lead-lag | 1 | *p.u.* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | TC | :math:`T_C` | Lead time constant in lead-lag | 1 | *p.u.* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | VRMAX | :math:`V_{RMAX}` | Max. exc. limit (0-unlimited) | 7.300 | *p.u.* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | VRMIN | :math:`V_{RMIN}` | Min. excitation limit | -7.300 | *p.u.* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | KE | :math:`K_E` | Saturation feedback gain | 1 | *p.u.* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | TE | :math:`T_E` | Integrator time constant | 0.800 | *p.u.* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | KF | :math:`K_F` | Feedback gain | 0.100 | | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | TF1 | :math:`T_{F1}` | Feedback washout time constant | 1 | *p.u.* | non_zero,non_negative | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | Switch | :math:`S_w` | Switch that PSS/E did not implement | 0 | *bool* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | E1 | :math:`E_1` | First saturation point | 0 | *p.u.* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | SE1 | :math:`S_{E1}` | Value at first saturation point | 0 | *p.u.* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | E2 | :math:`E_2` | Second saturation point | 0 | *p.u.* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | SE2 | :math:`S_{E2}` | Value at second saturation point | 0 | *p.u.* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | ug | :math:`u_g` | Generator online status | 0 | *bool* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | Sn | :math:`S_m` | Rated power from generator | 0 | *MVA* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | Vn | :math:`V_m` | Rated voltage from generator | 0 | *kV* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | bus | :math:`bus` | Bus idx of the generators | 0 | | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ Variables --------- +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +=========+================================+==========+=======================================+========+============+ | LG_y | :math:`y_{LG}` | State | State in lag transfer function | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | LL_x | :math:`x'_{LL}` | State | State in lead-lag | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | LA_y | :math:`y_{LA}` | State | State in lag TF | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | INT_y | :math:`y_{INT}` | State | Integrator output | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | WF_x | :math:`x'_{WF}` | State | State in washout filter | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | v | :math:`E_{term}` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | vout | :math:`v_{out}` | Algeb | Exciter final output voltage | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | vref | :math:`V_{ref}` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | vi | :math:`V_{i}` | Algeb | Total input voltages | *p.u.* | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | LL_y | :math:`y_{LL}` | Algeb | Output of lead-lag | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | UEL | :math:`U_{EL}` | Algeb | Interface var for under exc. limiter | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | HG_y | :math:`y_{HG}` | Algeb | HVGate output | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | Se | :math:`V_{out}*S_e(|V_{out}|)` | Algeb | saturation output | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | VFE | :math:`V_{FE}` | Algeb | Combined saturation feedback | *p.u.* | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | WF_y | :math:`y_{WF}` | Algeb | Output of washout filter | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | vf | :math:`v_{f}` | ExtAlgeb | Excitation field voltage to generator | | | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | Armature excitation current | | | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | a | :math:`\theta` | ExtAlgeb | Bus voltage phase angle | | | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | vbus | :math:`V` | ExtAlgeb | Bus voltage magnitude | | | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ Initialization Equations ------------------------ +---------+--------------------------------+----------+-----------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+================================+==========+===============================================+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term}` | +---------+--------------------------------+----------+-----------------------------------------------+ | LL_x | :math:`x'_{LL}` | State | :math:`V_{i}` | +---------+--------------------------------+----------+-----------------------------------------------+ | LA_y | :math:`y_{LA}` | State | :math:`K_{A} y_{LL}` | +---------+--------------------------------+----------+-----------------------------------------------+ | INT_y | :math:`y_{INT}` | State | :math:`v_{f0}` | +---------+--------------------------------+----------+-----------------------------------------------+ | WF_x | :math:`x'_{WF}` | State | :math:`y_{INT}` | +---------+--------------------------------+----------+-----------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+--------------------------------+----------+-----------------------------------------------+ | v | :math:`E_{term}` | Algeb | :math:`V` | +---------+--------------------------------+----------+-----------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} v_{f0}` | +---------+--------------------------------+----------+-----------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`E_{term} + \frac{V_{FE0}}{K_{A}}` | +---------+--------------------------------+----------+-----------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`\frac{V_{FE0}}{K_{A}}` | +---------+--------------------------------+----------+-----------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`V_{i}` | +---------+--------------------------------+----------+-----------------------------------------------+ | UEL | :math:`U_{EL}` | Algeb | :math:`0` | +---------+--------------------------------+----------+-----------------------------------------------+ | HG_y | :math:`y_{HG}` | Algeb | :math:`HG_{lt z0} U_{EL} + HG_{lt z1} y_{LL}` | +---------+--------------------------------+----------+-----------------------------------------------+ | Se | :math:`V_{out}*S_e(|V_{out}|)` | Algeb | :math:`S_{e0}` | +---------+--------------------------------+----------+-----------------------------------------------+ | VFE | :math:`V_{FE}` | Algeb | :math:`V_{FE0}` | +---------+--------------------------------+----------+-----------------------------------------------+ | WF_y | :math:`y_{WF}` | Algeb | :math:`0` | +---------+--------------------------------+----------+-----------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | | +---------+--------------------------------+----------+-----------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | | +---------+--------------------------------+----------+-----------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | | +---------+--------------------------------+----------+-----------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | | +---------+--------------------------------+----------+-----------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+----------------------------------------------+----------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+==============================================+================+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term} - y_{LG}` | :math:`T_R` | +--------+-----------------+----------+----------------------------------------------+----------------+ | LL_x | :math:`x'_{LL}` | State | :math:`V_{i} - x'_{LL}` | :math:`T_B` | +--------+-----------------+----------+----------------------------------------------+----------------+ | LA_y | :math:`y_{LA}` | State | :math:`K_{A} y_{LL} - y_{LA}` | :math:`T_A` | +--------+-----------------+----------+----------------------------------------------+----------------+ | INT_y | :math:`y_{INT}` | State | :math:`u_{e} \left(- V_{FE} + y_{LA}\right)` | :math:`T_E` | +--------+-----------------+----------+----------------------------------------------+----------------+ | WF_x | :math:`x'_{WF}` | State | :math:`- x'_{WF} + y_{INT}` | :math:`T_{F1}` | +--------+-----------------+----------+----------------------------------------------+----------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+----------------------------------------------+----------------+ Algebraic Equations ----------------------------- +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+================================+==========+=====================================================================================================================================+ | v | :math:`E_{term}` | Algeb | :math:`- E_{term} + V` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`- v_{out} + y_{INT}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`V_{ref0} - V_{ref}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`- E_{term} - V_{i} + V_{ref} - y_{WF}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- x'_{LL} + y_{LL}\right) + T_{B} x'_{LL} - T_{B} y_{LL} + T_{C} \left(V_{i} - x'_{LL}\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`U_{EL}` | Algeb | :math:`- U_{EL}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | HG_y | :math:`y_{HG}` | Algeb | :math:`HG_{lt z0} U_{EL} + HG_{lt z1} y_{LL} - y_{HG}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`V_{out}*S_e(|V_{out}|)` | Algeb | :math:`B^q_{SAT} z_{0}^{SL} \left(- A^q_{SAT} + y_{INT}\right)^{2} - V_{out}*S_e(|V_{out}|)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | VFE | :math:`V_{FE}` | Algeb | :math:`K_{E} y_{INT} - V_{FE} + V_{out}*S_e(|V_{out}|)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`y_{WF}` | Algeb | :math:`K_{F} \left(- x'_{WF} + y_{INT}\right) - T_{F1} y_{WF}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | :math:`u_{e} \left(- v_{f0} + v_{out}\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | :math:`0` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | :math:`0` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | :math:`0` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +==========+=======================+=============================================================================================================================================================================================================================================+=================+ | ue | :math:`u_e` | :math:`u u_{g}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VRMAXc | :math:`VRMAXc` | :math:`V_{RMAX} - 999 z_{VRMAX} + 999` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E1 | :math:`E^{1c}_{SAT}` | :math:`E_{1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E2 | :math:`E^{2c}_{SAT}` | :math:`E_{2} - 2 z^{SE2}_{SAT} + 2` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE1 | :math:`SE^{1c}_{SAT}` | :math:`S_{E1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE2 | :math:`SE^{2c}_{SAT}` | :math:`S_{E2} - 2 z^{SE2}_{SAT} + 2` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_a | :math:`a_{SAT}` | :math:`\sqrt{\frac{E^{1c}_{SAT} SE^{1c}_{SAT}}{E^{2c}_{SAT} SE^{2c}_{SAT}}} \left(\operatorname{Indicator}{\left(SE^{2c}_{SAT} > 0 \right)} + \operatorname{Indicator}{\left(SE^{2c}_{SAT} < 0 \right)}\right)` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_A | :math:`A^q_{SAT}` | :math:`E^{2c}_{SAT} - \frac{E^{1c}_{SAT} - E^{2c}_{SAT}}{a_{SAT} - 1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_B | :math:`B^q_{SAT}` | :math:`\frac{E^{2c}_{SAT} SE^{2c}_{SAT} \left(a_{SAT} - 1\right)^{2} \left(\operatorname{Indicator}{\left(a_{SAT} > 0 \right)} + \operatorname{Indicator}{\left(a_{SAT} < 0 \right)}\right)}{\left(E^{1c}_{SAT} - E^{2c}_{SAT}\right)^{2}}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Se0 | :math:`S_{e0}` | :math:`B^q_{SAT} \left(A^q_{SAT} - v_{f0}\right)^{2} \operatorname{Indicator}{\left(v_{f0} > A^q_{SAT} \right)}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vfe0 | :math:`V_{FE0}` | :math:`K_{E} v_{f0} + S_{e0}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`V_{ref}` | PostInitService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VRU | :math:`V_{RMAX}` | :math:`VRMAXc` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VRL | :math:`V_{RMIN}` | :math:`V_{RMIN}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ Discretes ----------- +---------+-------------------+------------+----------------+ | Name | Symbol | Type | Info | +=========+===================+============+================+ | LL_LT1 | :math:`LT_{LL}` | LessThan | | +---------+-------------------+------------+----------------+ | LL_LT2 | :math:`LT_{LL}` | LessThan | | +---------+-------------------+------------+----------------+ | HG_lt | :math:`None_{HG}` | LessThan | | +---------+-------------------+------------+----------------+ | LA_lim | :math:`lim_{LA}` | AntiWindup | Limiter in Lag | +---------+-------------------+------------+----------------+ | SL | :math:`SL` | LessThan | | +---------+-------------------+------------+----------------+ Blocks ------- +------+-------------+---------------+-----------------------------+ | Name | Symbol | Type | Info | +======+=============+===============+=============================+ | LG | :math:`LG` | Lag | Transducer delay | +------+-------------+---------------+-----------------------------+ | SAT | :math:`SAT` | ExcQuadSat | Field voltage saturation | +------+-------------+---------------+-----------------------------+ | LL | :math:`LL` | LeadLag | Lead-lag compensator | +------+-------------+---------------+-----------------------------+ | HG | :math:`HG` | HVGate | HVGate for under excitation | +------+-------------+---------------+-----------------------------+ | LA | :math:`LA` | LagAntiWindup | Anti-windup lag | +------+-------------+---------------+-----------------------------+ | INT | :math:`INT` | Integrator | Integrator | +------+-------------+---------------+-----------------------------+ | WF | :math:`WF` | Washout | Feedback to input | +------+-------------+---------------+-----------------------------+ Config Fields in [ESDC1A] +---------------+--------+-------+---------------------------------------+-----------------+ | Option | Symbol | Value | Info | Accepted values | +===============+========+=======+=======================================+=================+ | allow_adjust | | 1 | allow adjusting upper or lower limits | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_lower | | 0 | adjust lower limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_upper | | 1 | adjust upper limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _ESDC2A: -------------------------------------------------------------------------------- ESDC2A -------------------------------------------------------------------------------- ESDC2A model. This model is implemented as described in the PSS/E manual, except that the HVGate is not in use. Due to the HVGate and saturation function, the results are close to but different from TSAT. Parameters ---------- +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | Name | Symbol | Description | Default | Unit | Properties | +=========+==================+=====================================+=========+========+=======================+ | idx | | unique device idx | | | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | u | :math:`u` | connection status | 1 | *bool* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | name | | device name | | | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | syn | | Synchronous generator idx | | | mandatory | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | TR | :math:`T_R` | Sensing time constant | 0.010 | *p.u.* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | KA | :math:`K_A` | Regulator gain | 80 | | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | TA | :math:`T_A` | Lag time constant in regulator | 0.040 | *p.u.* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | TB | :math:`T_B` | Lag time constant in lead-lag | 1 | *p.u.* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | TC | :math:`T_C` | Lead time constant in lead-lag | 1 | *p.u.* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | VRMAX | :math:`V_{RMAX}` | Max. exc. limit (0-unlimited) | 7.300 | *p.u.* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | VRMIN | :math:`V_{RMIN}` | Min. excitation limit | -7.300 | *p.u.* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | KE | :math:`K_E` | Saturation feedback gain | 1 | *p.u.* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | TE | :math:`T_E` | Integrator time constant | 0.800 | *p.u.* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | KF | :math:`K_F` | Feedback gain | 0.100 | | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | TF1 | :math:`T_{F1}` | Feedback washout time constant | 1 | *p.u.* | non_zero,non_negative | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | Switch | :math:`S_w` | Switch that PSS/E did not implement | 0 | *bool* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | E1 | :math:`E_1` | First saturation point | 0 | *p.u.* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | SE1 | :math:`S_{E1}` | Value at first saturation point | 0 | *p.u.* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | E2 | :math:`E_2` | Second saturation point | 0 | *p.u.* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | SE2 | :math:`S_{E2}` | Value at second saturation point | 0 | *p.u.* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | ug | :math:`u_g` | Generator online status | 0 | *bool* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | Sn | :math:`S_m` | Rated power from generator | 0 | *MVA* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | Vn | :math:`V_m` | Rated voltage from generator | 0 | *kV* | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ | bus | :math:`bus` | Bus idx of the generators | 0 | | | +---------+------------------+-------------------------------------+---------+--------+-----------------------+ Variables --------- +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +=========+================================+==========+=======================================+========+============+ | LG_y | :math:`y_{LG}` | State | State in lag transfer function | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | LL_x | :math:`x'_{LL}` | State | State in lead-lag | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | LA_y | :math:`y_{LA}` | State | State in lag TF | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | INT_y | :math:`y_{INT}` | State | Integrator output | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | WF_x | :math:`x'_{WF}` | State | State in washout filter | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | v | :math:`E_{term}` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | vout | :math:`v_{out}` | Algeb | Exciter final output voltage | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | vref | :math:`V_{ref}` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | vi | :math:`V_{i}` | Algeb | Total input voltages | *p.u.* | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | LL_y | :math:`y_{LL}` | Algeb | Output of lead-lag | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | UEL | :math:`U_{EL}` | Algeb | Interface var for under exc. limiter | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | HG_y | :math:`y_{HG}` | Algeb | HVGate output | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | Se | :math:`V_{out}*S_e(|V_{out}|)` | Algeb | saturation output | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | VFE | :math:`V_{FE}` | Algeb | Combined saturation feedback | *p.u.* | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | WF_y | :math:`y_{WF}` | Algeb | Output of washout filter | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | vf | :math:`v_{f}` | ExtAlgeb | Excitation field voltage to generator | | | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | Armature excitation current | | | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | a | :math:`\theta` | ExtAlgeb | Bus voltage phase angle | | | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | vbus | :math:`V` | ExtAlgeb | Bus voltage magnitude | | | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ Initialization Equations ------------------------ +---------+--------------------------------+----------+-----------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+================================+==========+===============================================+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term}` | +---------+--------------------------------+----------+-----------------------------------------------+ | LL_x | :math:`x'_{LL}` | State | :math:`V_{i}` | +---------+--------------------------------+----------+-----------------------------------------------+ | LA_y | :math:`y_{LA}` | State | :math:`K_{A} y_{LL}` | +---------+--------------------------------+----------+-----------------------------------------------+ | INT_y | :math:`y_{INT}` | State | :math:`v_{f0}` | +---------+--------------------------------+----------+-----------------------------------------------+ | WF_x | :math:`x'_{WF}` | State | :math:`y_{INT}` | +---------+--------------------------------+----------+-----------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+--------------------------------+----------+-----------------------------------------------+ | v | :math:`E_{term}` | Algeb | :math:`V` | +---------+--------------------------------+----------+-----------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} v_{f0}` | +---------+--------------------------------+----------+-----------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`E_{term} + \frac{V_{FE0}}{K_{A}}` | +---------+--------------------------------+----------+-----------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`\frac{V_{FE0}}{K_{A}}` | +---------+--------------------------------+----------+-----------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`V_{i}` | +---------+--------------------------------+----------+-----------------------------------------------+ | UEL | :math:`U_{EL}` | Algeb | :math:`0` | +---------+--------------------------------+----------+-----------------------------------------------+ | HG_y | :math:`y_{HG}` | Algeb | :math:`HG_{lt z0} U_{EL} + HG_{lt z1} y_{LL}` | +---------+--------------------------------+----------+-----------------------------------------------+ | Se | :math:`V_{out}*S_e(|V_{out}|)` | Algeb | :math:`S_{e0}` | +---------+--------------------------------+----------+-----------------------------------------------+ | VFE | :math:`V_{FE}` | Algeb | :math:`V_{FE0}` | +---------+--------------------------------+----------+-----------------------------------------------+ | WF_y | :math:`y_{WF}` | Algeb | :math:`0` | +---------+--------------------------------+----------+-----------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | | +---------+--------------------------------+----------+-----------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | | +---------+--------------------------------+----------+-----------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | | +---------+--------------------------------+----------+-----------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | | +---------+--------------------------------+----------+-----------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+----------------------------------------------+----------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+==============================================+================+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term} - y_{LG}` | :math:`T_R` | +--------+-----------------+----------+----------------------------------------------+----------------+ | LL_x | :math:`x'_{LL}` | State | :math:`V_{i} - x'_{LL}` | :math:`T_B` | +--------+-----------------+----------+----------------------------------------------+----------------+ | LA_y | :math:`y_{LA}` | State | :math:`K_{A} y_{LL} - y_{LA}` | :math:`T_A` | +--------+-----------------+----------+----------------------------------------------+----------------+ | INT_y | :math:`y_{INT}` | State | :math:`u_{e} \left(- V_{FE} + y_{LA}\right)` | :math:`T_E` | +--------+-----------------+----------+----------------------------------------------+----------------+ | WF_x | :math:`x'_{WF}` | State | :math:`- x'_{WF} + y_{INT}` | :math:`T_{F1}` | +--------+-----------------+----------+----------------------------------------------+----------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+----------------------------------------------+----------------+ Algebraic Equations ----------------------------- +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+================================+==========+=====================================================================================================================================+ | v | :math:`E_{term}` | Algeb | :math:`- E_{term} + V` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`- v_{out} + y_{INT}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`V_{ref0} - V_{ref}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`- E_{term} - V_{i} + V_{ref} - y_{WF}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- x'_{LL} + y_{LL}\right) + T_{B} x'_{LL} - T_{B} y_{LL} + T_{C} \left(V_{i} - x'_{LL}\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`U_{EL}` | Algeb | :math:`- U_{EL}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | HG_y | :math:`y_{HG}` | Algeb | :math:`HG_{lt z0} U_{EL} + HG_{lt z1} y_{LL} - y_{HG}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`V_{out}*S_e(|V_{out}|)` | Algeb | :math:`B^q_{SAT} z_{0}^{SL} \left(- A^q_{SAT} + y_{INT}\right)^{2} - V_{out}*S_e(|V_{out}|)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | VFE | :math:`V_{FE}` | Algeb | :math:`K_{E} y_{INT} - V_{FE} + V_{out}*S_e(|V_{out}|)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`y_{WF}` | Algeb | :math:`K_{F} \left(- x'_{WF} + y_{INT}\right) - T_{F1} y_{WF}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | :math:`u_{e} \left(- v_{f0} + v_{out}\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | :math:`0` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | :math:`0` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | :math:`0` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +==========+=======================+=============================================================================================================================================================================================================================================+=================+ | ue | :math:`u_e` | :math:`u u_{g}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VRMAXc | :math:`VRMAXc` | :math:`V_{RMAX} - 999 z_{VRMAX} + 999` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E1 | :math:`E^{1c}_{SAT}` | :math:`E_{1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E2 | :math:`E^{2c}_{SAT}` | :math:`E_{2} - 2 z^{SE2}_{SAT} + 2` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE1 | :math:`SE^{1c}_{SAT}` | :math:`S_{E1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE2 | :math:`SE^{2c}_{SAT}` | :math:`S_{E2} - 2 z^{SE2}_{SAT} + 2` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_a | :math:`a_{SAT}` | :math:`\sqrt{\frac{E^{1c}_{SAT} SE^{1c}_{SAT}}{E^{2c}_{SAT} SE^{2c}_{SAT}}} \left(\operatorname{Indicator}{\left(SE^{2c}_{SAT} > 0 \right)} + \operatorname{Indicator}{\left(SE^{2c}_{SAT} < 0 \right)}\right)` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_A | :math:`A^q_{SAT}` | :math:`E^{2c}_{SAT} - \frac{E^{1c}_{SAT} - E^{2c}_{SAT}}{a_{SAT} - 1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_B | :math:`B^q_{SAT}` | :math:`\frac{E^{2c}_{SAT} SE^{2c}_{SAT} \left(a_{SAT} - 1\right)^{2} \left(\operatorname{Indicator}{\left(a_{SAT} > 0 \right)} + \operatorname{Indicator}{\left(a_{SAT} < 0 \right)}\right)}{\left(E^{1c}_{SAT} - E^{2c}_{SAT}\right)^{2}}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Se0 | :math:`S_{e0}` | :math:`B^q_{SAT} \left(A^q_{SAT} - v_{f0}\right)^{2} \operatorname{Indicator}{\left(v_{f0} > A^q_{SAT} \right)}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vfe0 | :math:`V_{FE0}` | :math:`K_{E} v_{f0} + S_{e0}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`V_{ref}` | PostInitService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VRU | :math:`V_T V_{RMAX}` | :math:`E_{term} VRMAXc` | VarService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VRL | :math:`V_T V_{RMIN}` | :math:`E_{term} V_{RMIN}` | VarService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ Discretes ----------- +---------+-------------------+------------+----------------+ | Name | Symbol | Type | Info | +=========+===================+============+================+ | LL_LT1 | :math:`LT_{LL}` | LessThan | | +---------+-------------------+------------+----------------+ | LL_LT2 | :math:`LT_{LL}` | LessThan | | +---------+-------------------+------------+----------------+ | HG_lt | :math:`None_{HG}` | LessThan | | +---------+-------------------+------------+----------------+ | LA_lim | :math:`lim_{LA}` | AntiWindup | Limiter in Lag | +---------+-------------------+------------+----------------+ | SL | :math:`SL` | LessThan | | +---------+-------------------+------------+----------------+ Blocks ------- +------+-------------+---------------+-----------------------------+ | Name | Symbol | Type | Info | +======+=============+===============+=============================+ | LG | :math:`LG` | Lag | Transducer delay | +------+-------------+---------------+-----------------------------+ | SAT | :math:`SAT` | ExcQuadSat | Field voltage saturation | +------+-------------+---------------+-----------------------------+ | LL | :math:`LL` | LeadLag | Lead-lag compensator | +------+-------------+---------------+-----------------------------+ | HG | :math:`HG` | HVGate | HVGate for under excitation | +------+-------------+---------------+-----------------------------+ | LA | :math:`LA` | LagAntiWindup | Anti-windup lag | +------+-------------+---------------+-----------------------------+ | INT | :math:`INT` | Integrator | Integrator | +------+-------------+---------------+-----------------------------+ | WF | :math:`WF` | Washout | Feedback to input | +------+-------------+---------------+-----------------------------+ Config Fields in [ESDC2A] +---------------+--------+-------+---------------------------------------+-----------------+ | Option | Symbol | Value | Info | Accepted values | +===============+========+=======+=======================================+=================+ | allow_adjust | | 1 | allow adjusting upper or lower limits | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_lower | | 0 | adjust lower limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_upper | | 1 | adjust upper limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _EXST1: -------------------------------------------------------------------------------- EXST1 -------------------------------------------------------------------------------- EXST1-type static excitation system. Parameters ---------- +--------+------------------+------------------------------+---------+--------+-----------------------+ | Name | Symbol | Description | Default | Unit | Properties | +========+==================+==============================+=========+========+=======================+ | idx | | unique device idx | | | | +--------+------------------+------------------------------+---------+--------+-----------------------+ | u | :math:`u` | connection status | 1 | *bool* | | +--------+------------------+------------------------------+---------+--------+-----------------------+ | name | | device name | | | | +--------+------------------+------------------------------+---------+--------+-----------------------+ | syn | | Synchronous generator idx | | | mandatory | +--------+------------------+------------------------------+---------+--------+-----------------------+ | TR | :math:`T_R` | Measurement delay | 0.010 | | | +--------+------------------+------------------------------+---------+--------+-----------------------+ | VIMAX | :math:`V_{IMAX}` | Max. input voltage | 0.200 | | | +--------+------------------+------------------------------+---------+--------+-----------------------+ | VIMIN | :math:`V_{IMIN}` | Min. input voltage | 0 | | | +--------+------------------+------------------------------+---------+--------+-----------------------+ | TC | :math:`T_C` | LL numerator | 1 | | | +--------+------------------+------------------------------+---------+--------+-----------------------+ | TB | :math:`T_B` | LL denominator | 1 | | | +--------+------------------+------------------------------+---------+--------+-----------------------+ | KA | :math:`K_A` | Regulator gain | 80 | | | +--------+------------------+------------------------------+---------+--------+-----------------------+ | TA | :math:`T_A` | Regulator delay | 0.050 | | | +--------+------------------+------------------------------+---------+--------+-----------------------+ | VRMAX | :math:`V_{RMAX}` | Max. regulator output | 8 | | | +--------+------------------+------------------------------+---------+--------+-----------------------+ | VRMIN | :math:`V_{RMIN}` | Min. regulator output | -3 | | | +--------+------------------+------------------------------+---------+--------+-----------------------+ | KC | :math:`K_C` | Coef. for Ifd | 0.200 | | | +--------+------------------+------------------------------+---------+--------+-----------------------+ | KF | :math:`K_F` | Feedback gain | 0.100 | | | +--------+------------------+------------------------------+---------+--------+-----------------------+ | TF | :math:`T_F` | Feedback delay | 1 | | non_zero,non_negative | +--------+------------------+------------------------------+---------+--------+-----------------------+ | ug | :math:`u_g` | Generator online status | 0 | *bool* | | +--------+------------------+------------------------------+---------+--------+-----------------------+ | Sn | :math:`S_m` | Rated power from generator | 0 | *MVA* | | +--------+------------------+------------------------------+---------+--------+-----------------------+ | Vn | :math:`V_m` | Rated voltage from generator | 0 | *kV* | | +--------+------------------+------------------------------+---------+--------+-----------------------+ | bus | :math:`bus` | Bus idx of the generators | 0 | | | +--------+------------------+------------------------------+---------+--------+-----------------------+ Variables --------- +---------+----------------------+----------+---------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +=========+======================+==========+=======================================+========+============+ | LG_y | :math:`y_{LG}` | State | State in lag transfer function | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | LL_x | :math:`x'_{LL}` | State | State in lead-lag | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | LR_y | :math:`y_{LR}` | State | State in lag transfer function | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | WF_x | :math:`x'_{WF}` | State | State in washout filter | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | v | :math:`E_{term}` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vout | :math:`v_{out}` | Algeb | Exciter final output voltage | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vref | :math:`V_{ref}` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vi | :math:`V_{i}` | Algeb | Total input voltages | *p.u.* | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vl | :math:`V_{l}` | Algeb | Input after limiter | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | LL_y | :math:`y_{LL}` | Algeb | Output of lead-lag | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | WF_y | :math:`y_{WF}` | Algeb | Output of washout filter | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vfmax | :math:`V_{fmax}` | Algeb | Upper bound of output limiter | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vfmin | :math:`V_{fmin}` | Algeb | Lower bound of output limiter | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vf | :math:`v_{f}` | ExtAlgeb | Excitation field voltage to generator | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | Armature excitation current | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | a | :math:`\theta` | ExtAlgeb | Bus voltage phase angle | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vbus | :math:`V` | ExtAlgeb | Bus voltage magnitude | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ Initialization Equations ------------------------ +---------+----------------------+----------+-------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+======================+==========+=========================================================================+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term}` | +---------+----------------------+----------+-------------------------------------------------------------------------+ | LL_x | :math:`x'_{LL}` | State | :math:`V_{l}` | +---------+----------------------+----------+-------------------------------------------------------------------------+ | LR_y | :math:`y_{LR}` | State | :math:`K_{A} y_{LL}` | +---------+----------------------+----------+-------------------------------------------------------------------------+ | WF_x | :math:`x'_{WF}` | State | :math:`y_{LR}` | +---------+----------------------+----------+-------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+----------------------+----------+-------------------------------------------------------------------------+ | v | :math:`E_{term}` | Algeb | :math:`V` | +---------+----------------------+----------+-------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} v_{f0}` | +---------+----------------------+----------+-------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`E_{term} + \frac{v_{f0}}{K_{A}}` | +---------+----------------------+----------+-------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`\frac{v_{f0}}{K_{A}}` | +---------+----------------------+----------+-------------------------------------------------------------------------+ | vl | :math:`V_{l}` | Algeb | :math:`V_{i} z_{i}^{HLI} + V_{IMAX} z_{u}^{HLI} + V_{IMIN} z_{l}^{HLI}` | +---------+----------------------+----------+-------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`V_{l}` | +---------+----------------------+----------+-------------------------------------------------------------------------+ | WF_y | :math:`y_{WF}` | Algeb | :math:`0` | +---------+----------------------+----------+-------------------------------------------------------------------------+ | vfmax | :math:`V_{fmax}` | Algeb | :math:`- K_{C} X_{ad}I_{fd} + V_{RMAX}` | +---------+----------------------+----------+-------------------------------------------------------------------------+ | vfmin | :math:`V_{fmin}` | Algeb | :math:`- K_{C} X_{ad}I_{fd} + V_{RMIN}` | +---------+----------------------+----------+-------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+----------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+==================================+=============+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term} - y_{LG}` | :math:`T_R` | +--------+-----------------+----------+----------------------------------+-------------+ | LL_x | :math:`x'_{LL}` | State | :math:`V_{l} - x'_{LL}` | :math:`T_B` | +--------+-----------------+----------+----------------------------------+-------------+ | LR_y | :math:`y_{LR}` | State | :math:`K_{A} y_{LL} - y_{LR}` | :math:`T_A` | +--------+-----------------+----------+----------------------------------+-------------+ | WF_x | :math:`x'_{WF}` | State | :math:`- x'_{WF} + y_{LR}` | :math:`T_F` | +--------+-----------------+----------+----------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+----------------------------------+-------------+ Algebraic Equations ----------------------------- +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+======================+==========+=====================================================================================================================================+ | v | :math:`E_{term}` | Algeb | :math:`- E_{term} + V` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} \left(V_{fmax} z_{u}^{HLR} + V_{fmin} z_{l}^{HLR} + y_{LR} z_{i}^{HLR}\right) - v_{out}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`V_{ref0} - V_{ref}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`- V_{i} + V_{ref} - y_{LG} - y_{WF}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vl | :math:`V_{l}` | Algeb | :math:`V_{i} z_{i}^{HLI} - V_{l} + V_{IMAX} z_{u}^{HLI} + V_{IMIN} z_{l}^{HLI}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- x'_{LL} + y_{LL}\right) + T_{B} x'_{LL} - T_{B} y_{LL} + T_{C} \left(V_{l} - x'_{LL}\right)` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`y_{WF}` | Algeb | :math:`K_{F} \left(- x'_{WF} + y_{LR}\right) - T_{F} y_{WF}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vfmax | :math:`V_{fmax}` | Algeb | :math:`- K_{C} X_{ad}I_{fd} + V_{RMAX} - V_{fmax}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vfmin | :math:`V_{fmin}` | Algeb | :math:`- K_{C} X_{ad}I_{fd} + V_{RMIN} - V_{fmin}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | :math:`u_{e} \left(- v_{f0} + v_{out}\right)` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +--------+------------------+-----------------+-----------------+ | Name | Symbol | Equation | Type | +========+==================+=================+=================+ | ue | :math:`u_e` | :math:`u u_{g}` | ConstService | +--------+------------------+-----------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`V_{ref}` | PostInitService | +--------+------------------+-----------------+-----------------+ Discretes ----------- +---------+-----------------+-------------+----------------------------------+ | Name | Symbol | Type | Info | +=========+=================+=============+==================================+ | HLI | :math:`HLI` | HardLimiter | Hard limiter on input | +---------+-----------------+-------------+----------------------------------+ | LL_LT1 | :math:`LT_{LL}` | LessThan | | +---------+-----------------+-------------+----------------------------------+ | LL_LT2 | :math:`LT_{LL}` | LessThan | | +---------+-----------------+-------------+----------------------------------+ | HLR | :math:`HLR` | HardLimiter | Hard limiter on regulator output | +---------+-----------------+-------------+----------------------------------+ Blocks ------- +------+------------+---------+-----------------------------+ | Name | Symbol | Type | Info | +======+============+=========+=============================+ | LG | :math:`LG` | Lag | Sensing delay | +------+------------+---------+-----------------------------+ | LL | :math:`LL` | LeadLag | Lead-lag compensator | +------+------------+---------+-----------------------------+ | LR | :math:`LR` | Lag | Regulator | +------+------------+---------+-----------------------------+ | WF | :math:`WF` | Washout | Stablizing circuit feedback | +------+------------+---------+-----------------------------+ Config Fields in [EXST1] +---------------+--------+-------+---------------------------------------+-----------------+ | Option | Symbol | Value | Info | Accepted values | +===============+========+=======+=======================================+=================+ | allow_adjust | | 1 | allow adjusting upper or lower limits | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_lower | | 0 | adjust lower limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_upper | | 1 | adjust upper limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _ESST3A: -------------------------------------------------------------------------------- ESST3A -------------------------------------------------------------------------------- Static exciter type 3A model Parameters ---------- +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +=========+==================+================================================================+=========+==========+============+ | idx | | unique device idx | | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | name | | device name | | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | syn | | Synchronous generator idx | | | mandatory | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | TR | :math:`T_R` | Sensing time constant | 0.010 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | VIMAX | :math:`V_{IMAX}` | Max. input voltage | 0.800 | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | VIMIN | :math:`V_{IMIN}` | Min. input voltage | -0.100 | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | KM | :math:`K_M` | Forward gain constant | 500 | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | TC | :math:`T_C` | Lead time constant in lead-lag | 3 | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | TB | :math:`T_B` | Lag time constant in lead-lag | 15 | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | KA | :math:`K_A` | Gain in anti-windup lag TF | 50 | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | TA | :math:`T_A` | Lag time constant in anti-windup lag | 0.100 | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | VRMAX | :math:`V_{RMAX}` | Maximum excitation limit | 8 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | VRMIN | :math:`V_{RMIN}` | Minimum excitation limit | 0 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | KG | :math:`K_G` | Feedback gain of inner field regulator | 1 | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | KP | :math:`K_P` | Potential circuit gain coeff. | 4 | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | KI | :math:`K_I` | Potential circuit gain coeff. | 0.100 | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | VBMAX | :math:`V_{BMAX}` | VB upper limit | 18 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | KC | :math:`K_C` | Rectifier loading factor proportional to commutating reactance | 0.100 | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | XL | :math:`X_L` | Potential source reactance | 0.010 | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | VGMAX | :math:`V_{GMAX}` | VG upper limit | 4 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | THETAP | :math:`\theta_P` | Rectifier firing angle | 0 | *degree* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | TM | :math:`K_C` | Inner field regulator forward time constant | 0.100 | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | VMMAX | :math:`V_{MMAX}` | Maximum VM limit | 1 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | VMMIN | :math:`V_{RMIN}` | Minimum VM limit | 0.100 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | ug | :math:`u_g` | Generator online status | 0 | *bool* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | Sn | :math:`S_m` | Rated power from generator | 0 | *MVA* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | Vn | :math:`V_m` | Rated voltage from generator | 0 | *kV* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | bus | :math:`bus` | Bus idx of the generators | 0 | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ Variables --------- +---------+----------------------+----------+---------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +=========+======================+==========+=======================================+========+============+ | LG_y | :math:`y_{LG}` | State | State in lag transfer function | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | LL_x | :math:`x'_{LL}` | State | State in lead-lag | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | LAW1_y | :math:`y_{LAW1}` | State | State in lag TF | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | LAW2_y | :math:`y_{LAW2}` | State | State in lag TF | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | v | :math:`E_{term}` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vout | :math:`v_{out}` | Algeb | Exciter final output voltage | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | UEL | :math:`U_{EL}` | Algeb | Interface var for under exc. limiter | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | IN | :math:`I_{N}` | Algeb | Input to FEX | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | FEX_y | :math:`y_{FEX}` | Algeb | Output of piecewise | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | VB_x | :math:`x_{VB}` | Algeb | Value before limiter | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | VB_y | :math:`y_{VB}` | Algeb | Output after limiter and post gain | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | VG_x | :math:`x_{VG}` | Algeb | Value before limiter | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | VG_y | :math:`y_{VG}` | Algeb | Output after limiter and post gain | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vrs | :math:`V_{RS}` | Algeb | VR subtract feedback VG | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vref | :math:`V_{ref}` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vi | :math:`V_{i}` | Algeb | Total input voltages | *p.u.* | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vil | :math:`V_{il}` | Algeb | Input voltage after limit | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | HG_y | :math:`y_{HG}` | Algeb | HVGate output | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | LL_y | :math:`y_{LL}` | Algeb | Output of lead-lag | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vf | :math:`v_{f}` | ExtAlgeb | Excitation field voltage to generator | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | Armature excitation current | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | a | :math:`\theta` | ExtAlgeb | Bus voltage phase angle | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vbus | :math:`V` | ExtAlgeb | Bus voltage magnitude | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vd | :math:`V_{d}` | ExtAlgeb | d-axis machine voltage | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vq | :math:`V_{q}` | ExtAlgeb | q-axis machine voltage | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | Id | :math:`I_{d}` | ExtAlgeb | d-axis machine current | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | Iq | :math:`I_{q}` | ExtAlgeb | q-axis machine current | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ Initialization Equations ------------------------ +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+======================+==========+=====================================================================================================================================================================================================================================================================================+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_x | :math:`x'_{LL}` | State | :math:`y_{HG}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LAW1_y | :math:`y_{LAW1}` | State | :math:`K_{A} y_{LL}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LAW2_y | :math:`y_{LAW2}` | State | :math:`K_{M} V_{RS}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`E_{term}` | Algeb | :math:`V` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} v_{f0}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`U_{EL}` | Algeb | :math:`U_{EL0}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`I_{N}` | Algeb | :math:`\operatorname{safe}_{div}{\left(K_{C} X_{ad}I_{fd},V_{E} \right)}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | FEX_y | :math:`y_{FEX}` | Algeb | :math:`\operatorname{FixPiecewise}{\left(\left( 1, \ I_{N} \leq 0\right),\left( 1 - 0.577 I_{N}, \ I_{N} \leq 0.433\right),\left( \sqrt{0.75 - I_{N}^{2}}, \ I_{N} \leq 0.75\right),\left( 1.732 - 1.732 I_{N}, \ I_{N} \leq 1\right),\left( 0, \ \text{True}\right) \right)}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VB_x | :math:`x_{VB}` | Algeb | :math:`V_{E} y_{FEX}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VB_y | :math:`y_{VB}` | Algeb | :math:`VB_{lim zi} x_{VB} + VB_{lim zu} V_{BMAX}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VG_x | :math:`x_{VG}` | Algeb | :math:`K_{G} v_{out}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VG_y | :math:`y_{VG}` | Algeb | :math:`VG_{lim zi} x_{VG} + VG_{lim zu} V_{GMAX}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vrs | :math:`V_{RS}` | Algeb | :math:`\frac{\operatorname{safe}_{div}{\left(v_{f0},y_{VB} \right)}}{K_{M}}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`E_{term} + \frac{V_{RS} + y_{VG}}{K_{A}}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`- E_{term} + V_{ref}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vil | :math:`V_{il}` | Algeb | :math:`V_{i} z_{i}^{HLI} + V_{IMAX} z_{u}^{HLI} + V_{IMIN} z_{l}^{HLI}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | HG_y | :math:`y_{HG}` | Algeb | :math:`HG_{lt z0} U_{EL} + HG_{lt z1} V_{il}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`y_{HG}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vd | :math:`V_{d}` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vq | :math:`V_{q}` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Id | :math:`I_{d}` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iq | :math:`I_{q}` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +---------+------------------+----------+----------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +=========+==================+==========+==================================+=============+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term} - y_{LG}` | :math:`T_R` | +---------+------------------+----------+----------------------------------+-------------+ | LL_x | :math:`x'_{LL}` | State | :math:`- x'_{LL} + y_{HG}` | :math:`T_B` | +---------+------------------+----------+----------------------------------+-------------+ | LAW1_y | :math:`y_{LAW1}` | State | :math:`K_{A} y_{LL} - y_{LAW1}` | :math:`T_A` | +---------+------------------+----------+----------------------------------+-------------+ | LAW2_y | :math:`y_{LAW2}` | State | :math:`K_{M} V_{RS} - y_{LAW2}` | :math:`K_C` | +---------+------------------+----------+----------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +---------+------------------+----------+----------------------------------+-------------+ Algebraic Equations ----------------------------- +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+======================+==========+=================================================================================================================================================================================================================================================================================================+ | v | :math:`E_{term}` | Algeb | :math:`- E_{term} + V` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} y_{LAW2} y_{VB} - v_{out}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`U_{EL}` | Algeb | :math:`U_{EL0} - U_{EL}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`I_{N}` | Algeb | :math:`u_{e} \left(- I_{N} V_{E} + K_{C} X_{ad}I_{fd}\right)` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | FEX_y | :math:`y_{FEX}` | Algeb | :math:`- y_{FEX} + \operatorname{FixPiecewise}{\left(\left( 1, \ I_{N} \leq 0\right),\left( 1 - 0.577 I_{N}, \ I_{N} \leq 0.433\right),\left( \sqrt{0.75 - I_{N}^{2}}, \ I_{N} \leq 0.75\right),\left( 1.732 - 1.732 I_{N}, \ I_{N} \leq 1\right),\left( 0, \ \text{True}\right) \right)}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VB_x | :math:`x_{VB}` | Algeb | :math:`V_{E} y_{FEX} - x_{VB}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VB_y | :math:`y_{VB}` | Algeb | :math:`VB_{lim zi} x_{VB} + VB_{lim zu} V_{BMAX} - y_{VB}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VG_x | :math:`x_{VG}` | Algeb | :math:`K_{G} v_{out} - x_{VG}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VG_y | :math:`y_{VG}` | Algeb | :math:`VG_{lim zi} x_{VG} + VG_{lim zu} V_{GMAX} - y_{VG}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vrs | :math:`V_{RS}` | Algeb | :math:`- V_{RS} + y_{LAW1} - y_{VG}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`V_{ref0} - V_{ref}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`- V_{i} + V_{ref} - y_{LG}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vil | :math:`V_{il}` | Algeb | :math:`V_{i} z_{i}^{HLI} + V_{IMAX} z_{u}^{HLI} + V_{IMIN} z_{l}^{HLI} - V_{il}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | HG_y | :math:`y_{HG}` | Algeb | :math:`HG_{lt z0} U_{EL} + HG_{lt z1} V_{il} - y_{HG}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- x'_{LL} + y_{LL}\right) + T_{B} x'_{LL} - T_{B} y_{LL} + T_{C} \left(- x'_{LL} + y_{HG}\right)` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | :math:`u_{e} \left(- v_{f0} + v_{out}\right)` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vd | :math:`V_{d}` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vq | :math:`V_{q}` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Id | :math:`I_{d}` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iq | :math:`I_{q}` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +--------+------------------+-------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +========+==================+===============================================================================================================================+=================+ | ue | :math:`u_e` | :math:`u u_{g}` | ConstService | +--------+------------------+-------------------------------------------------------------------------------------------------------------------------------+-----------------+ | KPC | :math:`K_{PC}` | :math:`K_{P} e^{i \operatorname{radians}{\left(\theta_{P} \right)}}` | ConstService | +--------+------------------+-------------------------------------------------------------------------------------------------------------------------------+-----------------+ | UEL0 | :math:`U_{EL0}` | :math:`-9999` | ConstService | +--------+------------------+-------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VE | :math:`V_E` | :math:`\left|{K_{PC} \left(V_{d} + i V_{q}\right) + i \left(I_{d} + i I_{q}\right) \left(K_{I} + K_{PC} X_{L}\right)}\right|` | VarService | +--------+------------------+-------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`V_{ref}` | PostInitService | +--------+------------------+-------------------------------------------------------------------------------------------------------------------------------+-----------------+ Discretes ----------- +-----------+--------------------+-------------+----------------+ | Name | Symbol | Type | Info | +===========+====================+=============+================+ | VB_lim | :math:`lim_{VB}` | HardLimiter | | +-----------+--------------------+-------------+----------------+ | VG_lim | :math:`lim_{VG}` | HardLimiter | | +-----------+--------------------+-------------+----------------+ | HG_lt | :math:`None_{HG}` | LessThan | | +-----------+--------------------+-------------+----------------+ | LL_LT1 | :math:`LT_{LL}` | LessThan | | +-----------+--------------------+-------------+----------------+ | LL_LT2 | :math:`LT_{LL}` | LessThan | | +-----------+--------------------+-------------+----------------+ | LAW1_lim | :math:`lim_{LAW1}` | AntiWindup | Limiter in Lag | +-----------+--------------------+-------------+----------------+ | HLI | :math:`HLI` | HardLimiter | Input limiter | +-----------+--------------------+-------------+----------------+ | LAW2_lim | :math:`lim_{LAW2}` | AntiWindup | Limiter in Lag | +-----------+--------------------+-------------+----------------+ Blocks ------- +-------+--------------+---------------+-----------------------------+ | Name | Symbol | Type | Info | +=======+==============+===============+=============================+ | LG | :math:`LG` | Lag | Voltage transducer | +-------+--------------+---------------+-----------------------------+ | FEX | :math:`FEX` | Piecewise | Piecewise function FEX | +-------+--------------+---------------+-----------------------------+ | VB | :math:`VB` | GainLimiter | VB with limiter | +-------+--------------+---------------+-----------------------------+ | VG | :math:`VG` | GainLimiter | Feedback gain with HL | +-------+--------------+---------------+-----------------------------+ | HG | :math:`HG` | HVGate | HVGate for under excitation | +-------+--------------+---------------+-----------------------------+ | LL | :math:`LL` | LeadLag | Regulator | +-------+--------------+---------------+-----------------------------+ | LAW1 | :math:`LAW1` | LagAntiWindup | Lag AW on VR | +-------+--------------+---------------+-----------------------------+ | LAW2 | :math:`LAW2` | LagAntiWindup | Lag AW on VM | +-------+--------------+---------------+-----------------------------+ Config Fields in [ESST3A] +---------------+--------+-------+---------------------------------------+-----------------+ | Option | Symbol | Value | Info | Accepted values | +===============+========+=======+=======================================+=================+ | allow_adjust | | 1 | allow adjusting upper or lower limits | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_lower | | 0 | adjust lower limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_upper | | 1 | adjust upper limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _SEXS: -------------------------------------------------------------------------------- SEXS -------------------------------------------------------------------------------- Simplified Excitation System Parameters ---------- +-------+-----------------+------------------------------+---------+--------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +=======+=================+==============================+=========+========+============+ | idx | | unique device idx | | | | +-------+-----------------+------------------------------+---------+--------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +-------+-----------------+------------------------------+---------+--------+------------+ | name | | device name | | | | +-------+-----------------+------------------------------+---------+--------+------------+ | syn | | Synchronous generator idx | | | mandatory | +-------+-----------------+------------------------------+---------+--------+------------+ | TATB | :math:`T_A/T_B` | Time constant TA/TB | 0.400 | | | +-------+-----------------+------------------------------+---------+--------+------------+ | TB | :math:`T_B` | Time constant TB in LL | 5 | | | +-------+-----------------+------------------------------+---------+--------+------------+ | K | :math:`K` | Gain | 20 | | non_zero | +-------+-----------------+------------------------------+---------+--------+------------+ | TE | :math:`T_E` | AW Lag time constant | 1 | | | +-------+-----------------+------------------------------+---------+--------+------------+ | EMIN | :math:`E_{MIN}` | lower limit | -99 | | | +-------+-----------------+------------------------------+---------+--------+------------+ | EMAX | :math:`E_{MAX}` | upper limit | 99 | | | +-------+-----------------+------------------------------+---------+--------+------------+ | ug | :math:`u_g` | Generator online status | 0 | *bool* | | +-------+-----------------+------------------------------+---------+--------+------------+ | Sn | :math:`S_m` | Rated power from generator | 0 | *MVA* | | +-------+-----------------+------------------------------+---------+--------+------------+ | Vn | :math:`V_m` | Rated voltage from generator | 0 | *kV* | | +-------+-----------------+------------------------------+---------+--------+------------+ | bus | :math:`bus` | Bus idx of the generators | 0 | | | +-------+-----------------+------------------------------+---------+--------+------------+ Variables --------- +---------+----------------------+----------+---------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +=========+======================+==========+=======================================+========+============+ | LL_x | :math:`x'_{LL}` | State | State in lead-lag | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | LAW_y | :math:`y_{LAW}` | State | State in lag TF | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | v | :math:`E_{term}` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vout | :math:`v_{out}` | Algeb | Exciter final output voltage | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vref | :math:`V_{ref}` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vi | :math:`V_{i}` | Algeb | Total input voltages | *p.u.* | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | LL_y | :math:`y_{LL}` | Algeb | Output of lead-lag | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vf | :math:`v_{f}` | ExtAlgeb | Excitation field voltage to generator | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | Armature excitation current | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | a | :math:`\theta` | ExtAlgeb | Bus voltage phase angle | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vbus | :math:`V` | ExtAlgeb | Bus voltage magnitude | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ Initialization Equations ------------------------ +---------+----------------------+----------+-------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+======================+==========+=====================================+ | LL_x | :math:`x'_{LL}` | State | :math:`V_{i}` | +---------+----------------------+----------+-------------------------------------+ | LAW_y | :math:`y_{LAW}` | State | :math:`K y_{LL}` | +---------+----------------------+----------+-------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+----------------------+----------+-------------------------------------+ | v | :math:`E_{term}` | Algeb | :math:`V` | +---------+----------------------+----------+-------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} v_{f0}` | +---------+----------------------+----------+-------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`E_{term} + \frac{v_{f0}}{K}` | +---------+----------------------+----------+-------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`\frac{v_{f0}}{K}` | +---------+----------------------+----------+-------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`V_{i}` | +---------+----------------------+----------+-------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------+ | a | :math:`\theta` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------+ | vbus | :math:`V` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+----------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+==================================+=============+ | LL_x | :math:`x'_{LL}` | State | :math:`V_{i} - x'_{LL}` | :math:`T_B` | +--------+-----------------+----------+----------------------------------+-------------+ | LAW_y | :math:`y_{LAW}` | State | :math:`K y_{LL} - y_{LAW}` | :math:`T_E` | +--------+-----------------+----------+----------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+----------------------------------+-------------+ Algebraic Equations ----------------------------- +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+======================+==========+==================================================================================================================================+ | v | :math:`E_{term}` | Algeb | :math:`- E_{term} + V` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} y_{LAW} - v_{out}` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`V_{ref0} - V_{ref}` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`- E_{term} - V_{i} + V_{ref}` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- x'_{LL} + y_{LL}\right) + TA \left(V_{i} - x'_{LL}\right) + T_{B} x'_{LL} - T_{B} y_{LL}` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | :math:`u_{e} \left(- v_{f0} + v_{out}\right)` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +--------+------------------+-------------------------+-----------------+ | Name | Symbol | Equation | Type | +========+==================+=========================+=================+ | ue | :math:`u_e` | :math:`u u_{g}` | ConstService | +--------+------------------+-------------------------+-----------------+ | TA | :math:`TA` | :math:`T_{A/T B} T_{B}` | ConstService | +--------+------------------+-------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`V_{ref}` | PostInitService | +--------+------------------+-------------------------+-----------------+ Discretes ----------- +----------+-------------------+------------+----------------+ | Name | Symbol | Type | Info | +==========+===================+============+================+ | LL_LT1 | :math:`LT_{LL}` | LessThan | | +----------+-------------------+------------+----------------+ | LL_LT2 | :math:`LT_{LL}` | LessThan | | +----------+-------------------+------------+----------------+ | LAW_lim | :math:`lim_{LAW}` | AntiWindup | Limiter in Lag | +----------+-------------------+------------+----------------+ Blocks ------- +------+-------------+---------------+------+ | Name | Symbol | Type | Info | +======+=============+===============+======+ | LL | :math:`LL` | LeadLag | | +------+-------------+---------------+------+ | LAW | :math:`LAW` | LagAntiWindup | | +------+-------------+---------------+------+ Config Fields in [SEXS] +---------------+--------+-------+---------------------------------------+-----------------+ | Option | Symbol | Value | Info | Accepted values | +===============+========+=======+=======================================+=================+ | allow_adjust | | 1 | allow adjusting upper or lower limits | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_lower | | 0 | adjust lower limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_upper | | 1 | adjust upper limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _IEEET1: -------------------------------------------------------------------------------- IEEET1 -------------------------------------------------------------------------------- IEEET1 exciter. Parameters ---------- +---------+------------------+--------------------------------------+---------+--------+-----------------------+ | Name | Symbol | Description | Default | Unit | Properties | +=========+==================+======================================+=========+========+=======================+ | idx | | unique device idx | | | | +---------+------------------+--------------------------------------+---------+--------+-----------------------+ | u | :math:`u` | connection status | 1 | *bool* | | +---------+------------------+--------------------------------------+---------+--------+-----------------------+ | name | | device name | | | | +---------+------------------+--------------------------------------+---------+--------+-----------------------+ | syn | | Synchronous generator idx | | | mandatory | +---------+------------------+--------------------------------------+---------+--------+-----------------------+ | TR | :math:`T_R` | Sensing time constant | 0.020 | *p.u.* | | +---------+------------------+--------------------------------------+---------+--------+-----------------------+ | KA | :math:`K_A` | Regulator gain | 5 | *p.u.* | | +---------+------------------+--------------------------------------+---------+--------+-----------------------+ | TA | :math:`T_A` | Lag time constant in anti-windup lag | 0.040 | *p.u.* | | +---------+------------------+--------------------------------------+---------+--------+-----------------------+ | VRMAX | :math:`V_{RMAX}` | Maximum excitation limit | 7.300 | *p.u.* | | +---------+------------------+--------------------------------------+---------+--------+-----------------------+ | VRMIN | :math:`V_{RMIN}` | Minimum excitation limit | -7.300 | *p.u.* | | +---------+------------------+--------------------------------------+---------+--------+-----------------------+ | KE | :math:`K_E` | Gain added to saturation | 1 | *p.u.* | | +---------+------------------+--------------------------------------+---------+--------+-----------------------+ | TE | :math:`T_E` | Exciter integrator time constant | 0.800 | *p.u.* | | +---------+------------------+--------------------------------------+---------+--------+-----------------------+ | KF | :math:`K_F` | Feedback gain | 0.100 | | | +---------+------------------+--------------------------------------+---------+--------+-----------------------+ | TF | :math:`T_F` | Feedback delay | 1 | | non_zero,non_negative | +---------+------------------+--------------------------------------+---------+--------+-----------------------+ | Switch | :math:`S_w` | Switch unused in PSS/E | 0 | *bool* | | +---------+------------------+--------------------------------------+---------+--------+-----------------------+ | E1 | :math:`E_1` | First saturation point | 0 | *p.u.* | | +---------+------------------+--------------------------------------+---------+--------+-----------------------+ | SE1 | :math:`S_{E1}` | Value at first saturation point | 0 | *p.u.* | | +---------+------------------+--------------------------------------+---------+--------+-----------------------+ | E2 | :math:`E_2` | Second saturation point | 1 | *p.u.* | | +---------+------------------+--------------------------------------+---------+--------+-----------------------+ | SE2 | :math:`S_{E2}` | Value at second saturation point | 1 | *p.u.* | | +---------+------------------+--------------------------------------+---------+--------+-----------------------+ | ug | :math:`u_g` | Generator online status | 0 | *bool* | | +---------+------------------+--------------------------------------+---------+--------+-----------------------+ | Sn | :math:`S_m` | Rated power from generator | 0 | *MVA* | | +---------+------------------+--------------------------------------+---------+--------+-----------------------+ | Vn | :math:`V_m` | Rated voltage from generator | 0 | *kV* | | +---------+------------------+--------------------------------------+---------+--------+-----------------------+ | bus | :math:`bus` | Bus idx of the generators | 0 | | | +---------+------------------+--------------------------------------+---------+--------+-----------------------+ Variables --------- +---------+------------------------+----------+---------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +=========+========================+==========+=======================================+========+============+ | LG_y | :math:`y_{LG}` | State | State in lag transfer function | | v_str | +---------+------------------------+----------+---------------------------------------+--------+------------+ | LA_y | :math:`y_{LA}` | State | State in lag TF | | v_str | +---------+------------------------+----------+---------------------------------------+--------+------------+ | INT_y | :math:`y_{INT}` | State | Integrator output | | v_str | +---------+------------------------+----------+---------------------------------------+--------+------------+ | WF_x | :math:`x'_{WF}` | State | State in washout filter | | v_str | +---------+------------------------+----------+---------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+------------------------+----------+---------------------------------------+--------+------------+ | v | :math:`E_{term}` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+------------------------+----------+---------------------------------------+--------+------------+ | vout | :math:`v_{out}` | Algeb | Exciter final output voltage | | v_str | +---------+------------------------+----------+---------------------------------------+--------+------------+ | vref | :math:`V_{ref}` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+------------------------+----------+---------------------------------------+--------+------------+ | vi | :math:`V_{i}` | Algeb | Total input voltages | *p.u.* | v_str | +---------+------------------------+----------+---------------------------------------+--------+------------+ | VFE | :math:`V_{FE}` | Algeb | Combined saturation feedback | *p.u.* | v_str | +---------+------------------------+----------+---------------------------------------+--------+------------+ | Se | :math:`S_e(|V_{out}|)` | Algeb | saturation output | | v_str | +---------+------------------------+----------+---------------------------------------+--------+------------+ | WF_y | :math:`y_{WF}` | Algeb | Output of washout filter | | v_str | +---------+------------------------+----------+---------------------------------------+--------+------------+ | vf | :math:`v_{f}` | ExtAlgeb | Excitation field voltage to generator | | | +---------+------------------------+----------+---------------------------------------+--------+------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | Armature excitation current | | | +---------+------------------------+----------+---------------------------------------+--------+------------+ | a | :math:`\theta` | ExtAlgeb | Bus voltage phase angle | | | +---------+------------------------+----------+---------------------------------------+--------+------------+ | vbus | :math:`V` | ExtAlgeb | Bus voltage magnitude | | | +---------+------------------------+----------+---------------------------------------+--------+------------+ Initialization Equations ------------------------ +---------+------------------------+----------+-------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+========================+==========+=================================================+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term}` | +---------+------------------------+----------+-------------------------------------------------+ | LA_y | :math:`y_{LA}` | State | :math:`K_{A} u_{e} \left(V_{i} - y_{WF}\right)` | +---------+------------------------+----------+-------------------------------------------------+ | INT_y | :math:`y_{INT}` | State | :math:`v_{f0}` | +---------+------------------------+----------+-------------------------------------------------+ | WF_x | :math:`x'_{WF}` | State | :math:`v_{out}` | +---------+------------------------+----------+-------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+------------------------+----------+-------------------------------------------------+ | v | :math:`E_{term}` | Algeb | :math:`V` | +---------+------------------------+----------+-------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} v_{f0}` | +---------+------------------------+----------+-------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`E_{term} + V_{b0}` | +---------+------------------------+----------+-------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`- E_{term} + V_{ref}` | +---------+------------------------+----------+-------------------------------------------------+ | VFE | :math:`V_{FE}` | Algeb | :math:`V_{FE0}` | +---------+------------------------+----------+-------------------------------------------------+ | Se | :math:`S_e(|V_{out}|)` | Algeb | :math:`S_{e0}` | +---------+------------------------+----------+-------------------------------------------------+ | WF_y | :math:`y_{WF}` | Algeb | :math:`0` | +---------+------------------------+----------+-------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | | +---------+------------------------+----------+-------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | | +---------+------------------------+----------+-------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | | +---------+------------------------+----------+-------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | | +---------+------------------------+----------+-------------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+----------------------------------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+==========================================================+=============+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term} - y_{LG}` | :math:`T_R` | +--------+-----------------+----------+----------------------------------------------------------+-------------+ | LA_y | :math:`y_{LA}` | State | :math:`K_{A} u_{e} \left(V_{i} - y_{WF}\right) - y_{LA}` | :math:`T_A` | +--------+-----------------+----------+----------------------------------------------------------+-------------+ | INT_y | :math:`y_{INT}` | State | :math:`u_{e} \left(- V_{FE} + y_{LA}\right)` | :math:`T_E` | +--------+-----------------+----------+----------------------------------------------------------+-------------+ | WF_x | :math:`x'_{WF}` | State | :math:`v_{out} - x'_{WF}` | :math:`T_F` | +--------+-----------------+----------+----------------------------------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+----------------------------------------------------------+-------------+ Algebraic Equations ----------------------------- +---------+------------------------+----------+--------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+========================+==========+======================================================================================+ | v | :math:`E_{term}` | Algeb | :math:`- E_{term} + V` | +---------+------------------------+----------+--------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} \left(- v_{out} + y_{INT}\right)` | +---------+------------------------+----------+--------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`V_{ref0} - V_{ref}` | +---------+------------------------+----------+--------------------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`u_{e} \left(- V_{i} + V_{ref} - y_{LG}\right)` | +---------+------------------------+----------+--------------------------------------------------------------------------------------+ | VFE | :math:`V_{FE}` | Algeb | :math:`u_{e} \left(K_{E} y_{INT} + S_e(|V_{out}|) - V_{FE}\right)` | +---------+------------------------+----------+--------------------------------------------------------------------------------------+ | Se | :math:`S_e(|V_{out}|)` | Algeb | :math:`B^q_{SAT} z_{0}^{SL} \left(- A^q_{SAT} + y_{INT}\right)^{2} - S_e(|V_{out}|)` | +---------+------------------------+----------+--------------------------------------------------------------------------------------+ | WF_y | :math:`y_{WF}` | Algeb | :math:`K_{F} \left(v_{out} - x'_{WF}\right) - T_{F} y_{WF}` | +---------+------------------------+----------+--------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | :math:`u_{e} \left(- v_{f0} + v_{out}\right)` | +---------+------------------------+----------+--------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | :math:`0` | +---------+------------------------+----------+--------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | :math:`0` | +---------+------------------------+----------+--------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | :math:`0` | +---------+------------------------+----------+--------------------------------------------------------------------------------------+ Services ---------- +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +==========+=======================+=============================================================================================================================================================================================================================================+=================+ | ue | :math:`u_e` | :math:`u u_{g}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VRMAXc | :math:`VRMAXc` | :math:`V_{RMAX} - 999 z_{VRMAX} + 999` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E1 | :math:`E^{1c}_{SAT}` | :math:`E_{1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E2 | :math:`E^{2c}_{SAT}` | :math:`E_{2} - 2 z^{SE2}_{SAT} + 2` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE1 | :math:`SE^{1c}_{SAT}` | :math:`S_{E1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE2 | :math:`SE^{2c}_{SAT}` | :math:`S_{E2} - 2 z^{SE2}_{SAT} + 2` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_a | :math:`a_{SAT}` | :math:`\sqrt{\frac{E^{1c}_{SAT} SE^{1c}_{SAT}}{E^{2c}_{SAT} SE^{2c}_{SAT}}} \left(\operatorname{Indicator}{\left(SE^{2c}_{SAT} > 0 \right)} + \operatorname{Indicator}{\left(SE^{2c}_{SAT} < 0 \right)}\right)` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_A | :math:`A^q_{SAT}` | :math:`E^{2c}_{SAT} - \frac{E^{1c}_{SAT} - E^{2c}_{SAT}}{a_{SAT} - 1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_B | :math:`B^q_{SAT}` | :math:`\frac{E^{2c}_{SAT} SE^{2c}_{SAT} \left(a_{SAT} - 1\right)^{2} \left(\operatorname{Indicator}{\left(a_{SAT} > 0 \right)} + \operatorname{Indicator}{\left(a_{SAT} < 0 \right)}\right)}{\left(E^{1c}_{SAT} - E^{2c}_{SAT}\right)^{2}}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Se0 | :math:`S_{e0}` | :math:`B^q_{SAT} \left(A^q_{SAT} - v_{f0}\right)^{2} \operatorname{Indicator}{\left(v_{f0} > A^q_{SAT} \right)}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vr0 | :math:`V_{r0}` | :math:`K_{E} v_{f0} + S_{e0}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vb0 | :math:`V_{b0}` | :math:`\frac{V_{r0}}{K_{A}}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vfe0 | :math:`V_{FE0}` | :math:`K_{E} v_{f0} + S_{e0}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`V_{ref}` | PostInitService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ Discretes ----------- +---------+------------------+------------+----------------+ | Name | Symbol | Type | Info | +=========+==================+============+================+ | LA_lim | :math:`lim_{LA}` | AntiWindup | Limiter in Lag | +---------+------------------+------------+----------------+ | SL | :math:`SL` | LessThan | | +---------+------------------+------------+----------------+ Blocks ------- +------+-------------+---------------+-----------------------------+ | Name | Symbol | Type | Info | +======+=============+===============+=============================+ | SAT | :math:`SAT` | ExcQuadSat | Field voltage saturation | +------+-------------+---------------+-----------------------------+ | LG | :math:`LG` | Lag | Sensing delay | +------+-------------+---------------+-----------------------------+ | LA | :math:`LA` | LagAntiWindup | Anti-windup lag | +------+-------------+---------------+-----------------------------+ | INT | :math:`INT` | Integrator | Integrator | +------+-------------+---------------+-----------------------------+ | WF | :math:`WF` | Washout | Stablizing circuit feedback | +------+-------------+---------------+-----------------------------+ Config Fields in [IEEET1] +---------------+--------+-------+---------------------------------------+-----------------+ | Option | Symbol | Value | Info | Accepted values | +===============+========+=======+=======================================+=================+ | allow_adjust | | 1 | allow adjusting upper or lower limits | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_lower | | 0 | adjust lower limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_upper | | 1 | adjust upper limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _EXAC1: -------------------------------------------------------------------------------- EXAC1 -------------------------------------------------------------------------------- EXAC1 model. Ref: https://www.powerworld.com/WebHelp/Content/TransientModels_HTML/Exciter%20EXAC1.htm Parameters ---------- +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | Name | Symbol | Description | Default | Unit | Properties | +========+==================+================================================================+=========+========+=======================+ | idx | | unique device idx | | | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | u | :math:`u` | connection status | 1 | *bool* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | name | | device name | | | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | syn | | Synchronous generator idx | | | mandatory | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | TR | :math:`T_R` | Sensing time constant | 0.010 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | TB | :math:`T_B` | Lag time constant in lead-lag | 1 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | TC | :math:`T_C` | Lead time constant in lead-lag | 1 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | KA | :math:`K_A` | Regulator gain | 80 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | TA | :math:`T_A` | Lag time constant in regulator | 0.040 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | VRMAX | :math:`V_{RMAX}` | Maximum regulator output | 8 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | VRMIN | :math:`V_{RMIN}` | Minimum regulator output | 0 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | TE | :math:`T_E` | Exciter integrator time constant | 0.800 | *p.u.* | non_negative | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | KF | :math:`K_F` | Feedback gain | 0.100 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | TF | :math:`T_F` | Feedback delay | 1 | | non_zero,non_negative | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | KC | :math:`K_C` | Rectifier loading factor proportional to commutating reactance | 0.100 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | KD | :math:`K_C` | Ifd feedback gain | 0 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | KE | :math:`K_E` | Saturation feedback gain | 1 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | E1 | :math:`E_1` | First saturation point | 0 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | SE1 | :math:`S_{E1}` | Value at first saturation point | 0 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | E2 | :math:`E_2` | Second saturation point | 1 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | SE2 | :math:`S_{E2}` | Value at second saturation point | 1 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | ug | :math:`u_g` | Generator online status | 0 | *bool* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | Sn | :math:`S_m` | Rated power from generator | 0 | *MVA* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | Vn | :math:`V_m` | Rated voltage from generator | 0 | *kV* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | bus | :math:`bus` | Bus idx of the generators | 0 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ Variables --------- +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | Name | Symbol | Type | Description | Unit | Properties | +=========+================================+==========+=======================================+========+==============+ | LG_y | :math:`y_{LG}` | State | State in lag transfer function | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | LL_x | :math:`x'_{LL}` | State | State in lead-lag | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | LA_y | :math:`y_{LA}` | State | State in lag TF | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | INT_y | :math:`y_{INT}` | State | Integrator output | | v_str,v_iter | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | WF_x | :math:`x'_{WF}` | State | State in washout filter | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | v | :math:`E_{term}` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | vout | :math:`v_{out}` | Algeb | Exciter final output voltage | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | IN | :math:`I_{N}` | Algeb | Input to FEX | | v_str,v_iter | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | FEX_y | :math:`y_{FEX}` | Algeb | Output of piecewise | | v_str,v_iter | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | vi | :math:`V_{i}` | Algeb | Total input voltages | *p.u.* | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | LL_y | :math:`y_{LL}` | Algeb | Output of lead-lag | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | Se | :math:`V_{out}*S_e(|V_{out}|)` | Algeb | saturation output | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | VFE | :math:`V_{FE}` | Algeb | Combined saturation feedback | *p.u.* | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | vref | :math:`V_{ref}` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | WF_y | :math:`y_{WF}` | Algeb | Output of washout filter | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | vf | :math:`v_{f}` | ExtAlgeb | Excitation field voltage to generator | | | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | Armature excitation current | | | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | a | :math:`\theta` | ExtAlgeb | Bus voltage phase angle | | | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | vbus | :math:`V` | ExtAlgeb | Bus voltage magnitude | | | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ Initialization Equations ------------------------ +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+================================+==========+=================================================================================================================================================================================================================================================================================================+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_x | :math:`x'_{LL}` | State | :math:`V_{i}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LA_y | :math:`y_{LA}` | State | :math:`K_{A} y_{LL}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | INT_y | :math:`y_{INT}` | State | :math:`- v_{f0} + y_{FEX} y_{INT}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_x | :math:`x'_{WF}` | State | :math:`V_{FE}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`E_{term}` | Algeb | :math:`V` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} v_{f0}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`I_{N}` | Algeb | :math:`- I_{N} y_{INT} + K_{C} X_{ad}I_{fd}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | FEX_y | :math:`y_{FEX}` | Algeb | :math:`- y_{FEX} + \operatorname{FixPiecewise}{\left(\left( 1, \ I_{N} \leq 0\right),\left( 1 - 0.577 I_{N}, \ I_{N} \leq 0.433\right),\left( \sqrt{0.75 - I_{N}^{2}}, \ I_{N} \leq 0.75\right),\left( 1.732 - 1.732 I_{N}, \ I_{N} \leq 1\right),\left( 0, \ \text{True}\right) \right)}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`- E_{term} + V_{ref}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`V_{i}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`V_{out}*S_e(|V_{out}|)` | Algeb | :math:`B^q_{SAT} \left(- A^q_{SAT} + y_{INT}\right)^{2} \operatorname{Indicator}{\left(y_{INT} > A^q_{SAT} \right)}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VFE | :math:`V_{FE}` | Algeb | :math:`K_{C} X_{ad}I_{fd} + K_{E} y_{INT} + V_{out}*S_e(|V_{out}|)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`E_{term} + \frac{V_{FE}}{K_{A}}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`y_{WF}` | Algeb | :math:`0` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+----------------------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+==============================================+=============+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term} - y_{LG}` | :math:`T_R` | +--------+-----------------+----------+----------------------------------------------+-------------+ | LL_x | :math:`x'_{LL}` | State | :math:`V_{i} - x'_{LL}` | :math:`T_B` | +--------+-----------------+----------+----------------------------------------------+-------------+ | LA_y | :math:`y_{LA}` | State | :math:`K_{A} y_{LL} - y_{LA}` | :math:`T_A` | +--------+-----------------+----------+----------------------------------------------+-------------+ | INT_y | :math:`y_{INT}` | State | :math:`u_{e} \left(- V_{FE} + y_{LA}\right)` | :math:`T_E` | +--------+-----------------+----------+----------------------------------------------+-------------+ | WF_x | :math:`x'_{WF}` | State | :math:`V_{FE} - x'_{WF}` | :math:`T_F` | +--------+-----------------+----------+----------------------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+----------------------------------------------+-------------+ Algebraic Equations ----------------------------- +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+================================+==========+=================================================================================================================================================================================================================================================================================================+ | v | :math:`E_{term}` | Algeb | :math:`- E_{term} + V` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} \left(- v_{out} + y_{FEX} y_{INT}\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`I_{N}` | Algeb | :math:`u_{e} \left(- I_{N} y_{INT} + K_{C} X_{ad}I_{fd}\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | FEX_y | :math:`y_{FEX}` | Algeb | :math:`- y_{FEX} + \operatorname{FixPiecewise}{\left(\left( 1, \ I_{N} \leq 0\right),\left( 1 - 0.577 I_{N}, \ I_{N} \leq 0.433\right),\left( \sqrt{0.75 - I_{N}^{2}}, \ I_{N} \leq 0.75\right),\left( 1.732 - 1.732 I_{N}, \ I_{N} \leq 1\right),\left( 0, \ \text{True}\right) \right)}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`u_{e} \left(- E_{term} - V_{i} + V_{ref} - y_{WF}\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- x'_{LL} + y_{LL}\right) + T_{B} x'_{LL} - T_{B} y_{LL} + T_{C} \left(V_{i} - x'_{LL}\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`V_{out}*S_e(|V_{out}|)` | Algeb | :math:`u_{e} \left(B^q_{SAT} z_{0}^{SL} \left(- A^q_{SAT} + y_{INT}\right)^{2} - V_{out}*S_e(|V_{out}|)\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VFE | :math:`V_{FE}` | Algeb | :math:`u_{e} \left(K_{C} X_{ad}I_{fd} + K_{E} y_{INT} - V_{FE} + V_{out}*S_e(|V_{out}|)\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`V_{ref0} - V_{ref}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`y_{WF}` | Algeb | :math:`K_{F} \left(V_{FE} - x'_{WF}\right) - T_{F} y_{WF}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | :math:`u_{e} \left(- v_{f0} + v_{out}\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | :math:`0` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | :math:`0` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | :math:`0` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +==========+=======================+=============================================================================================================================================================================================================================================+=================+ | ue | :math:`u_e` | :math:`u u_{g}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E1 | :math:`E^{1c}_{SAT}` | :math:`E_{1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E2 | :math:`E^{2c}_{SAT}` | :math:`E_{2} - 2 z^{SE2}_{SAT} + 2` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE1 | :math:`SE^{1c}_{SAT}` | :math:`S_{E1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE2 | :math:`SE^{2c}_{SAT}` | :math:`S_{E2} - 2 z^{SE2}_{SAT} + 2` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_a | :math:`a_{SAT}` | :math:`\sqrt{\frac{E^{1c}_{SAT} SE^{1c}_{SAT}}{E^{2c}_{SAT} SE^{2c}_{SAT}}} \left(\operatorname{Indicator}{\left(SE^{2c}_{SAT} > 0 \right)} + \operatorname{Indicator}{\left(SE^{2c}_{SAT} < 0 \right)}\right)` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_A | :math:`A^q_{SAT}` | :math:`E^{2c}_{SAT} - \frac{E^{1c}_{SAT} - E^{2c}_{SAT}}{a_{SAT} - 1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_B | :math:`B^q_{SAT}` | :math:`\frac{E^{2c}_{SAT} SE^{2c}_{SAT} \left(a_{SAT} - 1\right)^{2} \left(\operatorname{Indicator}{\left(a_{SAT} > 0 \right)} + \operatorname{Indicator}{\left(a_{SAT} < 0 \right)}\right)}{\left(E^{1c}_{SAT} - E^{2c}_{SAT}\right)^{2}}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`V_{ref}` | PostInitService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ Discretes ----------- +---------+------------------+------------+----------------+ | Name | Symbol | Type | Info | +=========+==================+============+================+ | LL_LT1 | :math:`LT_{LL}` | LessThan | | +---------+------------------+------------+----------------+ | LL_LT2 | :math:`LT_{LL}` | LessThan | | +---------+------------------+------------+----------------+ | LA_lim | :math:`lim_{LA}` | AntiWindup | Limiter in Lag | +---------+------------------+------------+----------------+ | SL | :math:`SL` | LessThan | | +---------+------------------+------------+----------------+ Blocks ------- +------+-------------+---------------+-----------------------------+ | Name | Symbol | Type | Info | +======+=============+===============+=============================+ | SAT | :math:`SAT` | ExcQuadSat | Field voltage saturation | +------+-------------+---------------+-----------------------------+ | FEX | :math:`FEX` | Piecewise | Piecewise function FEX | +------+-------------+---------------+-----------------------------+ | LG | :math:`LG` | Lag | Voltage transducer | +------+-------------+---------------+-----------------------------+ | LL | :math:`LL` | LeadLag | Regulator | +------+-------------+---------------+-----------------------------+ | LA | :math:`LA` | LagAntiWindup | Lag AW on VR | +------+-------------+---------------+-----------------------------+ | INT | :math:`INT` | Integrator | Integrator | +------+-------------+---------------+-----------------------------+ | WF | :math:`WF` | Washout | Stablizing circuit feedback | +------+-------------+---------------+-----------------------------+ Config Fields in [EXAC1] +---------------+--------+-------+---------------------------------------+-----------------+ | Option | Symbol | Value | Info | Accepted values | +===============+========+=======+=======================================+=================+ | allow_adjust | | 1 | allow adjusting upper or lower limits | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_lower | | 0 | adjust lower limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_upper | | 1 | adjust upper limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _EXAC2: -------------------------------------------------------------------------------- EXAC2 -------------------------------------------------------------------------------- EXAC2 model. Ref: https://www.powerworld.com/WebHelp/Content/TransientModels_HTML/Exciter%20EXAC2.htm Notes ----- ``VLR`` is an input parameter, but to initialize the LVGate, an internal ``VLRx`` will be computed as a contant upon initialization. The constant ``VLRx`` will be used in the place of ``VLR`` in the block diagram. Parameters ---------- +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | Name | Symbol | Description | Default | Unit | Properties | +========+==================+================================================================+=========+========+=======================+ | idx | | unique device idx | | | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | u | :math:`u` | connection status | 1 | *bool* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | name | | device name | | | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | syn | | Synchronous generator idx | | | mandatory | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | TR | :math:`T_R` | Sensing time constant | 0.010 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | TB | :math:`T_B` | Lag time constant in lead-lag | 1 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | TC | :math:`T_C` | Lead time constant in lead-lag | 1 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | KA | :math:`K_A` | Regulator gain | 80 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | TA | :math:`T_A` | Lag time constant in regulator | 0.040 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | VRMAX | :math:`V_{RMAX}` | Maximum regulator output | 8 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | VRMIN | :math:`V_{RMIN}` | Minimum regulator output | 0 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | TE | :math:`T_E` | Exciter integrator time constant | 0.800 | *p.u.* | non_negative | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | KF | :math:`K_F` | Feedback gain | 0.100 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | TF | :math:`T_F` | Feedback delay | 1 | | non_zero,non_negative | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | KC | :math:`K_C` | Rectifier loading factor proportional to commutating reactance | 0.100 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | KD | :math:`K_C` | Ifd feedback gain | 0 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | KE | :math:`K_E` | Saturation feedback gain | 1 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | E1 | :math:`E_1` | First saturation point | 0 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | SE1 | :math:`S_{E1}` | Value at first saturation point | 0 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | E2 | :math:`E_2` | Second saturation point | 1 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | SE2 | :math:`S_{E2}` | Value at second saturation point | 1 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | VAMAX | :math:`V_{RMAX}` | Maximum KA block output | 8 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | VAMIN | :math:`V_{RMIN}` | Minimum KA block output | 0 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | VLR | :math:`V_{LR}` | low voltage constant | 0 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | KL | :math:`K_L` | gain for low voltage | 1 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | KH | :math:`K_H` | gain for high voltage | 1 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | KB | :math:`K_B` | gain KB for regulator | 1 | *p.u.* | non_negative | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | ug | :math:`u_g` | Generator online status | 0 | *bool* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | Sn | :math:`S_m` | Rated power from generator | 0 | *MVA* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | Vn | :math:`V_m` | Rated voltage from generator | 0 | *kV* | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | bus | :math:`bus` | Bus idx of the generators | 0 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ Variables --------- +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | Name | Symbol | Type | Description | Unit | Properties | +=========+================================+==========+=======================================+========+==============+ | LG_y | :math:`y_{LG}` | State | State in lag transfer function | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | LL_x | :math:`x'_{LL}` | State | State in lead-lag | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | LA_y | :math:`y_{LA}` | State | State in lag TF | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | INT_y | :math:`y_{INT}` | State | Integrator output | | v_str,v_iter | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | WF_x | :math:`x'_{WF}` | State | State in washout filter | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | v | :math:`E_{term}` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | vout | :math:`v_{out}` | Algeb | Exciter final output voltage | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | IN | :math:`I_{N}` | Algeb | Input to FEX | | v_str,v_iter | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | FEX_y | :math:`y_{FEX}` | Algeb | Output of piecewise | | v_str,v_iter | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | vi | :math:`V_{i}` | Algeb | Total input voltages | *p.u.* | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | LL_y | :math:`y_{LL}` | Algeb | Output of lead-lag | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | Se | :math:`V_{out}*S_e(|V_{out}|)` | Algeb | saturation output | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | VFE | :math:`V_{FE}` | Algeb | Combined saturation feedback | *p.u.* | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | vref | :math:`V_{ref}` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | WF_y | :math:`y_{WF}` | Algeb | Output of washout filter | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | VHA | :math:`VHA` | Algeb | | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | VL | :math:`VL` | Algeb | | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | LVG_y | :math:`y_{LVG}` | Algeb | LVGate output | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | VR_x | :math:`x_{VR}` | Algeb | Value before limiter | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | VR_y | :math:`y_{VR}` | Algeb | Output after limiter and post gain | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | VLRx | :math:`VLRx` | Algeb | | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | vf | :math:`v_{f}` | ExtAlgeb | Excitation field voltage to generator | | | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | Armature excitation current | | | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | a | :math:`\theta` | ExtAlgeb | Bus voltage phase angle | | | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | vbus | :math:`V` | ExtAlgeb | Bus voltage magnitude | | | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ Initialization Equations ------------------------ +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+================================+==========+=================================================================================================================================================================================================================================================================================================+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_x | :math:`x'_{LL}` | State | :math:`V_{i}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LA_y | :math:`y_{LA}` | State | :math:`K_{A} y_{LL}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | INT_y | :math:`y_{INT}` | State | :math:`- v_{f0} + y_{FEX} y_{INT}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_x | :math:`x'_{WF}` | State | :math:`V_{FE}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`E_{term}` | Algeb | :math:`V` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} v_{f0}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`I_{N}` | Algeb | :math:`- I_{N} y_{INT} + K_{C} X_{ad}I_{fd}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | FEX_y | :math:`y_{FEX}` | Algeb | :math:`- y_{FEX} + \operatorname{FixPiecewise}{\left(\left( 1, \ I_{N} \leq 0\right),\left( 1 - 0.577 I_{N}, \ I_{N} \leq 0.433\right),\left( \sqrt{0.75 - I_{N}^{2}}, \ I_{N} \leq 0.75\right),\left( 1.732 - 1.732 I_{N}, \ I_{N} \leq 1\right),\left( 0, \ \text{True}\right) \right)}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`- E_{term} + V_{ref}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`V_{i}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`V_{out}*S_e(|V_{out}|)` | Algeb | :math:`B^q_{SAT} \left(- A^q_{SAT} + y_{INT}\right)^{2} \operatorname{Indicator}{\left(y_{INT} > A^q_{SAT} \right)}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VFE | :math:`V_{FE}` | Algeb | :math:`K_{C} X_{ad}I_{fd} + K_{E} y_{INT} + V_{out}*S_e(|V_{out}|)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`E_{term} + \frac{K_{L} V_{FE} + \frac{V_{FE}}{K_{B}}}{K_{A}}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`y_{WF}` | Algeb | :math:`0` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VHA | :math:`VHA` | Algeb | :math:`- K_{H} V_{FE} + y_{LA}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VL | :math:`VL` | Algeb | :math:`K_{L} \left(VLRx - V_{FE}\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LVG_y | :math:`y_{LVG}` | Algeb | :math:`LVG_{lt z0} VL + LVG_{lt z1} VHA` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VR_x | :math:`x_{VR}` | Algeb | :math:`K_{B} y_{LVG}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VR_y | :math:`y_{VR}` | Algeb | :math:`VR_{lim zi} x_{VR} + VR_{lim zl} V_{RMIN} + VR_{lim zu} V_{RMAX}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VLRx | :math:`VLRx` | Algeb | :math:`V_{LR} \operatorname{Indicator}{\left(V_{FE} + \frac{V_{FE}}{K_{B} K_{L}} < V_{LR} \right)} + \left(V_{FE} + \frac{V_{FE}}{K_{B} K_{L}}\right) \operatorname{Indicator}{\left(V_{FE} + \frac{V_{FE}}{K_{B} K_{L}} > V_{LR} \right)}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+----------------------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+==============================================+=============+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term} - y_{LG}` | :math:`T_R` | +--------+-----------------+----------+----------------------------------------------+-------------+ | LL_x | :math:`x'_{LL}` | State | :math:`V_{i} - x'_{LL}` | :math:`T_B` | +--------+-----------------+----------+----------------------------------------------+-------------+ | LA_y | :math:`y_{LA}` | State | :math:`K_{A} y_{LL} - y_{LA}` | :math:`T_A` | +--------+-----------------+----------+----------------------------------------------+-------------+ | INT_y | :math:`y_{INT}` | State | :math:`u_{e} \left(- V_{FE} + y_{VR}\right)` | :math:`T_E` | +--------+-----------------+----------+----------------------------------------------+-------------+ | WF_x | :math:`x'_{WF}` | State | :math:`V_{FE} - x'_{WF}` | :math:`T_F` | +--------+-----------------+----------+----------------------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+----------------------------------------------+-------------+ Algebraic Equations ----------------------------- +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+================================+==========+=================================================================================================================================================================================================================================================================================================+ | v | :math:`E_{term}` | Algeb | :math:`- E_{term} + V` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} \left(- v_{out} + y_{FEX} y_{INT}\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`I_{N}` | Algeb | :math:`u_{e} \left(- I_{N} y_{INT} + K_{C} X_{ad}I_{fd}\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | FEX_y | :math:`y_{FEX}` | Algeb | :math:`- y_{FEX} + \operatorname{FixPiecewise}{\left(\left( 1, \ I_{N} \leq 0\right),\left( 1 - 0.577 I_{N}, \ I_{N} \leq 0.433\right),\left( \sqrt{0.75 - I_{N}^{2}}, \ I_{N} \leq 0.75\right),\left( 1.732 - 1.732 I_{N}, \ I_{N} \leq 1\right),\left( 0, \ \text{True}\right) \right)}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`u_{e} \left(- E_{term} - V_{i} + V_{ref} - y_{WF}\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- x'_{LL} + y_{LL}\right) + T_{B} x'_{LL} - T_{B} y_{LL} + T_{C} \left(V_{i} - x'_{LL}\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`V_{out}*S_e(|V_{out}|)` | Algeb | :math:`u_{e} \left(B^q_{SAT} z_{0}^{SL} \left(- A^q_{SAT} + y_{INT}\right)^{2} - V_{out}*S_e(|V_{out}|)\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VFE | :math:`V_{FE}` | Algeb | :math:`u_{e} \left(K_{C} X_{ad}I_{fd} + K_{E} y_{INT} - V_{FE} + V_{out}*S_e(|V_{out}|)\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`V_{ref0} - V_{ref}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`y_{WF}` | Algeb | :math:`K_{F} \left(V_{FE} - x'_{WF}\right) - T_{F} y_{WF}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VHA | :math:`VHA` | Algeb | :math:`- K_{H} V_{FE} - VHA + y_{LA}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VL | :math:`VL` | Algeb | :math:`K_{L} \left(VLRx - V_{FE}\right) - VL` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LVG_y | :math:`y_{LVG}` | Algeb | :math:`LVG_{lt z0} VL + LVG_{lt z1} VHA - y_{LVG}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VR_x | :math:`x_{VR}` | Algeb | :math:`K_{B} y_{LVG} - x_{VR}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VR_y | :math:`y_{VR}` | Algeb | :math:`VR_{lim zi} x_{VR} + VR_{lim zl} V_{RMIN} + VR_{lim zu} V_{RMAX} - y_{VR}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VLRx | :math:`VLRx` | Algeb | :math:`VLR_{0} - VLRx` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | :math:`u_{e} \left(- v_{f0} + v_{out}\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | :math:`0` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | :math:`0` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | :math:`0` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +==========+=======================+=============================================================================================================================================================================================================================================+=================+ | ue | :math:`u_e` | :math:`u u_{g}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E1 | :math:`E^{1c}_{SAT}` | :math:`E_{1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E2 | :math:`E^{2c}_{SAT}` | :math:`E_{2} - 2 z^{SE2}_{SAT} + 2` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE1 | :math:`SE^{1c}_{SAT}` | :math:`S_{E1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE2 | :math:`SE^{2c}_{SAT}` | :math:`S_{E2} - 2 z^{SE2}_{SAT} + 2` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_a | :math:`a_{SAT}` | :math:`\sqrt{\frac{E^{1c}_{SAT} SE^{1c}_{SAT}}{E^{2c}_{SAT} SE^{2c}_{SAT}}} \left(\operatorname{Indicator}{\left(SE^{2c}_{SAT} > 0 \right)} + \operatorname{Indicator}{\left(SE^{2c}_{SAT} < 0 \right)}\right)` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_A | :math:`A^q_{SAT}` | :math:`E^{2c}_{SAT} - \frac{E^{1c}_{SAT} - E^{2c}_{SAT}}{a_{SAT} - 1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_B | :math:`B^q_{SAT}` | :math:`\frac{E^{2c}_{SAT} SE^{2c}_{SAT} \left(a_{SAT} - 1\right)^{2} \left(\operatorname{Indicator}{\left(a_{SAT} > 0 \right)} + \operatorname{Indicator}{\left(a_{SAT} < 0 \right)}\right)}{\left(E^{1c}_{SAT} - E^{2c}_{SAT}\right)^{2}}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`V_{ref}` | PostInitService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VLR0 | :math:`VLR0` | :math:`VLRx` | PostInitService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ Discretes ----------- +---------+--------------------+-------------+----------------+ | Name | Symbol | Type | Info | +=========+====================+=============+================+ | LL_LT1 | :math:`LT_{LL}` | LessThan | | +---------+--------------------+-------------+----------------+ | LL_LT2 | :math:`LT_{LL}` | LessThan | | +---------+--------------------+-------------+----------------+ | LA_lim | :math:`lim_{LA}` | AntiWindup | Limiter in Lag | +---------+--------------------+-------------+----------------+ | SL | :math:`SL` | LessThan | | +---------+--------------------+-------------+----------------+ | LVG_lt | :math:`None_{LVG}` | LessThan | | +---------+--------------------+-------------+----------------+ | VR_lim | :math:`lim_{VR}` | HardLimiter | | +---------+--------------------+-------------+----------------+ Blocks ------- +------+-------------+---------------+-----------------------------+ | Name | Symbol | Type | Info | +======+=============+===============+=============================+ | SAT | :math:`SAT` | ExcQuadSat | Field voltage saturation | +------+-------------+---------------+-----------------------------+ | FEX | :math:`FEX` | Piecewise | Piecewise function FEX | +------+-------------+---------------+-----------------------------+ | LG | :math:`LG` | Lag | Voltage transducer | +------+-------------+---------------+-----------------------------+ | LL | :math:`LL` | LeadLag | Regulator | +------+-------------+---------------+-----------------------------+ | LA | :math:`LA` | LagAntiWindup | Lag AW on VR | +------+-------------+---------------+-----------------------------+ | INT | :math:`INT` | Integrator | Integrator | +------+-------------+---------------+-----------------------------+ | WF | :math:`WF` | Washout | Stablizing circuit feedback | +------+-------------+---------------+-----------------------------+ | LVG | :math:`LVG` | LVGate | | +------+-------------+---------------+-----------------------------+ | VR | :math:`VR` | GainLimiter | | +------+-------------+---------------+-----------------------------+ Config Fields in [EXAC2] +---------------+--------+-------+---------------------------------------+-----------------+ | Option | Symbol | Value | Info | Accepted values | +===============+========+=======+=======================================+=================+ | allow_adjust | | 1 | allow adjusting upper or lower limits | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_lower | | 0 | adjust lower limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_upper | | 1 | adjust upper limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _EXAC4: -------------------------------------------------------------------------------- EXAC4 -------------------------------------------------------------------------------- IEEE Type AC4 excitation system model. Parameters ---------- +--------+------------------+----------------------------------+---------+--------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +========+==================+==================================+=========+========+============+ | idx | | unique device idx | | | | +--------+------------------+----------------------------------+---------+--------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +--------+------------------+----------------------------------+---------+--------+------------+ | name | | device name | | | | +--------+------------------+----------------------------------+---------+--------+------------+ | syn | | Synchronous generator idx | | | mandatory | +--------+------------------+----------------------------------+---------+--------+------------+ | TR | :math:`T_R` | Sensing time constant | 0.010 | *p.u.