.. _TurbineGov: ================================================================================ TurbineGov ================================================================================ Turbine governor group for synchronous generator. Common Parameters: u, name Common Variables: pout Available models: TG2_, TGOV1_, TGOV1DB_, TGOV1N_, TGOV1NDB_, IEEEG1_, IEESGO_, GAST_, HYGOV_, HYGOVDB_, HYGOV4_ .. _TG2: -------------------------------------------------------------------------------- TG2 -------------------------------------------------------------------------------- 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,unique | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Tn | :math:`T_n` | Turbine power rating. Equal to `Sn` if not provided. | 0 | *MVA* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | wref0 | :math:`\omega_{ref0}` | Base speed reference | 1 | *p.u.* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | R | :math:`R` | Speed regulation gain (mach. base default) | 0.050 | *p.u.* | ipower | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | pmax | :math:`p_{max}` | Maximum power output | 999 | *p.u.* | power | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | pmin | :math:`p_{min}` | Minimum power output | 0 | *p.u.* | power | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | dbl | :math:`L_{db}` | Deadband lower limit | -0.000 | *p.u.* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | dbu | :math:`U_{db}` | Deadband upper limit | 0.000 | *p.u.* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | dbc | :math:`C_{db}` | Deadband neutral value | 0 | *p.u.* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | T1 | :math:`T_1` | Transient gain time | 0.200 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | T2 | :math:`T_2` | Governor time constant | 10 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Sg | :math:`S_n` | Rated power from generator | 0 | *MVA* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | ug | :math:`u_g` | Generator connection status | 0 | *bool* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Vn | :math:`V_n` | Rated voltage from generator | 0 | *kV* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ Variables --------- +--------+----------------------+----------+-----------------------------------------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +========+======================+==========+=======================================================================+========+============+ | ll_x | :math:`x'_{ll}` | State | State in lead-lag | | v_str | +--------+----------------------+----------+-----------------------------------------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | *p.u.* | | +--------+----------------------+----------+-----------------------------------------------------------------------+--------+------------+ | paux | :math:`P_{aux}` | Algeb | Auxiliary power input | | v_str | +--------+----------------------+----------+-----------------------------------------------------------------------+--------+------------+ | pout | :math:`P_{out}` | Algeb | Turbine final output power | | v_str | +--------+----------------------+----------+-----------------------------------------------------------------------+--------+------------+ | wref | :math:`\omega_{ref}` | Algeb | Speed reference variable | | v_str | +--------+----------------------+----------+-----------------------------------------------------------------------+--------+------------+ | w_d | :math:`\omega_{dev}` | Algeb | Generator speed deviation before dead band (positive for under speed) | | v_str | +--------+----------------------+----------+-----------------------------------------------------------------------+--------+------------+ | w_dm | :math:`\omega_{dm}` | Algeb | Measured speed deviation after dead band | | v_str | +--------+----------------------+----------+-----------------------------------------------------------------------+--------+------------+ | w_dmg | :math:`\omega_{dmG}` | Algeb | Speed deviation after dead band after gain | | v_str | +--------+----------------------+----------+-----------------------------------------------------------------------+--------+------------+ | ll_y | :math:`y_{ll}` | Algeb | Output of lead-lag | | v_str | +--------+----------------------+----------+-----------------------------------------------------------------------+--------+------------+ | pnl | :math:`P_{nl}` | Algeb | Power output before hard limiter | | v_str | +--------+----------------------+----------+-----------------------------------------------------------------------+--------+------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | Mechanical power interface to SynGen | | | +--------+----------------------+----------+-----------------------------------------------------------------------+--------+------------+ Initialization Equations ------------------------ +--------+----------------------+----------+-------------------------+ | Name | Symbol | Type | Initial Value | +========+======================+==========+=========================+ | ll_x | :math:`x'_{ll}` | State | :math:`\omega_{dmG}` | +--------+----------------------+----------+-------------------------+ | omega | :math:`\omega` | ExtState | | +--------+----------------------+----------+-------------------------+ | paux | :math:`P_{aux}` | Algeb | :math:`P_{aux0}` | +--------+----------------------+----------+-------------------------+ | pout | :math:`P_{out}` | Algeb | :math:`\tau_{m0} u_{e}` | +--------+----------------------+----------+-------------------------+ | wref | :math:`\omega_{ref}` | Algeb | :math:`\omega_{ref0}` | +--------+----------------------+----------+-------------------------+ | w_d | :math:`\omega_{dev}` | Algeb | :math:`0` | +--------+----------------------+----------+-------------------------+ | w_dm | :math:`\omega_{dm}` | Algeb | :math:`0` | +--------+----------------------+----------+-------------------------+ | w_dmg | :math:`\omega_{dmG}` | Algeb | :math:`0` | +--------+----------------------+----------+-------------------------+ | ll_y | :math:`y_{ll}` | Algeb | :math:`\omega_{dmG}` | +--------+----------------------+----------+-------------------------+ | pnl | :math:`P_{nl}` | Algeb | :math:`\tau_{m0}` | +--------+----------------------+----------+-------------------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | | +--------+----------------------+----------+-------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+----------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+==================================+=============+ | ll_x | :math:`x'_{ll}` | State | :math:`\omega_{dmG} - x'_{ll}` | :math:`T_2` | +--------+-----------------+----------+----------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+----------------------------------+-------------+ Algebraic Equations ----------------------------- +--------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +========+======================+==========+============================================================================================================================================+ | paux | :math:`P_{aux}` | Algeb | :math:`P_{aux0} - P_{aux}` | +--------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------+ | pout | :math:`P_{out}` | Algeb | :math:`P_{nl} z_{i}^{plim} - P_{out} + p_{max} z_{u}^{plim} + p_{min} z_{l}^{plim}` | +--------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------+ | wref | :math:`\omega_{ref}` | Algeb | :math:`\omega_{ref0} - \omega_{ref}` | +--------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------+ | w_d | :math:`\omega_{dev}` | Algeb | :math:`- \omega_{dev} + u_{e} \left(- \omega + \omega_{ref}\right)` | +--------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------+ | w_dm | :math:`\omega_{dm}` | Algeb | :math:`L_{db} z_{lr}^{w_{db}} + U_{db} z_{ur}^{w_{db}} + \omega_{dev} \left(1 - z_{i}^{w_{db}}\right) - \omega_{dm}` | +--------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------+ | w_dmg | :math:`\omega_{dmG}` | Algeb | :math:`G \omega_{dm} - \omega_{dmG}` | +--------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------+ | ll_y | :math:`y_{ll}` | Algeb | :math:`T_{1} \left(\omega_{dmG} - x'_{ll}\right) + T_{2} x'_{ll} - T_{2} y_{ll} + ll_{LT1 z1} ll_{LT2 z1} \left(- x'_{ll} + y_{ll}\right)` | +--------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------+ | pnl | :math:`P_{nl}` | Algeb | :math:`- P_{nl} + P_{ref0} + y_{ll}` | +--------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | :math:`u_{e} \left(P_{out} - \tau_{m0}\right)` | +--------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +--------+------------------+---------------------+--------------+ | Name | Symbol | Equation | Type | +========+==================+=====================+==============+ | ue | :math:`u_{e}` | :math:`u u_{g}` | ConstService | +--------+------------------+---------------------+--------------+ | pref0 | :math:`P_{ref0}` | :math:`\tau_{m0}` | ConstService | +--------+------------------+---------------------+--------------+ | paux0 | :math:`P_{aux0}` | :math:`0` | ConstService | +--------+------------------+---------------------+--------------+ | gain | :math:`G` | :math:`\frac{u}{R}` | ConstService | +--------+------------------+---------------------+--------------+ Discretes ----------- +---------+-----------------+-------------+------+ | Name | Symbol | Type | Info | +=========+=================+=============+======+ | w_db | :math:`w_db` | DeadBandRT | | +---------+-----------------+-------------+------+ | ll_LT1 | :math:`LT_{ll}` | LessThan | | +---------+-----------------+-------------+------+ | ll_LT2 | :math:`LT_{ll}` | LessThan | | +---------+-----------------+-------------+------+ | plim | :math:`plim` | HardLimiter | | +---------+-----------------+-------------+------+ Blocks ------- +------+------------+---------+------+ | Name | Symbol | Type | Info | +======+============+=========+======+ | ll | :math:`ll` | LeadLag | | +------+------------+---------+------+ Config Fields in [TG2] +---------------+-----------------------+-------+---------------------------------------+-----------------+ | 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) | +---------------+-----------------------+-------+---------------------------------------+-----------------+ | deadband | :math:`z_{deadband}` | 0 | enable input dead band | (0, 1) | +---------------+-----------------------+-------+---------------------------------------+-----------------+ | hardlimit | :math:`z_{hardlimit}` | 1 | enable output hard limit | (0, 1) | +---------------+-----------------------+-------+---------------------------------------+-----------------+ .. _TGOV1: -------------------------------------------------------------------------------- TGOV1 -------------------------------------------------------------------------------- TGOV1 turbine governor model. Implements the PSS/E TGOV1 model without deadband. 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,unique | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Tn | :math:`T_n` | Turbine power rating. Equal to `Sn` if not provided. | 0 | *MVA* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | wref0 | :math:`\omega_{ref0}` | Base speed reference | 1 | *p.u.* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | R | :math:`R` | Speed regulation gain (mach. base default) | 0.050 | *p.u.* | ipower | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | VMAX | :math:`V_{max}` | Maximum valve position | 1.200 | *p.u.* | power | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | VMIN | :math:`V_{min}` | Minimum valve position | 0 | *p.u.* | power | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | T1 | :math:`T_1` | Valve time constant | 0.100 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | T2 | :math:`T_2` | Lead-lag lead time constant | 0.200 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | T3 | :math:`T_3` | Lead-lag lag time constant | 10 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Dt | :math:`D_t` | Turbine damping coefficient | 0 | | power | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Sg | :math:`S_n` | Rated power from generator | 0 | *MVA* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | ug | :math:`u_g` | Generator connection status | 0 | *bool* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Vn | :math:`V_n` | Rated voltage from generator | 0 | *kV* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ Variables --------- +--------+----------------------+----------+--------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +========+======================+==========+======================================+========+============+ | LAG_y | :math:`y_{LAG}` | State | State in lag TF | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | LL_x | :math:`x'_{LL}` | State | State in lead-lag | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | *p.u.* | | +--------+----------------------+----------+--------------------------------------+--------+------------+ | paux | :math:`P_{aux}` | Algeb | Auxiliary power input | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | pout | :math:`P_{out}` | Algeb | Turbine final output power | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | wref | :math:`\omega_{ref}` | Algeb | Speed reference variable | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | pref | :math:`P_{ref}` | Algeb | Reference power input | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | wd | :math:`\omega_{dev}` | Algeb | Generator speed deviation | *p.u.* | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | pd | :math:`P_{d}` | Algeb | Pref plus speed deviation times gain | *p.u.* | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | LL_y | :math:`y_{LL}` | Algeb | Output of lead-lag | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | Mechanical power interface to SynGen | | | +--------+----------------------+----------+--------------------------------------+--------+------------+ Initialization Equations ------------------------ +--------+----------------------+----------+-------------------------+ | Name | Symbol | Type | Initial Value | +========+======================+==========+=========================+ | LAG_y | :math:`y_{LAG}` | State | :math:`P_{d}` | +--------+----------------------+----------+-------------------------+ | LL_x | :math:`x'_{LL}` | State | :math:`y_{LAG}` | +--------+----------------------+----------+-------------------------+ | omega | :math:`\omega` | ExtState | | +--------+----------------------+----------+-------------------------+ | paux | :math:`P_{aux}` | Algeb | :math:`P_{aux0}` | +--------+----------------------+----------+-------------------------+ | pout | :math:`P_{out}` | Algeb | :math:`\tau_{m0} u_{e}` | +--------+----------------------+----------+-------------------------+ | wref | :math:`\omega_{ref}` | Algeb | :math:`\omega_{ref0}` | +--------+----------------------+----------+-------------------------+ | pref | :math:`P_{ref}` | Algeb | :math:`R \tau_{m0}` | +--------+----------------------+----------+-------------------------+ | wd | :math:`\omega_{dev}` | Algeb | :math:`0` | +--------+----------------------+----------+-------------------------+ | pd | :math:`P_{d}` | Algeb | :math:`\tau_{m0} u_{e}` | +--------+----------------------+----------+-------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`y_{LAG}` | +--------+----------------------+----------+-------------------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | | +--------+----------------------+----------+-------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+----------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+==================================+=============+ | LAG_y | :math:`y_{LAG}` | State | :math:`P_{d} - y_{LAG}` | :math:`T_1` | +--------+-----------------+----------+----------------------------------+-------------+ | LL_x | :math:`x'_{LL}` | State | :math:`- x'_{LL} + y_{LAG}` | :math:`T_3` | +--------+-----------------+----------+----------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+----------------------------------+-------------+ Algebraic Equations ----------------------------- +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=======+======================+==========+=========================================================================================================================================+ | paux | :math:`P_{aux}` | Algeb | :math:`P_{aux0} - P_{aux}` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | pout | :math:`P_{out}` | Algeb | :math:`- P_{out} + u_{e} \left(- D_{t} \omega_{dev} + y_{LL}\right)` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | wref | :math:`\omega_{ref}` | Algeb | :math:`\omega_{ref0} - \omega_{ref}` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | pref | :math:`P_{ref}` | Algeb | :math:`P_{ref0} R - P_{ref}` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | wd | :math:`\omega_{dev}` | Algeb | :math:`- \omega_{dev} + u_{e} \left(\omega - \omega_{ref}\right)` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | pd | :math:`P_{d}` | Algeb | :math:`G u_{e} \left(P_{aux} + P_{ref} - \omega_{dev}\right) - P_{d}` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- x'_{LL} + y_{LL}\right) + T_{2} \left(- x'_{LL} + y_{LAG}\right) + T_{3} x'_{LL} - T_{3} y_{LL}` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | :math:`u_{e} \left(P_{out} - \tau_{m0}\right)` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +--------+------------------+-------------------------+--------------+ | Name | Symbol | Equation | Type | +========+==================+=========================+==============+ | ue | :math:`u_{e}` | :math:`u u_{g}` | ConstService | +--------+------------------+-------------------------+--------------+ | pref0 | :math:`P_{ref0}` | :math:`\tau_{m0}` | ConstService | +--------+------------------+-------------------------+--------------+ | paux0 | :math:`P_{aux0}` | :math:`0` | ConstService | +--------+------------------+-------------------------+--------------+ | gain | :math:`G` | :math:`\frac{u_{e}}{R}` | ConstService | +--------+------------------+-------------------------+--------------+ Discretes ----------- +----------+-------------------+------------+----------------+ | Name | Symbol | Type | Info | +==========+===================+============+================+ | LAG_lim | :math:`lim_{LAG}` | AntiWindup | Limiter in Lag | +----------+-------------------+------------+----------------+ | LL_LT1 | :math:`LT_{LL}` | LessThan | | +----------+-------------------+------------+----------------+ | LL_LT2 | :math:`LT_{LL}` | LessThan | | +----------+-------------------+------------+----------------+ Blocks ------- +------+-------------+---------------+------+ | Name | Symbol | Type | Info | +======+=============+===============+======+ | LAG | :math:`LAG` | LagAntiWindup | | +------+-------------+---------------+------+ | LL | :math:`LL` | LeadLag | | +------+-------------+---------------+------+ Config Fields in [TGOV1] +---------------+--------+-------+---------------------------------------+-----------------+ | 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) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _TGOV1DB: -------------------------------------------------------------------------------- TGOV1DB -------------------------------------------------------------------------------- TGOV1 turbine governor model with speed input deadband. 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,unique | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Tn | :math:`T_n` | Turbine power rating. Equal to `Sn` if not provided. | 0 | *MVA* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | wref0 | :math:`\omega_{ref0}` | Base speed reference | 1 | *p.u.* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | R | :math:`R` | Speed regulation gain (mach. base default) | 0.050 | *p.u.* | ipower | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | VMAX | :math:`V_{max}` | Maximum valve position | 1.200 | *p.u.* | power | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | VMIN | :math:`V_{min}` | Minimum valve position | 0 | *p.u.* | power | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | T1 | :math:`T_1` | Valve time constant | 0.100 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | T2 | :math:`T_2` | Lead-lag lead time constant | 0.200 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | T3 | :math:`T_3` | Lead-lag lag time constant | 10 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Dt | :math:`D_t` | Turbine damping coefficient | 0 | | power | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | dbL | :math:`db_L` | Lower bound of deadband | 0 | *p.u.* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | dbU | :math:`db_U` | Upper bound of deadband | 0 | *p.u.* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Sg | :math:`S_n` | Rated power from generator | 0 | *MVA* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | ug | :math:`u_g` | Generator connection status | 0 | *bool* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Vn | :math:`V_n` | Rated voltage from generator | 0 | *kV* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ Variables --------- +--------+----------------------+----------+--------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +========+======================+==========+======================================+========+============+ | LAG_y | :math:`y_{LAG}` | State | State in lag TF | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | LL_x | :math:`x'_{LL}` | State | State in lead-lag | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | *p.u.* | | +--------+----------------------+----------+--------------------------------------+--------+------------+ | paux | :math:`P_{aux}` | Algeb | Auxiliary power input | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | pout | :math:`P_{out}` | Algeb | Turbine final output power | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | wref | :math:`\omega_{ref}` | Algeb | Speed reference variable | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | pref | :math:`P_{ref}` | Algeb | Reference power input | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | wd | :math:`\omega_{dev}` | Algeb | Generator speed deviation | *p.u.* | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | pd | :math:`P_{d}` | Algeb | Pref plus speed deviation times gain | *p.u.* | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | LL_y | :math:`y_{LL}` | Algeb | Output of lead-lag | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | DB_y | :math:`y_{DB}` | Algeb | Deadband type 1 output | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | Mechanical power interface to SynGen | | | +--------+----------------------+----------+--------------------------------------+--------+------------+ Initialization Equations ------------------------ +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +========+======================+==========+===============================================================================================================+ | LAG_y | :math:`y_{LAG}` | State | :math:`P_{d}` | +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ | LL_x | :math:`x'_{LL}` | State | :math:`y_{LAG}` | +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ | paux | :math:`P_{aux}` | Algeb | :math:`P_{aux0}` | +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ | pout | :math:`P_{out}` | Algeb | :math:`\tau_{m0} u_{e}` | +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ | wref | :math:`\omega_{ref}` | Algeb | :math:`\omega_{ref0}` | +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ | pref | :math:`P_{ref}` | Algeb | :math:`R \tau_{m0}` | +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ | wd | :math:`\omega_{dev}` | Algeb | :math:`0` | +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ | pd | :math:`P_{d}` | Algeb | :math:`\tau_{m0} u_{e}` | +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`y_{LAG}` | +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ | DB_y | :math:`y_{DB}` | Algeb | :math:`1.0 DB_{db zl} \left(\omega_{dev} - db_{L}\right) + 1.0 DB_{db zu} \left(\omega_{dev} - db_{U}\right)` | +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | | +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+----------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+==================================+=============+ | LAG_y | :math:`y_{LAG}` | State | :math:`P_{d} - y_{LAG}` | :math:`T_1` | +--------+-----------------+----------+----------------------------------+-------------+ | LL_x | :math:`x'_{LL}` | State | :math:`- x'_{LL} + y_{LAG}` | :math:`T_3` | +--------+-----------------+----------+----------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+----------------------------------+-------------+ Algebraic Equations ----------------------------- +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=======+======================+==========+=========================================================================================================================================+ | paux | :math:`P_{aux}` | Algeb | :math:`P_{aux0} - P_{aux}` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | pout | :math:`P_{out}` | Algeb | :math:`- D_{t} y_{DB} - P_{out} + y_{LL}` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | wref | :math:`\omega_{ref}` | Algeb | :math:`\omega_{ref0} - \omega_{ref}` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | pref | :math:`P_{ref}` | Algeb | :math:`P_{ref0} R - P_{ref}` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | wd | :math:`\omega_{dev}` | Algeb | :math:`- \omega_{dev} + u_{e} \left(\omega - \omega_{ref}\right)` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | pd | :math:`P_{d}` | Algeb | :math:`G u_{e} \left(P_{aux} + P_{ref} - y_{DB}\right) - P_{d}` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- x'_{LL} + y_{LL}\right) + T_{2} \left(- x'_{LL} + y_{LAG}\right) + T_{3} x'_{LL} - T_{3} y_{LL}` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | DB_y | :math:`y_{DB}` | Algeb | :math:`1.0 DB_{db zl} \left(\omega_{dev} - db_{L}\right) + 1.0 DB_{db zu} \left(\omega_{dev} - db_{U}\right) - y_{DB}` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | :math:`u_{e} \left(P_{out} - \tau_{m0}\right)` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +--------+------------------+-------------------------+--------------+ | Name | Symbol | Equation | Type | +========+==================+=========================+==============+ | ue | :math:`u_{e}` | :math:`u u_{g}` | ConstService | +--------+------------------+-------------------------+--------------+ | pref0 | :math:`P_{ref0}` | :math:`\tau_{m0}` | ConstService | +--------+------------------+-------------------------+--------------+ | paux0 | :math:`P_{aux0}` | :math:`0` | ConstService | +--------+------------------+-------------------------+--------------+ | gain | :math:`G` | :math:`\frac{u_{e}}{R}` | ConstService | +--------+------------------+-------------------------+--------------+ Discretes ----------- +----------+-------------------+------------+----------------+ | Name | Symbol | Type | Info | +==========+===================+============+================+ | LAG_lim | :math:`lim_{LAG}` | AntiWindup | Limiter in Lag | +----------+-------------------+------------+----------------+ | LL_LT1 | :math:`LT_{LL}` | LessThan | | +----------+-------------------+------------+----------------+ | LL_LT2 | :math:`LT_{LL}` | LessThan | | +----------+-------------------+------------+----------------+ | DB_db | :math:`db_{DB}` | DeadBand | | +----------+-------------------+------------+----------------+ Blocks ------- +------+-------------+---------------+------------------------------+ | Name | Symbol | Type | Info | +======+=============+===============+==============================+ | LAG | :math:`LAG` | LagAntiWindup | | +------+-------------+---------------+------------------------------+ | LL | :math:`LL` | LeadLag | | +------+-------------+---------------+------------------------------+ | DB | :math:`DB` | DeadBand1 | deadband for speed deviation | +------+-------------+---------------+------------------------------+ Config Fields in [TGOV1DB] +---------------+--------+-------+---------------------------------------+-----------------+ | 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) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _TGOV1N: -------------------------------------------------------------------------------- TGOV1N -------------------------------------------------------------------------------- New TGOV1 (TGOV1N) turbine governor model. The TGOV1N model that sums ``pref`` and ``paux`` signals after the droop. This model is useful for incorporating AGC and scheduling signals, which will not be multiplied by ``1/R`` like in the original TGOV1 model. Scheduling changes should write to ``pref0.v`` in place. AGC signal should write to ``paux0.v`` in place. Modifying ``tm0`` is not allowed. Examples -------- To update all ``paux0`` values to ``paux_new``, which contains the new values, do .. code:: python ss.TGOV1N.paux0.v[:] = paux_new # in-place update of the `paux0.v` array instead of .. code:: python ss.TGOV1N.paux0.v = paux_new # error; changes the reference of `paux0.v` 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,unique | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Tn | :math:`T_n` | Turbine power rating. Equal to `Sn` if not provided. | 0 | *MVA* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | wref0 | :math:`\omega_{ref0}` | Base speed reference | 1 | *p.u.* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | R | :math:`R` | Speed regulation gain (mach. base default) | 0.050 | *p.u.* | ipower | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | VMAX | :math:`V_{max}` | Maximum valve position | 1.200 | *p.u.* | power | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | VMIN | :math:`V_{min}` | Minimum valve position | 0 | *p.u.* | power | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | T1 | :math:`T_1` | Valve time constant | 0.100 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | T2 | :math:`T_2` | Lead-lag lead time constant | 0.200 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | T3 | :math:`T_3` | Lead-lag lag time constant | 10 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Dt | :math:`D_t` | Turbine damping coefficient | 0 | | power | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Sg | :math:`S_n` | Rated power from generator | 0 | *MVA* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | ug | :math:`u_g` | Generator connection status | 0 | *bool* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Vn | :math:`V_n` | Rated voltage from generator | 0 | *kV* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ Variables --------- +--------+----------------------+----------+--------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +========+======================+==========+======================================+========+============+ | LAG_y | :math:`y_{LAG}` | State | State in lag TF | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | LL_x | :math:`x'_{LL}` | State | State in lead-lag | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | *p.u.* | | +--------+----------------------+----------+--------------------------------------+--------+------------+ | paux | :math:`P_{aux}` | Algeb | Auxiliary power input | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | pout | :math:`P_{out}` | Algeb | Turbine final output power | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | wref | :math:`\omega_{ref}` | Algeb | Speed reference variable | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | pref | :math:`P_{ref}` | Algeb | Reference power input | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | wd | :math:`\omega_{dev}` | Algeb | Generator speed deviation | *p.u.* | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | pd | :math:`P_{d}` | Algeb | Pref plus speed deviation times gain | *p.u.* | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | LL_y | :math:`y_{LL}` | Algeb | Output of lead-lag | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | Mechanical power interface to SynGen | | | +--------+----------------------+----------+--------------------------------------+--------+------------+ Initialization Equations ------------------------ +--------+----------------------+----------+-------------------------+ | Name | Symbol | Type | Initial Value | +========+======================+==========+=========================+ | LAG_y | :math:`y_{LAG}` | State | :math:`P_{d}` | +--------+----------------------+----------+-------------------------+ | LL_x | :math:`x'_{LL}` | State | :math:`y_{LAG}` | +--------+----------------------+----------+-------------------------+ | omega | :math:`\omega` | ExtState | | +--------+----------------------+----------+-------------------------+ | paux | :math:`P_{aux}` | Algeb | :math:`P_{aux0}` | +--------+----------------------+----------+-------------------------+ | pout | :math:`P_{out}` | Algeb | :math:`\tau_{m0} u_{e}` | +--------+----------------------+----------+-------------------------+ | wref | :math:`\omega_{ref}` | Algeb | :math:`\omega_{ref0}` | +--------+----------------------+----------+-------------------------+ | pref | :math:`P_{ref}` | Algeb | :math:`\tau_{m0}` | +--------+----------------------+----------+-------------------------+ | wd | :math:`\omega_{dev}` | Algeb | :math:`0` | +--------+----------------------+----------+-------------------------+ | pd | :math:`P_{d}` | Algeb | :math:`\tau_{m0} u_{e}` | +--------+----------------------+----------+-------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`y_{LAG}` | +--------+----------------------+----------+-------------------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | | +--------+----------------------+----------+-------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+----------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+==================================+=============+ | LAG_y | :math:`y_{LAG}` | State | :math:`P_{d} - y_{LAG}` | :math:`T_1` | +--------+-----------------+----------+----------------------------------+-------------+ | LL_x | :math:`x'_{LL}` | State | :math:`- x'_{LL} + y_{LAG}` | :math:`T_3` | +--------+-----------------+----------+----------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+----------------------------------+-------------+ Algebraic Equations ----------------------------- +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=======+======================+==========+=========================================================================================================================================+ | paux | :math:`P_{aux}` | Algeb | :math:`P_{aux0} - P_{aux}` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | pout | :math:`P_{out}` | Algeb | :math:`- P_{out} + u_{e} \left(- D_{t} \omega_{dev} + y_{LL}\right)` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | wref | :math:`\omega_{ref}` | Algeb | :math:`\omega_{ref0} - \omega_{ref}` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | pref | :math:`P_{ref}` | Algeb | :math:`P_{ref0} - P_{ref}` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | wd | :math:`\omega_{dev}` | Algeb | :math:`- \omega_{dev} + u_{e} \left(\omega - \omega_{ref}\right)` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | pd | :math:`P_{d}` | Algeb | :math:`- P_{d} + u_{e} \left(- G \omega_{dev} + P_{aux} + P_{ref}\right)` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- x'_{LL} + y_{LL}\right) + T_{2} \left(- x'_{LL} + y_{LAG}\right) + T_{3} x'_{LL} - T_{3} y_{LL}` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | :math:`u_{e} \left(P_{out} - \tau_{m0}\right)` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +--------+------------------+-------------------------+--------------+ | Name | Symbol | Equation | Type | +========+==================+=========================+==============+ | ue | :math:`u_{e}` | :math:`u u_{g}` | ConstService | +--------+------------------+-------------------------+--------------+ | pref0 | :math:`P_{ref0}` | :math:`\tau_{m0}` | ConstService | +--------+------------------+-------------------------+--------------+ | paux0 | :math:`P_{aux0}` | :math:`0` | ConstService | +--------+------------------+-------------------------+--------------+ | gain | :math:`G` | :math:`\frac{u_{e}}{R}` | ConstService | +--------+------------------+-------------------------+--------------+ Discretes ----------- +----------+-------------------+------------+----------------+ | Name | Symbol | Type | Info | +==========+===================+============+================+ | LAG_lim | :math:`lim_{LAG}` | AntiWindup | Limiter in Lag | +----------+-------------------+------------+----------------+ | LL_LT1 | :math:`LT_{LL}` | LessThan | | +----------+-------------------+------------+----------------+ | LL_LT2 | :math:`LT_{LL}` | LessThan | | +----------+-------------------+------------+----------------+ Blocks ------- +------+-------------+---------------+------+ | Name | Symbol | Type | Info | +======+=============+===============+======+ | LAG | :math:`LAG` | LagAntiWindup | | +------+-------------+---------------+------+ | LL | :math:`LL` | LeadLag | | +------+-------------+---------------+------+ Config Fields in [TGOV1N] +---------------+--------+-------+---------------------------------------+-----------------+ | 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) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _TGOV1NDB: -------------------------------------------------------------------------------- TGOV1NDB -------------------------------------------------------------------------------- TGOV1N turbine governor model with speed input deadband. 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,unique | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Tn | :math:`T_n` | Turbine power rating. Equal to `Sn` if not provided. | 0 | *MVA* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | wref0 | :math:`\omega_{ref0}` | Base speed reference | 1 | *p.u.* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | R | :math:`R` | Speed regulation gain (mach. base default) | 0.050 | *p.u.* | ipower | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | VMAX | :math:`V_{max}` | Maximum valve position | 1.200 | *p.u.* | power | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | VMIN | :math:`V_{min}` | Minimum valve position | 0 | *p.u.* | power | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | T1 | :math:`T_1` | Valve time constant | 0.100 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | T2 | :math:`T_2` | Lead-lag lead time constant | 0.200 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | T3 | :math:`T_3` | Lead-lag lag time constant | 10 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Dt | :math:`D_t` | Turbine damping coefficient | 0 | | power | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | dbL | :math:`db_L` | Lower bound of deadband | 0 | *p.u.* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | dbU | :math:`db_U` | Upper bound of deadband | 0 | *p.u.* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Sg | :math:`S_n` | Rated power from generator | 0 | *MVA* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | ug | :math:`u_g` | Generator connection status | 0 | *bool* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Vn | :math:`V_n` | Rated voltage from generator | 0 | *kV* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ Variables --------- +--------+----------------------+----------+--------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +========+======================+==========+======================================+========+============+ | LAG_y | :math:`y_{LAG}` | State | State in lag TF | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | LL_x | :math:`x'_{LL}` | State | State in lead-lag | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | *p.u.* | | +--------+----------------------+----------+--------------------------------------+--------+------------+ | paux | :math:`P_{aux}` | Algeb | Auxiliary power input | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | pout | :math:`P_{out}` | Algeb | Turbine final output power | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | wref | :math:`\omega_{ref}` | Algeb | Speed reference variable | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | pref | :math:`P_{ref}` | Algeb | Reference power input | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | wd | :math:`\omega_{dev}` | Algeb | Generator speed deviation | *p.u.* | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | pd | :math:`P_{d}` | Algeb | Pref plus speed deviation times gain | *p.u.* | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | LL_y | :math:`y_{LL}` | Algeb | Output of lead-lag | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | DB_y | :math:`y_{DB}` | Algeb | Deadband type 1 output | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | Mechanical power interface to SynGen | | | +--------+----------------------+----------+--------------------------------------+--------+------------+ Initialization Equations ------------------------ +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +========+======================+==========+===============================================================================================================+ | LAG_y | :math:`y_{LAG}` | State | :math:`P_{d}` | +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ | LL_x | :math:`x'_{LL}` | State | :math:`y_{LAG}` | +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ | paux | :math:`P_{aux}` | Algeb | :math:`P_{aux0}` | +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ | pout | :math:`P_{out}` | Algeb | :math:`\tau_{m0} u_{e}` | +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ | wref | :math:`\omega_{ref}` | Algeb | :math:`\omega_{ref0}` | +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ | pref | :math:`P_{ref}` | Algeb | :math:`\tau_{m0}` | +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ | wd | :math:`\omega_{dev}` | Algeb | :math:`0` | +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ | pd | :math:`P_{d}` | Algeb | :math:`\tau_{m0} u_{e}` | +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`y_{LAG}` | +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ | DB_y | :math:`y_{DB}` | Algeb | :math:`1.0 DB_{db zl} \left(\omega_{dev} - db_{L}\right) + 1.0 DB_{db zu} \left(\omega_{dev} - db_{U}\right)` | +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | | +--------+----------------------+----------+---------------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+----------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+==================================+=============+ | LAG_y | :math:`y_{LAG}` | State | :math:`P_{d} - y_{LAG}` | :math:`T_1` | +--------+-----------------+----------+----------------------------------+-------------+ | LL_x | :math:`x'_{LL}` | State | :math:`- x'_{LL} + y_{LAG}` | :math:`T_3` | +--------+-----------------+----------+----------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+----------------------------------+-------------+ Algebraic Equations ----------------------------- +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=======+======================+==========+=========================================================================================================================================+ | paux | :math:`P_{aux}` | Algeb | :math:`P_{aux0} - P_{aux}` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | pout | :math:`P_{out}` | Algeb | :math:`- D_{t} y_{DB} - P_{out} + y_{LL}` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | wref | :math:`\omega_{ref}` | Algeb | :math:`\omega_{ref0} - \omega_{ref}` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | pref | :math:`P_{ref}` | Algeb | :math:`P_{ref0} - P_{ref}` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | wd | :math:`\omega_{dev}` | Algeb | :math:`- \omega_{dev} + u_{e} \left(\omega - \omega_{ref}\right)` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | pd | :math:`P_{d}` | Algeb | :math:`- P_{d} + u_{e} \left(G y_{DB} + P_{aux} + P_{ref}\right)` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- x'_{LL} + y_{LL}\right) + T_{2} \left(- x'_{LL} + y_{LAG}\right) + T_{3} x'_{LL} - T_{3} y_{LL}` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | DB_y | :math:`y_{DB}` | Algeb | :math:`1.0 DB_{db zl} \left(\omega_{dev} - db_{L}\right) + 1.0 DB_{db zu} \left(\omega_{dev} - db_{U}\right) - y_{DB}` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | :math:`u_{e} \left(P_{out} - \tau_{m0}\right)` | +-------+----------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +--------+------------------+-------------------------+--------------+ | Name | Symbol | Equation | Type | +========+==================+=========================+==============+ | ue | :math:`u_{e}` | :math:`u u_{g}` | ConstService | +--------+------------------+-------------------------+--------------+ | pref0 | :math:`P_{ref0}` | :math:`\tau_{m0}` | ConstService | +--------+------------------+-------------------------+--------------+ | paux0 | :math:`P_{aux0}` | :math:`0` | ConstService | +--------+------------------+-------------------------+--------------+ | gain | :math:`G` | :math:`\frac{u_{e}}{R}` | ConstService | +--------+------------------+-------------------------+--------------+ Discretes ----------- +----------+-------------------+------------+----------------+ | Name | Symbol | Type | Info | +==========+===================+============+================+ | LAG_lim | :math:`lim_{LAG}` | AntiWindup | Limiter in Lag | +----------+-------------------+------------+----------------+ | LL_LT1 | :math:`LT_{LL}` | LessThan | | +----------+-------------------+------------+----------------+ | LL_LT2 | :math:`LT_{LL}` | LessThan | | +----------+-------------------+------------+----------------+ | DB_db | :math:`db_{DB}` | DeadBand | | +----------+-------------------+------------+----------------+ Blocks ------- +------+-------------+---------------+------------------------------+ | Name | Symbol | Type | Info | +======+=============+===============+==============================+ | LAG | :math:`LAG` | LagAntiWindup | | +------+-------------+---------------+------------------------------+ | LL | :math:`LL` | LeadLag | | +------+-------------+---------------+------------------------------+ | DB | :math:`DB` | DeadBand1 | deadband for speed deviation | +------+-------------+---------------+------------------------------+ Config Fields in [TGOV1NDB] +---------------+--------+-------+---------------------------------------+-----------------+ | 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) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _IEEEG1: -------------------------------------------------------------------------------- IEEEG1 -------------------------------------------------------------------------------- IEEE Type 1 Speed-Governing Model. If only one generator is connected, its `idx` must be given to `syn`, and `syn2` must be left blank. Each generator must provide data in its `Sn` base. `syn` is connected to the high-pressure output (PHP) and the optional `syn2` is connected to the low- pressure output (PLP). The speed deviation of generator 1 (syn) is measured. If the turbine rating `Tn` is not specified, the sum of `Sn` of all connected generators will be used. Normally, K1 + K2 + ... + K8 = 1.0. If the second generator is not connected, K1 + K3 + K5 + K7 = 1, and K2 + K4 + K6 + K8 = 0. If K1 to K8 do not sum up to 1.0, they will be normalized. The normalized parameters are called ``K1n`` through ``K8n``. If initialization error occurs for variable ``vs``, it is due to the limits ``PMIN`` and ``PMAX``. IEEEG1 does not yet support the change of reference (scheduling). 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,unique | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | Tn | :math:`T_n` | Turbine power rating. Equal to `Sn` if not provided. | 0 | *MVA* | | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | wref0 | :math:`\omega_{ref0}` | Base speed reference | 1 | *p.u.* | | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | syn2 | | Optional SynGen idx | | | | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | K | :math:`K` | Gain (1/R) in mach. base | 20 | *p.u. (power)* | power | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | T1 | :math:`T_1` | Gov. lag time const. | 1 | | | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | T2 | :math:`T_2` | Gov. lead time const. | 1 | | | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | T3 | :math:`T_3` | Valve controller time const. | 0.100 | | | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | UO | :math:`U_o` | Max. valve opening rate | 0.100 | *p.u./sec* | | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | UC | :math:`U_c` | Max. valve closing rate | -0.100 | *p.u./sec* | | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | PMAX | :math:`P_{MAX}` | Max. turbine power | 5 | | power | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | PMIN | :math:`P_{MIN}` | Min. turbine power | 0 | | power | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | T4 | :math:`T_4` | Inlet piping/steam bowl time constant | 0.400 | | | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | K1 | :math:`K_1` | Fraction of power from HP | 0.500 | | | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | K2 | :math:`K_2` | Fraction of power from LP | 0 | | | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | T5 | :math:`T_5` | Time constant of 2nd boiler pass | 8 | | | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | K3 | :math:`K_3` | Fraction of HP shaft power after 2nd boiler pass | 0.500 | | | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | K4 | :math:`K_4` | Fraction of LP shaft power after 2nd boiler pass | 0 | | | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | T6 | :math:`T_6` | Time constant of 3rd boiler pass | 0.500 | | | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | K5 | :math:`K_5` | Fraction of HP shaft power after 3rd boiler pass | 0 | | | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | K6 | :math:`K_6` | Fraction of LP shaft power after 3rd boiler pass | 0 | | | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | T7 | :math:`T_7` | Time constant of 4th boiler pass | 0.050 | | | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | K7 | :math:`K_7` | Fraction of HP shaft power after 4th boiler pass | 0 | | | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | K8 | :math:`K_8` | Fraction of LP shaft power after 4th boiler pass | 0 | | | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | Sg | :math:`S_n` | Rated power from generator | 0 | *MVA* | | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | ug | :math:`u_g` | Generator connection status | 0 | *bool* | | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | Vn | :math:`V_n` | Rated voltage from generator | 0 | *kV* | | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ | Sg2 | :math:`S_{n2}` | Rated power of Syn2 | 0 | *MVA* | | +--------+-----------------------+------------------------------------------------------+---------+----------------+------------------+ Variables --------- +--------+----------------------+----------+--------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +========+======================+==========+======================================+========+============+ | LL_x | :math:`x'_{LL}` | State | State in lead-lag | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | IAW_y | :math:`y_{IAW}` | State | AW Integrator output | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | L4_y | :math:`y_{L4}` | State | State in lag transfer function | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | L5_y | :math:`y_{L5}` | State | State in lag transfer function | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | L6_y | :math:`y_{L6}` | State | State in lag transfer function | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | L7_y | :math:`y_{L7}` | State | State in lag transfer function | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | *p.u.* | | +--------+----------------------+----------+--------------------------------------+--------+------------+ | paux | :math:`P_{aux}` | Algeb | Auxiliary power input | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | pout | :math:`P_{out}` | Algeb | Turbine final output power | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | wref | :math:`\omega_{ref}` | Algeb | Speed reference variable | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | wd | :math:`\omega_{dev}` | Algeb | Generator under speed | *p.u.* | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | LL_y | :math:`y_{LL}` | Algeb | Output of lead-lag | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | vs | :math:`V_{s}` | Algeb | Valve speed | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | vsl | :math:`V_{sl}` | Algeb | Valve move speed after limiter | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | PHP | :math:`P_{HP}` | Algeb | HP output | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | PLP | :math:`P_{LP}` | Algeb | LP output | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | Mechanical power interface to SynGen | | | +--------+----------------------+----------+--------------------------------------+--------+------------+ | tm2 | :math:`\tau_{m2}` | ExtAlgeb | Mechanical power to syn2 | | | +--------+----------------------+----------+--------------------------------------+--------+------------+ Initialization Equations ------------------------ +--------+----------------------+----------+------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +========+======================+==========+==========================================================================================+ | LL_x | :math:`x'_{LL}` | State | :math:`\omega_{dev}` | +--------+----------------------+----------+------------------------------------------------------------------------------------------+ | IAW_y | :math:`y_{IAW}` | State | :math:`tm_{012}` | +--------+----------------------+----------+------------------------------------------------------------------------------------------+ | L4_y | :math:`y_{L4}` | State | :math:`y_{IAW}` | +--------+----------------------+----------+------------------------------------------------------------------------------------------+ | L5_y | :math:`y_{L5}` | State | :math:`y_{L4}` | +--------+----------------------+----------+------------------------------------------------------------------------------------------+ | L6_y | :math:`y_{L6}` | State | :math:`y_{L5}` | +--------+----------------------+----------+------------------------------------------------------------------------------------------+ | L7_y | :math:`y_{L7}` | State | :math:`y_{L6}` | +--------+----------------------+----------+------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +--------+----------------------+----------+------------------------------------------------------------------------------------------+ | paux | :math:`P_{aux}` | Algeb | :math:`P_{aux0}` | +--------+----------------------+----------+------------------------------------------------------------------------------------------+ | pout | :math:`P_{out}` | Algeb | :math:`\tau_{m0} u_{e}` | +--------+----------------------+----------+------------------------------------------------------------------------------------------+ | wref | :math:`\omega_{ref}` | Algeb | :math:`\omega_{ref0}` | +--------+----------------------+----------+------------------------------------------------------------------------------------------+ | wd | :math:`\omega_{dev}` | Algeb | :math:`0` | +--------+----------------------+----------+------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`\omega_{dev}` | +--------+----------------------+----------+------------------------------------------------------------------------------------------+ | vs | :math:`V_{s}` | Algeb | :math:`0` | +--------+----------------------+----------+------------------------------------------------------------------------------------------+ | vsl | :math:`V_{sl}` | Algeb | :math:`U_{c} z_{l}^{HL} + U_{o} z_{u}^{HL} + V_{s} z_{i}^{HL}` | +--------+----------------------+----------+------------------------------------------------------------------------------------------+ | PHP | :math:`P_{HP}` | Algeb | :math:`u_{e} \left(K_{1n} y_{L4} + K_{3n} y_{L5} + K_{5n} y_{L6} + K_{7n} y_{L7}\right)` | +--------+----------------------+----------+------------------------------------------------------------------------------------------+ | PLP | :math:`P_{LP}` | Algeb | :math:`u_{e} \left(K_{2n} y_{L4} + K_{4n} y_{L5} + K_{6n} y_{L6} + K_{8n} y_{L7}\right)` | +--------+----------------------+----------+------------------------------------------------------------------------------------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | | +--------+----------------------+----------+------------------------------------------------------------------------------------------+ | tm2 | :math:`\tau_{m2}` | ExtAlgeb | | +--------+----------------------+----------+------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+----------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+==================================+=============+ | LL_x | :math:`x'_{LL}` | State | :math:`\omega_{dev} - x'_{LL}` | :math:`T_1` | +--------+-----------------+----------+----------------------------------+-------------+ | IAW_y | :math:`y_{IAW}` | State | :math:`V_{sl}` | :math:`1` | +--------+-----------------+----------+----------------------------------+-------------+ | L4_y | :math:`y_{L4}` | State | :math:`y_{IAW} - y_{L4}` | :math:`T_4` | +--------+-----------------+----------+----------------------------------+-------------+ | L5_y | :math:`y_{L5}` | State | :math:`y_{L4} - y_{L5}` | :math:`T_5` | +--------+-----------------+----------+----------------------------------+-------------+ | L6_y | :math:`y_{L6}` | State | :math:`y_{L5} - y_{L6}` | :math:`T_6` | +--------+-----------------+----------+----------------------------------+-------------+ | L7_y | :math:`y_{L7}` | State | :math:`y_{L6} - y_{L7}` | :math:`T_7` | +--------+-----------------+----------+----------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+----------------------------------+-------------+ Algebraic Equations ----------------------------- +-------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=======+======================+==========+==================================================================================================================================================+ | paux | :math:`P_{aux}` | Algeb | :math:`P_{aux0} - P_{aux}` | +-------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------+ | pout | :math:`P_{out}` | Algeb | :math:`P_{HP} u_{e} - P_{out}` | +-------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------+ | wref | :math:`\omega_{ref}` | Algeb | :math:`\omega_{ref0} - \omega_{ref}` | +-------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------+ | wd | :math:`\omega_{dev}` | Algeb | :math:`- \omega_{dev} + u_{e} \left(- \omega + \omega_{ref}\right)` | +-------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`y_{LL}` | Algeb | :math:`K T_{1} x'_{LL} + K T_{2} \left(\omega_{dev} - x'_{LL}\right) + LL_{LT1 z1} LL_{LT2 z1} \left(- K x'_{LL} + y_{LL}\right) - T_{1} y_{LL}` | +-------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------+ | vs | :math:`V_{s}` | Algeb | :math:`- V_{s} + \frac{u_{e} \left(P_{aux} + tm_{012} - y_{IAW} + y_{LL}\right)}{T_{3}}` | +-------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------+ | vsl | :math:`V_{sl}` | Algeb | :math:`U_{c} z_{l}^{HL} + U_{o} z_{u}^{HL} + V_{s} z_{i}^{HL} - V_{sl}` | +-------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------+ | PHP | :math:`P_{HP}` | Algeb | :math:`- P_{HP} + u_{e} \left(K_{1n} y_{L4} + K_{3n} y_{L5} + K_{5n} y_{L6} + K_{7n} y_{L7}\right)` | +-------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------+ | PLP | :math:`P_{LP}` | Algeb | :math:`- P_{LP} + u_{e} \left(K_{2n} y_{L4} + K_{4n} y_{L5} + K_{6n} y_{L6} + K_{8n} y_{L7}\right)` | +-------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | :math:`u_{e} \left(P_{out} - \tau_{m0}\right)` | +-------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------+ | tm2 | :math:`\tau_{m2}` | ExtAlgeb | :math:`u_{e} z_{syn2} \left(P_{LP} - \tau_{m02}\right)` | +-------+----------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +----------+--------------------------+---------------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +==========+==========================+===========================================================================+=================+ | ue | :math:`u_{e}` | :math:`u u_{g}` | ConstService | +----------+--------------------------+---------------------------------------------------------------------------+-----------------+ | pref0 | :math:`P_{ref0}` | :math:`\tau_{m0}` | ConstService | +----------+--------------------------+---------------------------------------------------------------------------+-----------------+ | paux0 | :math:`P_{aux0}` | :math:`0` | ConstService | +----------+--------------------------+---------------------------------------------------------------------------+-----------------+ | _sumK18 | :math:`\sum_{i=1}^8 K_i` | :math:`K_{1} + K_{2} + K_{3} + K_{4} + K_{5} + K_{6} + K_{7} + K_{8}` | ConstService | +----------+--------------------------+---------------------------------------------------------------------------+-----------------+ | _Kcoeff | :math:`K_{coeff}` | :math:`\frac{1}{\sum_{i=1}^8 K_i}` | ConstService | +----------+--------------------------+---------------------------------------------------------------------------+-----------------+ | K1n | :math:`K_{1n}` | :math:`K_{1} K_{coeff}` | ConstService | +----------+--------------------------+---------------------------------------------------------------------------+-----------------+ | K2n | :math:`K_{2n}` | :math:`K_{2} K_{coeff}` | ConstService | +----------+--------------------------+---------------------------------------------------------------------------+-----------------+ | K3n | :math:`K_{3n}` | :math:`K_{3} K_{coeff}` | ConstService | +----------+--------------------------+---------------------------------------------------------------------------+-----------------+ | K4n | :math:`K_{4n}` | :math:`K_{4} K_{coeff}` | ConstService | +----------+--------------------------+---------------------------------------------------------------------------+-----------------+ | K5n | :math:`K_{5n}` | :math:`K_{5} K_{coeff}` | ConstService | +----------+--------------------------+---------------------------------------------------------------------------+-----------------+ | K6n | :math:`K_{6n}` | :math:`K_{6} K_{coeff}` | ConstService | +----------+--------------------------+---------------------------------------------------------------------------+-----------------+ | K7n | :math:`K_{7n}` | :math:`K_{7} K_{coeff}` | ConstService | +----------+--------------------------+---------------------------------------------------------------------------+-----------------+ | K8n | :math:`K_{8n}` | :math:`K_{8} K_{coeff}` | ConstService | +----------+--------------------------+---------------------------------------------------------------------------+-----------------+ | _tm0K2 | :math:`_tm0K2` | :math:`\tau_{m0} z_{syn2} \left(K_{2n} + K_{4n} + K_{6n} + K_{8n}\right)` | PostInitService | +----------+--------------------------+---------------------------------------------------------------------------+-----------------+ | _tm02K1 | :math:`_tm02K1` | :math:`\tau_{m02} \left(K_{1n} + K_{3n} + K_{5n} + K_{7n}\right)` | PostInitService | +----------+--------------------------+---------------------------------------------------------------------------+-----------------+ | tm012 | :math:`tm012` | :math:`\tau_{m02} + \tau_{m0}` | ConstService | +----------+--------------------------+---------------------------------------------------------------------------+-----------------+ Discretes ----------- +----------+-------------------+-------------+------------------------+ | Name | Symbol | Type | Info | +==========+===================+=============+========================+ | LL_LT1 | :math:`LT_{LL}` | LessThan | | +----------+-------------------+-------------+------------------------+ | LL_LT2 | :math:`LT_{LL}` | LessThan | | +----------+-------------------+-------------+------------------------+ | HL | :math:`HL` | HardLimiter | Limiter on valve speed | +----------+-------------------+-------------+------------------------+ | IAW_lim | :math:`lim_{IAW}` | AntiWindup | Limiter in integrator | +----------+-------------------+-------------+------------------------+ Blocks ------- +------+-------------+----------------------+--------------------------------+ | Name | Symbol | Type | Info | +======+=============+======================+================================+ | LL | :math:`LL` | LeadLag | Signal conditioning for wd | +------+-------------+----------------------+--------------------------------+ | IAW | :math:`IAW` | IntegratorAntiWindup | Valve position integrator | +------+-------------+----------------------+--------------------------------+ | L4 | :math:`L4` | Lag | first process | +------+-------------+----------------------+--------------------------------+ | L5 | :math:`L5` | Lag | second (reheat) process | +------+-------------+----------------------+--------------------------------+ | L6 | :math:`L6` | Lag | third process | +------+-------------+----------------------+--------------------------------+ | L7 | :math:`L7` | Lag | fourth (second reheat) process | +------+-------------+----------------------+--------------------------------+ Config Fields in [IEEEG1] +---------------+--------+-------+---------------------------------------+-----------------+ | 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) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _IEESGO: -------------------------------------------------------------------------------- IEESGO -------------------------------------------------------------------------------- IEEE Standard Governor (IEESGO). 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,unique | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Tn | :math:`T_n` | Turbine power rating. Equal to `Sn` if not provided. | 0 | *MVA* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | wref0 | :math:`\omega_{ref0}` | Base speed reference | 1 | *p.u.* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | T1 | :math:`T_1` | Controller lag | 0.020 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | T2 | :math:`T_2` | Lead compensation | 1 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | T3 | :math:`T_3` | Governor lag | 1 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | T4 | :math:`T_4` | Steam inlet delay | 0.500 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | T5 | :math:`T_5` | Reheater delay | 10 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | T6 | :math:`T_6` | Crossover delay | 0.500 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | K1 | :math:`K_1` | 1/pu regulation | 0.020 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | K2 | :math:`K_2` | fraction K2 | 1 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | K3 | :math:`K_3` | fraction K3 | 1 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | PMAX | :math:`P_{MAX}` | Max. turbine power | 5 | | power | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | PMIN | :math:`P_{MIN}` | Min. turbine power | 0 | | power | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Sg | :math:`S_n` | Rated power from generator | 0 | *MVA* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | ug | :math:`u_g` | Generator connection status | 0 | *bool* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Vn | :math:`V_n` | Rated voltage from generator | 0 | *kV* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ Variables --------- +--------+----------------------+----------+--------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +========+======================+==========+======================================+========+============+ | F1_y | :math:`y_{F1}` | State | State in lag transfer function | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | F2_x | :math:`x'_{F2}` | State | State in lead-lag | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | F3_y | :math:`y_{F3}` | State | State in lag transfer function | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | F4_y | :math:`y_{F4}` | State | State in lag transfer function | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | F5_y | :math:`y_{F5}` | State | State in lag transfer function | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | *p.u.* | | +--------+----------------------+----------+--------------------------------------+--------+------------+ | paux | :math:`P_{aux}` | Algeb | Auxiliary power input | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | pout | :math:`P_{out}` | Algeb | Turbine final output power | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | wref | :math:`\omega_{ref}` | Algeb | Speed reference variable | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | F2_y | :math:`y_{F2}` | Algeb | Output of lead-lag | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | HL_x | :math:`x_{HL}` | Algeb | Value before limiter | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | HL_y | :math:`y_{HL}` | Algeb | Output after limiter and post gain | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | Mechanical power interface to SynGen | | | +--------+----------------------+----------+--------------------------------------+--------+------------+ Initialization Equations ------------------------ +--------+----------------------+----------+------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +========+======================+==========+====================================================================================+ | F1_y | :math:`y_{F1}` | State | :math:`K_{1} u_{e} \left(\omega - \omega_{ref}\right)` | +--------+----------------------+----------+------------------------------------------------------------------------------------+ | F2_x | :math:`x'_{F2}` | State | :math:`y_{F1}` | +--------+----------------------+----------+------------------------------------------------------------------------------------+ | F3_y | :math:`y_{F3}` | State | :math:`1.0 y_{HL}` | +--------+----------------------+----------+------------------------------------------------------------------------------------+ | F4_y | :math:`y_{F4}` | State | :math:`K_{2} y_{F3}` | +--------+----------------------+----------+------------------------------------------------------------------------------------+ | F5_y | :math:`y_{F5}` | State | :math:`K_{3} y_{F4}` | +--------+----------------------+----------+------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +--------+----------------------+----------+------------------------------------------------------------------------------------+ | paux | :math:`P_{aux}` | Algeb | :math:`P_{aux0}` | +--------+----------------------+----------+------------------------------------------------------------------------------------+ | pout | :math:`P_{out}` | Algeb | :math:`\tau_{m0} u_{e}` | +--------+----------------------+----------+------------------------------------------------------------------------------------+ | wref | :math:`\omega_{ref}` | Algeb | :math:`\omega_{ref0}` | +--------+----------------------+----------+------------------------------------------------------------------------------------+ | F2_y | :math:`y_{F2}` | Algeb | :math:`y_{F1}` | +--------+----------------------+----------+------------------------------------------------------------------------------------+ | HL_x | :math:`x_{HL}` | Algeb | :math:`1.0 u_{e} \left(P_{aux} + P_{ref0} - y_{F2}\right)` | +--------+----------------------+----------+------------------------------------------------------------------------------------+ | HL_y | :math:`y_{HL}` | Algeb | :math:`1.0 HL_{lim zi} x_{HL} + 1.0 HL_{lim zl} P_{MIN} + 1.0 HL_{lim zu} P_{MAX}` | +--------+----------------------+----------+------------------------------------------------------------------------------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | | +--------+----------------------+----------+------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+-----------------------------------------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+=================================================================+=============+ | F1_y | :math:`y_{F1}` | State | :math:`K_{1} u_{e} \left(\omega - \omega_{ref}\right) - y_{F1}` | :math:`T_1` | +--------+-----------------+----------+-----------------------------------------------------------------+-------------+ | F2_x | :math:`x'_{F2}` | State | :math:`- x'_{F2} + y_{F1}` | :math:`T_3` | +--------+-----------------+----------+-----------------------------------------------------------------+-------------+ | F3_y | :math:`y_{F3}` | State | :math:`- y_{F3} + 1.0 y_{HL}` | :math:`T_4` | +--------+-----------------+----------+-----------------------------------------------------------------+-------------+ | F4_y | :math:`y_{F4}` | State | :math:`K_{2} y_{F3} - y_{F4}` | :math:`T_5` | +--------+-----------------+----------+-----------------------------------------------------------------+-------------+ | F5_y | :math:`y_{F5}` | State | :math:`K_{3} y_{F4} - y_{F5}` | :math:`T_6` | +--------+-----------------+----------+-----------------------------------------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+-----------------------------------------------------------------+-------------+ Algebraic Equations ----------------------------- +-------+----------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=======+======================+==========+======================================================================================================================================================+ | paux | :math:`P_{aux}` | Algeb | :math:`P_{aux0} - P_{aux}` | +-------+----------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | pout | :math:`P_{out}` | Algeb | :math:`- P_{out} + u_{e} \left(y_{F3} \cdot \left(1 - K_{2}\right) + y_{F4} \cdot \left(1 - K_{3}\right) + y_{F5}\right)` | +-------+----------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | wref | :math:`\omega_{ref}` | Algeb | :math:`\omega_{ref0} - \omega_{ref}` | +-------+----------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | F2_y | :math:`y_{F2}` | Algeb | :math:`F_{2 LT1 z1} F_{2 LT2 z1} \left(- 1.0 x'_{F2} + y_{F2}\right) + 1.0 T_{2} \left(- x'_{F2} + y_{F1}\right) + 1.0 T_{3} x'_{F2} - T_{3} y_{F2}` | +-------+----------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | HL_x | :math:`x_{HL}` | Algeb | :math:`1.0 u_{e} \left(P_{aux} + P_{ref0} - y_{F2}\right) - x_{HL}` | +-------+----------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | HL_y | :math:`y_{HL}` | Algeb | :math:`1.0 HL_{lim zi} x_{HL} + 1.0 HL_{lim zl} P_{MIN} + 1.0 HL_{lim zu} P_{MAX} - y_{HL}` | +-------+----------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | :math:`u_{e} \left(P_{out} - \tau_{m0}\right)` | +-------+----------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +--------+------------------+-------------------+--------------+ | Name | Symbol | Equation | Type | +========+==================+===================+==============+ | ue | :math:`u_{e}` | :math:`u u_{g}` | ConstService | +--------+------------------+-------------------+--------------+ | pref0 | :math:`P_{ref0}` | :math:`\tau_{m0}` | ConstService | +--------+------------------+-------------------+--------------+ | paux0 | :math:`P_{aux0}` | :math:`0` | ConstService | +--------+------------------+-------------------+--------------+ Discretes ----------- +---------+------------------+-------------+------+ | Name | Symbol | Type | Info | +=========+==================+=============+======+ | F2_LT1 | :math:`LT_{F2}` | LessThan | | +---------+------------------+-------------+------+ | F2_LT2 | :math:`LT_{F2}` | LessThan | | +---------+------------------+-------------+------+ | HL_lim | :math:`lim_{HL}` | HardLimiter | | +---------+------------------+-------------+------+ Blocks ------- +------+------------+-------------+------+ | Name | Symbol | Type | Info | +======+============+=============+======+ | F1 | :math:`F1` | Lag | | +------+------------+-------------+------+ | F2 | :math:`F2` | LeadLag | | +------+------------+-------------+------+ | HL | :math:`HL` | GainLimiter | | +------+------------+-------------+------+ | F3 | :math:`F3` | Lag | | +------+------------+-------------+------+ | F4 | :math:`F4` | Lag | | +------+------------+-------------+------+ | F5 | :math:`F5` | Lag | | +------+------------+-------------+------+ Config Fields in [IEESGO] +---------------+--------+-------+---------------------------------------+-----------------+ | 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) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _GAST: -------------------------------------------------------------------------------- GAST -------------------------------------------------------------------------------- GAST turbine governor model. Reference: [1] Neplan, TURBINE-GOVERNOR GAST, [Online], Available: https://www.neplan.ch/wp-content/uploads/2015/08/Nep_TURBINES_GOV.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,unique | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Tn | :math:`T_n` | Turbine power rating. Equal to `Sn` if not provided. | 0 | *MVA* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | wref0 | :math:`\omega_{ref0}` | Base speed reference | 1 | *p.u.* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | R | :math:`R` | Speed regulation gain (mach. base default) | 0.050 | *p.u.* | ipower | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | VMAX | :math:`V_{max}` | Maximum valve position | 1.200 | *p.u.* | power | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | VMIN | :math:`V_{min}` | Minimum valve position | 0 | *p.u.