.. _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:`vp` | State | Voltage after saturation feedback, before speed term | *p.u.* | v_str | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | LS_y | :math:`LS_{y}` | State | State in lag transfer function | | v_str | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | LL_x | :math:`LL_{x}` | State | State in lead-lag | | v_str | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | LA_y | :math:`LA_{y}` | State | State in lag TF | | v_str | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | W_x | :math:`W_{x}` | State | State in washout filter | | v_str | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | v | :math:`v` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | vout | :math:`vout` | Algeb | Exciter final output voltage | | v_str | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | vref | :math:`vref` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | Se | :math:`Se` | Algeb | saturation output | | v_str | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | vi | :math:`vi` | Algeb | Total input voltages | *p.u.* | v_str | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | LL_y | :math:`LL_{y}` | Algeb | Output of lead-lag | | v_str | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | W_y | :math:`W_{y}` | Algeb | Output of washout filter | | v_str | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | vf | :math:`vf` | ExtAlgeb | Excitation field voltage to generator | | | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | Armature excitation current | | | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | a | :math:`a` | ExtAlgeb | Bus voltage phase angle | | | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | vbus | :math:`vbus` | ExtAlgeb | Bus voltage magnitude | | | +---------+----------------+----------+------------------------------------------------------+--------+------------+ Initialization Equations ------------------------ +---------+----------------+----------+--------------------+ | Name | Symbol | Type | Initial Value | +=========+================+==========+====================+ | vp | :math:`vp` | State | :math:`vf_{0}` | +---------+----------------+----------+--------------------+ | LS_y | :math:`LS_{y}` | State | :math:`1.0 v` | +---------+----------------+----------+--------------------+ | LL_x | :math:`LL_{x}` | State | :math:`vi` | +---------+----------------+----------+--------------------+ | LA_y | :math:`LA_{y}` | State | :math:`KA LL_{y}` | +---------+----------------+----------+--------------------+ | W_x | :math:`W_{x}` | State | :math:`vp` | +---------+----------------+----------+--------------------+ | omega | :math:`\omega` | ExtState | | +---------+----------------+----------+--------------------+ | v | :math:`v` | Algeb | :math:`vbus` | +---------+----------------+----------+--------------------+ | vout | :math:`vout` | Algeb | :math:`ue vf_{0}` | +---------+----------------+----------+--------------------+ | vref | :math:`vref` | Algeb | :math:`v + vb_{0}` | +---------+----------------+----------+--------------------+ | Se | :math:`Se` | Algeb | :math:`Se_{0}` | +---------+----------------+----------+--------------------+ | vi | :math:`vi` | Algeb | :math:`vb_{0}` | +---------+----------------+----------+--------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`vi` | +---------+----------------+----------+--------------------+ | W_y | :math:`W_{y}` | Algeb | :math:`0` | +---------+----------------+----------+--------------------+ | vf | :math:`vf` | ExtAlgeb | | +---------+----------------+----------+--------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | | +---------+----------------+----------+--------------------+ | a | :math:`a` | ExtAlgeb | | +---------+----------------+----------+--------------------+ | vbus | :math:`vbus` | ExtAlgeb | | +---------+----------------+----------+--------------------+ Differential Equations ----------------------------- +--------+----------------+----------+--------------------------------------------------+----------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+================+==========+==================================================+================+ | vp | :math:`vp` | State | :math:`ue \left(- KE vp + LA_{y} - Se vp\right)` | :math:`T_E` | +--------+----------------+----------+--------------------------------------------------+----------------+ | LS_y | :math:`LS_{y}` | State | :math:`- LS_{y} + 1.0 v` | :math:`T_R` | +--------+----------------+----------+--------------------------------------------------+----------------+ | LL_x | :math:`LL_{x}` | State | :math:`- LL_{x} + vi` | :math:`T_B` | +--------+----------------+----------+--------------------------------------------------+----------------+ | LA_y | :math:`LA_{y}` | State | :math:`KA LL_{y} - LA_{y}` | :math:`T_A` | +--------+----------------+----------+--------------------------------------------------+----------------+ | W_x | :math:`W_{x}` | State | :math:`- W_{x} + vp` | :math:`T_{F1}` | +--------+----------------+----------+--------------------------------------------------+----------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+----------------+----------+--------------------------------------------------+----------------+ Algebraic Equations ----------------------------- +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+================+==========+========================================================================================================================+ | v | :math:`v` | Algeb | :math:`- v + vbus` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`\omega ue vp - vout` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`- vref + vref_{0}` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`Se` | Algeb | :math:`SAT_{B} SL_{z0} \left(- SAT_{A} + vp\right)^{2} - Se vp` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`- LS_{y} - W_{y} - vi + vref` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- LL_{x} + LL_{y}\right) + LL_{x} TB - LL_{y} TB + TC \left(- LL_{x} + vi\right)` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | W_y | :math:`W_{y}` | Algeb | :math:`KF_{1} \left(- W_{x} + vp\right) - TF_{1} W_{y}` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | :math:`ue \left(- vf_{0} + vout\right)` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | :math:`0` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | :math:`0` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | :math:`0` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ Services ---------- +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +==========+=======================+=============================================================================================================================================================================================================================+=================+ | ue | :math:`u_e` | :math:`u ug` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E1 | :math:`E^{1c}_{SAT}` | :math:`E_{1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E2 | :math:`E^{2c}_{SAT}` | :math:`E_{2} - 2 SAT_{zSE2} + 2` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE1 | :math:`SE^{1c}_{SAT}` | :math:`SE_{1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE2 | :math:`SE^{2c}_{SAT}` | :math:`- 2 SAT_{zSE2} + SE_{2} + 2` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_a | :math:`a_{SAT}` | :math:`\sqrt{\frac{SAT_{E1} SAT_{SE1}}{SAT_{E2} SAT_{SE2}}} \left(\operatorname{Indicator}{\left(SAT_{SE2} > 0 \right)} + \operatorname{Indicator}{\left(SAT_{SE2} < 0 \right)}\right)` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_A | :math:`A^q_{SAT}` | :math:`SAT_{E2} - \frac{SAT_{E1} - SAT_{E2}}{SAT_{a} - 1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_B | :math:`B^q_{SAT}` | :math:`\frac{SAT_{E2} SAT_{SE2} \left(SAT_{a} - 1\right)^{2} \left(\operatorname{Indicator}{\left(SAT_{a} > 0 \right)} + \operatorname{Indicator}{\left(SAT_{a} < 0 \right)}\right)}{\left(SAT_{E1} - SAT_{E2}\right)^{2}}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Se0 | :math:`S_{e0}` | :math:`\frac{SAT_{B} \left(SAT_{A} - vf_{0}\right)^{2} \operatorname{Indicator}{\left(vf_{0} > SAT_{A} \right)}}{- ug + vf_{0} + 1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vr0 | :math:`V_{r0}` | :math:`vf_{0} \left(KE + Se_{0}\right)` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vb0 | :math:`V_{b0}` | :math:`\frac{vr_{0}}{KA}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`vref` | 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:`vp` | State | Voltage after saturation feedback, before speed term | *p.u.* | v_str | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | LS_y | :math:`LS_{y}` | State | State in lag transfer function | | v_str | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | LL_x | :math:`LL_{x}` | State | State in lead-lag | | v_str | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | LA_y | :math:`LA_{y}` | State | State in lag TF | | v_str | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | W_x | :math:`W_{x}` | State | State in washout filter | | v_str | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | v | :math:`v` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | vout | :math:`vout` | Algeb | Exciter final output voltage | | v_str | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | vref | :math:`vref` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | Se | :math:`Se` | Algeb | saturation output | | v_str | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | vi | :math:`vi` | Algeb | Total input voltages | *p.u.* | v_str | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | LL_y | :math:`LL_{y}` | Algeb | Output of lead-lag | | v_str | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | W_y | :math:`W_{y}` | Algeb | Output of washout filter | | v_str | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | vf | :math:`vf` | ExtAlgeb | Excitation field voltage to generator | | | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | Armature excitation current | | | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | a | :math:`a` | ExtAlgeb | Bus voltage phase angle | | | +---------+----------------+----------+------------------------------------------------------+--------+------------+ | vbus | :math:`vbus` | ExtAlgeb | Bus voltage magnitude | | | +---------+----------------+----------+------------------------------------------------------+--------+------------+ Initialization Equations ------------------------ +---------+----------------+----------+--------------------+ | Name | Symbol | Type | Initial Value | +=========+================+==========+====================+ | vp | :math:`vp` | State | :math:`vf_{0}` | +---------+----------------+----------+--------------------+ | LS_y | :math:`LS_{y}` | State | :math:`1.0 v` | +---------+----------------+----------+--------------------+ | LL_x | :math:`LL_{x}` | State | :math:`vi` | +---------+----------------+----------+--------------------+ | LA_y | :math:`LA_{y}` | State | :math:`KA LL_{y}` | +---------+----------------+----------+--------------------+ | W_x | :math:`W_{x}` | State | :math:`vp` | +---------+----------------+----------+--------------------+ | omega | :math:`\omega` | ExtState | | +---------+----------------+----------+--------------------+ | v | :math:`v` | Algeb | :math:`vbus` | +---------+----------------+----------+--------------------+ | vout | :math:`vout` | Algeb | :math:`ue vf_{0}` | +---------+----------------+----------+--------------------+ | vref | :math:`vref` | Algeb | :math:`v + vb_{0}` | +---------+----------------+----------+--------------------+ | Se | :math:`Se` | Algeb | :math:`Se_{0}` | +---------+----------------+----------+--------------------+ | vi | :math:`vi` | Algeb | :math:`vb_{0}` | +---------+----------------+----------+--------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`vi` | +---------+----------------+----------+--------------------+ | W_y | :math:`W_{y}` | Algeb | :math:`0` | +---------+----------------+----------+--------------------+ | vf | :math:`vf` | ExtAlgeb | | +---------+----------------+----------+--------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | | +---------+----------------+----------+--------------------+ | a | :math:`a` | ExtAlgeb | | +---------+----------------+----------+--------------------+ | vbus | :math:`vbus` | ExtAlgeb | | +---------+----------------+----------+--------------------+ Differential Equations ----------------------------- +--------+----------------+----------+--------------------------------------------------+----------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+================+==========+==================================================+================+ | vp | :math:`vp` | State | :math:`ue \left(- KE vp + LA_{y} - Se vp\right)` | :math:`T_E` | +--------+----------------+----------+--------------------------------------------------+----------------+ | LS_y | :math:`LS_{y}` | State | :math:`- LS_{y} + 1.0 v` | :math:`T_R` | +--------+----------------+----------+--------------------------------------------------+----------------+ | LL_x | :math:`LL_{x}` | State | :math:`- LL_{x} + vi` | :math:`T_B` | +--------+----------------+----------+--------------------------------------------------+----------------+ | LA_y | :math:`LA_{y}` | State | :math:`KA LL_{y} - LA_{y}` | :math:`T_A` | +--------+----------------+----------+--------------------------------------------------+----------------+ | W_x | :math:`W_{x}` | State | :math:`- W_{x} + vp` | :math:`T_{F1}` | +--------+----------------+----------+--------------------------------------------------+----------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+----------------+----------+--------------------------------------------------+----------------+ Algebraic Equations ----------------------------- +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+================+==========+========================================================================================================================+ | v | :math:`v` | Algeb | :math:`- v + vbus` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`ue vp - vout` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`- vref + vref_{0}` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`Se` | Algeb | :math:`SAT_{B} SL_{z0} \left(- SAT_{A} + vp\right)^{2} - Se vp` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`- LS_{y} - W_{y} - vi + vref` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- LL_{x} + LL_{y}\right) + LL_{x} TB - LL_{y} TB + TC \left(- LL_{x} + vi\right)` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | W_y | :math:`W_{y}` | Algeb | :math:`KF_{1} \left(- W_{x} + vp\right) - TF_{1} W_{y}` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | :math:`ue \left(- vf_{0} + vout\right)` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | :math:`0` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | :math:`0` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | :math:`0` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ Services ---------- +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +==========+=======================+=============================================================================================================================================================================================================================+=================+ | ue | :math:`u_e` | :math:`u ug` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E1 | :math:`E^{1c}_{SAT}` | :math:`E_{1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E2 | :math:`E^{2c}_{SAT}` | :math:`E_{2} - 2 SAT_{zSE2} + 2` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE1 | :math:`SE^{1c}_{SAT}` | :math:`SE_{1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE2 | :math:`SE^{2c}_{SAT}` | :math:`- 2 SAT_{zSE2} + SE_{2} + 2` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_a | :math:`a_{SAT}` | :math:`\sqrt{\frac{SAT_{E1} SAT_{SE1}}{SAT_{E2} SAT_{SE2}}} \left(\operatorname{Indicator}{\left(SAT_{SE2} > 0 \right)} + \operatorname{Indicator}{\left(SAT_{SE2} < 0 \right)}\right)` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_A | :math:`A^q_{SAT}` | :math:`SAT_{E2} - \frac{SAT_{E1} - SAT_{E2}}{SAT_{a} - 1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_B | :math:`B^q_{SAT}` | :math:`\frac{SAT_{E2} SAT_{SE2} \left(SAT_{a} - 1\right)^{2} \left(\operatorname{Indicator}{\left(SAT_{a} > 0 \right)} + \operatorname{Indicator}{\left(SAT_{a} < 0 \right)}\right)}{\left(SAT_{E1} - SAT_{E2}\right)^{2}}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Se0 | :math:`S_{e0}` | :math:`\frac{SAT_{B} \left(SAT_{A} - vf_{0}\right)^{2} \operatorname{Indicator}{\left(vf_{0} > SAT_{A} \right)}}{- ug + vf_{0} + 1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vr0 | :math:`V_{r0}` | :math:`vf_{0} \left(KE + Se_{0}\right)` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vb0 | :math:`V_{b0}` | :math:`\frac{vr_{0}}{KA}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`vref` | PostInitService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VRTMAX | :math:`V_{RMAX}V_T` | :math:`VRMAX v` | VarService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VRTMIN | :math:`V_{RMIN}V_T` | :math:`VRMIN v` | 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:`LG_{y}` | State | State in lag transfer function | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | LL_x | :math:`LL_{x}` | State | State in lead-lag | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | LA_y | :math:`LA_{y}` | State | State in lag TF | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | INT_y | :math:`INT_{y}` | State | Integrator output | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | WF_x | :math:`WF_{x}` | State | State in washout filter | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ | v | :math:`v` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vout | :math:`vout` | Algeb | Exciter final output voltage | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vref | :math:`vref` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vi | :math:`vi` | Algeb | Total input voltages | *p.u.* | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | LL_y | :math:`LL_{y}` | Algeb | Output of lead-lag | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | UEL | :math:`UEL` | Algeb | Interface var for under exc. limiter | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | HG_y | :math:`HG_{y}` | Algeb | HVGate output | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | Se | :math:`Se` | Algeb | saturation output | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | VFE | :math:`VFE` | Algeb | Combined saturation feedback | *p.u.* | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | WF_y | :math:`WF_{y}` | Algeb | Output of washout filter | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vf | :math:`vf` | ExtAlgeb | Excitation field voltage to generator | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | Armature excitation current | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ | a | :math:`a` | ExtAlgeb | Bus voltage phase angle | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vbus | :math:`vbus` | ExtAlgeb | Bus voltage magnitude | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ Initialization Equations ------------------------ +---------+-----------------+----------+--------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+=================+==========+============================================+ | LG_y | :math:`LG_{y}` | State | :math:`v` | +---------+-----------------+----------+--------------------------------------------+ | LL_x | :math:`LL_{x}` | State | :math:`vi` | +---------+-----------------+----------+--------------------------------------------+ | LA_y | :math:`LA_{y}` | State | :math:`KA LL_{y}` | +---------+-----------------+----------+--------------------------------------------+ | INT_y | :math:`INT_{y}` | State | :math:`vf_{0}` | +---------+-----------------+----------+--------------------------------------------+ | WF_x | :math:`WF_{x}` | State | :math:`INT_{y}` | +---------+-----------------+----------+--------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+-----------------+----------+--------------------------------------------+ | v | :math:`v` | Algeb | :math:`vbus` | +---------+-----------------+----------+--------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`ue vf_{0}` | +---------+-----------------+----------+--------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`v + \frac{vfe_{0}}{KA}` | +---------+-----------------+----------+--------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`\frac{vfe_{0}}{KA}` | +---------+-----------------+----------+--------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`vi` | +---------+-----------------+----------+--------------------------------------------+ | UEL | :math:`UEL` | Algeb | :math:`0` | +---------+-----------------+----------+--------------------------------------------+ | HG_y | :math:`HG_{y}` | Algeb | :math:`HG_{lt z0} UEL + HG_{lt z1} LL_{y}` | +---------+-----------------+----------+--------------------------------------------+ | Se | :math:`Se` | Algeb | :math:`Se_{0}` | +---------+-----------------+----------+--------------------------------------------+ | VFE | :math:`VFE` | Algeb | :math:`vfe_{0}` | +---------+-----------------+----------+--------------------------------------------+ | WF_y | :math:`WF_{y}` | Algeb | :math:`0` | +---------+-----------------+----------+--------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | | +---------+-----------------+----------+--------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | | +---------+-----------------+----------+--------------------------------------------+ | a | :math:`a` | ExtAlgeb | | +---------+-----------------+----------+--------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | | +---------+-----------------+----------+--------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+--------------------------------------+----------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+======================================+================+ | LG_y | :math:`LG_{y}` | State | :math:`- LG_{y} + v` | :math:`T_R` | +--------+-----------------+----------+--------------------------------------+----------------+ | LL_x | :math:`LL_{x}` | State | :math:`- LL_{x} + vi` | :math:`T_B` | +--------+-----------------+----------+--------------------------------------+----------------+ | LA_y | :math:`LA_{y}` | State | :math:`KA LL_{y} - LA_{y}` | :math:`T_A` | +--------+-----------------+----------+--------------------------------------+----------------+ | INT_y | :math:`INT_{y}` | State | :math:`ue \left(LA_{y} - VFE\right)` | :math:`T_E` | +--------+-----------------+----------+--------------------------------------+----------------+ | WF_x | :math:`WF_{x}` | State | :math:`INT_{y} - WF_{x}` | :math:`T_{F1}` | +--------+-----------------+----------+--------------------------------------+----------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+--------------------------------------+----------------+ Algebraic Equations ----------------------------- +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+================+==========+========================================================================================================================+ | v | :math:`v` | Algeb | :math:`- v + vbus` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`INT_{y} - vout` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`- vref + vref_{0}` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`- WF_{y} - v - vi + vref` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- LL_{x} + LL_{y}\right) + LL_{x} TB - LL_{y} TB + TC \left(- LL_{x} + vi\right)` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`UEL` | Algeb | :math:`- UEL` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | HG_y | :math:`HG_{y}` | Algeb | :math:`HG_{lt z0} UEL + HG_{lt z1} LL_{y} - HG_{y}` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`Se` | Algeb | :math:`SAT_{B} SL_{z0} \left(INT_{y} - SAT_{A}\right)^{2} - Se` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | VFE | :math:`VFE` | Algeb | :math:`INT_{y} KE + Se - VFE` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`WF_{y}` | Algeb | :math:`KF \left(INT_{y} - WF_{x}\right) - TF_{1} WF_{y}` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | :math:`ue \left(- vf_{0} + vout\right)` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | :math:`0` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | :math:`0` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | :math:`0` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ Services ---------- +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +==========+=======================+=============================================================================================================================================================================================================================+=================+ | ue | :math:`u_e` | :math:`u ug` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VRMAXc | :math:`VRMAXc` | :math:`VRMAX - 999 _zVRM + 999` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E1 | :math:`E^{1c}_{SAT}` | :math:`E_{1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E2 | :math:`E^{2c}_{SAT}` | :math:`E_{2} - 2 SAT_{zSE2} + 2` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE1 | :math:`SE^{1c}_{SAT}` | :math:`SE_{1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE2 | :math:`SE^{2c}_{SAT}` | :math:`- 2 SAT_{zSE2} + SE_{2} + 2` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_a | :math:`a_{SAT}` | :math:`\sqrt{\frac{SAT_{E1} SAT_{SE1}}{SAT_{E2} SAT_{SE2}}} \left(\operatorname{Indicator}{\left(SAT_{SE2} > 0 \right)} + \operatorname{Indicator}{\left(SAT_{SE2} < 0 \right)}\right)` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_A | :math:`A^q_{SAT}` | :math:`SAT_{E2} - \frac{SAT_{E1} - SAT_{E2}}{SAT_{a} - 1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_B | :math:`B^q_{SAT}` | :math:`\frac{SAT_{E2} SAT_{SE2} \left(SAT_{a} - 1\right)^{2} \left(\operatorname{Indicator}{\left(SAT_{a} > 0 \right)} + \operatorname{Indicator}{\left(SAT_{a} < 0 \right)}\right)}{\left(SAT_{E1} - SAT_{E2}\right)^{2}}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Se0 | :math:`S_{e0}` | :math:`SAT_{B} \left(SAT_{A} - vf_{0}\right)^{2} \operatorname{Indicator}{\left(vf_{0} > SAT_{A} \right)}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vfe0 | :math:`V_{FE0}` | :math:`KE vf_{0} + Se_{0}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`vref` | PostInitService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VRU | :math:`V_{RMAX}` | :math:`VRMAXc` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VRL | :math:`V_{RMIN}` | :math:`VRMIN` | 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:`LG_{y}` | State | State in lag transfer function | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | LL_x | :math:`LL_{x}` | State | State in lead-lag | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | LA_y | :math:`LA_{y}` | State | State in lag TF | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | INT_y | :math:`INT_{y}` | State | Integrator output | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | WF_x | :math:`WF_{x}` | State | State in washout filter | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ | v | :math:`v` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vout | :math:`vout` | Algeb | Exciter final output voltage | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vref | :math:`vref` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vi | :math:`vi` | Algeb | Total input voltages | *p.u.* | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | LL_y | :math:`LL_{y}` | Algeb | Output of lead-lag | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | UEL | :math:`UEL` | Algeb | Interface var for under exc. limiter | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | HG_y | :math:`HG_{y}` | Algeb | HVGate output | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | Se | :math:`Se` | Algeb | saturation output | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | VFE | :math:`VFE` | Algeb | Combined saturation feedback | *p.u.* | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | WF_y | :math:`WF_{y}` | Algeb | Output of washout filter | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vf | :math:`vf` | ExtAlgeb | Excitation field voltage to generator | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | Armature excitation current | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ | a | :math:`a` | ExtAlgeb | Bus voltage phase angle | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vbus | :math:`vbus` | ExtAlgeb | Bus voltage magnitude | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ Initialization Equations ------------------------ +---------+-----------------+----------+--------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+=================+==========+============================================+ | LG_y | :math:`LG_{y}` | State | :math:`v` | +---------+-----------------+----------+--------------------------------------------+ | LL_x | :math:`LL_{x}` | State | :math:`vi` | +---------+-----------------+----------+--------------------------------------------+ | LA_y | :math:`LA_{y}` | State | :math:`KA LL_{y}` | +---------+-----------------+----------+--------------------------------------------+ | INT_y | :math:`INT_{y}` | State | :math:`vf_{0}` | +---------+-----------------+----------+--------------------------------------------+ | WF_x | :math:`WF_{x}` | State | :math:`INT_{y}` | +---------+-----------------+----------+--------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+-----------------+----------+--------------------------------------------+ | v | :math:`v` | Algeb | :math:`vbus` | +---------+-----------------+----------+--------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`ue vf_{0}` | +---------+-----------------+----------+--------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`v + \frac{vfe_{0}}{KA}` | +---------+-----------------+----------+--------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`\frac{vfe_{0}}{KA}` | +---------+-----------------+----------+--------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`vi` | +---------+-----------------+----------+--------------------------------------------+ | UEL | :math:`UEL` | Algeb | :math:`0` | +---------+-----------------+----------+--------------------------------------------+ | HG_y | :math:`HG_{y}` | Algeb | :math:`HG_{lt z0} UEL + HG_{lt z1} LL_{y}` | +---------+-----------------+----------+--------------------------------------------+ | Se | :math:`Se` | Algeb | :math:`Se_{0}` | +---------+-----------------+----------+--------------------------------------------+ | VFE | :math:`VFE` | Algeb | :math:`vfe_{0}` | +---------+-----------------+----------+--------------------------------------------+ | WF_y | :math:`WF_{y}` | Algeb | :math:`0` | +---------+-----------------+----------+--------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | | +---------+-----------------+----------+--------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | | +---------+-----------------+----------+--------------------------------------------+ | a | :math:`a` | ExtAlgeb | | +---------+-----------------+----------+--------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | | +---------+-----------------+----------+--------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+--------------------------------------+----------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+======================================+================+ | LG_y | :math:`LG_{y}` | State | :math:`- LG_{y} + v` | :math:`T_R` | +--------+-----------------+----------+--------------------------------------+----------------+ | LL_x | :math:`LL_{x}` | State | :math:`- LL_{x} + vi` | :math:`T_B` | +--------+-----------------+----------+--------------------------------------+----------------+ | LA_y | :math:`LA_{y}` | State | :math:`KA LL_{y} - LA_{y}` | :math:`T_A` | +--------+-----------------+----------+--------------------------------------+----------------+ | INT_y | :math:`INT_{y}` | State | :math:`ue \left(LA_{y} - VFE\right)` | :math:`T_E` | +--------+-----------------+----------+--------------------------------------+----------------+ | WF_x | :math:`WF_{x}` | State | :math:`INT_{y} - WF_{x}` | :math:`T_{F1}` | +--------+-----------------+----------+--------------------------------------+----------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+--------------------------------------+----------------+ Algebraic Equations ----------------------------- +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+================+==========+========================================================================================================================+ | v | :math:`v` | Algeb | :math:`- v + vbus` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`INT_{y} - vout` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`- vref + vref_{0}` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`- WF_{y} - v - vi + vref` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- LL_{x} + LL_{y}\right) + LL_{x} TB - LL_{y} TB + TC \left(- LL_{x} + vi\right)` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`UEL` | Algeb | :math:`- UEL` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | HG_y | :math:`HG_{y}` | Algeb | :math:`HG_{lt z0} UEL + HG_{lt z1} LL_{y} - HG_{y}` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`Se` | Algeb | :math:`SAT_{B} SL_{z0} \left(INT_{y} - SAT_{A}\right)^{2} - Se` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | VFE | :math:`VFE` | Algeb | :math:`INT_{y} KE + Se - VFE` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`WF_{y}` | Algeb | :math:`KF \left(INT_{y} - WF_{x}\right) - TF_{1} WF_{y}` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | :math:`ue \left(- vf_{0} + vout\right)` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | :math:`0` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | :math:`0` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | :math:`0` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ Services ---------- +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +==========+=======================+=============================================================================================================================================================================================================================+=================+ | ue | :math:`u_e` | :math:`u ug` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VRMAXc | :math:`VRMAXc` | :math:`VRMAX - 999 _zVRM + 999` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E1 | :math:`E^{1c}_{SAT}` | :math:`E_{1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E2 | :math:`E^{2c}_{SAT}` | :math:`E_{2} - 2 SAT_{zSE2} + 2` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE1 | :math:`SE^{1c}_{SAT}` | :math:`SE_{1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE2 | :math:`SE^{2c}_{SAT}` | :math:`- 2 SAT_{zSE2} + SE_{2} + 2` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_a | :math:`a_{SAT}` | :math:`\sqrt{\frac{SAT_{E1} SAT_{SE1}}{SAT_{E2} SAT_{SE2}}} \left(\operatorname{Indicator}{\left(SAT_{SE2} > 0 \right)} + \operatorname{Indicator}{\left(SAT_{SE2} < 0 \right)}\right)` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_A | :math:`A^q_{SAT}` | :math:`SAT_{E2} - \frac{SAT_{E1} - SAT_{E2}}{SAT_{a} - 1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_B | :math:`B^q_{SAT}` | :math:`\frac{SAT_{E2} SAT_{SE2} \left(SAT_{a} - 1\right)^{2} \left(\operatorname{Indicator}{\left(SAT_{a} > 0 \right)} + \operatorname{Indicator}{\left(SAT_{a} < 0 \right)}\right)}{\left(SAT_{E1} - SAT_{E2}\right)^{2}}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Se0 | :math:`S_{e0}` | :math:`SAT_{B} \left(SAT_{A} - vf_{0}\right)^{2} \operatorname{Indicator}{\left(vf_{0} > SAT_{A} \right)}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vfe0 | :math:`V_{FE0}` | :math:`KE vf_{0} + Se_{0}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`vref` | PostInitService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VRU | :math:`V_T V_{RMAX}` | :math:`VRMAXc v` | VarService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VRL | :math:`V_T V_{RMIN}` | :math:`VRMIN v` | 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:`LG_{y}` | State | State in lag transfer function | | v_str | +---------+----------------+----------+---------------------------------------+--------+------------+ | LL_x | :math:`LL_{x}` | State | State in lead-lag | | v_str | +---------+----------------+----------+---------------------------------------+--------+------------+ | LR_y | :math:`LR_{y}` | State | State in lag transfer function | | v_str | +---------+----------------+----------+---------------------------------------+--------+------------+ | WF_x | :math:`WF_{x}` | State | State in washout filter | | v_str | +---------+----------------+----------+---------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+----------------+----------+---------------------------------------+--------+------------+ | v | :math:`v` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+----------------+----------+---------------------------------------+--------+------------+ | vout | :math:`vout` | Algeb | Exciter final output voltage | | v_str | +---------+----------------+----------+---------------------------------------+--------+------------+ | vref | :math:`vref` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+----------------+----------+---------------------------------------+--------+------------+ | vi | :math:`vi` | Algeb | Total input voltages | *p.u.* | v_str | +---------+----------------+----------+---------------------------------------+--------+------------+ | vl | :math:`vl` | Algeb | Input after limiter | | v_str | +---------+----------------+----------+---------------------------------------+--------+------------+ | LL_y | :math:`LL_{y}` | Algeb | Output of lead-lag | | v_str | +---------+----------------+----------+---------------------------------------+--------+------------+ | WF_y | :math:`WF_{y}` | Algeb | Output of washout filter | | v_str | +---------+----------------+----------+---------------------------------------+--------+------------+ | vfmax | :math:`vfmax` | Algeb | Upper bound of output limiter | | v_str | +---------+----------------+----------+---------------------------------------+--------+------------+ | vfmin | :math:`vfmin` | Algeb | Lower bound of output limiter | | v_str | +---------+----------------+----------+---------------------------------------+--------+------------+ | vf | :math:`vf` | ExtAlgeb | Excitation field voltage to generator | | | +---------+----------------+----------+---------------------------------------+--------+------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | Armature excitation current | | | +---------+----------------+----------+---------------------------------------+--------+------------+ | a | :math:`a` | ExtAlgeb | Bus voltage phase angle | | | +---------+----------------+----------+---------------------------------------+--------+------------+ | vbus | :math:`vbus` | ExtAlgeb | Bus voltage magnitude | | | +---------+----------------+----------+---------------------------------------+--------+------------+ Initialization Equations ------------------------ +---------+----------------+----------+-------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+================+==========+=======================================================+ | LG_y | :math:`LG_{y}` | State | :math:`v` | +---------+----------------+----------+-------------------------------------------------------+ | LL_x | :math:`LL_{x}` | State | :math:`vl` | +---------+----------------+----------+-------------------------------------------------------+ | LR_y | :math:`LR_{y}` | State | :math:`KA LL_{y}` | +---------+----------------+----------+-------------------------------------------------------+ | WF_x | :math:`WF_{x}` | State | :math:`LR_{y}` | +---------+----------------+----------+-------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+----------------+----------+-------------------------------------------------------+ | v | :math:`v` | Algeb | :math:`vbus` | +---------+----------------+----------+-------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`ue vf_{0}` | +---------+----------------+----------+-------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`v + \frac{vf_{0}}{KA}` | +---------+----------------+----------+-------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`\frac{vf_{0}}{KA}` | +---------+----------------+----------+-------------------------------------------------------+ | vl | :math:`vl` | Algeb | :math:`HLI_{zi} vi + HLI_{zl} VIMIN + HLI_{zu} VIMAX` | +---------+----------------+----------+-------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`vl` | +---------+----------------+----------+-------------------------------------------------------+ | WF_y | :math:`WF_{y}` | Algeb | :math:`0` | +---------+----------------+----------+-------------------------------------------------------+ | vfmax | :math:`vfmax` | Algeb | :math:`- KC XadIfd + VRMAX` | +---------+----------------+----------+-------------------------------------------------------+ | vfmin | :math:`vfmin` | Algeb | :math:`- KC XadIfd + VRMIN` | +---------+----------------+----------+-------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | | +---------+----------------+----------+-------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | | +---------+----------------+----------+-------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | | +---------+----------------+----------+-------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | | +---------+----------------+----------+-------------------------------------------------------+ Differential Equations ----------------------------- +--------+----------------+----------+----------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+================+==========+==================================+=============+ | LG_y | :math:`LG_{y}` | State | :math:`- LG_{y} + v` | :math:`T_R` | +--------+----------------+----------+----------------------------------+-------------+ | LL_x | :math:`LL_{x}` | State | :math:`- LL_{x} + vl` | :math:`T_B` | +--------+----------------+----------+----------------------------------+-------------+ | LR_y | :math:`LR_{y}` | State | :math:`KA