* | | +--------+------------------+----------------------------------+---------+--------+------------+ | VIMAX | :math:`V_{IMAX}` | Max. input voltage | 5 | | | +--------+------------------+----------------------------------+---------+--------+------------+ | VIMIN | :math:`V_{IMIN}` | Min. input voltage | -0.100 | | | +--------+------------------+----------------------------------+---------+--------+------------+ | TC | :math:`T_C` | Lead time constant in lead-lag | 1 | *p.u.* | | +--------+------------------+----------------------------------+---------+--------+------------+ | TB | :math:`T_B` | Lag time constant in lead-lag | 1 | *p.u.* | | +--------+------------------+----------------------------------+---------+--------+------------+ | KA | :math:`K_A` | Regulator gain | 80 | | | +--------+------------------+----------------------------------+---------+--------+------------+ | TA | :math:`T_A` | Lag time constant in regulator | 0.040 | *p.u.* | | +--------+------------------+----------------------------------+---------+--------+------------+ | VRMAX | :math:`V_{RMAX}` | Maximum excitation limit | 8 | *p.u.* | | +--------+------------------+----------------------------------+---------+--------+------------+ | VRMIN | :math:`V_{RMIN}` | Minimum excitation limit | 0 | *p.u.* | | +--------+------------------+----------------------------------+---------+--------+------------+ | KC | :math:`K_C` | Reactive power compensation gain | 0 | | | +--------+------------------+----------------------------------+---------+--------+------------+ | ug | :math:`u_g` | Generator online status | 0 | *bool* | | +--------+------------------+----------------------------------+---------+--------+------------+ | Sn | :math:`S_m` | Rated power from generator | 0 | *MVA* | | +--------+------------------+----------------------------------+---------+--------+------------+ | Vn | :math:`V_m` | Rated voltage from generator | 0 | *kV* | | +--------+------------------+----------------------------------+---------+--------+------------+ | bus | :math:`bus` | Bus idx of the generators | 0 | | | +--------+------------------+----------------------------------+---------+--------+------------+ Variables --------- +---------+----------------------+----------+---------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +=========+======================+==========+=======================================+========+============+ | LG_y | :math:`y_{LG}` | State | State in lag transfer function | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | LL_x | :math:`x'_{LL}` | State | State in lead-lag | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | LR_y | :math:`y_{LR}` | State | State in lag transfer function | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | v | :math:`E_{term}` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vout | :math:`v_{out}` | Algeb | Exciter final output voltage | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vi | :math:`V_{i}` | Algeb | Total input voltages | *p.u.* | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | LL_y | :math:`y_{LL}` | Algeb | Output of lead-lag | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vfmax | :math:`V_{fmax}` | Algeb | Upper bound of output limiter | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vfmin | :math:`V_{fmin}` | Algeb | Lower bound of output limiter | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vf | :math:`v_{f}` | ExtAlgeb | Excitation field voltage to generator | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | Armature excitation current | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | a | :math:`\theta` | ExtAlgeb | Bus voltage phase angle | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vbus | :math:`V` | ExtAlgeb | Bus voltage magnitude | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ Initialization Equations ------------------------ +---------+----------------------+----------+-------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+======================+==========+=========================================================================+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term}` | +---------+----------------------+----------+-------------------------------------------------------------------------+ | LL_x | :math:`x'_{LL}` | State | :math:`V_{i} z_{i}^{HLI} + V_{IMAX} z_{u}^{HLI} + V_{IMIN} z_{l}^{HLI}` | +---------+----------------------+----------+-------------------------------------------------------------------------+ | LR_y | :math:`y_{LR}` | State | :math:`K_{A} y_{LL}` | +---------+----------------------+----------+-------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+----------------------+----------+-------------------------------------------------------------------------+ | v | :math:`E_{term}` | Algeb | :math:`V` | +---------+----------------------+----------+-------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} v_{f0}` | +---------+----------------------+----------+-------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`\frac{v_{f0}}{K_{A}}` | +---------+----------------------+----------+-------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`V_{i} z_{i}^{HLI} + V_{IMAX} z_{u}^{HLI} + V_{IMIN} z_{l}^{HLI}` | +---------+----------------------+----------+-------------------------------------------------------------------------+ | vfmax | :math:`V_{fmax}` | Algeb | :math:`- K_{C} X_{ad}I_{fd} + V_{RMAX}` | +---------+----------------------+----------+-------------------------------------------------------------------------+ | vfmin | :math:`V_{fmin}` | Algeb | :math:`- K_{C} X_{ad}I_{fd} + V_{RMIN}` | +---------+----------------------+----------+-------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+-----------------------------------------------------------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+===================================================================================+=============+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term} - y_{LG}` | :math:`T_R` | +--------+-----------------+----------+-----------------------------------------------------------------------------------+-------------+ | LL_x | :math:`x'_{LL}` | State | :math:`V_{i} z_{i}^{HLI} + V_{IMAX} z_{u}^{HLI} + V_{IMIN} z_{l}^{HLI} - x'_{LL}` | :math:`T_B` | +--------+-----------------+----------+-----------------------------------------------------------------------------------+-------------+ | LR_y | :math:`y_{LR}` | State | :math:`K_{A} y_{LL} - y_{LR}` | :math:`T_A` | +--------+-----------------+----------+-----------------------------------------------------------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+-----------------------------------------------------------------------------------+-------------+ Algebraic Equations ----------------------------- +---------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+======================+==========+===============================================================================================================================================================================================+ | v | :math:`E_{term}` | Algeb | :math:`- E_{term} + V` | +---------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} \left(V_{fmax} z_{u}^{HLR} + V_{fmin} z_{l}^{HLR} + y_{LR} z_{i}^{HLR}\right) - v_{out}` | +---------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`- V_{i} + V_{ref0} - y_{LG}` | +---------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- x'_{LL} + y_{LL}\right) + T_{B} x'_{LL} - T_{B} y_{LL} + T_{C} \left(V_{i} z_{i}^{HLI} + V_{IMAX} z_{u}^{HLI} + V_{IMIN} z_{l}^{HLI} - x'_{LL}\right)` | +---------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vfmax | :math:`V_{fmax}` | Algeb | :math:`- K_{C} X_{ad}I_{fd} + V_{RMAX} - V_{fmax}` | +---------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vfmin | :math:`V_{fmin}` | Algeb | :math:`- K_{C} X_{ad}I_{fd} + V_{RMIN} - V_{fmin}` | +---------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | :math:`u_{e} \left(- v_{f0} + v_{out}\right)` | +---------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +--------+------------------+-----------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +========+==================+=========================================+=================+ | ue | :math:`u_e` | :math:`u u_{g}` | ConstService | +--------+------------------+-----------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`E_{term} + \frac{v_{f0}}{K_{A}}` | PostInitService | +--------+------------------+-----------------------------------------+-----------------+ Discretes ----------- +---------+-----------------+-------------+----------------------------------+ | Name | Symbol | Type | Info | +=========+=================+=============+==================================+ | HLI | :math:`HLI` | HardLimiter | Hard limiter on input | +---------+-----------------+-------------+----------------------------------+ | LL_LT1 | :math:`LT_{LL}` | LessThan | | +---------+-----------------+-------------+----------------------------------+ | LL_LT2 | :math:`LT_{LL}` | LessThan | | +---------+-----------------+-------------+----------------------------------+ | HLR | :math:`HLR` | HardLimiter | Hard limiter on regulator output | +---------+-----------------+-------------+----------------------------------+ Blocks ------- +------+------------+---------+----------------------+ | Name | Symbol | Type | Info | +======+============+=========+======================+ | LG | :math:`LG` | Lag | Sensing delay | +------+------------+---------+----------------------+ | LL | :math:`LL` | LeadLag | Lead-lag compensator | +------+------------+---------+----------------------+ | LR | :math:`LR` | Lag | Regulator | +------+------------+---------+----------------------+ Config Fields in [EXAC4] +---------------+--------+-------+---------------------------------------+-----------------+ | Option | Symbol | Value | Info | Accepted values | +===============+========+=======+=======================================+=================+ | allow_adjust | | 1 | allow adjusting upper or lower limits | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_lower | | 0 | adjust lower limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_upper | | 1 | adjust upper limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _ESST4B: -------------------------------------------------------------------------------- ESST4B -------------------------------------------------------------------------------- Parameters ---------- +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +=========+==================+================================================================+=========+==========+============+ | idx | | unique device idx | | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | name | | device name | | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | syn | | Synchronous generator idx | | | mandatory | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | TR | :math:`T_R` | Sensing time constant | 0.010 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | KPR | :math:`K_{PR}` | Proportional gain 1 | 1 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | KIR | :math:`K_{IR}` | Integral gain 1 | 0 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | VRMAX | :math:`V_{RMAX}` | Maximum regulator limit | 8 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | VRMIN | :math:`V_{RMIN}` | Minimum regulator limit | 0 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | TA | :math:`T_A` | Lag time constant | 0.100 | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | KPM | :math:`K_{PM}` | Proportional gain 2 | 1 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | KIM | :math:`K_{IM}` | Integral gain 2 | 0 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | VMMAX | :math:`V_{RMAX}` | Maximum inner loop limit | 8 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | VMMIN | :math:`V_{RMIN}` | Minimum inner loop limit | 0 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | KG | :math:`K_G` | Feedback gain of inner field regulator | 1 | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | KP | :math:`K_P` | Potential circuit gain coeff. | 4 | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | KI | :math:`K_I` | Potential circuit gain coeff. | 0.100 | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | VBMAX | :math:`V_{BMAX}` | VB upper limit | 18 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | KC | :math:`K_C` | Rectifier loading factor proportional to commutating reactance | 0.100 | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | XL | :math:`X_L` | Potential source reactance | 0.010 | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | THETAP | :math:`\theta_P` | Rectifier firing angle | 0 | *degree* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | VGMAX | :math:`V_{GMAX}` | VG upper limit | 20 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | ug | :math:`u_g` | Generator online status | 0 | *bool* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | Sn | :math:`S_m` | Rated power from generator | 0 | *MVA* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | Vn | :math:`V_m` | Rated voltage from generator | 0 | *kV* | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ | bus | :math:`bus` | Bus idx of the generators | 0 | | | +---------+------------------+----------------------------------------------------------------+---------+----------+------------+ Variables --------- +---------+----------------------+----------+---------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +=========+======================+==========+=======================================+========+============+ | LG_y | :math:`y_{LG}` | State | State in lag transfer function | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | PI1_xi | :math:`xi_{PI1}` | State | Integrator output | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | LA_y | :math:`y_{LA}` | State | State in lag transfer function | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | PI2_xi | :math:`xi_{PI2}` | State | Integrator output | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | v | :math:`E_{term}` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vout | :math:`v_{out}` | Algeb | Exciter final output voltage | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | UEL | :math:`U_{EL}` | Algeb | Interface var for under exc. limiter | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | IN | :math:`I_{N}` | Algeb | Input to FEX | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | FEX_y | :math:`y_{FEX}` | Algeb | Output of piecewise | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | VB_x | :math:`x_{VB}` | Algeb | Value before limiter | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | VB_y | :math:`y_{VB}` | Algeb | Output after limiter and post gain | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | VG_x | :math:`x_{VG}` | Algeb | Value before limiter | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | VG_y | :math:`y_{VG}` | Algeb | Output after limiter and post gain | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vref | :math:`V_{ref}` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vi | :math:`V_{i}` | Algeb | Total input voltages | *p.u.* | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | PI1_ys | :math:`ys_{PI1}` | Algeb | PI summation before limit | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | PI1_y | :math:`y_{PI1}` | Algeb | PI output | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | PI2_ys | :math:`ys_{PI2}` | Algeb | PI summation before limit | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | PI2_y | :math:`y_{PI2}` | Algeb | PI output | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vf | :math:`v_{f}` | ExtAlgeb | Excitation field voltage to generator | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | Armature excitation current | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | a | :math:`\theta` | ExtAlgeb | Bus voltage phase angle | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vbus | :math:`V` | ExtAlgeb | Bus voltage magnitude | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vd | :math:`V_{d}` | ExtAlgeb | d-axis machine voltage | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vq | :math:`V_{q}` | ExtAlgeb | q-axis machine voltage | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | Id | :math:`I_{d}` | ExtAlgeb | d-axis machine current | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | Iq | :math:`I_{q}` | ExtAlgeb | q-axis machine current | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ Initialization Equations ------------------------ +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+======================+==========+=====================================================================================================================================================================================================================================================================================+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PI1_xi | :math:`xi_{PI1}` | State | :math:`y_{VG}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LA_y | :math:`y_{LA}` | State | :math:`1.0 y_{PI1}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PI2_xi | :math:`xi_{PI2}` | State | :math:`\operatorname{safe}_{div}{\left(v_{f0},y_{VB} \right)}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`E_{term}` | Algeb | :math:`V` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} v_{f0}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`U_{EL}` | Algeb | :math:`0` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`I_{N}` | Algeb | :math:`\operatorname{safe}_{div}{\left(K_{C} X_{ad}I_{fd},V_{E} \right)}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | FEX_y | :math:`y_{FEX}` | Algeb | :math:`\operatorname{FixPiecewise}{\left(\left( 1, \ I_{N} \leq 0\right),\left( 1 - 0.577 I_{N}, \ I_{N} \leq 0.433\right),\left( \sqrt{0.75 - I_{N}^{2}}, \ I_{N} \leq 0.75\right),\left( 1.732 - 1.732 I_{N}, \ I_{N} \leq 1\right),\left( 0, \ \text{True}\right) \right)}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VB_x | :math:`x_{VB}` | Algeb | :math:`V_{E} y_{FEX}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VB_y | :math:`y_{VB}` | Algeb | :math:`VB_{lim zi} x_{VB} + VB_{lim zu} V_{BMAX}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VG_x | :math:`x_{VG}` | Algeb | :math:`K_{G} v_{out}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VG_y | :math:`y_{VG}` | Algeb | :math:`VG_{lim zi} x_{VG} + VG_{lim zu} V_{GMAX}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`E_{term}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`- E_{term} + V_{ref}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PI1_ys | :math:`ys_{PI1}` | Algeb | :math:`K_{PR} V_{i} + y_{VG}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PI1_y | :math:`y_{PI1}` | Algeb | :math:`\pi_{1 lim zi} ys_{PI1} + \pi_{1 lim zl} V_{RMIN} + \pi_{1 lim zu} V_{RMAX}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PI2_ys | :math:`ys_{PI2}` | Algeb | :math:`K_{PM} \left(y_{LA} - y_{VG}\right) + \operatorname{safe}_{div}{\left(v_{f0},y_{VB} \right)}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PI2_y | :math:`y_{PI2}` | Algeb | :math:`\pi_{2 lim zi} ys_{PI2} + \pi_{2 lim zl} V_{RMIN} + \pi_{2 lim zu} V_{RMAX}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vd | :math:`V_{d}` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vq | :math:`V_{q}` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Id | :math:`I_{d}` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iq | :math:`I_{q}` | ExtAlgeb | | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +---------+------------------+----------+----------------------------------------------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +=========+==================+==========+======================================================================+=============+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term} - y_{LG}` | :math:`T_R` | +---------+------------------+----------+----------------------------------------------------------------------+-------------+ | PI1_xi | :math:`xi_{PI1}` | State | :math:`K_{IR} \left(V_{i} + 2 y_{PI1} - 2 ys_{PI1}\right)` | | +---------+------------------+----------+----------------------------------------------------------------------+-------------+ | LA_y | :math:`y_{LA}` | State | :math:`- y_{LA} + 1.0 y_{PI1}` | :math:`T_A` | +---------+------------------+----------+----------------------------------------------------------------------+-------------+ | PI2_xi | :math:`xi_{PI2}` | State | :math:`K_{IM} \left(y_{LA} + 2 y_{PI2} - y_{VG} - 2 ys_{PI2}\right)` | | +---------+------------------+----------+----------------------------------------------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +---------+------------------+----------+----------------------------------------------------------------------+-------------+ Algebraic Equations ----------------------------- +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+======================+==========+=================================================================================================================================================================================================================================================================================================+ | v | :math:`E_{term}` | Algeb | :math:`- E_{term} + V` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} y_{PI2} y_{VB} - v_{out}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`U_{EL}` | Algeb | :math:`- U_{EL}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`I_{N}` | Algeb | :math:`u_{e} \left(- I_{N} V_{E} + K_{C} X_{ad}I_{fd}\right)` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | FEX_y | :math:`y_{FEX}` | Algeb | :math:`- y_{FEX} + \operatorname{FixPiecewise}{\left(\left( 1, \ I_{N} \leq 0\right),\left( 1 - 0.577 I_{N}, \ I_{N} \leq 0.433\right),\left( \sqrt{0.75 - I_{N}^{2}}, \ I_{N} \leq 0.75\right),\left( 1.732 - 1.732 I_{N}, \ I_{N} \leq 1\right),\left( 0, \ \text{True}\right) \right)}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VB_x | :math:`x_{VB}` | Algeb | :math:`V_{E} y_{FEX} - x_{VB}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VB_y | :math:`y_{VB}` | Algeb | :math:`VB_{lim zi} x_{VB} + VB_{lim zu} V_{BMAX} - y_{VB}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VG_x | :math:`x_{VG}` | Algeb | :math:`K_{G} v_{out} - x_{VG}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VG_y | :math:`y_{VG}` | Algeb | :math:`VG_{lim zi} x_{VG} + VG_{lim zu} V_{GMAX} - y_{VG}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`V_{ref0} - V_{ref}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`- V_{i} + V_{ref} - y_{LG}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PI1_ys | :math:`ys_{PI1}` | Algeb | :math:`K_{PR} V_{i} + xi_{PI1} - ys_{PI1}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PI1_y | :math:`y_{PI1}` | Algeb | :math:`\pi_{1 lim zi} ys_{PI1} + \pi_{1 lim zl} V_{RMIN} + \pi_{1 lim zu} V_{RMAX} - y_{PI1}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PI2_ys | :math:`ys_{PI2}` | Algeb | :math:`K_{PM} \left(y_{LA} - y_{VG}\right) + xi_{PI2} - ys_{PI2}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PI2_y | :math:`y_{PI2}` | Algeb | :math:`\pi_{2 lim zi} ys_{PI2} + \pi_{2 lim zl} V_{RMIN} + \pi_{2 lim zu} V_{RMAX} - y_{PI2}` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | :math:`u_{e} \left(- v_{f0} + v_{out}\right)` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vd | :math:`V_{d}` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vq | :math:`V_{q}` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Id | :math:`I_{d}` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iq | :math:`I_{q}` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +--------+------------------+-------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +========+==================+===============================================================================================================================+=================+ | ue | :math:`u_e` | :math:`u u_{g}` | ConstService | +--------+------------------+-------------------------------------------------------------------------------------------------------------------------------+-----------------+ | KPC | :math:`K_{PC}` | :math:`K_{P} e^{i \operatorname{radians}{\left(\theta_{P} \right)}}` | ConstService | +--------+------------------+-------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VE | :math:`V_E` | :math:`\left|{K_{PC} \left(V_{d} + i V_{q}\right) + i \left(I_{d} + i I_{q}\right) \left(K_{I} + K_{PC} X_{L}\right)}\right|` | VarService | +--------+------------------+-------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`V_{ref}` | PostInitService | +--------+------------------+-------------------------------------------------------------------------------------------------------------------------------+-----------------+ Discretes ----------- +----------+-------------------+-------------+------+ | Name | Symbol | Type | Info | +==========+===================+=============+======+ | VB_lim | :math:`lim_{VB}` | HardLimiter | | +----------+-------------------+-------------+------+ | VG_lim | :math:`lim_{VG}` | HardLimiter | | +----------+-------------------+-------------+------+ | PI1_lim | :math:`lim_{PI1}` | HardLimiter | | +----------+-------------------+-------------+------+ | PI2_lim | :math:`lim_{PI2}` | HardLimiter | | +----------+-------------------+-------------+------+ Blocks ------- +------+-------------+-------------+------------------------+ | Name | Symbol | Type | Info | +======+=============+=============+========================+ | LG | :math:`LG` | Lag | Voltage transducer | +------+-------------+-------------+------------------------+ | FEX | :math:`FEX` | Piecewise | Piecewise function FEX | +------+-------------+-------------+------------------------+ | VB | :math:`VB` | GainLimiter | VB with limiter | +------+-------------+-------------+------------------------+ | VG | :math:`VG` | GainLimiter | Feedback gain with HL | +------+-------------+-------------+------------------------+ | PI1 | :math:`PI1` | PITrackAW | | +------+-------------+-------------+------------------------+ | LA | :math:`LA` | Lag | Regulation delay | +------+-------------+-------------+------------------------+ | PI2 | :math:`PI2` | PITrackAW | | +------+-------------+-------------+------------------------+ Config Fields in [ESST4B] +---------------+----------------+-------+---------------------------------------+-----------------+ | Option | Symbol | Value | Info | Accepted values | +===============+================+=======+=======================================+=================+ | allow_adjust | | 1 | allow adjusting upper or lower limits | (0, 1) | +---------------+----------------+-------+---------------------------------------+-----------------+ | adjust_lower | | 0 | adjust lower limit | (0, 1) | +---------------+----------------+-------+---------------------------------------+-----------------+ | adjust_upper | | 1 | adjust upper limit | (0, 1) | +---------------+----------------+-------+---------------------------------------+-----------------+ | ksr | :math:`K_{sr}` | 2 | Tracking gain for outer PI controller | | +---------------+----------------+-------+---------------------------------------+-----------------+ | ksm | :math:`K_{sm}` | 2 | Tracking gain for inner PI controller | | +---------------+----------------+-------+---------------------------------------+-----------------+ .. _AC8B: -------------------------------------------------------------------------------- AC8B -------------------------------------------------------------------------------- Exciter AC8B model. Reference: [1]_, [2]_ .. [1] Powerworld, Exciter AC8B, [Online], Available: https://www.powerworld.com/WebHelp/Content/TransientModels_HTML/Exciter%20AC8B.htm .. [2] NEPLAN, Exciters Models, [Online], Available: https://www.neplan.ch/wp-content/uploads/2015/08/Nep_EXCITERS1.pdf Parameters ---------- +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +=========+===================+================================================================+=========+========+============+ | idx | | unique device idx | | | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | name | | device name | | | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | syn | | Synchronous generator idx | | | mandatory | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | TR | :math:`T_R` | Sensing time constant | 0.010 | *p.u.* | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | kP | :math:`k_P` | PID proportional coeff. | 10 | | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | kI | :math:`k_I` | PID integrative coeff. | 10 | | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | kD | :math:`k_D` | PID derivative coeff. | 10 | | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | Td | :math:`T_d` | PID derivative time constant. | 0.200 | | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | VPMAX | :math:`V_{PMAX}` | PID maximum limit | 999 | *p.u.* | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | VPMIN | :math:`V_{PMIN}` | PID minimum limit | -999 | *p.u.* | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | VRMAX | :math:`V_{RMAX}` | Maximum regulator limit | 7.300 | *p.u.* | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | VRMIN | :math:`V_{RMIN}` | Minimum regulator limit | 1 | *p.u.* | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | VFEMAX | :math:`V_{FEMAX}` | Exciter field current limit | 999 | *p.u.* | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | VEMIN | :math:`V_{EMIN}` | Minimum exciter voltage output | -999 | *p.u.* | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | TA | :math:`T_A` | Lag time constant in anti-windup lag | 0.040 | *p.u.* | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | KA | :math:`K_A` | Gain in anti-windup lag TF | 40 | *p.u.* | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | TE | :math:`T_E` | Exciter integrator time constant | 0.800 | *p.u.* | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | E1 | :math:`E_1` | First saturation point | 0 | *p.u.* | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | SE1 | :math:`S_{E1}` | Value at first saturation point | 0 | *p.u.* | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | E2 | :math:`E_2` | Second saturation point | 1 | *p.u.* | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | SE2 | :math:`S_{E2}` | Value at second saturation point | 1 | *p.u.* | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | KE | :math:`K_E` | Gain added to saturation | 1 | *p.u.* | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | KD | :math:`K_D` | Ifd feedback gain | 0 | | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | KC | :math:`K_C` | Rectifier loading factor proportional to commutating reactance | 0.100 | | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | ug | :math:`u_g` | Generator online status | 0 | *bool* | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | Sn | :math:`S_m` | Rated power from generator | 0 | *MVA* | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | Vn | :math:`V_m` | Rated voltage from generator | 0 | *kV* | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ | bus | :math:`bus` | Bus idx of the generators | 0 | | | +---------+-------------------+----------------------------------------------------------------+---------+--------+------------+ Variables --------- +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | Name | Symbol | Type | Description | Unit | Properties | +===========+================================+==========+=======================================+========+==============+ | LG_y | :math:`y_{LG}` | State | State in lag transfer function | | v_str | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | PID_xi | :math:`xi_{PID}` | State | Integrator output | | v_str | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | PID_WO_x | :math:`x'_{PID\ {WO}_{PID}}` | State | State in washout filter | | v_str | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | LA_y | :math:`y_{LA}` | State | State in lag TF | | v_str | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | INT_y | :math:`y_{INT}` | State | Integrator output | | v_str,v_iter | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | v | :math:`E_{term}` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | vout | :math:`v_{out}` | Algeb | Exciter final output voltage | | v_str | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | IN | :math:`I_{N}` | Algeb | Input to FEX | | v_str,v_iter | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | FEX_y | :math:`y_{FEX}` | Algeb | Output of piecewise | | v_str,v_iter | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | UEL | :math:`U_{EL}` | Algeb | Interface var for under exc. limiter | | v_str | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | OEL | :math:`O_{EL}` | Algeb | Interface var for over exc. limiter | | v_str | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | Vs | :math:`V_{s}` | Algeb | Voltage compensation from PSS | | v_str | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | vref | :math:`V_{ref}` | Algeb | Reference voltage input | *p.u.* | v_str | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | vi | :math:`V_{i}` | Algeb | Total input voltages | *p.u.* | v_str | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | PID_uin | :math:`uin_{PID}` | Algeb | PID input | | v_str | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | PID_WO_y | :math:`y_{PID\ {WO}_{PID}}` | Algeb | Output of washout filter | | v_str | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | PID_ys | :math:`ys_{PID}` | Algeb | PI summation before limit | | v_str | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | PID_y | :math:`y_{PID}` | Algeb | PI output | | v_str | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | Se | :math:`V_{out}*S_e(|V_{out}|)` | Algeb | saturation output | | v_str | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | VFE | :math:`V_{FE}` | Algeb | Combined saturation feedback | *p.u.* | v_str | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | vf | :math:`v_{f}` | ExtAlgeb | Excitation field voltage to generator | | | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | Armature excitation current | | | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | a | :math:`\theta` | ExtAlgeb | Bus voltage phase angle | | | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ | vbus | :math:`V` | ExtAlgeb | Bus voltage magnitude | | | +-----------+--------------------------------+----------+---------------------------------------+--------+--------------+ Initialization Equations ------------------------ +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +===========+================================+==========+=================================================================================================================================================================================================================================================================================================+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term}` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PID_xi | :math:`xi_{PID}` | State | :math:`\frac{V_{FE}}{K_{A}}` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PID_WO_x | :math:`x'_{PID\ {WO}_{PID}}` | State | :math:`uin_{PID}` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LA_y | :math:`y_{LA}` | State | :math:`K_{A} y_{PID}` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | INT_y | :math:`y_{INT}` | State | :math:`- v_{f0} + y_{FEX} y_{INT}` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`E_{term}` | Algeb | :math:`V` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} v_{f0}` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`I_{N}` | Algeb | :math:`- I_{N} y_{INT} + K_{C} X_{ad}I_{fd}` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | FEX_y | :math:`y_{FEX}` | Algeb | :math:`- y_{FEX} + \operatorname{FixPiecewise}{\left(\left( 1, \ I_{N} \leq 0\right),\left( 1 - 0.577 I_{N}, \ I_{N} \leq 0.433\right),\left( \sqrt{0.75 - I_{N}^{2}}, \ I_{N} \leq 0.75\right),\left( 1.732 - 1.732 I_{N}, \ I_{N} \leq 1\right),\left( 0, \ \text{True}\right) \right)}` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`U_{EL}` | Algeb | :math:`UEL_{0}` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | OEL | :math:`O_{EL}` | Algeb | :math:`OEL_{0}` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vs | :math:`V_{s}` | Algeb | :math:`0` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`E_{term}` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`- E_{term} + V_{ref}` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PID_uin | :math:`uin_{PID}` | Algeb | :math:`V_{i}` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PID_WO_y | :math:`y_{PID\ {WO}_{PID}}` | Algeb | :math:`0` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PID_ys | :math:`ys_{PID}` | Algeb | :math:`V_{i} k_{P} + \frac{V_{FE}}{K_{A}}` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PID_y | :math:`y_{PID}` | Algeb | :math:`PID_{lim zi} ys_{PID} + PID_{lim zl} V_{PMIN} + PID_{lim zu} V_{PMAX}` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`V_{out}*S_e(|V_{out}|)` | Algeb | :math:`B^q_{SAT} \left(- A^q_{SAT} + y_{INT}\right)^{2} \operatorname{Indicator}{\left(y_{INT} > A^q_{SAT} \right)}` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VFE | :math:`V_{FE}` | Algeb | :math:`K_{D} X_{ad}I_{fd} + K_{E} y_{INT} + V_{out}*S_e(|V_{out}|)` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +-----------+------------------------------+----------+-----------------------------------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +===========+==============================+==========+===========================================================+=============+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term} - y_{LG}` | :math:`T_R` | +-----------+------------------------------+----------+-----------------------------------------------------------+-------------+ | PID_xi | :math:`xi_{PID}` | State | :math:`k_{I} \left(V_{i} + 2 y_{PID} - 2 ys_{PID}\right)` | | +-----------+------------------------------+----------+-----------------------------------------------------------+-------------+ | PID_WO_x | :math:`x'_{PID\ {WO}_{PID}}` | State | :math:`uin_{PID} - x'_{PID\ {WO}_{PID}}` | :math:`T_d` | +-----------+------------------------------+----------+-----------------------------------------------------------+-------------+ | LA_y | :math:`y_{LA}` | State | :math:`K_{A} y_{PID} - y_{LA}` | :math:`T_A` | +-----------+------------------------------+----------+-----------------------------------------------------------+-------------+ | INT_y | :math:`y_{INT}` | State | :math:`u_{e} \left(- V_{FE} + y_{LA}\right)` | :math:`T_E` | +-----------+------------------------------+----------+-----------------------------------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +-----------+------------------------------+----------+-----------------------------------------------------------+-------------+ Algebraic Equations ----------------------------- +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +===========+================================+==========+=================================================================================================================================================================================================================================================================================================+ | v | :math:`E_{term}` | Algeb | :math:`- E_{term} + V` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} \left(- v_{out} + y_{FEX} y_{INT}\right)` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`I_{N}` | Algeb | :math:`u_{e} \left(- I_{N} y_{INT} + K_{C} X_{ad}I_{fd}\right)` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | FEX_y | :math:`y_{FEX}` | Algeb | :math:`- y_{FEX} + \operatorname{FixPiecewise}{\left(\left( 1, \ I_{N} \leq 0\right),\left( 1 - 0.577 I_{N}, \ I_{N} \leq 0.433\right),\left( \sqrt{0.75 - I_{N}^{2}}, \ I_{N} \leq 0.75\right),\left( 1.732 - 1.732 I_{N}, \ I_{N} \leq 1\right),\left( 0, \ \text{True}\right) \right)}` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`U_{EL}` | Algeb | :math:`UEL_{0} - U_{EL}` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | OEL | :math:`O_{EL}` | Algeb | :math:`OEL_{0} - O_{EL}` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vs | :math:`V_{s}` | Algeb | :math:`- V_{s}` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`V_{ref0} - V_{ref}` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`u_{e} \left(O_{EL} + U_{EL} - V_{i} + V_{ref} + V_{s} - y_{LG}\right)` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PID_uin | :math:`uin_{PID}` | Algeb | :math:`V_{i} - uin_{PID}` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PID_WO_y | :math:`y_{PID\ {WO}_{PID}}` | Algeb | :math:`- T_{d} y_{PID\ {WO}_{PID}} + k_{D} \left(uin_{PID} - x'_{PID\ {WO}_{PID}}\right)` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PID_ys | :math:`ys_{PID}` | Algeb | :math:`V_{i} k_{P} + xi_{PID} + y_{PID\ {WO}_{PID}} - ys_{PID}` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PID_y | :math:`y_{PID}` | Algeb | :math:`PID_{lim zi} ys_{PID} + PID_{lim zl} V_{PMIN} + PID_{lim zu} V_{PMAX} - y_{PID}` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`V_{out}*S_e(|V_{out}|)` | Algeb | :math:`u_{e} \left(B^q_{SAT} z_{0}^{SL} \left(- A^q_{SAT} + y_{INT}\right)^{2} - V_{out}*S_e(|V_{out}|)\right)` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VFE | :math:`V_{FE}` | Algeb | :math:`u_{e} \left(K_{D} X_{ad}I_{fd} + K_{E} y_{INT} - V_{FE} + V_{out}*S_e(|V_{out}|)\right)` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | :math:`u_{e} \left(- v_{f0} + v_{out}\right)` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | :math:`0` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | :math:`0` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | :math:`0` | +-----------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +==========+=======================+=============================================================================================================================================================================================================================================+=================+ | ue | :math:`u_e` | :math:`u u_{g}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | UEL0 | :math:`UEL0` | :math:`0` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | OEL0 | :math:`OEL0` | :math:`0` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E1 | :math:`E^{1c}_{SAT}` | :math:`E_{1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E2 | :math:`E^{2c}_{SAT}` | :math:`E_{2} - 2 z^{SE2}_{SAT} + 2` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE1 | :math:`SE^{1c}_{SAT}` | :math:`S_{E1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE2 | :math:`SE^{2c}_{SAT}` | :math:`S_{E2} - 2 z^{SE2}_{SAT} + 2` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_a | :math:`a_{SAT}` | :math:`\sqrt{\frac{E^{1c}_{SAT} SE^{1c}_{SAT}}{E^{2c}_{SAT} SE^{2c}_{SAT}}} \left(\operatorname{Indicator}{\left(SE^{2c}_{SAT} > 0 \right)} + \operatorname{Indicator}{\left(SE^{2c}_{SAT} < 0 \right)}\right)` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_A | :math:`A^q_{SAT}` | :math:`E^{2c}_{SAT} - \frac{E^{1c}_{SAT} - E^{2c}_{SAT}}{a_{SAT} - 1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_B | :math:`B^q_{SAT}` | :math:`\frac{E^{2c}_{SAT} SE^{2c}_{SAT} \left(a_{SAT} - 1\right)^{2} \left(\operatorname{Indicator}{\left(a_{SAT} > 0 \right)} + \operatorname{Indicator}{\left(a_{SAT} < 0 \right)}\right)}{\left(E^{1c}_{SAT} - E^{2c}_{SAT}\right)^{2}}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`E_{term}` | PostInitService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ Discretes ----------- +----------+-------------------+-------------+----------------+ | Name | Symbol | Type | Info | +==========+===================+=============+================+ | PID_lim | :math:`lim_{PID}` | HardLimiter | | +----------+-------------------+-------------+----------------+ | LA_lim | :math:`lim_{LA}` | AntiWindup | Limiter in Lag | +----------+-------------------+-------------+----------------+ | SL | :math:`SL` | LessThan | | +----------+-------------------+-------------+----------------+ Blocks ------- +---------+-------------------------+---------------+--------------------------+ | Name | Symbol | Type | Info | +=========+=========================+===============+==========================+ | FEX | :math:`FEX` | Piecewise | Piecewise function FEX | +---------+-------------------------+---------------+--------------------------+ | LG | :math:`LG` | Lag | Voltage transducer | +---------+-------------------------+---------------+--------------------------+ | PID | :math:`PID` | PIDTrackAW | PID | +---------+-------------------------+---------------+--------------------------+ | PID_WO | :math:`PID\ {WO}_{PID}` | Washout | Washout | +---------+-------------------------+---------------+--------------------------+ | LA | :math:`LA` | LagAntiWindup | V_{R}, Anti-windup lag | +---------+-------------------------+---------------+--------------------------+ | SAT | :math:`SAT` | ExcQuadSat | Field voltage saturation | +---------+-------------------------+---------------+--------------------------+ | INT | :math:`INT` | Integrator | V_E, integrator | +---------+-------------------------+---------------+--------------------------+ Config Fields in [AC8B] +---------------+--------+-------+---------------------------------------+-----------------+ | Option | Symbol | Value | Info | Accepted values | +===============+========+=======+=======================================+=================+ | allow_adjust | | 1 | allow adjusting upper or lower limits | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_lower | | 0 | adjust lower limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_upper | | 1 | adjust upper limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | ks | | 2 | Tracking gain for PID controller | | +---------------+--------+-------+---------------------------------------+-----------------+ .. _IEEET3: -------------------------------------------------------------------------------- IEEET3 -------------------------------------------------------------------------------- Exciter IEEET3. Reference: [1] PowerWorld, Exciter IEEET3, [Online], [2] NEPLAN, Exciters Models, [Online], Available: https://www.powerworld.com/WebHelp/Content/TransientModels_HTML/Exciter%20IEEET3.htm https://www.neplan.ch/wp-content/uploads/2015/08/Nep_EXCITERS1.pdf Parameters ---------- +--------+------------------+--------------------------------------+---------+--------+-----------------------+ | Name | Symbol | Description | Default | Unit | Properties | +========+==================+======================================+=========+========+=======================+ | idx | | unique device idx | | | | +--------+------------------+--------------------------------------+---------+--------+-----------------------+ | u | :math:`u` | connection status | 1 | *bool* | | +--------+------------------+--------------------------------------+---------+--------+-----------------------+ | name | | device name | | | | +--------+------------------+--------------------------------------+---------+--------+-----------------------+ | syn | | Synchronous generator idx | | | mandatory | +--------+------------------+--------------------------------------+---------+--------+-----------------------+ | TR | :math:`T_R` | Sensing time constant | 0.020 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+-----------------------+ | KA | :math:`K_A` | Regulator gain | 5 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+-----------------------+ | TA | :math:`T_A` | Lag time constant in anti-windup lag | 0.040 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+-----------------------+ | VRMAX | :math:`V_{RMAX}` | Maximum regulator limit | 7.300 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+-----------------------+ | VRMIN | :math:`V_{RMIN}` | Minimum regulator limit | -7.300 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+-----------------------+ | VBMAX | :math:`V_{BMAX}` | VB upper limit | 18 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+-----------------------+ | KE | :math:`K_E` | Exciter integrator constant | 1 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+-----------------------+ | TE | :math:`T_E` | Exciter integrator time constant | 1 | *p.u.* | | +--------+------------------+--------------------------------------+---------+--------+-----------------------+ | KF | :math:`K_F` | Feedback gain | 0.100 | | | +--------+------------------+--------------------------------------+---------+--------+-----------------------+ | TF | :math:`T_F` | Feedback delay | 1 | | non_zero,non_negative | +--------+------------------+--------------------------------------+---------+--------+-----------------------+ | KP | :math:`K_P` | Potential circuit gain coeff. | 4 | | | +--------+------------------+--------------------------------------+---------+--------+-----------------------+ | KI | :math:`K_I` | Potential circuit gain coeff. | 0.100 | | | +--------+------------------+--------------------------------------+---------+--------+-----------------------+ | ug | :math:`u_g` | Generator online status | 0 | *bool* | | +--------+------------------+--------------------------------------+---------+--------+-----------------------+ | Sn | :math:`S_m` | Rated power from generator | 0 | *MVA* | | +--------+------------------+--------------------------------------+---------+--------+-----------------------+ | Vn | :math:`V_m` | Rated voltage from generator | 0 | *kV* | | +--------+------------------+--------------------------------------+---------+--------+-----------------------+ | bus | :math:`bus` | Bus idx of the generators | 0 | | | +--------+------------------+--------------------------------------+---------+--------+-----------------------+ Variables --------- +---------+----------------------+----------+---------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +=========+======================+==========+=======================================+========+============+ | LG_y | :math:`y_{LG}` | State | State in lag transfer function | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | LA3_y | :math:`y_{LA3}` | State | State in lag TF | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | LA1_y | :math:`y_{LA1}` | State | State in lag transfer function | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | WF_x | :math:`x'_{WF}` | State | State in washout filter | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | v | :math:`E_{term}` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vout | :math:`v_{out}` | Algeb | Exciter final output voltage | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | UEL | :math:`U_{EL}` | Algeb | Interface var for under exc. limiter | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | OEL | :math:`O_{EL}` | Algeb | Interface var for over exc. limiter | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | Vs | :math:`V_{s}` | Algeb | Voltage compensation from PSS | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vref | :math:`V_{ref}` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vi | :math:`V_{i}` | Algeb | Total input voltages | *p.u.* | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | WF_y | :math:`y_{WF}` | Algeb | Output of washout filter | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | SQE | :math:`SQE` | Algeb | Square of error after mul | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | VB_y | :math:`y_{VB}` | Algeb | Output of piecewise | | v_str | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vf | :math:`v_{f}` | ExtAlgeb | Excitation field voltage to generator | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | Armature excitation current | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | a | :math:`\theta` | ExtAlgeb | Bus voltage phase angle | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vbus | :math:`V` | ExtAlgeb | Bus voltage magnitude | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vd | :math:`V_{d}` | ExtAlgeb | d-axis machine voltage | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | vq | :math:`V_{q}` | ExtAlgeb | q-axis machine voltage | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | Id | :math:`I_{d}` | ExtAlgeb | d-axis machine current | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ | Iq | :math:`I_{q}` | ExtAlgeb | q-axis machine current | | | +---------+----------------------+----------+---------------------------------------+--------+------------+ Initialization Equations ------------------------ +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+======================+==========+=====================================================================================================================================================================+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LA3_y | :math:`y_{LA3}` | State | :math:`K_{A} u_{e} \left(V_{i} - y_{WF}\right)` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LA1_y | :math:`y_{LA1}` | State | :math:`\frac{u_{e} \left(V_{BMAX} z_{u}^{HL} + y_{VB} z_{i}^{HL}\right)}{K_{E}}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_x | :math:`x'_{WF}` | State | :math:`y_{LA1}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`E_{term}` | Algeb | :math:`V` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} v_{f0}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`U_{EL}` | Algeb | :math:`UEL_{0}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | OEL | :math:`O_{EL}` | Algeb | :math:`OEL_{0}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vs | :math:`V_{s}` | Algeb | :math:`0` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`E_{term} + V_{b0}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`- E_{term} + V_{ref}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`y_{WF}` | Algeb | :math:`0` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | SQE | :math:`SQE` | Algeb | :math:`V_{E}^{2} - 0.6084 X_{ad}I_{fd}^{2}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VB_y | :math:`y_{VB}` | Algeb | :math:`\operatorname{FixPiecewise}{\left(\left( u_{e} y_{LA3}, \ SQE \leq 0\right),\left( u_{e} \left(\sqrt{SQE} + y_{LA3}\right), \ \text{True}\right) \right)}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vd | :math:`V_{d}` | ExtAlgeb | | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vq | :math:`V_{q}` | ExtAlgeb | | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Id | :math:`I_{d}` | ExtAlgeb | | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iq | :math:`I_{q}` | ExtAlgeb | | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+--------------------------------------------------------------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+======================================================================================+=============+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term} - y_{LG}` | :math:`T_R` | +--------+-----------------+----------+--------------------------------------------------------------------------------------+-------------+ | LA3_y | :math:`y_{LA3}` | State | :math:`K_{A} u_{e} \left(V_{i} - y_{WF}\right) - y_{LA3}` | :math:`T_A` | +--------+-----------------+----------+--------------------------------------------------------------------------------------+-------------+ | LA1_y | :math:`y_{LA1}` | State | :math:`- K_{E} y_{LA1} + u_{e} \left(V_{BMAX} z_{u}^{HL} + y_{VB} z_{i}^{HL}\right)` | :math:`T_E` | +--------+-----------------+----------+--------------------------------------------------------------------------------------+-------------+ | WF_x | :math:`x'_{WF}` | State | :math:`- x'_{WF} + y_{LA1}` | :math:`T_F` | +--------+-----------------+----------+--------------------------------------------------------------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+--------------------------------------------------------------------------------------+-------------+ Algebraic Equations ----------------------------- +---------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+======================+==========+================================================================================================================================================================================+ | v | :math:`E_{term}` | Algeb | :math:`- E_{term} + V` | +---------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} \left(- v_{out} + y_{LA1}\right)` | +---------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`U_{EL}` | Algeb | :math:`UEL_{0} - U_{EL}` | +---------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | OEL | :math:`O_{EL}` | Algeb | :math:`OEL_{0} - O_{EL}` | +---------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vs | :math:`V_{s}` | Algeb | :math:`- V_{s}` | +---------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`V_{ref0} - V_{ref}` | +---------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`u_{e} \left(O_{EL} + U_{EL} - V_{i} + V_{ref} + V_{s} - y_{LG}\right)` | +---------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`y_{WF}` | Algeb | :math:`K_{F} \left(- x'_{WF} + y_{LA1}\right) - T_{F} y_{WF}` | +---------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | SQE | :math:`SQE` | Algeb | :math:`- SQE + V_{E}^{2} - 0.6084 X_{ad}I_{fd}^{2}` | +---------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VB_y | :math:`y_{VB}` | Algeb | :math:`- y_{VB} + \operatorname{FixPiecewise}{\left(\left( u_{e} y_{LA3}, \ SQE \leq 0\right),\left( u_{e} \left(\sqrt{SQE} + y_{LA3}\right), \ \text{True}\right) \right)}` | +---------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | :math:`u_{e} \left(- v_{f0} + v_{out}\right)` | +---------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vd | :math:`V_{d}` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vq | :math:`V_{q}` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Id | :math:`I_{d}` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iq | :math:`I_{q}` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +---------+------------------+--------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +=========+==================+==================================================================================================+=================+ | ue | :math:`u_e` | :math:`u u_{g}` | ConstService | +---------+------------------+--------------------------------------------------------------------------------------------------+-----------------+ | VE | :math:`V_{E}` | :math:`\left|{i K_{I} \left(I_{d} + i I_{q}\right) + K_{P} \left(V_{d} + i V_{q}\right)}\right|` | VarService | +---------+------------------+--------------------------------------------------------------------------------------------------+-----------------+ | V40 | :math:`V40` | :math:`\sqrt{V_{E}^{2} - 0.6084 X_{ad}I_{fd}^{2}}` | ConstService | +---------+------------------+--------------------------------------------------------------------------------------------------+-----------------+ | VR0 | :math:`V_{R0}` | :math:`K_{E} v_{f0} - V_{40}` | ConstService | +---------+------------------+--------------------------------------------------------------------------------------------------+-----------------+ | vb0 | :math:`V_{b0}` | :math:`\frac{V_{R0}}{K_{A}}` | ConstService | +---------+------------------+--------------------------------------------------------------------------------------------------+-----------------+ | VRMAXc | :math:`VRMAXc` | :math:`V_{RMAX} - 999 z_{VRMAX} + 999` | ConstService | +---------+------------------+--------------------------------------------------------------------------------------------------+-----------------+ | UEL0 | :math:`UEL0` | :math:`0` | ConstService | +---------+------------------+--------------------------------------------------------------------------------------------------+-----------------+ | OEL0 | :math:`OEL0` | :math:`0` | ConstService | +---------+------------------+--------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`V_{ref}` | PostInitService | +---------+------------------+--------------------------------------------------------------------------------------------------+-----------------+ | zeros | :math:`zeros` | :math:`0.0` | ConstService | +---------+------------------+--------------------------------------------------------------------------------------------------+-----------------+ Discretes ----------- +----------+-------------------+-------------+---------------------+ | Name | Symbol | Type | Info | +==========+===================+=============+=====================+ | LA3_lim | :math:`lim_{LA3}` | AntiWindup | Limiter in Lag | +----------+-------------------+-------------+---------------------+ | SL | :math:`SL` | LessThan | | +----------+-------------------+-------------+---------------------+ | HL | :math:`HL` | HardLimiter | Hard limiter for VB | +----------+-------------------+-------------+---------------------+ Blocks ------- +------+-------------+---------------+-------------------------------------------+ | Name | Symbol | Type | Info | +======+=============+===============+===========================================+ | LG | :math:`LG` | Lag | Sensing delay | +------+-------------+---------------+-------------------------------------------+ | LA3 | :math:`LA3` | LagAntiWindup | V_{R}, Lag Anti-Windup | +------+-------------+---------------+-------------------------------------------+ | LA1 | :math:`LA1` | Lag | | +------+-------------+---------------+-------------------------------------------+ | WF | :math:`WF` | Washout | V_F, stablizing circuit feedback, washout | +------+-------------+---------------+-------------------------------------------+ | VB | :math:`VB` | Piecewise | | +------+-------------+---------------+-------------------------------------------+ Config Fields in [IEEET3] +---------------+--------+-------+---------------------------------------+-----------------+ | Option | Symbol | Value | Info | Accepted values | +===============+========+=======+=======================================+=================+ | allow_adjust | | 1 | allow adjusting upper or lower limits | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_lower | | 0 | adjust lower limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_upper | | 1 | adjust upper limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _ESAC1A: -------------------------------------------------------------------------------- ESAC1A -------------------------------------------------------------------------------- Exciter ESAC1A. Parameters ---------- +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | Name | Symbol | Description | Default | Unit | Properties | +=========+==================+================================================================+=========+========+=======================+ | idx | | unique device idx | | | | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | u | :math:`u` | connection status | 1 | *bool* | | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | name | | device name | | | | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | syn | | Synchronous generator idx | | | mandatory | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | TR | :math:`T_R` | Sensing time constant | 0.010 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | TB | :math:`T_B` | Lag time constant in lead-lag | 1 | *p.u.