* | power | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | KT | :math:`K_T` | Temperature limiter gain | 5 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | AT | :math:`A_T` | Ambient temperature load limit | 1 | | power | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | T1 | :math:`T_1` | Valve time constant | 0.100 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | T2 | :math:`T_2` | Lead-lag lead time constant | 0.200 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | T3 | :math:`T_3` | Lead-lag lag time constant | 10 | | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Dt | :math:`D_t` | Turbine damping coefficient | 0 | | power | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Sg | :math:`S_n` | Rated power from generator | 0 | *MVA* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | ug | :math:`u_g` | Generator connection status | 0 | *bool* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Vn | :math:`V_n` | Rated voltage from generator | 0 | *kV* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ Variables --------- +--------+----------------------+----------+--------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +========+======================+==========+======================================+========+============+ | LAG_y | :math:`y_{LAG}` | State | State in lag TF | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | LG2_y | :math:`y_{LG2}` | State | State in lag transfer function | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | LG3_y | :math:`y_{LG3}` | State | State in lag transfer function | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | *p.u.* | | +--------+----------------------+----------+--------------------------------------+--------+------------+ | paux | :math:`P_{aux}` | Algeb | Auxiliary power input | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | pout | :math:`P_{out}` | Algeb | Turbine final output power | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | wref | :math:`\omega_{ref}` | Algeb | Speed reference variable | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | pref | :math:`P_{ref}` | Algeb | Reference power input | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | wd | :math:`\omega_{dev}` | Algeb | Generator under speed | *p.u.* | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | pd | :math:`P_{d}` | Algeb | Pref plus under speed times gain | *p.u.* | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | v9 | :math:`V_{9}` | Algeb | V_9 for LVGate input | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | LVG_y | :math:`y_{LVG}` | Algeb | LVGate output | | v_str | +--------+----------------------+----------+--------------------------------------+--------+------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | Mechanical power interface to SynGen | | | +--------+----------------------+----------+--------------------------------------+--------+------------+ Initialization Equations ------------------------ +--------+----------------------+----------+-------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +========+======================+==========+=========================================================================+ | LAG_y | :math:`y_{LAG}` | State | :math:`y_{LVG}` | +--------+----------------------+----------+-------------------------------------------------------------------------+ | LG2_y | :math:`y_{LG2}` | State | :math:`y_{LAG}` | +--------+----------------------+----------+-------------------------------------------------------------------------+ | LG3_y | :math:`y_{LG3}` | State | :math:`y_{LG2}` | +--------+----------------------+----------+-------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +--------+----------------------+----------+-------------------------------------------------------------------------+ | paux | :math:`P_{aux}` | Algeb | :math:`P_{aux0}` | +--------+----------------------+----------+-------------------------------------------------------------------------+ | pout | :math:`P_{out}` | Algeb | :math:`\tau_{m0} u_{e}` | +--------+----------------------+----------+-------------------------------------------------------------------------+ | wref | :math:`\omega_{ref}` | Algeb | :math:`\omega_{ref0}` | +--------+----------------------+----------+-------------------------------------------------------------------------+ | pref | :math:`P_{ref}` | Algeb | :math:`R \tau_{m0}` | +--------+----------------------+----------+-------------------------------------------------------------------------+ | wd | :math:`\omega_{dev}` | Algeb | :math:`0` | +--------+----------------------+----------+-------------------------------------------------------------------------+ | pd | :math:`P_{d}` | Algeb | :math:`\tau_{m0} u_{e}` | +--------+----------------------+----------+-------------------------------------------------------------------------+ | v9 | :math:`V_{9}` | Algeb | :math:`u_{e} \left(A_{T} + K_{T} \left(A_{T} - \tau_{m0}\right)\right)` | +--------+----------------------+----------+-------------------------------------------------------------------------+ | LVG_y | :math:`y_{LVG}` | Algeb | :math:`LVG_{lt z0} V_{9} + LVG_{lt z1} P_{d}` | +--------+----------------------+----------+-------------------------------------------------------------------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | | +--------+----------------------+----------+-------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+----------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+==================================+=============+ | LAG_y | :math:`y_{LAG}` | State | :math:`- y_{LAG} + y_{LVG}` | :math:`T_1` | +--------+-----------------+----------+----------------------------------+-------------+ | LG2_y | :math:`y_{LG2}` | State | :math:`y_{LAG} - y_{LG2}` | :math:`T_2` | +--------+-----------------+----------+----------------------------------+-------------+ | LG3_y | :math:`y_{LG3}` | State | :math:`y_{LG2} - y_{LG3}` | :math:`T_3` | +--------+-----------------+----------+----------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+----------------------------------+-------------+ Algebraic Equations ----------------------------- +--------+----------------------+----------+---------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +========+======================+==========+=================================================================================+ | paux | :math:`P_{aux}` | Algeb | :math:`P_{aux0} - P_{aux}` | +--------+----------------------+----------+---------------------------------------------------------------------------------+ | pout | :math:`P_{out}` | Algeb | :math:`- P_{out} + u_{e} \left(- D_{t} \omega_{dev} + y_{LG2}\right)` | +--------+----------------------+----------+---------------------------------------------------------------------------------+ | wref | :math:`\omega_{ref}` | Algeb | :math:`\omega_{ref0} - \omega_{ref}` | +--------+----------------------+----------+---------------------------------------------------------------------------------+ | pref | :math:`P_{ref}` | Algeb | :math:`P_{ref0} R - P_{ref}` | +--------+----------------------+----------+---------------------------------------------------------------------------------+ | wd | :math:`\omega_{dev}` | Algeb | :math:`- \omega_{dev} + u_{e} \left(\omega - \omega_{ref}\right)` | +--------+----------------------+----------+---------------------------------------------------------------------------------+ | pd | :math:`P_{d}` | Algeb | :math:`G u_{e} \left(P_{aux} + P_{ref} - \omega_{dev}\right) - P_{d}` | +--------+----------------------+----------+---------------------------------------------------------------------------------+ | v9 | :math:`V_{9}` | Algeb | :math:`- V_{9} + u_{e} \left(A_{T} + K_{T} \left(A_{T} - y_{LG3}\right)\right)` | +--------+----------------------+----------+---------------------------------------------------------------------------------+ | LVG_y | :math:`y_{LVG}` | Algeb | :math:`LVG_{lt z0} V_{9} + LVG_{lt z1} P_{d} - y_{LVG}` | +--------+----------------------+----------+---------------------------------------------------------------------------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | :math:`u_{e} \left(P_{out} - \tau_{m0}\right)` | +--------+----------------------+----------+---------------------------------------------------------------------------------+ Services ---------- +--------+------------------+-------------------------+--------------+ | Name | Symbol | Equation | Type | +========+==================+=========================+==============+ | ue | :math:`u_{e}` | :math:`u u_{g}` | ConstService | +--------+------------------+-------------------------+--------------+ | pref0 | :math:`P_{ref0}` | :math:`\tau_{m0}` | ConstService | +--------+------------------+-------------------------+--------------+ | paux0 | :math:`P_{aux0}` | :math:`0` | ConstService | +--------+------------------+-------------------------+--------------+ | gain | :math:`G` | :math:`\frac{u_{e}}{R}` | ConstService | +--------+------------------+-------------------------+--------------+ Discretes ----------- +----------+--------------------+------------+----------------+ | Name | Symbol | Type | Info | +==========+====================+============+================+ | LVG_lt | :math:`None_{LVG}` | LessThan | | +----------+--------------------+------------+----------------+ | LAG_lim | :math:`lim_{LAG}` | AntiWindup | Limiter in Lag | +----------+--------------------+------------+----------------+ Blocks ------- +------+-------------+---------------+--------+ | Name | Symbol | Type | Info | +======+=============+===============+========+ | LVG | :math:`LVG` | LVGate | LVGate | +------+-------------+---------------+--------+ | LAG | :math:`LAG` | LagAntiWindup | | +------+-------------+---------------+--------+ | LG2 | :math:`LG2` | Lag | Lag T2 | +------+-------------+---------------+--------+ | LG3 | :math:`LG3` | Lag | Lag T3 | +------+-------------+---------------+--------+ Config Fields in [GAST] +---------------+--------+-------+---------------------------------------+-----------------+ | 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) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _HYGOV: -------------------------------------------------------------------------------- HYGOV -------------------------------------------------------------------------------- HYGOV turbine governor model. Implements the PSS/E HYGOV model without deadband. Reference: [1] PSSE, Model Library, HYGOV 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,unique | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | Tn | :math:`T_n` | Turbine power rating. Equal to `Sn` if not provided. | 0 | *MVA* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | wref0 | :math:`\omega_{ref0}` | Base speed reference | 1 | *p.u.* | | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | R | :math:`R` | Speed regulation gain (mach. base default) | 0.050 | *p.u.* | ipower | +--------+-----------------------+------------------------------------------------------+---------+--------+------------------+ | r | :math:`r` | Temporary droop (R