LL_{y} - LR_{y}` | :math:`T_A` | +--------+----------------+----------+----------------------------------+-------------+ | WF_x | :math:`WF_{x}` | State | :math:`LR_{y} - WF_{x}` | :math:`T_F` | +--------+----------------+----------+----------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+----------------+----------+----------------------------------+-------------+ Algebraic Equations ----------------------------- +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+================+==========+========================================================================================================================+ | v | :math:`v` | Algeb | :math:`- v + vbus` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`ue \left(HLR_{zi} LR_{y} + HLR_{zl} vfmin + HLR_{zu} vfmax\right) - vout` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`- vref + vref_{0}` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`- LG_{y} - WF_{y} - vi + vref` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vl | :math:`vl` | Algeb | :math:`HLI_{zi} vi + HLI_{zl} VIMIN + HLI_{zu} VIMAX - vl` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- LL_{x} + LL_{y}\right) + LL_{x} TB - LL_{y} TB + TC \left(- LL_{x} + vl\right)` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`WF_{y}` | Algeb | :math:`KF \left(LR_{y} - WF_{x}\right) - TF WF_{y}` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vfmax | :math:`vfmax` | Algeb | :math:`- KC XadIfd + VRMAX - vfmax` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vfmin | :math:`vfmin` | Algeb | :math:`- KC XadIfd + VRMIN - vfmin` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | :math:`ue \left(- vf_{0} + vout\right)` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | :math:`0` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | :math:`0` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | :math:`0` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ Services ---------- +--------+------------------+--------------+-----------------+ | Name | Symbol | Equation | Type | +========+==================+==============+=================+ | ue | :math:`u_e` | :math:`u ug` | ConstService | +--------+------------------+--------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`vref` | 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:`LG_{y}` | State | State in lag transfer function | | v_str | +---------+-------------------+----------+---------------------------------------+--------+------------+ | LL_x | :math:`LL_{x}` | State | State in lead-lag | | v_str | +---------+-------------------+----------+---------------------------------------+--------+------------+ | LAW1_y | :math:`LAW_{1 y}` | State | State in lag TF | | v_str | +---------+-------------------+----------+---------------------------------------+--------+------------+ | LAW2_y | :math:`LAW_{2 y}` | State | State in lag TF | | v_str | +---------+-------------------+----------+---------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+-------------------+----------+---------------------------------------+--------+------------+ | v | :math:`v` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+-------------------+----------+---------------------------------------+--------+------------+ | vout | :math:`vout` | Algeb | Exciter final output voltage | | v_str | +---------+-------------------+----------+---------------------------------------+--------+------------+ | UEL | :math:`UEL` | Algeb | Interface var for under exc. limiter | | v_str | +---------+-------------------+----------+---------------------------------------+--------+------------+ | IN | :math:`IN` | Algeb | Input to FEX | | v_str | +---------+-------------------+----------+---------------------------------------+--------+------------+ | FEX_y | :math:`FEX_{y}` | Algeb | Output of piecewise | | v_str | +---------+-------------------+----------+---------------------------------------+--------+------------+ | VB_x | :math:`VB_{x}` | Algeb | Value before limiter | | v_str | +---------+-------------------+----------+---------------------------------------+--------+------------+ | VB_y | :math:`VB_{y}` | Algeb | Output after limiter and post gain | | v_str | +---------+-------------------+----------+---------------------------------------+--------+------------+ | VG_x | :math:`VG_{x}` | Algeb | Value before limiter | | v_str | +---------+-------------------+----------+---------------------------------------+--------+------------+ | VG_y | :math:`VG_{y}` | Algeb | Output after limiter and post gain | | v_str | +---------+-------------------+----------+---------------------------------------+--------+------------+ | vrs | :math:`vrs` | Algeb | VR subtract feedback VG | | v_str | +---------+-------------------+----------+---------------------------------------+--------+------------+ | vref | :math:`vref` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+-------------------+----------+---------------------------------------+--------+------------+ | vi | :math:`vi` | Algeb | Total input voltages | *p.u.* | v_str | +---------+-------------------+----------+---------------------------------------+--------+------------+ | vil | :math:`vil` | Algeb | Input voltage after limit | | v_str | +---------+-------------------+----------+---------------------------------------+--------+------------+ | HG_y | :math:`HG_{y}` | Algeb | HVGate output | | v_str | +---------+-------------------+----------+---------------------------------------+--------+------------+ | LL_y | :math:`LL_{y}` | Algeb | Output of lead-lag | | v_str | +---------+-------------------+----------+---------------------------------------+--------+------------+ | vf | :math:`vf` | ExtAlgeb | Excitation field voltage to generator | | | +---------+-------------------+----------+---------------------------------------+--------+------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | Armature excitation current | | | +---------+-------------------+----------+---------------------------------------+--------+------------+ | a | :math:`a` | ExtAlgeb | Bus voltage phase angle | | | +---------+-------------------+----------+---------------------------------------+--------+------------+ | vbus | :math:`vbus` | ExtAlgeb | Bus voltage magnitude | | | +---------+-------------------+----------+---------------------------------------+--------+------------+ | vd | :math:`vd` | ExtAlgeb | d-axis machine voltage | | | +---------+-------------------+----------+---------------------------------------+--------+------------+ | vq | :math:`vq` | ExtAlgeb | q-axis machine voltage | | | +---------+-------------------+----------+---------------------------------------+--------+------------+ | Id | :math:`Id` | ExtAlgeb | d-axis machine current | | | +---------+-------------------+----------+---------------------------------------+--------+------------+ | Iq | :math:`Iq` | ExtAlgeb | q-axis machine current | | | +---------+-------------------+----------+---------------------------------------+--------+------------+ Initialization Equations ------------------------ +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+===================+==========+================================================================================================================================================================================================================================================================+ | LG_y | :math:`LG_{y}` | State | :math:`v` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_x | :math:`LL_{x}` | State | :math:`HG_{y}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LAW1_y | :math:`LAW_{1 y}` | State | :math:`KA LL_{y}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LAW2_y | :math:`LAW_{2 y}` | State | :math:`KM vrs` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`v` | Algeb | :math:`vbus` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`ue vf_{0}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`UEL` | Algeb | :math:`UEL_{0}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`IN` | Algeb | :math:`\operatorname{safe}_{div}{\left(KC XadIfd,VE \right)}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | FEX_y | :math:`FEX_{y}` | Algeb | :math:`\operatorname{FixPiecewise}{\left(\left( 1, \ IN \leq 0\right),\left( 1 - 0.577 IN, \ IN \leq 0.433\right),\left( \sqrt{0.75 - IN^{2}}, \ IN \leq 0.75\right),\left( 1.732 - 1.732 IN, \ IN \leq 1\right),\left( 0, \ \text{True}\right) \right)}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VB_x | :math:`VB_{x}` | Algeb | :math:`FEX_{y} VE` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VB_y | :math:`VB_{y}` | Algeb | :math:`VBMAX VB_{lim zu} + VB_{lim zi} VB_{x}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VG_x | :math:`VG_{x}` | Algeb | :math:`KG vout` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VG_y | :math:`VG_{y}` | Algeb | :math:`VGMAX VG_{lim zu} + VG_{lim zi} VG_{x}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vrs | :math:`vrs` | Algeb | :math:`\frac{\operatorname{safe}_{div}{\left(vf_{0},VB_{y} \right)}}{KM}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`v + \frac{VG_{y} + vrs}{KA}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`- v + vref` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vil | :math:`vil` | Algeb | :math:`HLI_{zi} vi + HLI_{zl} VIMIN + HLI_{zu} VIMAX` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | HG_y | :math:`HG_{y}` | Algeb | :math:`HG_{lt z0} UEL + HG_{lt z1} vil` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`HG_{y}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vd | :math:`vd` | ExtAlgeb | | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vq | :math:`vq` | ExtAlgeb | | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Id | :math:`Id` | ExtAlgeb | | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iq | :math:`Iq` | ExtAlgeb | | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +---------+-------------------+----------+----------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +=========+===================+==========+==================================+=============+ | LG_y | :math:`LG_{y}` | State | :math:`- LG_{y} + v` | :math:`T_R` | +---------+-------------------+----------+----------------------------------+-------------+ | LL_x | :math:`LL_{x}` | State | :math:`HG_{y} - LL_{x}` | :math:`T_B` | +---------+-------------------+----------+----------------------------------+-------------+ | LAW1_y | :math:`LAW_{1 y}` | State | :math:`KA LL_{y} - LAW_{1 y}` | :math:`T_A` | +---------+-------------------+----------+----------------------------------+-------------+ | LAW2_y | :math:`LAW_{2 y}` | State | :math:`KM vrs - LAW_{2 y}` | :math:`K_C` | +---------+-------------------+----------+----------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +---------+-------------------+----------+----------------------------------+-------------+ Algebraic Equations ----------------------------- +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+=================+==========+============================================================================================================================================================================================================================================================================+ | v | :math:`v` | Algeb | :math:`- v + vbus` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`LAW_{2 y} VB_{y} ue - vout` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`UEL` | Algeb | :math:`- UEL + UEL_{0}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`IN` | Algeb | :math:`ue \left(- IN VE + KC XadIfd\right)` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | FEX_y | :math:`FEX_{y}` | Algeb | :math:`- FEX_{y} + \operatorname{FixPiecewise}{\left(\left( 1, \ IN \leq 0\right),\left( 1 - 0.577 IN, \ IN \leq 0.433\right),\left( \sqrt{0.75 - IN^{2}}, \ IN \leq 0.75\right),\left( 1.732 - 1.732 IN, \ IN \leq 1\right),\left( 0, \ \text{True}\right) \right)}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VB_x | :math:`VB_{x}` | Algeb | :math:`FEX_{y} VE - VB_{x}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VB_y | :math:`VB_{y}` | Algeb | :math:`VBMAX VB_{lim zu} + VB_{lim zi} VB_{x} - VB_{y}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VG_x | :math:`VG_{x}` | Algeb | :math:`KG vout - VG_{x}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VG_y | :math:`VG_{y}` | Algeb | :math:`VGMAX VG_{lim zu} + VG_{lim zi} VG_{x} - VG_{y}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vrs | :math:`vrs` | Algeb | :math:`LAW_{1 y} - VG_{y} - vrs` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`- vref + vref_{0}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`- LG_{y} - vi + vref` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vil | :math:`vil` | Algeb | :math:`HLI_{zi} vi + HLI_{zl} VIMIN + HLI_{zu} VIMAX - vil` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | HG_y | :math:`HG_{y}` | Algeb | :math:`HG_{lt z0} UEL + HG_{lt z1} vil - HG_{y}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- LL_{x} + LL_{y}\right) + LL_{x} TB - LL_{y} TB + TC \left(HG_{y} - LL_{x}\right)` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | :math:`ue \left(- vf_{0} + vout\right)` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | :math:`0` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | :math:`0` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | :math:`0` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vd | :math:`vd` | ExtAlgeb | :math:`0` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vq | :math:`vq` | ExtAlgeb | :math:`0` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Id | :math:`Id` | ExtAlgeb | :math:`0` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iq | :math:`Iq` | ExtAlgeb | :math:`0` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +--------+------------------+-------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +========+==================+=======================================================================================================+=================+ | ue | :math:`u_e` | :math:`u ug` | ConstService | +--------+------------------+-------------------------------------------------------------------------------------------------------+-----------------+ | KPC | :math:`K_{PC}` | :math:`KP e^{i \operatorname{radians}{\left(THETAP \right)}}` | ConstService | +--------+------------------+-------------------------------------------------------------------------------------------------------+-----------------+ | UEL0 | :math:`U_{EL0}` | :math:`-9999` | ConstService | +--------+------------------+-------------------------------------------------------------------------------------------------------+-----------------+ | VE | :math:`V_E` | :math:`\left|{KPC \left(vd + i vq\right) + i \left(Id + i Iq\right) \left(KI + KPC XL\right)}\right|` | VarService | +--------+------------------+-------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`vref` | 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:`LL_{x}` | State | State in lead-lag | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | LAW_y | :math:`LAW_{y}` | State | State in lag TF | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ | v | :math:`v` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vout | :math:`vout` | Algeb | Exciter final output voltage | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vref | :math:`vref` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vi | :math:`vi` | Algeb | Total input voltages | *p.u.* | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | LL_y | :math:`LL_{y}` | Algeb | Output of lead-lag | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vf | :math:`vf` | ExtAlgeb | Excitation field voltage to generator | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | Armature excitation current | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ | a | :math:`a` | ExtAlgeb | Bus voltage phase angle | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vbus | :math:`vbus` | ExtAlgeb | Bus voltage magnitude | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ Initialization Equations ------------------------ +---------+-----------------+----------+------------------------------+ | Name | Symbol | Type | Initial Value | +=========+=================+==========+==============================+ | LL_x | :math:`LL_{x}` | State | :math:`vi` | +---------+-----------------+----------+------------------------------+ | LAW_y | :math:`LAW_{y}` | State | :math:`K LL_{y}` | +---------+-----------------+----------+------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+-----------------+----------+------------------------------+ | v | :math:`v` | Algeb | :math:`vbus` | +---------+-----------------+----------+------------------------------+ | vout | :math:`vout` | Algeb | :math:`ue vf_{0}` | +---------+-----------------+----------+------------------------------+ | vref | :math:`vref` | Algeb | :math:`v + \frac{vf_{0}}{K}` | +---------+-----------------+----------+------------------------------+ | vi | :math:`vi` | Algeb | :math:`\frac{vf_{0}}{K}` | +---------+-----------------+----------+------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`vi` | +---------+-----------------+----------+------------------------------+ | vf | :math:`vf` | ExtAlgeb | | +---------+-----------------+----------+------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | | +---------+-----------------+----------+------------------------------+ | a | :math:`a` | ExtAlgeb | | +---------+-----------------+----------+------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | | +---------+-----------------+----------+------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+----------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+==================================+=============+ | LL_x | :math:`LL_{x}` | State | :math:`- LL_{x} + vi` | :math:`T_B` | +--------+-----------------+----------+----------------------------------+-------------+ | LAW_y | :math:`LAW_{y}` | State | :math:`K LL_{y} - LAW_{y}` | :math:`T_E` | +--------+-----------------+----------+----------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+----------------------------------+-------------+ Algebraic Equations ----------------------------- +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+================+==========+========================================================================================================================+ | v | :math:`v` | Algeb | :math:`- v + vbus` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`LAW_{y} ue - vout` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`- vref + vref_{0}` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`- v - vi + vref` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- LL_{x} + LL_{y}\right) + LL_{x} TB - LL_{y} TB + TA \left(- LL_{x} + vi\right)` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | :math:`ue \left(- vf_{0} + vout\right)` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | :math:`0` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | :math:`0` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | :math:`0` | +---------+----------------+----------+------------------------------------------------------------------------------------------------------------------------+ Services ---------- +--------+------------------+-----------------+-----------------+ | Name | Symbol | Equation | Type | +========+==================+=================+=================+ | ue | :math:`u_e` | :math:`u ug` | ConstService | +--------+------------------+-----------------+-----------------+ | TA | :math:`TA` | :math:`TATB TB` | ConstService | +--------+------------------+-----------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`vref` | 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:`LG_{y}` | State | State in lag transfer function | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | LA_y | :math:`LA_{y}` | State | State in lag TF | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | INT_y | :math:`INT_{y}` | State | Integrator output | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | WF_x | :math:`WF_{x}` | State | State in washout filter | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ | v | :math:`v` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vout | :math:`vout` | Algeb | Exciter final output voltage | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vref | :math:`vref` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vi | :math:`vi` | Algeb | Total input voltages | *p.u.* | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | VFE | :math:`VFE` | Algeb | Combined saturation feedback | *p.u.* | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | Se | :math:`Se` | Algeb | saturation output | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | WF_y | :math:`WF_{y}` | Algeb | Output of washout filter | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vf | :math:`vf` | ExtAlgeb | Excitation field voltage to generator | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | Armature excitation current | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ | a | :math:`a` | ExtAlgeb | Bus voltage phase angle | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vbus | :math:`vbus` | ExtAlgeb | Bus voltage magnitude | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ Initialization Equations ------------------------ +---------+-----------------+----------+------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+=================+==========+==========================================+ | LG_y | :math:`LG_{y}` | State | :math:`v` | +---------+-----------------+----------+------------------------------------------+ | LA_y | :math:`LA_{y}` | State | :math:`KA ue \left(- WF_{y} + vi\right)` | +---------+-----------------+----------+------------------------------------------+ | INT_y | :math:`INT_{y}` | State | :math:`vf_{0}` | +---------+-----------------+----------+------------------------------------------+ | WF_x | :math:`WF_{x}` | State | :math:`vout` | +---------+-----------------+----------+------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+-----------------+----------+------------------------------------------+ | v | :math:`v` | Algeb | :math:`vbus` | +---------+-----------------+----------+------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`ue vf_{0}` | +---------+-----------------+----------+------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`v + vb_{0}` | +---------+-----------------+----------+------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`- v + vref` | +---------+-----------------+----------+------------------------------------------+ | VFE | :math:`VFE` | Algeb | :math:`vfe_{0}` | +---------+-----------------+----------+------------------------------------------+ | Se | :math:`Se` | Algeb | :math:`Se_{0}` | +---------+-----------------+----------+------------------------------------------+ | WF_y | :math:`WF_{y}` | Algeb | :math:`0` | +---------+-----------------+----------+------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | | +---------+-----------------+----------+------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | | +---------+-----------------+----------+------------------------------------------+ | a | :math:`a` | ExtAlgeb | | +---------+-----------------+----------+------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | | +---------+-----------------+----------+------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+---------------------------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+===================================================+=============+ | LG_y | :math:`LG_{y}` | State | :math:`- LG_{y} + v` | :math:`T_R` | +--------+-----------------+----------+---------------------------------------------------+-------------+ | LA_y | :math:`LA_{y}` | State | :math:`KA ue \left(- WF_{y} + vi\right) - LA_{y}` | :math:`T_A` | +--------+-----------------+----------+---------------------------------------------------+-------------+ | INT_y | :math:`INT_{y}` | State | :math:`ue \left(LA_{y} - VFE\right)` | :math:`T_E` | +--------+-----------------+----------+---------------------------------------------------+-------------+ | WF_x | :math:`WF_{x}` | State | :math:`- WF_{x} + vout` | :math:`T_F` | +--------+-----------------+----------+---------------------------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+---------------------------------------------------+-------------+ Algebraic Equations ----------------------------- +---------+----------------+----------+-----------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+================+==========+=================================================================+ | v | :math:`v` | Algeb | :math:`- v + vbus` | +---------+----------------+----------+-----------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`ue \left(INT_{y} - vout\right)` | +---------+----------------+----------+-----------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`- vref + vref_{0}` | +---------+----------------+----------+-----------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`ue \left(- LG_{y} - vi + vref\right)` | +---------+----------------+----------+-----------------------------------------------------------------+ | VFE | :math:`VFE` | Algeb | :math:`ue \left(INT_{y} KE + Se - VFE\right)` | +---------+----------------+----------+-----------------------------------------------------------------+ | Se | :math:`Se` | Algeb | :math:`SAT_{B} SL_{z0} \left(INT_{y} - SAT_{A}\right)^{2} - Se` | +---------+----------------+----------+-----------------------------------------------------------------+ | WF_y | :math:`WF_{y}` | Algeb | :math:`KF \left(- WF_{x} + vout\right) - TF WF_{y}` | +---------+----------------+----------+-----------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | :math:`ue \left(- vf_{0} + vout\right)` | +---------+----------------+----------+-----------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | :math:`0` | +---------+----------------+----------+-----------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | :math:`0` | +---------+----------------+----------+-----------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | :math:`0` | +---------+----------------+----------+-----------------------------------------------------------------+ Services ---------- +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +==========+=======================+=============================================================================================================================================================================================================================+=================+ | ue | :math:`u_e` | :math:`u ug` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VRMAXc | :math:`VRMAXc` | :math:`VRMAX - 999 _zVRM + 999` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E1 | :math:`E^{1c}_{SAT}` | :math:`E_{1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E2 | :math:`E^{2c}_{SAT}` | :math:`E_{2} - 2 SAT_{zSE2} + 2` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE1 | :math:`SE^{1c}_{SAT}` | :math:`SE_{1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE2 | :math:`SE^{2c}_{SAT}` | :math:`- 2 SAT_{zSE2} + SE_{2} + 2` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_a | :math:`a_{SAT}` | :math:`\sqrt{\frac{SAT_{E1} SAT_{SE1}}{SAT_{E2} SAT_{SE2}}} \left(\operatorname{Indicator}{\left(SAT_{SE2} > 0 \right)} + \operatorname{Indicator}{\left(SAT_{SE2} < 0 \right)}\right)` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_A | :math:`A^q_{SAT}` | :math:`SAT_{E2} - \frac{SAT_{E1} - SAT_{E2}}{SAT_{a} - 1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_B | :math:`B^q_{SAT}` | :math:`\frac{SAT_{E2} SAT_{SE2} \left(SAT_{a} - 1\right)^{2} \left(\operatorname{Indicator}{\left(SAT_{a} > 0 \right)} + \operatorname{Indicator}{\left(SAT_{a} < 0 \right)}\right)}{\left(SAT_{E1} - SAT_{E2}\right)^{2}}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Se0 | :math:`S_{e0}` | :math:`SAT_{B} \left(SAT_{A} - vf_{0}\right)^{2} \operatorname{Indicator}{\left(vf_{0} > SAT_{A} \right)}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vr0 | :math:`V_{r0}` | :math:`KE vf_{0} + Se_{0}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vb0 | :math:`V_{b0}` | :math:`\frac{vr_{0}}{KA}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vfe0 | :math:`V_{FE0}` | :math:`KE vf_{0} + Se_{0}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`vref` | 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:`LG_{y}` | State | State in lag transfer function | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | LL_x | :math:`LL_{x}` | State | State in lead-lag | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | LA_y | :math:`LA_{y}` | State | State in lag TF | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | INT_y | :math:`INT_{y}` | State | Integrator output | | v_str,v_iter | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | WF_x | :math:`WF_{x}` | State | State in washout filter | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | v | :math:`v` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | vout | :math:`vout` | Algeb | Exciter final output voltage | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | IN | :math:`IN` | Algeb | Input to FEX | | v_str,v_iter | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | FEX_y | :math:`FEX_{y}` | Algeb | Output of piecewise | | v_str,v_iter | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | vi | :math:`vi` | Algeb | Total input voltages | *p.u.* | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | LL_y | :math:`LL_{y}` | Algeb | Output of lead-lag | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | Se | :math:`Se` | Algeb | saturation output | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | VFE | :math:`VFE` | Algeb | Combined saturation feedback | *p.u.* | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | vref | :math:`vref` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | WF_y | :math:`WF_{y}` | Algeb | Output of washout filter | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | vf | :math:`vf` | ExtAlgeb | Excitation field voltage to generator | | | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | Armature excitation current | | | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | a | :math:`a` | ExtAlgeb | Bus voltage phase angle | | | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | vbus | :math:`vbus` | ExtAlgeb | Bus voltage magnitude | | | +---------+-----------------+----------+---------------------------------------+--------+--------------+ Initialization Equations ------------------------ +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+=================+==========+============================================================================================================================================================================================================================================================================+ | LG_y | :math:`LG_{y}` | State | :math:`v` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_x | :math:`LL_{x}` | State | :math:`vi` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LA_y | :math:`LA_{y}` | State | :math:`KA LL_{y}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | INT_y | :math:`INT_{y}` | State | :math:`FEX_{y} INT_{y} - vf_{0}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_x | :math:`WF_{x}` | State | :math:`VFE` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`v` | Algeb | :math:`vbus` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`ue vf_{0}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`IN` | Algeb | :math:`- IN INT_{y} + KC XadIfd` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | FEX_y | :math:`FEX_{y}` | Algeb | :math:`- FEX_{y} + \operatorname{FixPiecewise}{\left(\left( 1, \ IN \leq 0\right),\left( 1 - 0.577 IN, \ IN \leq 0.433\right),\left( \sqrt{0.75 - IN^{2}}, \ IN \leq 0.75\right),\left( 1.732 - 1.732 IN, \ IN \leq 1\right),\left( 0, \ \text{True}\right) \right)}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`- v + vref` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`vi` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`Se` | Algeb | :math:`SAT_{B} \left(INT_{y} - SAT_{A}\right)^{2} \operatorname{Indicator}{\left(INT_{y} > SAT_{A} \right)}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VFE | :math:`VFE` | Algeb | :math:`INT_{y} KE + KD XadIfd + Se` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`v + \frac{VFE}{KA}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`WF_{y}` | Algeb | :math:`0` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+--------------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+======================================+=============+ | LG_y | :math:`LG_{y}` | State | :math:`- LG_{y} + v` | :math:`T_R` | +--------+-----------------+----------+--------------------------------------+-------------+ | LL_x | :math:`LL_{x}` | State | :math:`- LL_{x} + vi` | :math:`T_B` | +--------+-----------------+----------+--------------------------------------+-------------+ | LA_y | :math:`LA_{y}` | State | :math:`KA LL_{y} - LA_{y}` | :math:`T_A` | +--------+-----------------+----------+--------------------------------------+-------------+ | INT_y | :math:`INT_{y}` | State | :math:`ue \left(LA_{y} - VFE\right)` | :math:`T_E` | +--------+-----------------+----------+--------------------------------------+-------------+ | WF_x | :math:`WF_{x}` | State | :math:`VFE - WF_{x}` | :math:`T_F` | +--------+-----------------+----------+--------------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+--------------------------------------+-------------+ Algebraic Equations ----------------------------- +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+=================+==========+============================================================================================================================================================================================================================================================================+ | v | :math:`v` | Algeb | :math:`- v + vbus` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`ue \left(FEX_{y} INT_{y} - vout\right)` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`IN` | Algeb | :math:`ue \left(- IN INT_{y} + KC XadIfd\right)` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | FEX_y | :math:`FEX_{y}` | Algeb | :math:`- FEX_{y} + \operatorname{FixPiecewise}{\left(\left( 1, \ IN \leq 0\right),\left( 1 - 0.577 IN, \ IN \leq 0.433\right),\left( \sqrt{0.75 - IN^{2}}, \ IN \leq 0.75\right),\left( 1.732 - 1.732 IN, \ IN \leq 1\right),\left( 0, \ \text{True}\right) \right)}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`ue \left(- WF_{y} - v - vi + vref\right)` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- LL_{x} + LL_{y}\right) + LL_{x} TB - LL_{y} TB + TC \left(- LL_{x} + vi\right)` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`Se` | Algeb | :math:`ue \left(SAT_{B} SL_{z0} \left(INT_{y} - SAT_{A}\right)^{2} - Se\right)` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VFE | :math:`VFE` | Algeb | :math:`ue \left(INT_{y} KE + KD XadIfd + Se - VFE\right)` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`- vref + vref_{0}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`WF_{y}` | Algeb | :math:`KF \left(VFE - WF_{x}\right) - TF WF_{y}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | :math:`ue \left(- vf_{0} + vout\right)` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | :math:`0` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | :math:`0` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | :math:`0` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +==========+=======================+=============================================================================================================================================================================================================================+=================+ | ue | :math:`u_e` | :math:`u ug` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E1 | :math:`E^{1c}_{SAT}` | :math:`E_{1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E2 | :math:`E^{2c}_{SAT}` | :math:`E_{2} - 2 SAT_{zSE2} + 2` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE1 | :math:`SE^{1c}_{SAT}` | :math:`SE_{1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE2 | :math:`SE^{2c}_{SAT}` | :math:`- 2 SAT_{zSE2} + SE_{2} + 2` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_a | :math:`a_{SAT}` | :math:`\sqrt{\frac{SAT_{E1} SAT_{SE1}}{SAT_{E2} SAT_{SE2}}} \left(\operatorname{Indicator}{\left(SAT_{SE2} > 0 \right)} + \operatorname{Indicator}{\left(SAT_{SE2} < 0 \right)}\right)` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_A | :math:`A^q_{SAT}` | :math:`SAT_{E2} - \frac{SAT_{E1} - SAT_{E2}}{SAT_{a} - 1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_B | :math:`B^q_{SAT}` | :math:`\frac{SAT_{E2} SAT_{SE2} \left(SAT_{a} - 1\right)^{2} \left(\operatorname{Indicator}{\left(SAT_{a} > 0 \right)} + \operatorname{Indicator}{\left(SAT_{a} < 0 \right)}\right)}{\left(SAT_{E1} - SAT_{E2}\right)^{2}}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`vref` | 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:`LG_{y}` | State | State in lag transfer function | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | LL_x | :math:`LL_{x}` | State | State in lead-lag | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | LA_y | :math:`LA_{y}` | State | State in lag TF | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | INT_y | :math:`INT_{y}` | State | Integrator output | | v_str,v_iter | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | WF_x | :math:`WF_{x}` | State | State in washout filter | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | v | :math:`v` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | vout | :math:`vout` | Algeb | Exciter final output voltage | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | IN | :math:`IN` | Algeb | Input to FEX | | v_str,v_iter | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | FEX_y | :math:`FEX_{y}` | Algeb | Output of piecewise | | v_str,v_iter | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | vi | :math:`vi` | Algeb | Total input voltages | *p.u.* | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | LL_y | :math:`LL_{y}` | Algeb | Output of lead-lag | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | Se | :math:`Se` | Algeb | saturation output | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | VFE | :math:`VFE` | Algeb | Combined saturation feedback | *p.u.* | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | vref | :math:`vref` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | WF_y | :math:`WF_{y}` | Algeb | Output of washout filter | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | VHA | :math:`VHA` | Algeb | | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | VL | :math:`VL` | Algeb | | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | LVG_y | :math:`LVG_{y}` | Algeb | LVGate output | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | VR_x | :math:`VR_{x}` | Algeb | Value before limiter | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | VR_y | :math:`VR_{y}` | Algeb | Output after limiter and post gain | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | VLRx | :math:`VLRx` | Algeb | | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | vf | :math:`vf` | ExtAlgeb | Excitation field voltage to generator | | | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | Armature excitation current | | | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | a | :math:`a` | ExtAlgeb | Bus voltage phase angle | | | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | vbus | :math:`vbus` | ExtAlgeb | Bus voltage magnitude | | | +---------+-----------------+----------+---------------------------------------+--------+--------------+ Initialization Equations ------------------------ +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+=================+==========+============================================================================================================================================================================================================================================================================+ | LG_y | :math:`LG_{y}` | State | :math:`v` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_x | :math:`LL_{x}` | State | :math:`vi` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LA_y | :math:`LA_{y}` | State | :math:`KA LL_{y}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | INT_y | :math:`INT_{y}` | State | :math:`FEX_{y} INT_{y} - vf_{0}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_x | :math:`WF_{x}` | State | :math:`VFE` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`v` | Algeb | :math:`vbus` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`ue vf_{0}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`IN` | Algeb | :math:`- IN INT_{y} + KC XadIfd` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | FEX_y | :math:`FEX_{y}` | Algeb | :math:`- FEX_{y} + \operatorname{FixPiecewise}{\left(\left( 1, \ IN \leq 0\right),\left( 1 - 0.577 IN, \ IN \leq 0.433\right),\left( \sqrt{0.75 - IN^{2}}, \ IN \leq 0.75\right),\left( 1.732 - 1.732 IN, \ IN \leq 1\right),\left( 0, \ \text{True}\right) \right)}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`- v + vref` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`vi` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`Se` | Algeb | :math:`SAT_{B} \left(INT_{y} - SAT_{A}\right)^{2} \operatorname{Indicator}{\left(INT_{y} > SAT_{A} \right)}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VFE | :math:`VFE` | Algeb | :math:`INT_{y} KE + KD XadIfd + Se` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`v + \frac{KL VFE + \frac{VFE}{KB}}{KA}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`WF_{y}` | Algeb | :math:`0` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VHA | :math:`VHA` | Algeb | :math:`- KH VFE + LA_{y}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VL | :math:`VL` | Algeb | :math:`KL \left(- VFE + VLRx\right)` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LVG_y | :math:`LVG_{y}` | Algeb | :math:`LVG_{lt z0} VL + LVG_{lt z1} VHA` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VR_x | :math:`VR_{x}` | Algeb | :math:`KB LVG_{y}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VR_y | :math:`VR_{y}` | Algeb | :math:`VRMAX VR_{lim zu} + VRMIN VR_{lim zl} + VR_{lim zi} VR_{x}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VLRx | :math:`VLRx` | Algeb | :math:`VLR \operatorname{Indicator}{\left(VFE + \frac{VFE}{KB KL} < VLR \right)} + \left(VFE + \frac{VFE}{KB KL}\right) \operatorname{Indicator}{\left(VFE + \frac{VFE}{KB KL} > VLR \right)}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+----------------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+========================================+=============+ | LG_y | :math:`LG_{y}` | State | :math:`- LG_{y} + v` | :math:`T_R` | +--------+-----------------+----------+----------------------------------------+-------------+ | LL_x | :math:`LL_{x}` | State | :math:`- LL_{x} + vi` | :math:`T_B` | +--------+-----------------+----------+----------------------------------------+-------------+ | LA_y | :math:`LA_{y}` | State | :math:`KA LL_{y} - LA_{y}` | :math:`T_A` | +--------+-----------------+----------+----------------------------------------+-------------+ | INT_y | :math:`INT_{y}` | State | :math:`ue \left(- VFE + VR_{y}\right)` | :math:`T_E` | +--------+-----------------+----------+----------------------------------------+-------------+ | WF_x | :math:`WF_{x}` | State | :math:`VFE - WF_{x}` | :math:`T_F` | +--------+-----------------+----------+----------------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+----------------------------------------+-------------+ Algebraic Equations ----------------------------- +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+=================+==========+============================================================================================================================================================================================================================================================================+ | v | :math:`v` | Algeb | :math:`- v + vbus` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`ue \left(FEX_{y} INT_{y} - vout\right)` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`IN` | Algeb | :math:`ue \left(- IN INT_{y} + KC XadIfd\right)` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | FEX_y | :math:`FEX_{y}` | Algeb | :math:`- FEX_{y} + \operatorname{FixPiecewise}{\left(\left( 1, \ IN \leq 0\right),\left( 1 - 0.577 IN, \ IN \leq 0.433\right),\left( \sqrt{0.75 - IN^{2}}, \ IN \leq 0.75\right),\left( 1.732 - 1.732 IN, \ IN \leq 1\right),\left( 0, \ \text{True}\right) \right)}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`ue \left(- WF_{y} - v - vi + vref\right)` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- LL_{x} + LL_{y}\right) + LL_{x} TB - LL_{y} TB + TC \left(- LL_{x} + vi\right)` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`Se` | Algeb | :math:`ue \left(SAT_{B} SL_{z0} \left(INT_{y} - SAT_{A}\right)^{2} - Se\right)` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VFE | :math:`VFE` | Algeb | :math:`ue \left(INT_{y} KE + KD XadIfd + Se - VFE\right)` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`- vref + vref_{0}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`WF_{y}` | Algeb | :math:`KF \left(VFE - WF_{x}\right) - TF WF_{y}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VHA | :math:`VHA` | Algeb | :math:`- KH VFE + LA_{y} - VHA` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VL | :math:`VL` | Algeb | :math:`KL \left(- VFE + VLRx\right) - VL` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LVG_y | :math:`LVG_{y}` | Algeb | :math:`LVG_{lt z0} VL + LVG_{lt z1} VHA - LVG_{y}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VR_x | :math:`VR_{x}` | Algeb | :math:`KB LVG_{y} - VR_{x}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VR_y | :math:`VR_{y}` | Algeb | :math:`VRMAX VR_{lim zu} + VRMIN VR_{lim zl} + VR_{lim zi} VR_{x} - VR_{y}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VLRx | :math:`VLRx` | Algeb | :math:`VLR_{0} - VLRx` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | :math:`ue \left(- vf_{0} + vout\right)` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | :math:`0` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | :math:`0` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | :math:`0` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +==========+=======================+=============================================================================================================================================================================================================================+=================+ | ue | :math:`u_e` | :math:`u ug` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E1 | :math:`E^{1c}_{SAT}` | :math:`E_{1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E2 | :math:`E^{2c}_{SAT}` | :math:`E_{2} - 2 SAT_{zSE2} + 2` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE1 | :math:`SE^{1c}_{SAT}` | :math:`SE_{1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE2 | :math:`SE^{2c}_{SAT}` | :math:`- 2 SAT_{zSE2} + SE_{2} + 2` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_a | :math:`a_{SAT}` | :math:`\sqrt{\frac{SAT_{E1} SAT_{SE1}}{SAT_{E2} SAT_{SE2}}} \left(\operatorname{Indicator}{\left(SAT_{SE2} > 0 \right)} + \operatorname{Indicator}{\left(SAT_{SE2} < 0 \right)}\right)` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_A | :math:`A^q_{SAT}` | :math:`SAT_{E2} - \frac{SAT_{E1} - SAT_{E2}}{SAT_{a} - 1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_B | :math:`B^q_{SAT}` | :math:`\frac{SAT_{E2} SAT_{SE2} \left(SAT_{a} - 1\right)^{2} \left(\operatorname{Indicator}{\left(SAT_{a} > 0 \right)} + \operatorname{Indicator}{\left(SAT_{a} < 0 \right)}\right)}{\left(SAT_{E1} - SAT_{E2}\right)^{2}}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`vref` | 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:`LG_{y}` | State | State in lag transfer function | | v_str | +---------+----------------+----------+---------------------------------------+--------+------------+ | LL_x | :math:`LL_{x}` | State | State in lead-lag | | v_str | +---------+----------------+----------+---------------------------------------+--------+------------+ | LR_y | :math:`LR_{y}` | State | State in lag transfer function | | v_str | +---------+----------------+----------+---------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+----------------+----------+---------------------------------------+--------+------------+ | v | :math:`v` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+----------------+----------+---------------------------------------+--------+------------+ | vout | :math:`vout` | Algeb | Exciter final output voltage | | v_str | +---------+----------------+----------+---------------------------------------+--------+------------+ | vi | :math:`vi` | Algeb | Total input voltages | *p.u.* | v_str | +---------+----------------+----------+---------------------------------------+--------+------------+ | LL_y | :math:`LL_{y}` | Algeb | Output of lead-lag | | v_str | +---------+----------------+----------+---------------------------------------+--------+------------+ | vfmax | :math:`vfmax` | Algeb | Upper bound of output limiter | | v_str | +---------+----------------+----------+---------------------------------------+--------+------------+ | vfmin | :math:`vfmin` | Algeb | Lower bound of output limiter | | v_str | +---------+----------------+----------+---------------------------------------+--------+------------+ | vf | :math:`vf` | ExtAlgeb | Excitation field voltage to generator | | | +---------+----------------+----------+---------------------------------------+--------+------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | Armature excitation current | | | +---------+----------------+----------+---------------------------------------+--------+------------+ | a | :math:`a` | ExtAlgeb | Bus voltage phase angle | | | +---------+----------------+----------+---------------------------------------+--------+------------+ | vbus | :math:`vbus` | ExtAlgeb | Bus voltage magnitude | | | +---------+----------------+----------+---------------------------------------+--------+------------+ Initialization Equations ------------------------ +---------+----------------+----------+-------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+================+==========+=======================================================+ | LG_y | :math:`LG_{y}` | State | :math:`v` | +---------+----------------+----------+-------------------------------------------------------+ | LL_x | :math:`LL_{x}` | State | :math:`HLI_{zi} vi + HLI_{zl} VIMIN + HLI_{zu} VIMAX` | +---------+----------------+----------+-------------------------------------------------------+ | LR_y | :math:`LR_{y}` | State | :math:`KA LL_{y}` | +---------+----------------+----------+-------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+----------------+----------+-------------------------------------------------------+ | v | :math:`v` | Algeb | :math:`vbus` | +---------+----------------+----------+-------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`ue vf_{0}` | +---------+----------------+----------+-------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`\frac{vf_{0}}{KA}` | +---------+----------------+----------+-------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`HLI_{zi} vi + HLI_{zl} VIMIN + HLI_{zu} VIMAX` | +---------+----------------+----------+-------------------------------------------------------+ | vfmax | :math:`vfmax` | Algeb | :math:`- KC XadIfd + VRMAX` | +---------+----------------+----------+-------------------------------------------------------+ | vfmin | :math:`vfmin` | Algeb | :math:`- KC XadIfd + VRMIN` | +---------+----------------+----------+-------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | | +---------+----------------+----------+-------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | | +---------+----------------+----------+-------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | | +---------+----------------+----------+-------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | | +---------+----------------+----------+-------------------------------------------------------+ Differential Equations ----------------------------- +--------+----------------+----------+----------------------------------------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+================+==========+================================================================+=============+ | LG_y | :math:`LG_{y}` | State | :math:`- LG_{y} + v` | :math:`T_R` | +--------+----------------+----------+----------------------------------------------------------------+-------------+ | LL_x | :math:`LL_{x}` | State | :math:`HLI_{zi} vi + HLI_{zl} VIMIN + HLI_{zu} VIMAX - LL_{x}` | :math:`T_B` | +--------+----------------+----------+----------------------------------------------------------------+-------------+ | LR_y | :math:`LR_{y}` | State | :math:`KA LL_{y} - LR_{y}` | :math:`T_A` | +--------+----------------+----------+----------------------------------------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+----------------+----------+----------------------------------------------------------------+-------------+ Algebraic Equations ----------------------------- +---------+----------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+================+==========+=================================================================================================================================================================+ | v | :math:`v` | Algeb | :math:`- v + vbus` | +---------+----------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`ue \left(HLR_{zi} LR_{y} + HLR_{zl} vfmin + HLR_{zu} vfmax\right) - vout` | +---------+----------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`- LG_{y} - vi + vref_{0}` | +---------+----------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- LL_{x} + LL_{y}\right) + LL_{x} TB - LL_{y} TB + TC \left(HLI_{zi} vi + HLI_{zl} VIMIN + HLI_{zu} VIMAX - LL_{x}\right)` | +---------+----------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vfmax | :math:`vfmax` | Algeb | :math:`- KC XadIfd + VRMAX - vfmax` | +---------+----------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vfmin | :math:`vfmin` | Algeb | :math:`- KC XadIfd + VRMIN - vfmin` | +---------+----------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | :math:`ue \left(- vf_{0} + vout\right)` | +---------+----------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | :math:`0` | +---------+----------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | :math:`0` | +---------+----------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | :math:`0` | +---------+----------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +--------+------------------+-------------------------------+-----------------+ | Name | Symbol | Equation | Type | +========+==================+===============================+=================+ | ue | :math:`u_e` | :math:`u ug` | ConstService | +--------+------------------+-------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`v + \frac{vf_{0}}{KA}` | 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:`LG_{y}` | State | State in lag transfer function | | v_str | +---------+---------------------+----------+---------------------------------------+--------+------------+ | PI1_xi | :math:`\pi_{1 \xi}` | State | Integrator output | | v_str | +---------+---------------------+----------+---------------------------------------+--------+------------+ | LA_y | :math:`LA_{y}` | State | State in lag transfer function | | v_str | +---------+---------------------+----------+---------------------------------------+--------+------------+ | PI2_xi | :math:`\pi_{2 \xi}` | State | Integrator output | | v_str | +---------+---------------------+----------+---------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+---------------------+----------+---------------------------------------+--------+------------+ | v | :math:`v` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+---------------------+----------+---------------------------------------+--------+------------+ | vout | :math:`vout` | Algeb | Exciter final output voltage | | v_str | +---------+---------------------+----------+---------------------------------------+--------+------------+ | UEL | :math:`UEL` | Algeb | Interface var for under exc. limiter | | v_str | +---------+---------------------+----------+---------------------------------------+--------+------------+ | IN | :math:`IN` | Algeb | Input to FEX | | v_str | +---------+---------------------+----------+---------------------------------------+--------+------------+ | FEX_y | :math:`FEX_{y}` | Algeb | Output of piecewise | | v_str | +---------+---------------------+----------+---------------------------------------+--------+------------+ | VB_x | :math:`VB_{x}` | Algeb | Value before limiter | | v_str | +---------+---------------------+----------+---------------------------------------+--------+------------+ | VB_y | :math:`VB_{y}` | Algeb | Output after limiter and post gain | | v_str | +---------+---------------------+----------+---------------------------------------+--------+------------+ | VG_x | :math:`VG_{x}` | Algeb | Value before limiter | | v_str | +---------+---------------------+----------+---------------------------------------+--------+------------+ | VG_y | :math:`VG_{y}` | Algeb | Output after limiter and post gain | | v_str | +---------+---------------------+----------+---------------------------------------+--------+------------+ | vref | :math:`vref` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+---------------------+----------+---------------------------------------+--------+------------+ | vi | :math:`vi` | Algeb | Total input voltages | *p.u.* | v_str | +---------+---------------------+----------+---------------------------------------+--------+------------+ | PI1_ys | :math:`\pi_{1 ys}` | Algeb | PI summation before limit | | v_str | +---------+---------------------+----------+---------------------------------------+--------+------------+ | PI1_y | :math:`\pi_{1 y}` | Algeb | PI output | | v_str | +---------+---------------------+----------+---------------------------------------+--------+------------+ | PI2_ys | :math:`\pi_{2 ys}` | Algeb | PI summation before limit | | v_str | +---------+---------------------+----------+---------------------------------------+--------+------------+ | PI2_y | :math:`\pi_{2 y}` | Algeb | PI output | | v_str | +---------+---------------------+----------+---------------------------------------+--------+------------+ | vf | :math:`vf` | ExtAlgeb | Excitation field voltage to generator | | | +---------+---------------------+----------+---------------------------------------+--------+------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | Armature excitation current | | | +---------+---------------------+----------+---------------------------------------+--------+------------+ | a | :math:`a` | ExtAlgeb | Bus voltage phase angle | | | +---------+---------------------+----------+---------------------------------------+--------+------------+ | vbus | :math:`vbus` | ExtAlgeb | Bus voltage magnitude | | | +---------+---------------------+----------+---------------------------------------+--------+------------+ | vd | :math:`vd` | ExtAlgeb | d-axis machine voltage | | | +---------+---------------------+----------+---------------------------------------+--------+------------+ | vq | :math:`vq` | ExtAlgeb | q-axis machine voltage | | | +---------+---------------------+----------+---------------------------------------+--------+------------+ | Id | :math:`Id` | ExtAlgeb | d-axis machine current | | | +---------+---------------------+----------+---------------------------------------+--------+------------+ | Iq | :math:`Iq` | ExtAlgeb | q-axis machine current | | | +---------+---------------------+----------+---------------------------------------+--------+------------+ Initialization Equations ------------------------ +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+=====================+==========+================================================================================================================================================================================================================================================================+ | LG_y | :math:`LG_{y}` | State | :math:`v` | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PI1_xi | :math:`\pi_{1 \xi}` | State | :math:`VG_{y}` | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LA_y | :math:`LA_{y}` | State | :math:`1.0 \pi_{1 y}` | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PI2_xi | :math:`\pi_{2 \xi}` | State | :math:`\operatorname{safe}_{div}{\left(vf_{0},VB_{y} \right)}` | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`v` | Algeb | :math:`vbus` | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`ue vf_{0}` | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`UEL` | Algeb | :math:`0` | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`IN` | Algeb | :math:`\operatorname{safe}_{div}{\left(KC XadIfd,VE \right)}` | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | FEX_y | :math:`FEX_{y}` | Algeb | :math:`\operatorname{FixPiecewise}{\left(\left( 1, \ IN \leq 0\right),\left( 1 - 0.577 IN, \ IN \leq 0.433\right),\left( \sqrt{0.75 - IN^{2}}, \ IN \leq 0.75\right),\left( 1.732 - 1.732 IN, \ IN \leq 1\right),\left( 0, \ \text{True}\right) \right)}` | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VB_x | :math:`VB_{x}` | Algeb | :math:`FEX_{y} VE` | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VB_y | :math:`VB_{y}` | Algeb | :math:`VBMAX VB_{lim zu} + VB_{lim zi} VB_{x}` | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VG_x | :math:`VG_{x}` | Algeb | :math:`KG vout` | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VG_y | :math:`VG_{y}` | Algeb | :math:`VGMAX VG_{lim zu} + VG_{lim zi} VG_{x}` | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`v` | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`- v + vref` | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PI1_ys | :math:`\pi_{1 ys}` | Algeb | :math:`KPR vi + VG_{y}` | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PI1_y | :math:`\pi_{1 y}` | Algeb | :math:`\pi_{1 lim zi} \pi_{1 ys} + \pi_{1 lim zl} VRMIN + \pi_{1 lim zu} VRMAX` | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PI2_ys | :math:`\pi_{2 ys}` | Algeb | :math:`KPM \left(LA_{y} - VG_{y}\right) + \operatorname{safe}_{div}{\left(vf_{0},VB_{y} \right)}` | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PI2_y | :math:`\pi_{2 y}` | Algeb | :math:`\pi_{2 lim zi} \pi_{2 ys} + \pi_{2 lim zl} VMMIN + \pi_{2 lim zu} VMMAX` | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vd | :math:`vd` | ExtAlgeb | | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vq | :math:`vq` | ExtAlgeb | | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Id | :math:`Id` | ExtAlgeb | | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iq | :math:`Iq` | ExtAlgeb | | +---------+---------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +---------+---------------------+----------+-----------------------------------------------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +=========+=====================+==========+=======================================================================+=============+ | LG_y | :math:`LG_{y}` | State | :math:`- LG_{y} + v` | :math:`T_R` | +---------+---------------------+----------+-----------------------------------------------------------------------+-------------+ | PI1_xi | :math:`\pi_{1 \xi}` | State | :math:`KIR \left(2 \pi_{1 y} - 2 \pi_{1 ys} + vi\right)` | | +---------+---------------------+----------+-----------------------------------------------------------------------+-------------+ | LA_y | :math:`LA_{y}` | State | :math:`- LA_{y} + 1.0 \pi_{1 y}` | :math:`T_A` | +---------+---------------------+----------+-----------------------------------------------------------------------+-------------+ | PI2_xi | :math:`\pi_{2 \xi}` | State | :math:`KIM \left(LA_{y} + 2 \pi_{2 y} - 2 \pi_{2 ys} - VG_{y}\right)` | | +---------+---------------------+----------+-----------------------------------------------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +---------+---------------------+----------+-----------------------------------------------------------------------+-------------+ Algebraic Equations ----------------------------- +---------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+====================+==========+============================================================================================================================================================================================================================================================================+ | v | :math:`v` | Algeb | :math:`- v + vbus` | +---------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`\pi_{2 y} VB_{y} ue - vout` | +---------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`UEL` | Algeb | :math:`- UEL` | +---------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`IN` | Algeb | :math:`ue \left(- IN VE + KC XadIfd\right)` | +---------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | FEX_y | :math:`FEX_{y}` | Algeb | :math:`- FEX_{y} + \operatorname{FixPiecewise}{\left(\left( 1, \ IN \leq 0\right),\left( 1 - 0.577 IN, \ IN \leq 0.433\right),\left( \sqrt{0.75 - IN^{2}}, \ IN \leq 0.75\right),\left( 1.732 - 1.732 IN, \ IN \leq 1\right),\left( 0, \ \text{True}\right) \right)}` | +---------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VB_x | :math:`VB_{x}` | Algeb | :math:`FEX_{y} VE - VB_{x}` | +---------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VB_y | :math:`VB_{y}` | Algeb | :math:`VBMAX VB_{lim zu} + VB_{lim zi} VB_{x} - VB_{y}` | +---------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VG_x | :math:`VG_{x}` | Algeb | :math:`KG vout - VG_{x}` | +---------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VG_y | :math:`VG_{y}` | Algeb | :math:`VGMAX VG_{lim zu} + VG_{lim zi} VG_{x} - VG_{y}` | +---------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`- vref + vref_{0}` | +---------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`- LG_{y} - vi + vref` | +---------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PI1_ys | :math:`\pi_{1 ys}` | Algeb | :math:`KPR vi + \pi_{1 \xi} - \pi_{1 ys}` | +---------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PI1_y | :math:`\pi_{1 y}` | Algeb | :math:`\pi_{1 lim zi} \pi_{1 ys} + \pi_{1 lim zl} VRMIN + \pi_{1 lim zu} VRMAX - \pi_{1 y}` | +---------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PI2_ys | :math:`\pi_{2 ys}` | Algeb | :math:`KPM \left(LA_{y} - VG_{y}\right) + \pi_{2 \xi} - \pi_{2 ys}` | +---------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PI2_y | :math:`\pi_{2 y}` | Algeb | :math:`\pi_{2 lim zi} \pi_{2 ys} + \pi_{2 lim zl} VMMIN + \pi_{2 lim zu} VMMAX - \pi_{2 y}` | +---------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | :math:`ue \left(- vf_{0} + vout\right)` | +---------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | :math:`0` | +---------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | :math:`0` | +---------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | :math:`0` | +---------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vd | :math:`vd` | ExtAlgeb | :math:`0` | +---------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vq | :math:`vq` | ExtAlgeb | :math:`0` | +---------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Id | :math:`Id` | ExtAlgeb | :math:`0` | +---------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iq | :math:`Iq` | ExtAlgeb | :math:`0` | +---------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +--------+------------------+-------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +========+==================+=======================================================================================================+=================+ | ue | :math:`u_e` | :math:`u ug` | ConstService | +--------+------------------+-------------------------------------------------------------------------------------------------------+-----------------+ | KPC | :math:`K_{PC}` | :math:`KP e^{i \operatorname{radians}{\left(THETAP \right)}}` | ConstService | +--------+------------------+-------------------------------------------------------------------------------------------------------+-----------------+ | VE | :math:`V_E` | :math:`\left|{KPC \left(vd + i vq\right) + i \left(Id + i Iq\right) \left(KI + KPC XL\right)}\right|` | VarService | +--------+------------------+-------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`vref` | 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:`LG_{y}` | State | State in lag transfer function | | v_str | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ | PID_xi | :math:`PID_{\xi}` | State | Integrator output | | v_str | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ | PID_WO_x | :math:`PID_{WO x}` | State | State in washout filter | | v_str | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ | LA_y | :math:`LA_{y}` | State | State in lag TF | | v_str | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ | INT_y | :math:`INT_{y}` | State | Integrator output | | v_str,v_iter | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ | v | :math:`v` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ | vout | :math:`vout` | Algeb | Exciter final output voltage | | v_str | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ | IN | :math:`IN` | Algeb | Input to FEX | | v_str,v_iter | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ | FEX_y | :math:`FEX_{y}` | Algeb | Output of piecewise | | v_str,v_iter | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ | UEL | :math:`UEL` | Algeb | Interface var for under exc. limiter | | v_str | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ | OEL | :math:`OEL` | Algeb | Interface var for over exc. limiter | | v_str | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ | Vs | :math:`Vs` | Algeb | Voltage compensation from PSS | | v_str | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ | vref | :math:`vref` | Algeb | Reference voltage input | *p.u.* | v_str | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ | vi | :math:`vi` | Algeb | Total input voltages | *p.u.* | v_str | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ | PID_uin | :math:`PID_{uin}` | Algeb | PID input | | v_str | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ | PID_WO_y | :math:`PID_{WO y}` | Algeb | Output of washout filter | | v_str | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ | PID_ys | :math:`PID_{ys}` | Algeb | PI summation before limit | | v_str | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ | PID_y | :math:`PID_{y}` | Algeb | PI output | | v_str | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ | Se | :math:`Se` | Algeb | saturation output | | v_str | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ | VFE | :math:`VFE` | Algeb | Combined saturation feedback | *p.u.* | v_str | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ | vf | :math:`vf` | ExtAlgeb | Excitation field voltage to generator | | | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | Armature excitation current | | | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ | a | :math:`a` | ExtAlgeb | Bus voltage phase angle | | | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ | vbus | :math:`vbus` | ExtAlgeb | Bus voltage magnitude | | | +-----------+--------------------+----------+---------------------------------------+--------+--------------+ Initialization Equations ------------------------ +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +===========+====================+==========+============================================================================================================================================================================================================================================================================+ | LG_y | :math:`LG_{y}` | State | :math:`v` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PID_xi | :math:`PID_{\xi}` | State | :math:`\frac{VFE}{KA}` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PID_WO_x | :math:`PID_{WO x}` | State | :math:`PID_{uin}` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LA_y | :math:`LA_{y}` | State | :math:`KA PID_{y}` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | INT_y | :math:`INT_{y}` | State | :math:`FEX_{y} INT_{y} - vf_{0}` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`v` | Algeb | :math:`vbus` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`ue vf_{0}` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`IN` | Algeb | :math:`- IN INT_{y} + KC XadIfd` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | FEX_y | :math:`FEX_{y}` | Algeb | :math:`- FEX_{y} + \operatorname{FixPiecewise}{\left(\left( 1, \ IN \leq 0\right),\left( 1 - 0.577 IN, \ IN \leq 0.433\right),\left( \sqrt{0.75 - IN^{2}}, \ IN \leq 0.75\right),\left( 1.732 - 1.732 IN, \ IN \leq 1\right),\left( 0, \ \text{True}\right) \right)}` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`UEL` | Algeb | :math:`UEL_{0}` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | OEL | :math:`OEL` | Algeb | :math:`OEL_{0}` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vs | :math:`Vs` | Algeb | :math:`0` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`v` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`- v + vref` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PID_uin | :math:`PID_{uin}` | Algeb | :math:`vi` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PID_WO_y | :math:`PID_{WO y}` | Algeb | :math:`0` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PID_ys | :math:`PID_{ys}` | Algeb | :math:`kP vi + \frac{VFE}{KA}` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PID_y | :math:`PID_{y}` | Algeb | :math:`PID_{lim zi} PID_{ys} + PID_{lim zl} VPMIN + PID_{lim zu} VPMAX` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`Se` | Algeb | :math:`SAT_{B} \left(INT_{y} - SAT_{A}\right)^{2} \operatorname{Indicator}{\left(INT_{y} > SAT_{A} \right)}` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VFE | :math:`VFE` | Algeb | :math:`INT_{y} KE + KD XadIfd + Se` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +-----------+--------------------+----------+-----------------------------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +===========+====================+==========+=====================================================+=============+ | LG_y | :math:`LG_{y}` | State | :math:`- LG_{y} + v` | :math:`T_R` | +-----------+--------------------+----------+-----------------------------------------------------+-------------+ | PID_xi | :math:`PID_{\xi}` | State | :math:`kI \left(2 PID_{y} - 2 PID_{ys} + vi\right)` | | +-----------+--------------------+----------+-----------------------------------------------------+-------------+ | PID_WO_x | :math:`PID_{WO x}` | State | :math:`- PID_{WO x} + PID_{uin}` | :math:`T_d` | +-----------+--------------------+----------+-----------------------------------------------------+-------------+ | LA_y | :math:`LA_{y}` | State | :math:`KA PID_{y} - LA_{y}` | :math:`T_A` | +-----------+--------------------+----------+-----------------------------------------------------+-------------+ | INT_y | :math:`INT_{y}` | State | :math:`ue \left(LA_{y} - VFE\right)` | :math:`T_E` | +-----------+--------------------+----------+-----------------------------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +-----------+--------------------+----------+-----------------------------------------------------+-------------+ Algebraic Equations ----------------------------- +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +===========+====================+==========+============================================================================================================================================================================================================================================================================+ | v | :math:`v` | Algeb | :math:`- v + vbus` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`ue \left(FEX_{y} INT_{y} - vout\right)` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`IN` | Algeb | :math:`ue \left(- IN INT_{y} + KC XadIfd\right)` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | FEX_y | :math:`FEX_{y}` | Algeb | :math:`- FEX_{y} + \operatorname{FixPiecewise}{\left(\left( 1, \ IN \leq 0\right),\left( 1 - 0.577 IN, \ IN \leq 0.433\right),\left( \sqrt{0.75 - IN^{2}}, \ IN \leq 0.75\right),\left( 1.732 - 1.732 IN, \ IN \leq 1\right),\left( 0, \ \text{True}\right) \right)}` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`UEL` | Algeb | :math:`- UEL + UEL_{0}` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | OEL | :math:`OEL` | Algeb | :math:`- OEL + OEL_{0}` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vs | :math:`Vs` | Algeb | :math:`- Vs` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`- vref + vref_{0}` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`ue \left(- LG_{y} + OEL + UEL + Vs - vi + vref\right)` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PID_uin | :math:`PID_{uin}` | Algeb | :math:`- PID_{uin} + vi` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PID_WO_y | :math:`PID_{WO y}` | Algeb | :math:`- PID_{WO y} Td + kD \left(- PID_{WO x} + PID_{uin}\right)` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PID_ys | :math:`PID_{ys}` | Algeb | :math:`PID_{WO y} + PID_{\xi} - PID_{ys} + kP vi` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PID_y | :math:`PID_{y}` | Algeb | :math:`PID_{lim zi} PID_{ys} + PID_{lim zl} VPMIN + PID_{lim zu} VPMAX - PID_{y}` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`Se` | Algeb | :math:`ue \left(SAT_{B} SL_{z0} \left(INT_{y} - SAT_{A}\right)^{2} - Se\right)` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VFE | :math:`VFE` | Algeb | :math:`ue \left(INT_{y} KE + KD XadIfd + Se - VFE\right)` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | :math:`ue \left(- vf_{0} + vout\right)` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | :math:`0` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | :math:`0` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | :math:`0` | +-----------+--------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +==========+=======================+=============================================================================================================================================================================================================================+=================+ | ue | :math:`u_e` | :math:`u ug` | 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 SAT_{zSE2} + 2` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE1 | :math:`SE^{1c}_{SAT}` | :math:`SE_{1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE2 | :math:`SE^{2c}_{SAT}` | :math:`- 2 SAT_{zSE2} + SE_{2} + 2` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_a | :math:`a_{SAT}` | :math:`\sqrt{\frac{SAT_{E1} SAT_{SE1}}{SAT_{E2} SAT_{SE2}}} \left(\operatorname{Indicator}{\left(SAT_{SE2} > 0 \right)} + \operatorname{Indicator}{\left(SAT_{SE2} < 0 \right)}\right)` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_A | :math:`A^q_{SAT}` | :math:`SAT_{E2} - \frac{SAT_{E1} - SAT_{E2}}{SAT_{a} - 1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_B | :math:`B^q_{SAT}` | :math:`\frac{SAT_{E2} SAT_{SE2} \left(SAT_{a} - 1\right)^{2} \left(\operatorname{Indicator}{\left(SAT_{a} > 0 \right)} + \operatorname{Indicator}{\left(SAT_{a} < 0 \right)}\right)}{\left(SAT_{E1} - SAT_{E2}\right)^{2}}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`v` | 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:`LG_{y}` | State | State in lag transfer function | | v_str | +---------+------------------+----------+---------------------------------------+--------+------------+ | LA3_y | :math:`LA_{3 y}` | State | State in lag TF | | v_str | +---------+------------------+----------+---------------------------------------+--------+------------+ | LA1_y | :math:`LA_{1 y}` | State | State in lag transfer function | | v_str | +---------+------------------+----------+---------------------------------------+--------+------------+ | WF_x | :math:`WF_{x}` | State | State in washout filter | | v_str | +---------+------------------+----------+---------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+------------------+----------+---------------------------------------+--------+------------+ | v | :math:`v` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+------------------+----------+---------------------------------------+--------+------------+ | vout | :math:`vout` | Algeb | Exciter final output voltage | | v_str | +---------+------------------+----------+---------------------------------------+--------+------------+ | UEL | :math:`UEL` | Algeb | Interface var for under exc. limiter | | v_str | +---------+------------------+----------+---------------------------------------+--------+------------+ | OEL | :math:`OEL` | Algeb | Interface var for over exc. limiter | | v_str | +---------+------------------+----------+---------------------------------------+--------+------------+ | Vs | :math:`Vs` | Algeb | Voltage compensation from PSS | | v_str | +---------+------------------+----------+---------------------------------------+--------+------------+ | vref | :math:`vref` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+------------------+----------+---------------------------------------+--------+------------+ | vi | :math:`vi` | Algeb | Total input voltages | *p.u.* | v_str | +---------+------------------+----------+---------------------------------------+--------+------------+ | WF_y | :math:`WF_{y}` | Algeb | Output of washout filter | | v_str | +---------+------------------+----------+---------------------------------------+--------+------------+ | SQE | :math:`SQE` | Algeb | Square of error after mul | | v_str | +---------+------------------+----------+---------------------------------------+--------+------------+ | VB_y | :math:`VB_{y}` | Algeb | Output of piecewise | | v_str | +---------+------------------+----------+---------------------------------------+--------+------------+ | vf | :math:`vf` | ExtAlgeb | Excitation field voltage to generator | | | +---------+------------------+----------+---------------------------------------+--------+------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | Armature excitation current | | | +---------+------------------+----------+---------------------------------------+--------+------------+ | a | :math:`a` | ExtAlgeb | Bus voltage phase angle | | | +---------+------------------+----------+---------------------------------------+--------+------------+ | vbus | :math:`vbus` | ExtAlgeb | Bus voltage magnitude | | | +---------+------------------+----------+---------------------------------------+--------+------------+ | vd | :math:`vd` | ExtAlgeb | d-axis machine voltage | | | +---------+------------------+----------+---------------------------------------+--------+------------+ | vq | :math:`vq` | ExtAlgeb | q-axis machine voltage | | | +---------+------------------+----------+---------------------------------------+--------+------------+ | Id | :math:`Id` | ExtAlgeb | d-axis machine current | | | +---------+------------------+----------+---------------------------------------+--------+------------+ | Iq | :math:`Iq` | ExtAlgeb | q-axis machine current | | | +---------+------------------+----------+---------------------------------------+--------+------------+ Initialization Equations ------------------------ +---------+------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+==================+==========+=================================================================================================================================================================+ | LG_y | :math:`LG_{y}` | State | :math:`v` | +---------+------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LA3_y | :math:`LA_{3 y}` | State | :math:`KA ue \left(- WF_{y} + vi\right)` | +---------+------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LA1_y | :math:`LA_{1 y}` | State | :math:`\frac{ue \left(HL_{zi} VB_{y} + HL_{zu} VBMAX\right)}{KE}` | +---------+------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_x | :math:`WF_{x}` | State | :math:`LA_{1 y}` | +---------+------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`v` | Algeb | :math:`vbus` | +---------+------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`ue vf_{0}` | +---------+------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`UEL` | Algeb | :math:`UEL_{0}` | +---------+------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | OEL | :math:`OEL` | Algeb | :math:`OEL_{0}` | +---------+------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vs | :math:`Vs` | Algeb | :math:`0` | +---------+------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`v + vb_{0}` | +---------+------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`- v + vref` | +---------+------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`WF_{y}` | Algeb | :math:`0` | +---------+------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | SQE | :math:`SQE` | Algeb | :math:`VE^{2} - 0.6084 XadIfd^{2}` | +---------+------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VB_y | :math:`VB_{y}` | Algeb | :math:`\operatorname{FixPiecewise}{\left(\left( LA_{3 y} ue, \ SQE \leq 0\right),\left( ue \left(LA_{3 y} + \sqrt{SQE}\right), \ \text{True}\right) \right)}` | +---------+------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | | +---------+------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | | +---------+------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | | +---------+------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | | +---------+------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vd | :math:`vd` | ExtAlgeb | | +---------+------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vq | :math:`vq` | ExtAlgeb | | +---------+------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Id | :math:`Id` | ExtAlgeb | | +---------+------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iq | :math:`Iq` | ExtAlgeb | | +---------+------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+------------------+----------+------------------------------------------------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+==================+==========+========================================================================+=============+ | LG_y | :math:`LG_{y}` | State | :math:`- LG_{y} + v` | :math:`T_R` | +--------+------------------+----------+------------------------------------------------------------------------+-------------+ | LA3_y | :math:`LA_{3 y}` | State | :math:`KA ue \left(- WF_{y} + vi\right) - LA_{3 y}` | :math:`T_A` | +--------+------------------+----------+------------------------------------------------------------------------+-------------+ | LA1_y | :math:`LA_{1 y}` | State | :math:`- KE LA_{1 y} + ue \left(HL_{zi} VB_{y} + HL_{zu} VBMAX\right)` | :math:`T_E` | +--------+------------------+----------+------------------------------------------------------------------------+-------------+ | WF_x | :math:`WF_{x}` | State | :math:`LA_{1 y} - WF_{x}` | :math:`T_F` | +--------+------------------+----------+------------------------------------------------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+------------------+----------+------------------------------------------------------------------------+-------------+ Algebraic Equations ----------------------------- +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+================+==========+============================================================================================================================================================================+ | v | :math:`v` | Algeb | :math:`- v + vbus` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`ue \left(LA_{1 y} - vout\right)` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`UEL` | Algeb | :math:`- UEL + UEL_{0}` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | OEL | :math:`OEL` | Algeb | :math:`- OEL + OEL_{0}` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vs | :math:`Vs` | Algeb | :math:`- Vs` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`- vref + vref_{0}` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`ue \left(- LG_{y} + OEL + UEL + Vs - vi + vref\right)` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`WF_{y}` | Algeb | :math:`KF \left(LA_{1 y} - WF_{x}\right) - TF WF_{y}` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | SQE | :math:`SQE` | Algeb | :math:`- SQE + VE^{2} - 0.6084 XadIfd^{2}` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VB_y | :math:`VB_{y}` | Algeb | :math:`- VB_{y} + \operatorname{FixPiecewise}{\left(\left( LA_{3 y} ue, \ SQE \leq 0\right),\left( ue \left(LA_{3 y} + \sqrt{SQE}\right), \ \text{True}\right) \right)}` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | :math:`ue \left(- vf_{0} + vout\right)` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | :math:`0` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | :math:`0` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | :math:`0` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vd | :math:`vd` | ExtAlgeb | :math:`0` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vq | :math:`vq` | ExtAlgeb | :math:`0` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Id | :math:`Id` | ExtAlgeb | :math:`0` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iq | :math:`Iq` | ExtAlgeb | :math:`0` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +---------+------------------+--------------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +=========+==================+==============================================================================================================+=================+ | ue | :math:`u_e` | :math:`u ug` | ConstService | +---------+------------------+--------------------------------------------------------------------------------------------------------------+-----------------+ | VE | :math:`V_{E}` | :math:`\sqrt{Id^{2} KI^{2} + 2 Id KI KP vq + Iq^{2} KI^{2} - 2 Iq KI KP vd + KP^{2} vd^{2} + KP^{2} vq^{2}}` | VarService | +---------+------------------+--------------------------------------------------------------------------------------------------------------+-----------------+ | V40 | :math:`V40` | :math:`\sqrt{VE^{2} - 0.6084 XadIfd^{2}}` | ConstService | +---------+------------------+--------------------------------------------------------------------------------------------------------------+-----------------+ | VR0 | :math:`V_{R0}` | :math:`KE vf_{0} - V_{40}` | ConstService | +---------+------------------+--------------------------------------------------------------------------------------------------------------+-----------------+ | vb0 | :math:`V_{b0}` | :math:`\frac{VR_{0}}{KA}` | ConstService | +---------+------------------+--------------------------------------------------------------------------------------------------------------+-----------------+ | VRMAXc | :math:`VRMAXc` | :math:`VRMAX - 999 _zVRM + 999` | ConstService | +---------+------------------+--------------------------------------------------------------------------------------------------------------+-----------------+ | UEL0 | :math:`UEL0` | :math:`0` | ConstService | +---------+------------------+--------------------------------------------------------------------------------------------------------------+-----------------+ | OEL0 | :math:`OEL0` | :math:`0` | ConstService | +---------+------------------+--------------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`vref` | 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:`LG_{y}` | State | State in lag transfer function | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | LL_x | :math:`LL_{x}` | State | State in lead-lag | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | LA_y | :math:`LA_{y}` | State | State in lag TF | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | INT_y | :math:`INT_{y}` | State | Integrator output | | v_str,v_iter | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | WF_x | :math:`WF_{x}` | State | State in washout filter | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | v | :math:`v` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | vout | :math:`vout` | Algeb | Exciter final output voltage | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | UEL | :math:`UEL` | Algeb | Interface var for under exc. limiter | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | OEL | :math:`OEL` | Algeb | Interface var for over exc. limiter | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | Vs | :math:`Vs` | Algeb | Voltage compensation from PSS | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | vref | :math:`vref` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | IN | :math:`IN` | Algeb | Input to FEX | | v_str,v_iter | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | FEX_y | :math:`FEX_{y}` | Algeb | Output of piecewise | | v_str,v_iter | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | vi | :math:`vi` | Algeb | Total input voltages | *p.u.* | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | LL_y | :math:`LL_{y}` | Algeb | Output of lead-lag | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | HVG_y | :math:`HVG_{y}` | Algeb | HVGate output | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | LVG_y | :math:`LVG_{y}` | Algeb | LVGate output | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | Se | :math:`Se` | Algeb | saturation output | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | VFE | :math:`VFE` | Algeb | Combined saturation feedback | *p.u.* | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | WF_y | :math:`WF_{y}` | Algeb | Output of washout filter | | v_str | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | vf | :math:`vf` | ExtAlgeb | Excitation field voltage to generator | | | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | Armature excitation current | | | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | a | :math:`a` | ExtAlgeb | Bus voltage phase angle | | | +---------+-----------------+----------+---------------------------------------+--------+--------------+ | vbus | :math:`vbus` | ExtAlgeb | Bus voltage magnitude | | | +---------+-----------------+----------+---------------------------------------+--------+--------------+ Initialization Equations ------------------------ +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+=================+==========+============================================================================================================================================================================================================================================================================+ | LG_y | :math:`LG_{y}` | State | :math:`v` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_x | :math:`LL_{x}` | State | :math:`vi` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LA_y | :math:`LA_{y}` | State | :math:`KA LL_{y}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | INT_y | :math:`INT_{y}` | State | :math:`FEX_{y} INT_{y} - vf_{0}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_x | :math:`WF_{x}` | State | :math:`VFE` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`v` | Algeb | :math:`vbus` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`ue vf_{0}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`UEL` | Algeb | :math:`UEL_{0}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | OEL | :math:`OEL` | Algeb | :math:`OEL_{0}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vs | :math:`Vs` | Algeb | :math:`0` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`v + \frac{VFE}{KA}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`IN` | Algeb | :math:`- IN INT_{y} + KC XadIfd` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | FEX_y | :math:`FEX_{y}` | Algeb | :math:`- FEX_{y} + \operatorname{FixPiecewise}{\left(\left( 1, \ IN \leq 0\right),\left( 1 - 0.577 IN, \ IN \leq 0.433\right),\left( \sqrt{0.75 - IN^{2}}, \ IN \leq 0.75\right),\left( 1.732 - 1.732 IN, \ IN \leq 1\right),\left( 0, \ \text{True}\right) \right)}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`- v + vref` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`vi` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | HVG_y | :math:`HVG_{y}` | Algeb | :math:`HVG_{lt z0} UEL + HVG_{lt z1} LA_{y}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LVG_y | :math:`LVG_{y}` | Algeb | :math:`HVG_{y} LVG_{lt z1} + LVG_{lt z0} OEL` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`Se` | Algeb | :math:`SAT_{B} \left(INT_{y} - SAT_{A}\right)^{2} \operatorname{Indicator}{\left(INT_{y} > SAT_{A} \right)}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VFE | :math:`VFE` | Algeb | :math:`INT_{y} KE + KD XadIfd + Se` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`WF_{y}` | Algeb | :math:`0` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+---------------------------------------+----------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+=======================================+================+ | LG_y | :math:`LG_{y}` | State | :math:`- LG_{y} + v` | :math:`T_R` | +--------+-----------------+----------+---------------------------------------+----------------+ | LL_x | :math:`LL_{x}` | State | :math:`- LL_{x} + vi` | :math:`T_B` | +--------+-----------------+----------+---------------------------------------+----------------+ | LA_y | :math:`LA_{y}` | State | :math:`KA LL_{y} - LA_{y}` | :math:`T_A` | +--------+-----------------+----------+---------------------------------------+----------------+ | INT_y | :math:`INT_{y}` | State | :math:`ue \left(LVG_{y} - VFE\right)` | :math:`T_E` | +--------+-----------------+----------+---------------------------------------+----------------+ | WF_x | :math:`WF_{x}` | State | :math:`VFE - WF_{x}` | :math:`T_{F1}` | +--------+-----------------+----------+---------------------------------------+----------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+---------------------------------------+----------------+ Algebraic Equations ----------------------------- +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+=================+==========+============================================================================================================================================================================================================================================================================+ | v | :math:`v` | Algeb | :math:`- v + vbus` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`FEX_{y} INT_{y} ue - vout` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`UEL` | Algeb | :math:`- UEL + UEL_{0}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | OEL | :math:`OEL` | Algeb | :math:`- OEL + OEL_{0}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vs | :math:`Vs` | Algeb | :math:`- Vs` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`- vref + vref_{0}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`IN` | Algeb | :math:`ue \left(- IN INT_{y} + KC XadIfd\right)` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | FEX_y | :math:`FEX_{y}` | Algeb | :math:`- FEX_{y} + \operatorname{FixPiecewise}{\left(\left( 1, \ IN \leq 0\right),\left( 1 - 0.577 IN, \ IN \leq 0.433\right),\left( \sqrt{0.75 - IN^{2}}, \ IN \leq 0.75\right),\left( 1.732 - 1.732 IN, \ IN \leq 1\right),\left( 0, \ \text{True}\right) \right)}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`ue \left(- LG_{y} + OEL + UEL + Vs - vi + vref\right)` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- LL_{x} + LL_{y}\right) + LL_{x} TB - LL_{y} TB + TC \left(- LL_{x} + vi\right)` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | HVG_y | :math:`HVG_{y}` | Algeb | :math:`HVG_{lt z0} UEL + HVG_{lt z1} LA_{y} - HVG_{y}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LVG_y | :math:`LVG_{y}` | Algeb | :math:`HVG_{y} LVG_{lt z1} + LVG_{lt z0} OEL - LVG_{y}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`Se` | Algeb | :math:`ue \left(SAT_{B} SL_{z0} \left(INT_{y} - SAT_{A}\right)^{2} - Se\right)` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VFE | :math:`VFE` | Algeb | :math:`ue \left(INT_{y} KE + KD XadIfd + Se - VFE\right)` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`WF_{y}` | Algeb | :math:`KF \left(VFE - WF_{x}\right) - TF WF_{y}` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | :math:`ue \left(- vf_{0} + vout\right)` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | :math:`0` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | :math:`0` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | :math:`0` | +---------+-----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +==========+=======================+=============================================================================================================================================================================================================================+=================+ | ue | :math:`u_e` | :math:`u ug` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | UEL0 | :math:`UEL0` | :math:`-999` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | OEL0 | :math:`OEL0` | :math:`999` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VAMAXu | :math:`VAMAXu` | :math:`VAMAX ue - 999 ue + 999` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VAMINu | :math:`VAMINu` | :math:`VAMIN ue + 999 ue - 999` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E1 | :math:`E^{1c}_{SAT}` | :math:`E_{1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E2 | :math:`E^{2c}_{SAT}` | :math:`E_{2} - 2 SAT_{zSE2} + 2` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE1 | :math:`SE^{1c}_{SAT}` | :math:`SE_{1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE2 | :math:`SE^{2c}_{SAT}` | :math:`- 2 SAT_{zSE2} + SE_{2} + 2` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_a | :math:`a_{SAT}` | :math:`\sqrt{\frac{SAT_{E1} SAT_{SE1}}{SAT_{E2} SAT_{SE2}}} \left(\operatorname{Indicator}{\left(SAT_{SE2} > 0 \right)} + \operatorname{Indicator}{\left(SAT_{SE2} < 0 \right)}\right)` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_A | :math:`A^q_{SAT}` | :math:`SAT_{E2} - \frac{SAT_{E1} - SAT_{E2}}{SAT_{a} - 1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_B | :math:`B^q_{SAT}` | :math:`\frac{SAT_{E2} SAT_{SE2} \left(SAT_{a} - 1\right)^{2} \left(\operatorname{Indicator}{\left(SAT_{a} > 0 \right)} + \operatorname{Indicator}{\left(SAT_{a} < 0 \right)}\right)}{\left(SAT_{E1} - SAT_{E2}\right)^{2}}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`vref` | 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:`LG_{y}` | State | State in lag transfer function | | v_str | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | LL_x | :math:`LL_{x}` | State | State in lead-lag | | v_str | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | LL1_x | :math:`LL_{1 x}` | State | State in lead-lag | | v_str | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | LA_y | :math:`LA_{y}` | State | State in lag TF | | v_str | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | WF_x | :math:`WF_{x}` | State | State in washout filter | | v_str | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | v | :math:`v` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | vout | :math:`vout` | Algeb | Exciter final output voltage | | v_str | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | UEL | :math:`UEL` | Algeb | Interface var for under exc. limiter | | v_str | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | OEL | :math:`OEL` | Algeb | Interface var for over exc. limiter | | v_str | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | Vs | :math:`Vs` | Algeb | Voltage compensation from PSS | | v_str | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | vref | :math:`vref` | Algeb | Reference voltage input | *p.u.* | v_str,v_iter | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | SG | :math:`SG` | Algeb | SG | | v_str | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | LR_x | :math:`LR_{x}` | Algeb | Value before limiter | | v_str | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | LR_y | :math:`LR_{y}` | Algeb | Output after limiter and post gain | | v_str | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | vi | :math:`vi` | Algeb | Total input voltages | *p.u.