* | non_negative | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | TC | :math:`T_C` | Lead time constant in lead-lag | 1 | *p.u.* | non_negative | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | VAMAX | :math:`V_{AMAX}` | V_A upper limit | 999 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | VAMIN | :math:`V_{AMIN}` | V_A lower limit | -999 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | KA | :math:`K_A` | Regulator gain | 80 | | | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | TA | :math:`T_A` | Lag time constant in regulator | 0.040 | *p.u.* | non_negative | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | VRMAX | :math:`V_{RMAX}` | Max. exc. limit (0-unlimited) | 7.300 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | VRMIN | :math:`V_{RMIN}` | Min. excitation limit | -7.300 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | TE | :math:`T_E` | Integrator time constant | 0.800 | *p.u.* | non_negative | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | E1 | :math:`E_1` | First saturation point | 0 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | SE1 | :math:`S_{E1}` | Value at first saturation point | 0 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | E2 | :math:`E_2` | Second saturation point | 1 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | SE2 | :math:`S_{E2}` | Value at second saturation point | 1 | *p.u.* | | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | KC | :math:`K_C` | Rectifier loading factor proportional to commutating reactance | 0.100 | | | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | KD | :math:`K_D` | Ifd feedback gain | 0 | | | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | KE | :math:`K_E` | Gain added to saturation | 1 | | | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | KF | :math:`K_F` | Feedback gain | 0.100 | | | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | TF | :math:`T_{F1}` | Feedback washout time constant | 1 | *p.u.* | non_zero,non_negative | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | Switch | :math:`S_w` | Switch that PSS/E did not implement | 0 | *bool* | | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | ug | :math:`u_g` | Generator online status | 0 | *bool* | | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | Sn | :math:`S_m` | Rated power from generator | 0 | *MVA* | | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | Vn | :math:`V_m` | Rated voltage from generator | 0 | *kV* | | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ | bus | :math:`bus` | Bus idx of the generators | 0 | | | +---------+------------------+----------------------------------------------------------------+---------+--------+-----------------------+ Variables --------- +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | Name | Symbol | Type | Description | Unit | Properties | +=========+================================+==========+=======================================+========+==============+ | LG_y | :math:`y_{LG}` | State | State in lag transfer function | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | LL_x | :math:`x'_{LL}` | State | State in lead-lag | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | LA_y | :math:`y_{LA}` | State | State in lag TF | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | INT_y | :math:`y_{INT}` | State | Integrator output | | v_str,v_iter | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | WF_x | :math:`x'_{WF}` | State | State in washout filter | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | v | :math:`E_{term}` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | vout | :math:`v_{out}` | Algeb | Exciter final output voltage | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | UEL | :math:`U_{EL}` | Algeb | Interface var for under exc. limiter | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | OEL | :math:`O_{EL}` | Algeb | Interface var for over exc. limiter | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | Vs | :math:`V_{s}` | Algeb | Voltage compensation from PSS | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | vref | :math:`V_{ref}` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | IN | :math:`I_{N}` | Algeb | Input to FEX | | v_str,v_iter | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | FEX_y | :math:`y_{FEX}` | Algeb | Output of piecewise | | v_str,v_iter | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | vi | :math:`V_{i}` | Algeb | Total input voltages | *p.u.* | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | LL_y | :math:`y_{LL}` | Algeb | Output of lead-lag | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | HVG_y | :math:`y_{HVG}` | Algeb | HVGate output | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | LVG_y | :math:`y_{LVG}` | Algeb | LVGate output | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | Se | :math:`V_{out}*S_e(|V_{out}|)` | Algeb | saturation output | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | VFE | :math:`V_{FE}` | Algeb | Combined saturation feedback | *p.u.* | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | WF_y | :math:`y_{WF}` | Algeb | Output of washout filter | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | vf | :math:`v_{f}` | ExtAlgeb | Excitation field voltage to generator | | | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | Armature excitation current | | | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | a | :math:`\theta` | ExtAlgeb | Bus voltage phase angle | | | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ | vbus | :math:`V` | ExtAlgeb | Bus voltage magnitude | | | +---------+--------------------------------+----------+---------------------------------------+--------+--------------+ Initialization Equations ------------------------ +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+================================+==========+=================================================================================================================================================================================================================================================================================================+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_x | :math:`x'_{LL}` | State | :math:`V_{i}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LA_y | :math:`y_{LA}` | State | :math:`K_{A} y_{LL}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | INT_y | :math:`y_{INT}` | State | :math:`- v_{f0} + y_{FEX} y_{INT}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_x | :math:`x'_{WF}` | State | :math:`V_{FE}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`E_{term}` | Algeb | :math:`V` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} v_{f0}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`U_{EL}` | Algeb | :math:`UEL_{0}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | OEL | :math:`O_{EL}` | Algeb | :math:`OEL_{0}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vs | :math:`V_{s}` | Algeb | :math:`0` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`E_{term} + \frac{V_{FE}}{K_{A}}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`I_{N}` | Algeb | :math:`- I_{N} y_{INT} + K_{C} X_{ad}I_{fd}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | FEX_y | :math:`y_{FEX}` | Algeb | :math:`- y_{FEX} + \operatorname{FixPiecewise}{\left(\left( 1, \ I_{N} \leq 0\right),\left( 1 - 0.577 I_{N}, \ I_{N} \leq 0.433\right),\left( \sqrt{0.75 - I_{N}^{2}}, \ I_{N} \leq 0.75\right),\left( 1.732 - 1.732 I_{N}, \ I_{N} \leq 1\right),\left( 0, \ \text{True}\right) \right)}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`- E_{term} + V_{ref}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`V_{i}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | HVG_y | :math:`y_{HVG}` | Algeb | :math:`HVG_{lt z0} U_{EL} + HVG_{lt z1} y_{LA}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LVG_y | :math:`y_{LVG}` | Algeb | :math:`LVG_{lt z0} O_{EL} + LVG_{lt z1} y_{HVG}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`V_{out}*S_e(|V_{out}|)` | Algeb | :math:`B^q_{SAT} \left(- A^q_{SAT} + y_{INT}\right)^{2} \operatorname{Indicator}{\left(y_{INT} > A^q_{SAT} \right)}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VFE | :math:`V_{FE}` | Algeb | :math:`K_{D} X_{ad}I_{fd} + K_{E} y_{INT} + V_{out}*S_e(|V_{out}|)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`y_{WF}` | Algeb | :math:`0` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+-----------------------------------------------+----------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+===============================================+================+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term} - y_{LG}` | :math:`T_R` | +--------+-----------------+----------+-----------------------------------------------+----------------+ | LL_x | :math:`x'_{LL}` | State | :math:`V_{i} - x'_{LL}` | :math:`T_B` | +--------+-----------------+----------+-----------------------------------------------+----------------+ | LA_y | :math:`y_{LA}` | State | :math:`K_{A} y_{LL} - y_{LA}` | :math:`T_A` | +--------+-----------------+----------+-----------------------------------------------+----------------+ | INT_y | :math:`y_{INT}` | State | :math:`u_{e} \left(- V_{FE} + y_{LVG}\right)` | :math:`T_E` | +--------+-----------------+----------+-----------------------------------------------+----------------+ | WF_x | :math:`x'_{WF}` | State | :math:`V_{FE} - x'_{WF}` | :math:`T_{F1}` | +--------+-----------------+----------+-----------------------------------------------+----------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+-----------------------------------------------+----------------+ Algebraic Equations ----------------------------- +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+================================+==========+=================================================================================================================================================================================================================================================================================================+ | v | :math:`E_{term}` | Algeb | :math:`- E_{term} + V` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} y_{FEX} y_{INT} - v_{out}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`U_{EL}` | Algeb | :math:`UEL_{0} - U_{EL}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | OEL | :math:`O_{EL}` | Algeb | :math:`OEL_{0} - O_{EL}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vs | :math:`V_{s}` | Algeb | :math:`- V_{s}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`V_{ref0} - V_{ref}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`I_{N}` | Algeb | :math:`u_{e} \left(- I_{N} y_{INT} + K_{C} X_{ad}I_{fd}\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | FEX_y | :math:`y_{FEX}` | Algeb | :math:`- y_{FEX} + \operatorname{FixPiecewise}{\left(\left( 1, \ I_{N} \leq 0\right),\left( 1 - 0.577 I_{N}, \ I_{N} \leq 0.433\right),\left( \sqrt{0.75 - I_{N}^{2}}, \ I_{N} \leq 0.75\right),\left( 1.732 - 1.732 I_{N}, \ I_{N} \leq 1\right),\left( 0, \ \text{True}\right) \right)}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`u_{e} \left(O_{EL} + U_{EL} - V_{i} + V_{ref} + V_{s} - y_{LG}\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- x'_{LL} + y_{LL}\right) + T_{B} x'_{LL} - T_{B} y_{LL} + T_{C} \left(V_{i} - x'_{LL}\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | HVG_y | :math:`y_{HVG}` | Algeb | :math:`HVG_{lt z0} U_{EL} + HVG_{lt z1} y_{LA} - y_{HVG}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LVG_y | :math:`y_{LVG}` | Algeb | :math:`LVG_{lt z0} O_{EL} + LVG_{lt z1} y_{HVG} - y_{LVG}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`V_{out}*S_e(|V_{out}|)` | Algeb | :math:`u_{e} \left(B^q_{SAT} z_{0}^{SL} \left(- A^q_{SAT} + y_{INT}\right)^{2} - V_{out}*S_e(|V_{out}|)\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VFE | :math:`V_{FE}` | Algeb | :math:`u_{e} \left(K_{D} X_{ad}I_{fd} + K_{E} y_{INT} - V_{FE} + V_{out}*S_e(|V_{out}|)\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`y_{WF}` | Algeb | :math:`K_{F} \left(V_{FE} - x'_{WF}\right) - T_{F1} y_{WF}` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | :math:`u_{e} \left(- v_{f0} + v_{out}\right)` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | :math:`0` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | :math:`0` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | :math:`0` | +---------+--------------------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +==========+=======================+=============================================================================================================================================================================================================================================+=================+ | ue | :math:`u_e` | :math:`u u_{g}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | UEL0 | :math:`UEL0` | :math:`-999` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | OEL0 | :math:`OEL0` | :math:`999` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VAMAXu | :math:`VAMAXu` | :math:`V_{AMAX} u_{e} - 999 u_{e} + 999` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VAMINu | :math:`VAMINu` | :math:`V_{AMIN} u_{e} + 999 u_{e} - 999` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E1 | :math:`E^{1c}_{SAT}` | :math:`E_{1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E2 | :math:`E^{2c}_{SAT}` | :math:`E_{2} - 2 z^{SE2}_{SAT} + 2` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE1 | :math:`SE^{1c}_{SAT}` | :math:`S_{E1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE2 | :math:`SE^{2c}_{SAT}` | :math:`S_{E2} - 2 z^{SE2}_{SAT} + 2` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_a | :math:`a_{SAT}` | :math:`\sqrt{\frac{E^{1c}_{SAT} SE^{1c}_{SAT}}{E^{2c}_{SAT} SE^{2c}_{SAT}}} \left(\operatorname{Indicator}{\left(SE^{2c}_{SAT} > 0 \right)} + \operatorname{Indicator}{\left(SE^{2c}_{SAT} < 0 \right)}\right)` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_A | :math:`A^q_{SAT}` | :math:`E^{2c}_{SAT} - \frac{E^{1c}_{SAT} - E^{2c}_{SAT}}{a_{SAT} - 1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_B | :math:`B^q_{SAT}` | :math:`\frac{E^{2c}_{SAT} SE^{2c}_{SAT} \left(a_{SAT} - 1\right)^{2} \left(\operatorname{Indicator}{\left(a_{SAT} > 0 \right)} + \operatorname{Indicator}{\left(a_{SAT} < 0 \right)}\right)}{\left(E^{1c}_{SAT} - E^{2c}_{SAT}\right)^{2}}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`V_{ref}` | PostInitService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ Discretes ----------- +---------+--------------------+------------+----------------+ | Name | Symbol | Type | Info | +=========+====================+============+================+ | LL_LT1 | :math:`LT_{LL}` | LessThan | | +---------+--------------------+------------+----------------+ | LL_LT2 | :math:`LT_{LL}` | LessThan | | +---------+--------------------+------------+----------------+ | LA_lim | :math:`lim_{LA}` | AntiWindup | Limiter in Lag | +---------+--------------------+------------+----------------+ | HVG_lt | :math:`None_{HVG}` | LessThan | | +---------+--------------------+------------+----------------+ | LVG_lt | :math:`None_{LVG}` | LessThan | | +---------+--------------------+------------+----------------+ | SL | :math:`SL` | LessThan | | +---------+--------------------+------------+----------------+ Blocks ------- +------+-------------+---------------+-----------------------------+ | Name | Symbol | Type | Info | +======+=============+===============+=============================+ | FEX | :math:`FEX` | Piecewise | Piecewise function FEX | +------+-------------+---------------+-----------------------------+ | LG | :math:`LG` | Lag | Voltage transducer | +------+-------------+---------------+-----------------------------+ | LL | :math:`LL` | LeadLag | V_A, Lead-lag compensator | +------+-------------+---------------+-----------------------------+ | LA | :math:`LA` | LagAntiWindup | V_A, Anti-windup lag | +------+-------------+---------------+-----------------------------+ | HVG | :math:`HVG` | HVGate | HVGate for under excitation | +------+-------------+---------------+-----------------------------+ | LVG | :math:`LVG` | LVGate | HVGate for under excitation | +------+-------------+---------------+-----------------------------+ | SAT | :math:`SAT` | ExcQuadSat | Field voltage saturation | +------+-------------+---------------+-----------------------------+ | INT | :math:`INT` | Integrator | V_E, integrator | +------+-------------+---------------+-----------------------------+ | WF | :math:`WF` | Washout | Stablizing circuit feedback | +------+-------------+---------------+-----------------------------+ Config Fields in [ESAC1A] +---------------+--------+-------+---------------------------------------+-----------------+ | Option | Symbol | Value | Info | Accepted values | +===============+========+=======+=======================================+=================+ | allow_adjust | | 1 | allow adjusting upper or lower limits | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_lower | | 0 | adjust lower limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_upper | | 1 | adjust upper limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _ESST1A: -------------------------------------------------------------------------------- ESST1A -------------------------------------------------------------------------------- Exciter ESST1A model. Reference: [1] PowerWorld, Exciter ESST1A, [Online], [2] NEPLAN, Exciters Models, [Online], Available: https://www.powerworld.com/WebHelp/Content/TransientModels_HTML/Exciter%20ESST1A.htm https://www.neplan.ch/wp-content/uploads/2015/08/Nep_EXCITERS1.pdf Parameters ---------- +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +========+==================+================================================================+=========+========+============+ | idx | | unique device idx | | | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | name | | device name | | | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | syn | | Synchronous generator idx | | | mandatory | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | TR | :math:`T_R` | Sensing time constant | 0.010 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | VIMAX | :math:`V_{IMAX}` | Max. input voltage | 0.800 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | VIMIN | :math:`V_{IMIN}` | Min. input voltage | -0.100 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | TB | :math:`T_B` | Lag time constant in lead-lag | 1 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | TC | :math:`T_C` | Lead time constant in lead-lag | 1 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | TB1 | :math:`T_{B1}` | Lag time constant in lead-lag 1 | 1 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | TC1 | :math:`T_{C1}` | Lead time constant in lead-lag 1 | 1 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | VAMAX | :math:`V_{AMAX}` | V_A upper limit | 999 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | VAMIN | :math:`V_{AMIN}` | V_A lower limit | -999 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | KA | :math:`K_A` | Regulator gain | 80 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | TA | :math:`T_A` | Lag time constant in regulator | 0.040 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | ILR | :math:`I_{LR}` | Exciter output current limite reference | 1 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | KLR | :math:`K_{LR}` | Exciter output current limiter gain | 1 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | VRMAX | :math:`V_{RMAX}` | Maximum voltage regulator output limit | 7.300 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | VRMIN | :math:`V_{RMIN}` | Minimum voltage regulator output limit | -7.300 | *p.u.* | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | KF | :math:`K_F` | Feedback gain | 0.100 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | TF | :math:`T_{F}` | Feedback washout time constant | 1 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | KC | :math:`K_C` | Rectifier loading factor proportional to commutating reactance | 0.100 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | UELc | :math:`UEL_c` | Alternate UEL inputs, input code 1-3 | 1 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | VOSc | :math:`VOS_c` | Alternate Stabilizer inputs, input code 1-2 | 1 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | ug | :math:`u_g` | Generator online status | 0 | *bool* | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | Sn | :math:`S_m` | Rated power from generator | 0 | *MVA* | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | Vn | :math:`V_m` | Rated voltage from generator | 0 | *kV* | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ | bus | :math:`bus` | Bus idx of the generators | 0 | | | +--------+------------------+----------------------------------------------------------------+---------+--------+------------+ Variables --------- +---------+----------------------+----------+---------------------------------------+--------+--------------+ | Name | Symbol | Type | Description | Unit | Properties | +=========+======================+==========+=======================================+========+==============+ | LG_y | :math:`y_{LG}` | State | State in lag transfer function | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | LL_x | :math:`x'_{LL}` | State | State in lead-lag | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | LL1_x | :math:`x'_{LL1}` | State | State in lead-lag | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | LA_y | :math:`y_{LA}` | State | State in lag TF | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | WF_x | :math:`x'_{WF}` | State | State in washout filter | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | v | :math:`E_{term}` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | vout | :math:`v_{out}` | Algeb | Exciter final output voltage | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | UEL | :math:`U_{EL}` | Algeb | Interface var for under exc. limiter | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | OEL | :math:`O_{EL}` | Algeb | Interface var for over exc. limiter | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | Vs | :math:`V_{s}` | Algeb | Voltage compensation from PSS | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | vref | :math:`V_{ref}` | Algeb | Reference voltage input | *p.u.* | v_str,v_iter | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | SG | :math:`SG` | Algeb | SG | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | LR_x | :math:`x_{LR}` | Algeb | Value before limiter | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | LR_y | :math:`y_{LR}` | Algeb | Output after limiter and post gain | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | vi | :math:`V_{i}` | Algeb | Total input voltages | *p.u.* | v_str,v_iter | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | vil_x | :math:`x_{vil}` | Algeb | Value before limiter | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | vil_y | :math:`y_{vil}` | Algeb | Output after limiter and post gain | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | UEL2 | :math:`UEL_{2}` | Algeb | UEL_2 as HVG1 u1 | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | HVG1_y | :math:`y_{HVG1}` | Algeb | HVGate output | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | LL_y | :math:`y_{LL}` | Algeb | Output of lead-lag | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | LL1_y | :math:`y_{LL1}` | Algeb | Output of lead-lag | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | vas | :math:`V_{As}` | Algeb | V_A after subtraction, as HVG u2 | | v_str,v_iter | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | UEL3 | :math:`UEL_{3}` | Algeb | UEL_3 as HVG u1 | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | HVG_y | :math:`y_{HVG}` | Algeb | HVGate output | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | LVG_y | :math:`y_{LVG}` | Algeb | LVGate output | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | vol_x | :math:`x_{vol}` | Algeb | Value before limiter | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | vol_y | :math:`y_{vol}` | Algeb | Output after limiter and post gain | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | WF_y | :math:`y_{WF}` | Algeb | Output of washout filter | | v_str | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | vf | :math:`v_{f}` | ExtAlgeb | Excitation field voltage to generator | | | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | Armature excitation current | | | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | a | :math:`\theta` | ExtAlgeb | Bus voltage phase angle | | | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | vbus | :math:`V` | ExtAlgeb | Bus voltage magnitude | | | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | vd | :math:`V_{d}` | ExtAlgeb | d-axis machine voltage | | | +---------+----------------------+----------+---------------------------------------+--------+--------------+ | vq | :math:`V_{q}` | ExtAlgeb | q-axis machine voltage | | | +---------+----------------------+----------+---------------------------------------+--------+--------------+ Initialization Equations ------------------------ +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+======================+==========+===========================================================================================================================+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | LL_x | :math:`x'_{LL}` | State | :math:`y_{HVG1}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | LL1_x | :math:`x'_{LL1}` | State | :math:`y_{LL}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | LA_y | :math:`y_{LA}` | State | :math:`K_{A} y_{LL1}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | WF_x | :math:`x'_{WF}` | State | :math:`y_{LVG}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | v | :math:`E_{term}` | Algeb | :math:`V` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} v_{f0}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`U_{EL}` | Algeb | :math:`UEL_{0}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | OEL | :math:`O_{EL}` | Algeb | :math:`OEL_{0}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | Vs | :math:`V_{s}` | Algeb | :math:`0` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`u_{e} \left(E_{term} - SG SWVOS_{s1} - SWUEL_{s1} U_{EL} + \frac{- SG SWVOS_{s2} + v_{f0} + y_{LR}}{K_{A}}\right)` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | SG | :math:`SG` | Algeb | :math:`SG_{0}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | LR_x | :math:`x_{LR}` | Algeb | :math:`K_{LR} \left(- I_{LR} + X_{ad}I_{fd}\right)` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | LR_y | :math:`y_{LR}` | Algeb | :math:`LR_{lim zi} x_{LR} + LR_{lim zl} zero` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`u_{e} \left(SG SWVOS_{s1} + SWUEL_{s1} U_{EL} + V_{ref} + V_{s} - y_{LG} - y_{WF}\right)` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | vil_x | :math:`x_{vil}` | Algeb | :math:`V_{i}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | vil_y | :math:`y_{vil}` | Algeb | :math:`V_{IMAX} vil_{lim zu} + V_{IMIN} vil_{lim zl} + vil_{lim zi} x_{vil}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | UEL2 | :math:`UEL_{2}` | Algeb | :math:`u_{e} \left(SWUEL_{s2} U_{EL} + llim \left(1 - SWUEL_{s2}\right)\right)` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | HVG1_y | :math:`y_{HVG1}` | Algeb | :math:`HVG_{1 lt z0} UEL_{2} + HVG_{1 lt z1} y_{vil}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`y_{HVG1}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | LL1_y | :math:`y_{LL1}` | Algeb | :math:`y_{LL}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | vas | :math:`V_{As}` | Algeb | :math:`u_{e} \left(SG SWVOS_{s2} + y_{LA} - y_{LR}\right)` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | UEL3 | :math:`UEL_{3}` | Algeb | :math:`u_{e} \left(SWUEL_{s3} U_{EL} + llim \left(1 - SWUEL_{s3}\right)\right)` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | HVG_y | :math:`y_{HVG}` | Algeb | :math:`HVG_{lt z0} UEL_{3} + HVG_{lt z1} V_{As}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | LVG_y | :math:`y_{LVG}` | Algeb | :math:`LVG_{lt z0} O_{EL} + LVG_{lt z1} y_{HVG}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | vol_x | :math:`x_{vol}` | Algeb | :math:`y_{LVG}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | vol_y | :math:`y_{vol}` | Algeb | :math:`efd_{l} vol_{lim zl} + efd_{u} vol_{lim zu} + vol_{lim zi} x_{vol}` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`y_{WF}` | Algeb | :math:`0` | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | vd | :math:`V_{d}` | ExtAlgeb | | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ | vq | :math:`V_{q}` | ExtAlgeb | | +---------+----------------------+----------+---------------------------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+------------------+----------+----------------------------------+----------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+==================+==========+==================================+================+ | LG_y | :math:`y_{LG}` | State | :math:`E_{term} - y_{LG}` | :math:`T_R` | +--------+------------------+----------+----------------------------------+----------------+ | LL_x | :math:`x'_{LL}` | State | :math:`- x'_{LL} + y_{HVG1}` | :math:`T_B` | +--------+------------------+----------+----------------------------------+----------------+ | LL1_x | :math:`x'_{LL1}` | State | :math:`- x'_{LL1} + y_{LL}` | :math:`T_{B1}` | +--------+------------------+----------+----------------------------------+----------------+ | LA_y | :math:`y_{LA}` | State | :math:`K_{A} y_{LL1} - y_{LA}` | :math:`T_A` | +--------+------------------+----------+----------------------------------+----------------+ | WF_x | :math:`x'_{WF}` | State | :math:`- x'_{WF} + y_{LVG}` | :math:`T_{F}` | +--------+------------------+----------+----------------------------------+----------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+------------------+----------+----------------------------------+----------------+ Algebraic Equations ----------------------------- +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+======================+==========+====================================================================================================================================================+ | v | :math:`E_{term}` | Algeb | :math:`- E_{term} + V` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} y_{vol} - v_{out}` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`U_{EL}` | Algeb | :math:`UEL_{0} - U_{EL}` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | OEL | :math:`O_{EL}` | Algeb | :math:`OEL_{0} - O_{EL}` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | Vs | :math:`V_{s}` | Algeb | :math:`- V_{s}` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`V_{ref0} - V_{ref}` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | SG | :math:`SG` | Algeb | :math:`- SG + SG_{0}` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | LR_x | :math:`x_{LR}` | Algeb | :math:`K_{LR} \left(- I_{LR} + X_{ad}I_{fd}\right) - x_{LR}` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | LR_y | :math:`y_{LR}` | Algeb | :math:`LR_{lim zi} x_{LR} + LR_{lim zl} zero - y_{LR}` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`V_{i}` | Algeb | :math:`- V_{i} + u_{e} \left(SG SWVOS_{s1} + SWUEL_{s1} U_{EL} + V_{ref} + V_{s} - y_{LG} - y_{WF}\right)` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | vil_x | :math:`x_{vil}` | Algeb | :math:`V_{i} - x_{vil}` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | vil_y | :math:`y_{vil}` | Algeb | :math:`V_{IMAX} vil_{lim zu} + V_{IMIN} vil_{lim zl} + vil_{lim zi} x_{vil} - y_{vil}` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL2 | :math:`UEL_{2}` | Algeb | :math:`- UEL_{2} + u_{e} \left(SWUEL_{s2} U_{EL} + llim \left(1 - SWUEL_{s2}\right)\right)` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | HVG1_y | :math:`y_{HVG1}` | Algeb | :math:`HVG_{1 lt z0} UEL_{2} + HVG_{1 lt z1} y_{vil} - y_{HVG1}` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- x'_{LL} + y_{LL}\right) + T_{B} x'_{LL} - T_{B} y_{LL} + T_{C} \left(- x'_{LL} + y_{HVG1}\right)` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | LL1_y | :math:`y_{LL1}` | Algeb | :math:`LL_{1 LT1 z1} LL_{1 LT2 z1} \left(- x'_{LL1} + y_{LL1}\right) + T_{B1} x'_{LL1} - T_{B1} y_{LL1} + T_{C1} \left(- x'_{LL1} + y_{LL}\right)` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | vas | :math:`V_{As}` | Algeb | :math:`- V_{As} + u_{e} \left(SG SWVOS_{s2} + y_{LA} - y_{LR}\right)` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL3 | :math:`UEL_{3}` | Algeb | :math:`- UEL_{3} + u_{e} \left(SWUEL_{s3} U_{EL} + llim \left(1 - SWUEL_{s3}\right)\right)` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | HVG_y | :math:`y_{HVG}` | Algeb | :math:`HVG_{lt z0} UEL_{3} + HVG_{lt z1} V_{As} - y_{HVG}` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | LVG_y | :math:`y_{LVG}` | Algeb | :math:`LVG_{lt z0} O_{EL} + LVG_{lt z1} y_{HVG} - y_{LVG}` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | vol_x | :math:`x_{vol}` | Algeb | :math:`- x_{vol} + y_{LVG}` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | vol_y | :math:`y_{vol}` | Algeb | :math:`efd_{l} vol_{lim zl} + efd_{u} vol_{lim zu} + vol_{lim zi} x_{vol} - y_{vol}` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`y_{WF}` | Algeb | :math:`K_{F} \left(- x'_{WF} + y_{LVG}\right) - T_{F} y_{WF}` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | :math:`u_{e} \left(- v_{f0} + v_{out}\right)` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | vd | :math:`V_{d}` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ | vq | :math:`V_{q}` | ExtAlgeb | :math:`0` | +---------+----------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +--------+------------------+------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +========+==================+========================================================================+=================+ | ue | :math:`u_e` | :math:`u u_{g}` | ConstService | +--------+------------------+------------------------------------------------------------------------+-----------------+ | UEL0 | :math:`UEL0` | :math:`-999` | ConstService | +--------+------------------+------------------------------------------------------------------------+-----------------+ | OEL0 | :math:`OEL0` | :math:`999` | ConstService | +--------+------------------+------------------------------------------------------------------------+-----------------+ | ulim | :math:`ulim` | :math:`9999` | ConstService | +--------+------------------+------------------------------------------------------------------------+-----------------+ | llim | :math:`llim` | :math:`-9999` | ConstService | +--------+------------------+------------------------------------------------------------------------+-----------------+ | SG0 | :math:`SG0` | :math:`0` | ConstService | +--------+------------------+------------------------------------------------------------------------+-----------------+ | zero | :math:`zero` | :math:`0` | ConstService | +--------+------------------+------------------------------------------------------------------------+-----------------+ | VA0 | :math:`V_{A0}` | :math:`- SG SWVOS_{s2} + v_{f0} + y_{LR}` | PostInitService | +--------+------------------+------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`V_{ref}` | PostInitService | +--------+------------------+------------------------------------------------------------------------+-----------------+ | efdu | :math:`efd_{u}` | :math:`- K_{C} X_{ad}I_{fd} + V_{RMAX} \left|{V_{d} + i V_{q}}\right|` | VarService | +--------+------------------+------------------------------------------------------------------------+-----------------+ | efdl | :math:`efd_{l}` | :math:`V_{RMIN} \left|{V_{d} + i V_{q}}\right|` | VarService | +--------+------------------+------------------------------------------------------------------------+-----------------+ Discretes ----------- +----------+---------------------+-------------+----------------+ | Name | Symbol | Type | Info | +==========+=====================+=============+================+ | SWUEL | :math:`SW_{UEL}` | Switcher | | +----------+---------------------+-------------+----------------+ | SWVOS | :math:`SW_{VOS}` | Switcher | | +----------+---------------------+-------------+----------------+ | LR_lim | :math:`lim_{LR}` | HardLimiter | | +----------+---------------------+-------------+----------------+ | vil_lim | :math:`lim_{vil}` | HardLimiter | | +----------+---------------------+-------------+----------------+ | HVG1_lt | :math:`None_{HVG1}` | LessThan | | +----------+---------------------+-------------+----------------+ | LL_LT1 | :math:`LT_{LL}` | LessThan | | +----------+---------------------+-------------+----------------+ | LL_LT2 | :math:`LT_{LL}` | LessThan | | +----------+---------------------+-------------+----------------+ | LL1_LT1 | :math:`LT_{LL1}` | LessThan | | +----------+---------------------+-------------+----------------+ | LL1_LT2 | :math:`LT_{LL1}` | LessThan | | +----------+---------------------+-------------+----------------+ | LA_lim | :math:`lim_{LA}` | AntiWindup | Limiter in Lag | +----------+---------------------+-------------+----------------+ | HVG_lt | :math:`None_{HVG}` | LessThan | | +----------+---------------------+-------------+----------------+ | LVG_lt | :math:`None_{LVG}` | LessThan | | +----------+---------------------+-------------+----------------+ | vol_lim | :math:`lim_{vol}` | HardLimiter | | +----------+---------------------+-------------+----------------+ Blocks ------- +-------+--------------+---------------+-------------------------------------+ | Name | Symbol | Type | Info | +=======+==============+===============+=====================================+ | LG | :math:`LG` | Lag | Voltage transducer | +-------+--------------+---------------+-------------------------------------+ | LR | :math:`LR` | GainLimiter | Exciter output current gain limiter | +-------+--------------+---------------+-------------------------------------+ | vil | :math:`vil` | GainLimiter | Exciter voltage input limiter | +-------+--------------+---------------+-------------------------------------+ | HVG1 | :math:`HVG1` | HVGate | HVGate after V_I | +-------+--------------+---------------+-------------------------------------+ | LL | :math:`LL` | LeadLag | Lead-lag compensator | +-------+--------------+---------------+-------------------------------------+ | LL1 | :math:`LL1` | LeadLag | Lead-lag compensator 1 | +-------+--------------+---------------+-------------------------------------+ | LA | :math:`LA` | LagAntiWindup | V_A, Anti-windup lag | +-------+--------------+---------------+-------------------------------------+ | HVG | :math:`HVG` | HVGate | HVGate for under excitation | +-------+--------------+---------------+-------------------------------------+ | LVG | :math:`LVG` | LVGate | HVGate for over excitation | +-------+--------------+---------------+-------------------------------------+ | vol | :math:`vol` | GainLimiter | Exciter output limiter | +-------+--------------+---------------+-------------------------------------+ | WF | :math:`WF` | Washout | V_F, Stablizing circuit feedback | +-------+--------------+---------------+-------------------------------------+ Config Fields in [ESST1A] +---------------+--------+-------+---------------------------------------+-----------------+ | Option | Symbol | Value | Info | Accepted values | +===============+========+=======+=======================================+=================+ | allow_adjust | | 1 | allow adjusting upper or lower limits | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_lower | | 0 | adjust lower limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_upper | | 1 | adjust upper limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _ESAC5A: -------------------------------------------------------------------------------- ESAC5A -------------------------------------------------------------------------------- Exciter ESAC5A. Parameters ---------- +--------+----------------+----------------------------------+---------+--------+--------------+ | Name | Symbol | Description | Default | Unit | Properties | +========+================+==================================+=========+========+==============+ | idx | | unique device idx | | | | +--------+----------------+----------------------------------+---------+--------+--------------+ | u | :math:`u` | connection status | 1 | *bool* | | +--------+----------------+----------------------------------+---------+--------+--------------+ | name | | device name | | | | +--------+----------------+----------------------------------+---------+--------+--------------+ | syn | | Synchronous generator idx | | | mandatory | +--------+----------------+----------------------------------+---------+--------+--------------+ | TR | :math:`T_R` | Sensing Time Constant | 0.010 | *p.u* | | +--------+----------------+----------------------------------+---------+--------+--------------+ | TA | :math:`T_A` | Voltage Regulator Time Constant | 0.040 | *p.u* | | +--------+----------------+----------------------------------+---------+--------+--------------+ | KA | :math:`K_A` | Voltage Regulator Gain | 80 | | | +--------+----------------+----------------------------------+---------+--------+--------------+ | VRMIN | :math:`V_Rmin` | V_R lower limit | -7.300 | *p.u* | | +--------+----------------+----------------------------------+---------+--------+--------------+ | VRMAX | :math:`V_Rmax` | V_R upper limit | 7.300 | *p.u* | | +--------+----------------+----------------------------------+---------+--------+--------------+ | TE | :math:`T_E` | Integrator Time Constant | 0.800 | *p.u* | non_negative | +--------+----------------+----------------------------------+---------+--------+--------------+ | KF | :math:`K_F` | Feedback Gain | 0.030 | | | +--------+----------------+----------------------------------+---------+--------+--------------+ | TF1 | :math:`T_F_1` | Lag Time Constant | 1 | *p.u* | | +--------+----------------+----------------------------------+---------+--------+--------------+ | TF2 | :math:`T_F_2` | Lead-Lag Time Constant (pole) | 0.800 | *p.u* | | +--------+----------------+----------------------------------+---------+--------+--------------+ | TF3 | :math:`T_F_3` | Lead-Lag Time Constant (zero) | 1 | *p.u* | | +--------+----------------+----------------------------------+---------+--------+--------------+ | KE | :math:`K_E` | Exciter Feedback Gain | 1 | | | +--------+----------------+----------------------------------+---------+--------+--------------+ | E1 | :math:`E_1` | First saturation point | 0 | *p.u.* | | +--------+----------------+----------------------------------+---------+--------+--------------+ | SE1 | :math:`S_E1` | Value at first saturation point | 0 | *p.u.* | | +--------+----------------+----------------------------------+---------+--------+--------------+ | E2 | :math:`E_2` | Second saturation point | 1 | *p.u.* | | +--------+----------------+----------------------------------+---------+--------+--------------+ | SE2 | :math:`S_E2` | Value at second saturation point | 1 | *p.u.* | | +--------+----------------+----------------------------------+---------+--------+--------------+ | ug | :math:`u_g` | Generator online status | 0 | *bool* | | +--------+----------------+----------------------------------+---------+--------+--------------+ | Sn | :math:`S_m` | Rated power from generator | 0 | *MVA* | | +--------+----------------+----------------------------------+---------+--------+--------------+ | Vn | :math:`V_m` | Rated voltage from generator | 0 | *kV* | | +--------+----------------+----------------------------------+---------+--------+--------------+ | bus | :math:`bus` | Bus idx of the generators | 0 | | | +--------+----------------+----------------------------------+---------+--------+--------------+ Variables --------- +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +=========+================================+==========+=======================================+========+============+ | LP_y | :math:`y_{LP}` | State | State in lag transfer function | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | VR_y | :math:`y_{VR}` | State | State in lag TF | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | LL_x | :math:`x'_{LL}` | State | State in lead-lag | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | WF_x | :math:`x'_{WF}` | State | State in washout filter | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | INT_y | :math:`y_{INT}` | State | Integrator output | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | v | :math:`E_{term}` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | vout | :math:`v_{out}` | Algeb | Exciter final output voltage | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | UEL | :math:`U_{EL}` | Algeb | Interface var for under exc. limiter | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | OEL | :math:`O_{EL}` | Algeb | Interface var for over exc. limiter | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | Vs | :math:`V_{s}` | Algeb | Voltage compensation from PSS | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | vref | :math:`V_{ref}` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | vi | :math:`vi` | Algeb | Total voltage input | *pu* | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | LL_y | :math:`y_{LL}` | Algeb | Output of lead-lag | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | WF_y | :math:`y_{WF}` | Algeb | Output of washout filter | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | Se | :math:`V_{out}*S_e(|V_{out}|)` | Algeb | saturation output | | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | VFE | :math:`V_{FE}` | Algeb | Combined saturation feedback | *p.u.* | v_str | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | vf | :math:`v_{f}` | ExtAlgeb | Excitation field voltage to generator | | | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | Armature excitation current | | | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | a | :math:`\theta` | ExtAlgeb | Bus voltage phase angle | | | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ | vbus | :math:`V` | ExtAlgeb | Bus voltage magnitude | | | +---------+--------------------------------+----------+---------------------------------------+--------+------------+ Initialization Equations ------------------------ +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+================================+==========+======================================================================================================================+ | LP_y | :math:`y_{LP}` | State | :math:`E_{term}` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------+ | VR_y | :math:`y_{VR}` | State | :math:`K_{A} vi` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------+ | LL_x | :math:`x'_{LL}` | State | :math:`y_{VR}` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------+ | WF_x | :math:`x'_{WF}` | State | :math:`y_{LL}` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------+ | INT_y | :math:`y_{INT}` | State | :math:`v_{f0}` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------+ | v | :math:`E_{term}` | Algeb | :math:`V` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} v_{f0}` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`U_{EL}` | Algeb | :math:`UEL_{0}` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------+ | OEL | :math:`O_{EL}` | Algeb | :math:`OEL_{0}` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------+ | Vs | :math:`V_{s}` | Algeb | :math:`0` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`E_{term} + \frac{V_{FE}}{K_{A}}` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`u_{e} \left(- E_{term} + V_{ref}\right)` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`y_{VR}` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`y_{WF}` | Algeb | :math:`0` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------+ | Se | :math:`V_{out}*S_e(|V_{out}|)` | Algeb | :math:`B^q_{SAT} \left(- A^q_{SAT} + y_{INT}\right)^{2} \operatorname{Indicator}{\left(y_{INT} > A^q_{SAT} \right)}` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------+ | VFE | :math:`V_{FE}` | Algeb | :math:`K_{E} y_{INT} + V_{out}*S_e(|V_{out}|)` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+----------------------------------------------+---------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+==============================================+===============+ | LP_y | :math:`y_{LP}` | State | :math:`E_{term} - y_{LP}` | :math:`T_R` | +--------+-----------------+----------+----------------------------------------------+---------------+ | VR_y | :math:`y_{VR}` | State | :math:`K_{A} vi - y_{VR}` | :math:`T_A` | +--------+-----------------+----------+----------------------------------------------+---------------+ | LL_x | :math:`x'_{LL}` | State | :math:`- x'_{LL} + y_{VR}` | :math:`T_F_2` | +--------+-----------------+----------+----------------------------------------------+---------------+ | WF_x | :math:`x'_{WF}` | State | :math:`- x'_{WF} + y_{LL}` | :math:`T_F_1` | +--------+-----------------+----------+----------------------------------------------+---------------+ | INT_y | :math:`y_{INT}` | State | :math:`u_{e} \left(- V_{FE} + y_{VR}\right)` | :math:`T_E` | +--------+-----------------+----------+----------------------------------------------+---------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+----------------------------------------------+---------------+ Algebraic Equations ----------------------------- +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+================================+==========+==============================================================================================================================================+ | v | :math:`E_{term}` | Algeb | :math:`- E_{term} + V` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`v_{out}` | Algeb | :math:`u_{e} y_{INT} - v_{out}` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`U_{EL}` | Algeb | :math:`UEL_{0} - U_{EL}` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------+ | OEL | :math:`O_{EL}` | Algeb | :math:`OEL_{0} - O_{EL}` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------+ | Vs | :math:`V_{s}` | Algeb | :math:`- V_{s}` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`V_{ref}` | Algeb | :math:`V_{ref0} - V_{ref}` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`u_{e} \left(V_{ref} + V_{s} - y_{LP} - y_{WF}\right) - vi` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- x'_{LL} + y_{LL}\right) + T_{F 2} x'_{LL} - T_{F 2} y_{LL} + T_{F 3} \left(- x'_{LL} + y_{VR}\right)` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`y_{WF}` | Algeb | :math:`K_{F} \left(- x'_{WF} + y_{LL}\right) - T_{F 1} y_{WF}` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`V_{out}*S_e(|V_{out}|)` | Algeb | :math:`u_{e} \left(B^q_{SAT} z_{0}^{SL} \left(- A^q_{SAT} + y_{INT}\right)^{2} - V_{out}*S_e(|V_{out}|)\right)` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------+ | VFE | :math:`V_{FE}` | Algeb | :math:`u_{e} \left(K_{E} y_{INT} - V_{FE} + V_{out}*S_e(|V_{out}|)\right)` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`v_{f}` | ExtAlgeb | :math:`u_{e} \left(- v_{f0} + v_{out}\right)` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`X_{ad}I_{fd}` | ExtAlgeb | :math:`0` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | :math:`0` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`V` | ExtAlgeb | :math:`0` | +---------+--------------------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +==========+=======================+=============================================================================================================================================================================================================================================+=================+ | ue | :math:`u_e` | :math:`u u_{g}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | UEL0 | :math:`UEL0` | :math:`0` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | OEL0 | :math:`OEL0` | :math:`0` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VRMAXu | :math:`VRMAXu` | :math:`V_{Rmax} u_{e} - 999 u_{e} + 999` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VRMINu | :math:`VRMINu` | :math:`V_{Rmin} u_{e} + 999 u_{e} - 999` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E1 | :math:`E^{1c}_{SAT}` | :math:`E_{1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E2 | :math:`E^{2c}_{SAT}` | :math:`E_{2} - 2 z^{SE2}_{SAT} + 2` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE1 | :math:`SE^{1c}_{SAT}` | :math:`S_{E1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE2 | :math:`SE^{2c}_{SAT}` | :math:`S_{E2} - 2 z^{SE2}_{SAT} + 2` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_a | :math:`a_{SAT}` | :math:`\sqrt{\frac{E^{1c}_{SAT} SE^{1c}_{SAT}}{E^{2c}_{SAT} SE^{2c}_{SAT}}} \left(\operatorname{Indicator}{\left(SE^{2c}_{SAT} > 0 \right)} + \operatorname{Indicator}{\left(SE^{2c}_{SAT} < 0 \right)}\right)` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_A | :math:`A^q_{SAT}` | :math:`E^{2c}_{SAT} - \frac{E^{1c}_{SAT} - E^{2c}_{SAT}}{a_{SAT} - 1}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_B | :math:`B^q_{SAT}` | :math:`\frac{E^{2c}_{SAT} SE^{2c}_{SAT} \left(a_{SAT} - 1\right)^{2} \left(\operatorname{Indicator}{\left(a_{SAT} > 0 \right)} + \operatorname{Indicator}{\left(a_{SAT} < 0 \right)}\right)}{\left(E^{1c}_{SAT} - E^{2c}_{SAT}\right)^{2}}` | ConstService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`V_{ref}` | PostInitService | +----------+-----------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ Discretes ----------- +---------+------------------+------------+----------------+ | Name | Symbol | Type | Info | +=========+==================+============+================+ | VR_lim | :math:`lim_{VR}` | AntiWindup | Limiter in Lag | +---------+------------------+------------+----------------+ | LL_LT1 | :math:`LT_{LL}` | LessThan | | +---------+------------------+------------+----------------+ | LL_LT2 | :math:`LT_{LL}` | LessThan | | +---------+------------------+------------+----------------+ | SL | :math:`SL` | LessThan | | +---------+------------------+------------+----------------+ Blocks ------- +------+-------------+---------------+--------------------------+ | Name | Symbol | Type | Info | +======+=============+===============+==========================+ | LP | :math:`LP` | Lag | Voltage transducer | +------+-------------+---------------+--------------------------+ | VR | :math:`VR` | LagAntiWindup | | +------+-------------+---------------+--------------------------+ | LL | :math:`LL` | LeadLag | | +------+-------------+---------------+--------------------------+ | WF | :math:`WF` | Washout | | +------+-------------+---------------+--------------------------+ | SAT | :math:`SAT` | ExcQuadSat | Field voltage saturation | +------+-------------+---------------+--------------------------+ | INT | :math:`INT` | Integrator | V_E, integrator | +------+-------------+---------------+--------------------------+ Config Fields in [ESAC5A] +---------------+--------+-------+---------------------------------------+-----------------+ | Option | Symbol | Value | Info | Accepted values | +===============+========+=======+=======================================+=================+ | allow_adjust | | 1 | allow adjusting upper or lower limits | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_lower | | 0 | adjust lower limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_upper | | 1 | adjust upper limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+