* | v_str,v_iter | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | vil_x | :math:`vil_{x}` | Algeb | Value before limiter | | v_str | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | vil_y | :math:`vil_{y}` | Algeb | Output after limiter and post gain | | v_str | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | UEL2 | :math:`UEL_{2}` | Algeb | UEL_2 as HVG1 u1 | | v_str | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | HVG1_y | :math:`HVG_{1 y}` | Algeb | HVGate output | | v_str | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | LL_y | :math:`LL_{y}` | Algeb | Output of lead-lag | | v_str | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | LL1_y | :math:`LL_{1 y}` | Algeb | Output of lead-lag | | v_str | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | vas | :math:`vas` | 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:`HVG_{y}` | Algeb | HVGate output | | v_str | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | LVG_y | :math:`LVG_{y}` | Algeb | LVGate output | | v_str | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | vol_x | :math:`vol_{x}` | Algeb | Value before limiter | | v_str | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | vol_y | :math:`vol_{y}` | Algeb | Output after limiter and post gain | | v_str | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | WF_y | :math:`WF_{y}` | Algeb | Output of washout filter | | v_str | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | vf | :math:`vf` | ExtAlgeb | Excitation field voltage to generator | | | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | Armature excitation current | | | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | a | :math:`a` | ExtAlgeb | Bus voltage phase angle | | | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | vbus | :math:`vbus` | ExtAlgeb | Bus voltage magnitude | | | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | vd | :math:`vd` | ExtAlgeb | d-axis machine voltage | | | +---------+-------------------+----------+---------------------------------------+--------+--------------+ | vq | :math:`vq` | ExtAlgeb | q-axis machine voltage | | | +---------+-------------------+----------+---------------------------------------+--------+--------------+ Initialization Equations ------------------------ +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+===================+==========+===========================================================================================================+ | LG_y | :math:`LG_{y}` | State | :math:`v` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | LL_x | :math:`LL_{x}` | State | :math:`HVG_{1 y}` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | LL1_x | :math:`LL_{1 x}` | State | :math:`LL_{y}` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | LA_y | :math:`LA_{y}` | State | :math:`KA LL_{1 y}` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | WF_x | :math:`WF_{x}` | State | :math:`LVG_{y}` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | v | :math:`v` | Algeb | :math:`vbus` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`ue vf_{0}` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | UEL | :math:`UEL` | Algeb | :math:`UEL_{0}` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | OEL | :math:`OEL` | Algeb | :math:`OEL_{0}` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | Vs | :math:`Vs` | Algeb | :math:`0` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`ue \left(- SG SWVOS_{s1} - SWUEL_{s1} UEL + v + \frac{LR_{y} - SG SWVOS_{s2} + vf_{0}}{KA}\right)` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | SG | :math:`SG` | Algeb | :math:`SG_{0}` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | LR_x | :math:`LR_{x}` | Algeb | :math:`KLR \left(- ILR + XadIfd\right)` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | LR_y | :math:`LR_{y}` | Algeb | :math:`LR_{lim zi} LR_{x} + LR_{lim zl} zero` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`ue \left(- LG_{y} + SG SWVOS_{s1} + SWUEL_{s1} UEL + Vs - WF_{y} + vref\right)` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | vil_x | :math:`vil_{x}` | Algeb | :math:`vi` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | vil_y | :math:`vil_{y}` | Algeb | :math:`VIMAX vil_{lim zu} + VIMIN vil_{lim zl} + vil_{lim zi} vil_{x}` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | UEL2 | :math:`UEL_{2}` | Algeb | :math:`ue \left(SWUEL_{s2} UEL + llim \left(1 - SWUEL_{s2}\right)\right)` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | HVG1_y | :math:`HVG_{1 y}` | Algeb | :math:`HVG_{1 lt z0} UEL_{2} + HVG_{1 lt z1} vil_{y}` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`HVG_{1 y}` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | LL1_y | :math:`LL_{1 y}` | Algeb | :math:`LL_{y}` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | vas | :math:`vas` | Algeb | :math:`ue \left(LA_{y} - LR_{y} + SG SWVOS_{s2}\right)` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | UEL3 | :math:`UEL_{3}` | Algeb | :math:`ue \left(SWUEL_{s3} UEL + llim \left(1 - SWUEL_{s3}\right)\right)` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | HVG_y | :math:`HVG_{y}` | Algeb | :math:`HVG_{lt z0} UEL_{3} + HVG_{lt z1} vas` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | LVG_y | :math:`LVG_{y}` | Algeb | :math:`HVG_{y} LVG_{lt z1} + LVG_{lt z0} OEL` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | vol_x | :math:`vol_{x}` | Algeb | :math:`LVG_{y}` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | vol_y | :math:`vol_{y}` | Algeb | :math:`efdl vol_{lim zl} + efdu vol_{lim zu} + vol_{lim zi} vol_{x}` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | WF_y | :math:`WF_{y}` | Algeb | :math:`0` | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | vd | :math:`vd` | ExtAlgeb | | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ | vq | :math:`vq` | ExtAlgeb | | +---------+-------------------+----------+-----------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+------------------+----------+----------------------------------+----------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+==================+==========+==================================+================+ | LG_y | :math:`LG_{y}` | State | :math:`- LG_{y} + v` | :math:`T_R` | +--------+------------------+----------+----------------------------------+----------------+ | LL_x | :math:`LL_{x}` | State | :math:`HVG_{1 y} - LL_{x}` | :math:`T_B` | +--------+------------------+----------+----------------------------------+----------------+ | LL1_x | :math:`LL_{1 x}` | State | :math:`- LL_{1 x} + LL_{y}` | :math:`T_{B1}` | +--------+------------------+----------+----------------------------------+----------------+ | LA_y | :math:`LA_{y}` | State | :math:`KA LL_{1 y} - LA_{y}` | :math:`T_A` | +--------+------------------+----------+----------------------------------+----------------+ | WF_x | :math:`WF_{x}` | State | :math:`LVG_{y} - WF_{x}` | :math:`T_{F}` | +--------+------------------+----------+----------------------------------+----------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+------------------+----------+----------------------------------+----------------+ Algebraic Equations ----------------------------- +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+===================+==========+======================================================================================================================================================+ | v | :math:`v` | Algeb | :math:`- v + vbus` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`ue vol_{y} - vout` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`UEL` | Algeb | :math:`- UEL + UEL_{0}` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | OEL | :math:`OEL` | Algeb | :math:`- OEL + OEL_{0}` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vs | :math:`Vs` | Algeb | :math:`- Vs` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`- vref + vref_{0}` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | SG | :math:`SG` | Algeb | :math:`- SG + SG_{0}` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | LR_x | :math:`LR_{x}` | Algeb | :math:`KLR \left(- ILR + XadIfd\right) - LR_{x}` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | LR_y | :math:`LR_{y}` | Algeb | :math:`LR_{lim zi} LR_{x} + LR_{lim zl} zero - LR_{y}` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`ue \left(- LG_{y} + SG SWVOS_{s1} + SWUEL_{s1} UEL + Vs - WF_{y} + vref\right) - vi` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | vil_x | :math:`vil_{x}` | Algeb | :math:`vi - vil_{x}` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | vil_y | :math:`vil_{y}` | Algeb | :math:`VIMAX vil_{lim zu} + VIMIN vil_{lim zl} + vil_{lim zi} vil_{x} - vil_{y}` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL2 | :math:`UEL_{2}` | Algeb | :math:`- UEL_{2} + ue \left(SWUEL_{s2} UEL + llim \left(1 - SWUEL_{s2}\right)\right)` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | HVG1_y | :math:`HVG_{1 y}` | Algeb | :math:`HVG_{1 lt z0} UEL_{2} + HVG_{1 lt z1} vil_{y} - HVG_{1 y}` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- LL_{x} + LL_{y}\right) + LL_{x} TB - LL_{y} TB + TC \left(HVG_{1 y} - LL_{x}\right)` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL1_y | :math:`LL_{1 y}` | Algeb | :math:`LL_{1 LT1 z1} LL_{1 LT2 z1} \left(- LL_{1 x} + LL_{1 y}\right) + LL_{1 x} TB_{1} - LL_{1 y} TB_{1} + TC_{1} \left(- LL_{1 x} + LL_{y}\right)` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | vas | :math:`vas` | Algeb | :math:`ue \left(LA_{y} - LR_{y} + SG SWVOS_{s2}\right) - vas` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | UEL3 | :math:`UEL_{3}` | Algeb | :math:`- UEL_{3} + ue \left(SWUEL_{s3} UEL + llim \left(1 - SWUEL_{s3}\right)\right)` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | HVG_y | :math:`HVG_{y}` | Algeb | :math:`HVG_{lt z0} UEL_{3} + HVG_{lt z1} vas - HVG_{y}` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | LVG_y | :math:`LVG_{y}` | Algeb | :math:`HVG_{y} LVG_{lt z1} + LVG_{lt z0} OEL - LVG_{y}` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | vol_x | :math:`vol_{x}` | Algeb | :math:`LVG_{y} - vol_{x}` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | vol_y | :math:`vol_{y}` | Algeb | :math:`efdl vol_{lim zl} + efdu vol_{lim zu} + vol_{lim zi} vol_{x} - vol_{y}` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`WF_{y}` | Algeb | :math:`KF \left(LVG_{y} - WF_{x}\right) - TF WF_{y}` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | :math:`ue \left(- vf_{0} + vout\right)` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | :math:`0` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | :math:`0` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | :math:`0` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | vd | :math:`vd` | ExtAlgeb | :math:`0` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | vq | :math:`vq` | ExtAlgeb | :math:`0` | +---------+-------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +--------+------------------+----------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +========+==================+====================================================+=================+ | ue | :math:`u_e` | :math:`u ug` | 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:`LR_{y} - SG SWVOS_{s2} + vf_{0}` | PostInitService | +--------+------------------+----------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`vref` | PostInitService | +--------+------------------+----------------------------------------------------+-----------------+ | efdu | :math:`efd_{u}` | :math:`- KC XadIfd + VRMAX \sqrt{vd^{2} + vq^{2}}` | VarService | +--------+------------------+----------------------------------------------------+-----------------+ | efdl | :math:`efd_{l}` | :math:`VRMIN \sqrt{vd^{2} + vq^{2}}` | 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:`LP_{y}` | State | State in lag transfer function | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | VR_y | :math:`VR_{y}` | State | State in lag TF | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | LL_x | :math:`LL_{x}` | State | State in lead-lag | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | WF_x | :math:`WF_{x}` | State | State in washout filter | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | INT_y | :math:`INT_{y}` | State | Integrator output | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ | v | :math:`v` | Algeb | Input to exciter (bus v or Eterm) | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vout | :math:`vout` | Algeb | Exciter final output voltage | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | UEL | :math:`UEL` | Algeb | Interface var for under exc. limiter | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | OEL | :math:`OEL` | Algeb | Interface var for over exc. limiter | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | Vs | :math:`Vs` | Algeb | Voltage compensation from PSS | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vref | :math:`vref` | Algeb | Reference voltage input | *p.u.* | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vi | :math:`vi` | Algeb | Total voltage input | *pu* | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | LL_y | :math:`LL_{y}` | Algeb | Output of lead-lag | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | WF_y | :math:`WF_{y}` | Algeb | Output of washout filter | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | Se | :math:`Se` | Algeb | saturation output | | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | VFE | :math:`VFE` | Algeb | Combined saturation feedback | *p.u.* | v_str | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vf | :math:`vf` | ExtAlgeb | Excitation field voltage to generator | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | Armature excitation current | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ | a | :math:`a` | ExtAlgeb | Bus voltage phase angle | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ | vbus | :math:`vbus` | ExtAlgeb | Bus voltage magnitude | | | +---------+-----------------+----------+---------------------------------------+--------+------------+ Initialization Equations ------------------------ +---------+-----------------+----------+--------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+=================+==========+==============================================================================================================+ | LP_y | :math:`LP_{y}` | State | :math:`v` | +---------+-----------------+----------+--------------------------------------------------------------------------------------------------------------+ | VR_y | :math:`VR_{y}` | State | :math:`KA vi` | +---------+-----------------+----------+--------------------------------------------------------------------------------------------------------------+ | LL_x | :math:`LL_{x}` | State | :math:`VR_{y}` | +---------+-----------------+----------+--------------------------------------------------------------------------------------------------------------+ | WF_x | :math:`WF_{x}` | State | :math:`LL_{y}` | +---------+-----------------+----------+--------------------------------------------------------------------------------------------------------------+ | INT_y | :math:`INT_{y}` | State | :math:`vf_{0}` | +---------+-----------------+----------+--------------------------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +---------+-----------------+----------+--------------------------------------------------------------------------------------------------------------+ | v | :math:`v` | Algeb | :math:`vbus` | +---------+-----------------+----------+--------------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`ue vf_{0}` | +---------+-----------------+----------+--------------------------------------------------------------------------------------------------------------+ | UEL | :math:`UEL` | Algeb | :math:`UEL_{0}` | +---------+-----------------+----------+--------------------------------------------------------------------------------------------------------------+ | OEL | :math:`OEL` | Algeb | :math:`OEL_{0}` | +---------+-----------------+----------+--------------------------------------------------------------------------------------------------------------+ | Vs | :math:`Vs` | Algeb | :math:`0` | +---------+-----------------+----------+--------------------------------------------------------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`v + \frac{VFE}{KA}` | +---------+-----------------+----------+--------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`ue \left(- v + vref\right)` | +---------+-----------------+----------+--------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`VR_{y}` | +---------+-----------------+----------+--------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`WF_{y}` | Algeb | :math:`0` | +---------+-----------------+----------+--------------------------------------------------------------------------------------------------------------+ | Se | :math:`Se` | Algeb | :math:`SAT_{B} \left(INT_{y} - SAT_{A}\right)^{2} \operatorname{Indicator}{\left(INT_{y} > SAT_{A} \right)}` | +---------+-----------------+----------+--------------------------------------------------------------------------------------------------------------+ | VFE | :math:`VFE` | Algeb | :math:`INT_{y} KE + Se` | +---------+-----------------+----------+--------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | | +---------+-----------------+----------+--------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | | +---------+-----------------+----------+--------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | | +---------+-----------------+----------+--------------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | | +---------+-----------------+----------+--------------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+----------------------------------------+---------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+========================================+===============+ | LP_y | :math:`LP_{y}` | State | :math:`- LP_{y} + v` | :math:`T_R` | +--------+-----------------+----------+----------------------------------------+---------------+ | VR_y | :math:`VR_{y}` | State | :math:`KA vi - VR_{y}` | :math:`T_A` | +--------+-----------------+----------+----------------------------------------+---------------+ | LL_x | :math:`LL_{x}` | State | :math:`- LL_{x} + VR_{y}` | :math:`T_F_2` | +--------+-----------------+----------+----------------------------------------+---------------+ | WF_x | :math:`WF_{x}` | State | :math:`LL_{y} - WF_{x}` | :math:`T_F_1` | +--------+-----------------+----------+----------------------------------------+---------------+ | INT_y | :math:`INT_{y}` | State | :math:`ue \left(- VFE + VR_{y}\right)` | :math:`T_E` | +--------+-----------------+----------+----------------------------------------+---------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+----------------------------------------+---------------+ Algebraic Equations ----------------------------- +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+================+==========+========================================================================================================================================+ | v | :math:`v` | Algeb | :math:`- v + vbus` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------+ | vout | :math:`vout` | Algeb | :math:`INT_{y} ue - vout` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------+ | UEL | :math:`UEL` | Algeb | :math:`- UEL + UEL_{0}` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------+ | OEL | :math:`OEL` | Algeb | :math:`- OEL + OEL_{0}` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------+ | Vs | :math:`Vs` | Algeb | :math:`- Vs` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------+ | vref | :math:`vref` | Algeb | :math:`- vref + vref_{0}` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`vi` | Algeb | :math:`ue \left(- LP_{y} + Vs - WF_{y} + vref\right) - vi` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- LL_{x} + LL_{y}\right) + LL_{x} TF_{2} - LL_{y} TF_{2} + TF_{3} \left(- LL_{x} + VR_{y}\right)` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------+ | WF_y | :math:`WF_{y}` | Algeb | :math:`KF \left(LL_{y} - WF_{x}\right) - TF_{1} WF_{y}` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`Se` | Algeb | :math:`ue \left(SAT_{B} SL_{z0} \left(INT_{y} - SAT_{A}\right)^{2} - Se\right)` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------+ | VFE | :math:`VFE` | Algeb | :math:`ue \left(INT_{y} KE + Se - VFE\right)` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | ExtAlgeb | :math:`ue \left(- vf_{0} + vout\right)` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | ExtAlgeb | :math:`0` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | :math:`0` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------+ | vbus | :math:`vbus` | ExtAlgeb | :math:`0` | +---------+----------------+----------+----------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +==========+=======================+=============================================================================================================================================================================================================================+=================+ | ue | :math:`u_e` | :math:`u ug` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | UEL0 | :math:`UEL0` | :math:`0` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | OEL0 | :math:`OEL0` | :math:`0` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VRMAXu | :math:`VRMAXu` | :math:`VRMAX ue - 999 ue + 999` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | VRMINu | :math:`VRMINu` | :math:`VRMIN ue + 999 ue - 999` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E1 | :math:`E^{1c}_{SAT}` | :math:`E_{1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_E2 | :math:`E^{2c}_{SAT}` | :math:`E_{2} - 2 SAT_{zSE2} + 2` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE1 | :math:`SE^{1c}_{SAT}` | :math:`SE_{1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_SE2 | :math:`SE^{2c}_{SAT}` | :math:`- 2 SAT_{zSE2} + SE_{2} + 2` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_a | :math:`a_{SAT}` | :math:`\sqrt{\frac{SAT_{E1} SAT_{SE1}}{SAT_{E2} SAT_{SE2}}} \left(\operatorname{Indicator}{\left(SAT_{SE2} > 0 \right)} + \operatorname{Indicator}{\left(SAT_{SE2} < 0 \right)}\right)` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_A | :math:`A^q_{SAT}` | :math:`SAT_{E2} - \frac{SAT_{E1} - SAT_{E2}}{SAT_{a} - 1}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | SAT_B | :math:`B^q_{SAT}` | :math:`\frac{SAT_{E2} SAT_{SE2} \left(SAT_{a} - 1\right)^{2} \left(\operatorname{Indicator}{\left(SAT_{a} > 0 \right)} + \operatorname{Indicator}{\left(SAT_{a} < 0 \right)}\right)}{\left(SAT_{E1} - SAT_{E2}\right)^{2}}` | ConstService | +----------+-----------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------+ | vref0 | :math:`V_{ref0}` | :math:`vref` | 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) | +---------------+--------+-------+---------------------------------------+-----------------+