.. _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:`ll_{x}` | State | State in lead-lag | | v_str | +--------+-----------------+----------+-----------------------------------------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | *p.u.* | | +--------+-----------------+----------+-----------------------------------------------------------------------+--------+------------+ | paux | :math:`paux` | Algeb | Auxiliary power input | | v_str | +--------+-----------------+----------+-----------------------------------------------------------------------+--------+------------+ | pout | :math:`pout` | Algeb | Turbine final output power | | v_str | +--------+-----------------+----------+-----------------------------------------------------------------------+--------+------------+ | wref | :math:`wref` | Algeb | Speed reference variable | | v_str | +--------+-----------------+----------+-----------------------------------------------------------------------+--------+------------+ | w_d | :math:`w_{d}` | Algeb | Generator speed deviation before dead band (positive for under speed) | | v_str | +--------+-----------------+----------+-----------------------------------------------------------------------+--------+------------+ | w_dm | :math:`w_{dm}` | Algeb | Measured speed deviation after dead band | | v_str | +--------+-----------------+----------+-----------------------------------------------------------------------+--------+------------+ | w_dmg | :math:`w_{dmg}` | Algeb | Speed deviation after dead band after gain | | v_str | +--------+-----------------+----------+-----------------------------------------------------------------------+--------+------------+ | ll_y | :math:`ll_{y}` | Algeb | Output of lead-lag | | v_str | +--------+-----------------+----------+-----------------------------------------------------------------------+--------+------------+ | pnl | :math:`pnl` | Algeb | Power output before hard limiter | | v_str | +--------+-----------------+----------+-----------------------------------------------------------------------+--------+------------+ | tm | :math:`tm` | ExtAlgeb | Mechanical power interface to SynGen | | | +--------+-----------------+----------+-----------------------------------------------------------------------+--------+------------+ Initialization Equations ------------------------ +--------+-----------------+----------+-------------------+ | Name | Symbol | Type | Initial Value | +========+=================+==========+===================+ | ll_x | :math:`ll_{x}` | State | :math:`w_{dmg}` | +--------+-----------------+----------+-------------------+ | omega | :math:`\omega` | ExtState | | +--------+-----------------+----------+-------------------+ | paux | :math:`paux` | Algeb | :math:`paux_{0}` | +--------+-----------------+----------+-------------------+ | pout | :math:`pout` | Algeb | :math:`tm_{0} ue` | +--------+-----------------+----------+-------------------+ | wref | :math:`wref` | Algeb | :math:`wref_{0}` | +--------+-----------------+----------+-------------------+ | w_d | :math:`w_{d}` | Algeb | :math:`0` | +--------+-----------------+----------+-------------------+ | w_dm | :math:`w_{dm}` | Algeb | :math:`0` | +--------+-----------------+----------+-------------------+ | w_dmg | :math:`w_{dmg}` | Algeb | :math:`0` | +--------+-----------------+----------+-------------------+ | ll_y | :math:`ll_{y}` | Algeb | :math:`w_{dmg}` | +--------+-----------------+----------+-------------------+ | pnl | :math:`pnl` | Algeb | :math:`tm_{0}` | +--------+-----------------+----------+-------------------+ | tm | :math:`tm` | ExtAlgeb | | +--------+-----------------+----------+-------------------+ Differential Equations ----------------------------- +--------+----------------+----------+----------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+================+==========+==================================+=============+ | ll_x | :math:`ll_{x}` | State | :math:`- ll_{x} + w_{dmg}` | :math:`T_2` | +--------+----------------+----------+----------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+----------------+----------+----------------------------------+-------------+ Algebraic Equations ----------------------------- +--------+-----------------+----------+--------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +========+=================+==========+======================================================================================================================================+ | paux | :math:`paux` | Algeb | :math:`- paux + paux_{0}` | +--------+-----------------+----------+--------------------------------------------------------------------------------------------------------------------------------------+ | pout | :math:`pout` | Algeb | :math:`plim_{zi} pnl + plim_{zl} pmin + plim_{zu} pmax - pout` | +--------+-----------------+----------+--------------------------------------------------------------------------------------------------------------------------------------+ | wref | :math:`wref` | Algeb | :math:`- wref + wref_{0}` | +--------+-----------------+----------+--------------------------------------------------------------------------------------------------------------------------------------+ | w_d | :math:`w_{d}` | Algeb | :math:`ue \left(- \omega + wref\right) - w_{d}` | +--------+-----------------+----------+--------------------------------------------------------------------------------------------------------------------------------------+ | w_dm | :math:`w_{dm}` | Algeb | :math:`dbl w_{db zlr} + dbu w_{db zur} + w_{d} \left(1 - w_{db zi}\right) - w_{dm}` | +--------+-----------------+----------+--------------------------------------------------------------------------------------------------------------------------------------+ | w_dmg | :math:`w_{dmg}` | Algeb | :math:`gain w_{dm} - w_{dmg}` | +--------+-----------------+----------+--------------------------------------------------------------------------------------------------------------------------------------+ | ll_y | :math:`ll_{y}` | Algeb | :math:`T_{1} \left(- ll_{x} + w_{dmg}\right) + T_{2} ll_{x} - T_{2} ll_{y} + ll_{LT1 z1} ll_{LT2 z1} \left(- ll_{x} + ll_{y}\right)` | +--------+-----------------+----------+--------------------------------------------------------------------------------------------------------------------------------------+ | pnl | :math:`pnl` | Algeb | :math:`ll_{y} - pnl + pref_{0}` | +--------+-----------------+----------+--------------------------------------------------------------------------------------------------------------------------------------+ | tm | :math:`tm` | ExtAlgeb | :math:`ue \left(pout - tm_{0}\right)` | +--------+-----------------+----------+--------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +--------+------------------+---------------------+--------------+ | Name | Symbol | Equation | Type | +========+==================+=====================+==============+ | ue | :math:`u_{e}` | :math:`u ug` | ConstService | +--------+------------------+---------------------+--------------+ | pref0 | :math:`P_{ref0}` | :math:`tm_{0}` | 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:`LAG_{y}` | State | State in lag TF | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | LL_x | :math:`LL_{x}` | State | State in lead-lag | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | *p.u.* | | +--------+-----------------+----------+--------------------------------------+--------+------------+ | paux | :math:`paux` | Algeb | Auxiliary power input | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | pout | :math:`pout` | Algeb | Turbine final output power | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | wref | :math:`wref` | Algeb | Speed reference variable | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | pref | :math:`pref` | Algeb | Reference power input | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | wd | :math:`wd` | Algeb | Generator speed deviation | *p.u.* | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | pd | :math:`pd` | Algeb | Pref plus speed deviation times gain | *p.u.* | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | LL_y | :math:`LL_{y}` | Algeb | Output of lead-lag | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | tm | :math:`tm` | ExtAlgeb | Mechanical power interface to SynGen | | | +--------+-----------------+----------+--------------------------------------+--------+------------+ Initialization Equations ------------------------ +--------+-----------------+----------+-------------------+ | Name | Symbol | Type | Initial Value | +========+=================+==========+===================+ | LAG_y | :math:`LAG_{y}` | State | :math:`pd` | +--------+-----------------+----------+-------------------+ | LL_x | :math:`LL_{x}` | State | :math:`LAG_{y}` | +--------+-----------------+----------+-------------------+ | omega | :math:`\omega` | ExtState | | +--------+-----------------+----------+-------------------+ | paux | :math:`paux` | Algeb | :math:`paux_{0}` | +--------+-----------------+----------+-------------------+ | pout | :math:`pout` | Algeb | :math:`tm_{0} ue` | +--------+-----------------+----------+-------------------+ | wref | :math:`wref` | Algeb | :math:`wref_{0}` | +--------+-----------------+----------+-------------------+ | pref | :math:`pref` | Algeb | :math:`R tm_{0}` | +--------+-----------------+----------+-------------------+ | wd | :math:`wd` | Algeb | :math:`0` | +--------+-----------------+----------+-------------------+ | pd | :math:`pd` | Algeb | :math:`tm_{0} ue` | +--------+-----------------+----------+-------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`LAG_{y}` | +--------+-----------------+----------+-------------------+ | tm | :math:`tm` | ExtAlgeb | | +--------+-----------------+----------+-------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+----------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+==================================+=============+ | LAG_y | :math:`LAG_{y}` | State | :math:`- LAG_{y} + pd` | :math:`T_1` | +--------+-----------------+----------+----------------------------------+-------------+ | LL_x | :math:`LL_{x}` | State | :math:`LAG_{y} - LL_{x}` | :math:`T_3` | +--------+-----------------+----------+----------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+----------------------------------+-------------+ Algebraic Equations ----------------------------- +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=======+================+==========+====================================================================================================================================+ | paux | :math:`paux` | Algeb | :math:`- paux + paux_{0}` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | pout | :math:`pout` | Algeb | :math:`- pout + ue \left(- Dt wd + LL_{y}\right)` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | wref | :math:`wref` | Algeb | :math:`- wref + wref_{0}` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | pref | :math:`pref` | Algeb | :math:`R pref_{0} - pref` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | wd | :math:`wd` | Algeb | :math:`ue \left(\omega - wref\right) - wd` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | pd | :math:`pd` | Algeb | :math:`gain ue \left(paux + pref - wd\right) - pd` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- LL_{x} + LL_{y}\right) + LL_{x} T_{3} - LL_{y} T_{3} + T_{2} \left(LAG_{y} - LL_{x}\right)` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | tm | :math:`tm` | ExtAlgeb | :math:`ue \left(pout - tm_{0}\right)` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +--------+------------------+----------------------+--------------+ | Name | Symbol | Equation | Type | +========+==================+======================+==============+ | ue | :math:`u_{e}` | :math:`u ug` | ConstService | +--------+------------------+----------------------+--------------+ | pref0 | :math:`P_{ref0}` | :math:`tm_{0}` | ConstService | +--------+------------------+----------------------+--------------+ | paux0 | :math:`P_{aux0}` | :math:`0` | ConstService | +--------+------------------+----------------------+--------------+ | gain | :math:`G` | :math:`\frac{ue}{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:`LAG_{y}` | State | State in lag TF | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | LL_x | :math:`LL_{x}` | State | State in lead-lag | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | *p.u.* | | +--------+-----------------+----------+--------------------------------------+--------+------------+ | paux | :math:`paux` | Algeb | Auxiliary power input | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | pout | :math:`pout` | Algeb | Turbine final output power | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | wref | :math:`wref` | Algeb | Speed reference variable | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | pref | :math:`pref` | Algeb | Reference power input | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | wd | :math:`wd` | Algeb | Generator speed deviation | *p.u.* | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | pd | :math:`pd` | Algeb | Pref plus speed deviation times gain | *p.u.* | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | LL_y | :math:`LL_{y}` | Algeb | Output of lead-lag | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | DB_y | :math:`DB_{y}` | Algeb | Deadband type 1 output | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | tm | :math:`tm` | ExtAlgeb | Mechanical power interface to SynGen | | | +--------+-----------------+----------+--------------------------------------+--------+------------+ Initialization Equations ------------------------ +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +========+=================+==========+=========================================================================================+ | LAG_y | :math:`LAG_{y}` | State | :math:`pd` | +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ | LL_x | :math:`LL_{x}` | State | :math:`LAG_{y}` | +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ | paux | :math:`paux` | Algeb | :math:`paux_{0}` | +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ | pout | :math:`pout` | Algeb | :math:`tm_{0} ue` | +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ | wref | :math:`wref` | Algeb | :math:`wref_{0}` | +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ | pref | :math:`pref` | Algeb | :math:`R tm_{0}` | +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ | wd | :math:`wd` | Algeb | :math:`0` | +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ | pd | :math:`pd` | Algeb | :math:`tm_{0} ue` | +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`LAG_{y}` | +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ | DB_y | :math:`DB_{y}` | Algeb | :math:`1.0 DB_{db zl} \left(- dbL + wd\right) + 1.0 DB_{db zu} \left(- dbU + wd\right)` | +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ | tm | :math:`tm` | ExtAlgeb | | +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+----------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+==================================+=============+ | LAG_y | :math:`LAG_{y}` | State | :math:`- LAG_{y} + pd` | :math:`T_1` | +--------+-----------------+----------+----------------------------------+-------------+ | LL_x | :math:`LL_{x}` | State | :math:`LAG_{y} - LL_{x}` | :math:`T_3` | +--------+-----------------+----------+----------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+----------------------------------+-------------+ Algebraic Equations ----------------------------- +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=======+================+==========+====================================================================================================================================+ | paux | :math:`paux` | Algeb | :math:`- paux + paux_{0}` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | pout | :math:`pout` | Algeb | :math:`- DB_{y} Dt + LL_{y} - pout` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | wref | :math:`wref` | Algeb | :math:`- wref + wref_{0}` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | pref | :math:`pref` | Algeb | :math:`R pref_{0} - pref` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | wd | :math:`wd` | Algeb | :math:`ue \left(\omega - wref\right) - wd` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | pd | :math:`pd` | Algeb | :math:`gain ue \left(- DB_{y} + paux + pref\right) - pd` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- LL_{x} + LL_{y}\right) + LL_{x} T_{3} - LL_{y} T_{3} + T_{2} \left(LAG_{y} - LL_{x}\right)` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | DB_y | :math:`DB_{y}` | Algeb | :math:`1.0 DB_{db zl} \left(- dbL + wd\right) + 1.0 DB_{db zu} \left(- dbU + wd\right) - DB_{y}` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | tm | :math:`tm` | ExtAlgeb | :math:`ue \left(pout - tm_{0}\right)` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +--------+------------------+----------------------+--------------+ | Name | Symbol | Equation | Type | +========+==================+======================+==============+ | ue | :math:`u_{e}` | :math:`u ug` | ConstService | +--------+------------------+----------------------+--------------+ | pref0 | :math:`P_{ref0}` | :math:`tm_{0}` | ConstService | +--------+------------------+----------------------+--------------+ | paux0 | :math:`P_{aux0}` | :math:`0` | ConstService | +--------+------------------+----------------------+--------------+ | gain | :math:`G` | :math:`\frac{ue}{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:`LAG_{y}` | State | State in lag TF | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | LL_x | :math:`LL_{x}` | State | State in lead-lag | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | *p.u.* | | +--------+-----------------+----------+--------------------------------------+--------+------------+ | paux | :math:`paux` | Algeb | Auxiliary power input | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | pout | :math:`pout` | Algeb | Turbine final output power | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | wref | :math:`wref` | Algeb | Speed reference variable | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | pref | :math:`pref` | Algeb | Reference power input | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | wd | :math:`wd` | Algeb | Generator speed deviation | *p.u.* | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | pd | :math:`pd` | Algeb | Pref plus speed deviation times gain | *p.u.* | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | LL_y | :math:`LL_{y}` | Algeb | Output of lead-lag | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | tm | :math:`tm` | ExtAlgeb | Mechanical power interface to SynGen | | | +--------+-----------------+----------+--------------------------------------+--------+------------+ Initialization Equations ------------------------ +--------+-----------------+----------+-------------------+ | Name | Symbol | Type | Initial Value | +========+=================+==========+===================+ | LAG_y | :math:`LAG_{y}` | State | :math:`pd` | +--------+-----------------+----------+-------------------+ | LL_x | :math:`LL_{x}` | State | :math:`LAG_{y}` | +--------+-----------------+----------+-------------------+ | omega | :math:`\omega` | ExtState | | +--------+-----------------+----------+-------------------+ | paux | :math:`paux` | Algeb | :math:`paux_{0}` | +--------+-----------------+----------+-------------------+ | pout | :math:`pout` | Algeb | :math:`tm_{0} ue` | +--------+-----------------+----------+-------------------+ | wref | :math:`wref` | Algeb | :math:`wref_{0}` | +--------+-----------------+----------+-------------------+ | pref | :math:`pref` | Algeb | :math:`tm_{0}` | +--------+-----------------+----------+-------------------+ | wd | :math:`wd` | Algeb | :math:`0` | +--------+-----------------+----------+-------------------+ | pd | :math:`pd` | Algeb | :math:`tm_{0} ue` | +--------+-----------------+----------+-------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`LAG_{y}` | +--------+-----------------+----------+-------------------+ | tm | :math:`tm` | ExtAlgeb | | +--------+-----------------+----------+-------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+----------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+==================================+=============+ | LAG_y | :math:`LAG_{y}` | State | :math:`- LAG_{y} + pd` | :math:`T_1` | +--------+-----------------+----------+----------------------------------+-------------+ | LL_x | :math:`LL_{x}` | State | :math:`LAG_{y} - LL_{x}` | :math:`T_3` | +--------+-----------------+----------+----------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+----------------------------------+-------------+ Algebraic Equations ----------------------------- +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=======+================+==========+====================================================================================================================================+ | paux | :math:`paux` | Algeb | :math:`- paux + paux_{0}` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | pout | :math:`pout` | Algeb | :math:`- pout + ue \left(- Dt wd + LL_{y}\right)` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | wref | :math:`wref` | Algeb | :math:`- wref + wref_{0}` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | pref | :math:`pref` | Algeb | :math:`- pref + pref_{0}` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | wd | :math:`wd` | Algeb | :math:`ue \left(\omega - wref\right) - wd` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | pd | :math:`pd` | Algeb | :math:`- pd + ue \left(- gain wd + paux + pref\right)` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- LL_{x} + LL_{y}\right) + LL_{x} T_{3} - LL_{y} T_{3} + T_{2} \left(LAG_{y} - LL_{x}\right)` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | tm | :math:`tm` | ExtAlgeb | :math:`ue \left(pout - tm_{0}\right)` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +--------+------------------+----------------------+--------------+ | Name | Symbol | Equation | Type | +========+==================+======================+==============+ | ue | :math:`u_{e}` | :math:`u ug` | ConstService | +--------+------------------+----------------------+--------------+ | pref0 | :math:`P_{ref0}` | :math:`tm_{0}` | ConstService | +--------+------------------+----------------------+--------------+ | paux0 | :math:`P_{aux0}` | :math:`0` | ConstService | +--------+------------------+----------------------+--------------+ | gain | :math:`G` | :math:`\frac{ue}{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:`LAG_{y}` | State | State in lag TF | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | LL_x | :math:`LL_{x}` | State | State in lead-lag | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | *p.u.* | | +--------+-----------------+----------+--------------------------------------+--------+------------+ | paux | :math:`paux` | Algeb | Auxiliary power input | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | pout | :math:`pout` | Algeb | Turbine final output power | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | wref | :math:`wref` | Algeb | Speed reference variable | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | pref | :math:`pref` | Algeb | Reference power input | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | wd | :math:`wd` | Algeb | Generator speed deviation | *p.u.* | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | pd | :math:`pd` | Algeb | Pref plus speed deviation times gain | *p.u.* | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | LL_y | :math:`LL_{y}` | Algeb | Output of lead-lag | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | DB_y | :math:`DB_{y}` | Algeb | Deadband type 1 output | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | tm | :math:`tm` | ExtAlgeb | Mechanical power interface to SynGen | | | +--------+-----------------+----------+--------------------------------------+--------+------------+ Initialization Equations ------------------------ +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +========+=================+==========+=========================================================================================+ | LAG_y | :math:`LAG_{y}` | State | :math:`pd` | +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ | LL_x | :math:`LL_{x}` | State | :math:`LAG_{y}` | +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ | paux | :math:`paux` | Algeb | :math:`paux_{0}` | +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ | pout | :math:`pout` | Algeb | :math:`tm_{0} ue` | +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ | wref | :math:`wref` | Algeb | :math:`wref_{0}` | +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ | pref | :math:`pref` | Algeb | :math:`tm_{0}` | +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ | wd | :math:`wd` | Algeb | :math:`0` | +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ | pd | :math:`pd` | Algeb | :math:`tm_{0} ue` | +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`LAG_{y}` | +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ | DB_y | :math:`DB_{y}` | Algeb | :math:`1.0 DB_{db zl} \left(- dbL + wd\right) + 1.0 DB_{db zu} \left(- dbU + wd\right)` | +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ | tm | :math:`tm` | ExtAlgeb | | +--------+-----------------+----------+-----------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+----------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+==================================+=============+ | LAG_y | :math:`LAG_{y}` | State | :math:`- LAG_{y} + pd` | :math:`T_1` | +--------+-----------------+----------+----------------------------------+-------------+ | LL_x | :math:`LL_{x}` | State | :math:`LAG_{y} - LL_{x}` | :math:`T_3` | +--------+-----------------+----------+----------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+----------------------------------+-------------+ Algebraic Equations ----------------------------- +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=======+================+==========+====================================================================================================================================+ | paux | :math:`paux` | Algeb | :math:`- paux + paux_{0}` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | pout | :math:`pout` | Algeb | :math:`- DB_{y} Dt + LL_{y} - pout` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | wref | :math:`wref` | Algeb | :math:`- wref + wref_{0}` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | pref | :math:`pref` | Algeb | :math:`- pref + pref_{0}` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | wd | :math:`wd` | Algeb | :math:`ue \left(\omega - wref\right) - wd` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | pd | :math:`pd` | Algeb | :math:`- pd + ue \left(DB_{y} gain + paux + pref\right)` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`LL_{LT1 z1} LL_{LT2 z1} \left(- LL_{x} + LL_{y}\right) + LL_{x} T_{3} - LL_{y} T_{3} + T_{2} \left(LAG_{y} - LL_{x}\right)` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | DB_y | :math:`DB_{y}` | Algeb | :math:`1.0 DB_{db zl} \left(- dbL + wd\right) + 1.0 DB_{db zu} \left(- dbU + wd\right) - DB_{y}` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ | tm | :math:`tm` | ExtAlgeb | :math:`ue \left(pout - tm_{0}\right)` | +-------+----------------+----------+------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +--------+------------------+----------------------+--------------+ | Name | Symbol | Equation | Type | +========+==================+======================+==============+ | ue | :math:`u_{e}` | :math:`u ug` | ConstService | +--------+------------------+----------------------+--------------+ | pref0 | :math:`P_{ref0}` | :math:`tm_{0}` | ConstService | +--------+------------------+----------------------+--------------+ | paux0 | :math:`P_{aux0}` | :math:`0` | ConstService | +--------+------------------+----------------------+--------------+ | gain | :math:`G` | :math:`\frac{ue}{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:`LL_{x}` | State | State in lead-lag | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | IAW_y | :math:`IAW_{y}` | State | AW Integrator output | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | L4_y | :math:`L_{4 y}` | State | State in lag transfer function | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | L5_y | :math:`L_{5 y}` | State | State in lag transfer function | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | L6_y | :math:`L_{6 y}` | State | State in lag transfer function | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | L7_y | :math:`L_{7 y}` | State | State in lag transfer function | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | *p.u.* | | +--------+-----------------+----------+--------------------------------------+--------+------------+ | paux | :math:`paux` | Algeb | Auxiliary power input | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | pout | :math:`pout` | Algeb | Turbine final output power | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | wref | :math:`wref` | Algeb | Speed reference variable | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | wd | :math:`wd` | Algeb | Generator under speed | *p.u.* | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | LL_y | :math:`LL_{y}` | Algeb | Output of lead-lag | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | vs | :math:`vs` | Algeb | Valve speed | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | vsl | :math:`vsl` | Algeb | Valve move speed after limiter | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | PHP | :math:`PHP` | Algeb | HP output | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | PLP | :math:`PLP` | Algeb | LP output | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | tm | :math:`tm` | ExtAlgeb | Mechanical power interface to SynGen | | | +--------+-----------------+----------+--------------------------------------+--------+------------+ | tm2 | :math:`tm_{2}` | ExtAlgeb | Mechanical power to syn2 | | | +--------+-----------------+----------+--------------------------------------+--------+------------+ Initialization Equations ------------------------ +--------+-----------------+----------+-------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +========+=================+==========+===============================================================================+ | LL_x | :math:`LL_{x}` | State | :math:`wd` | +--------+-----------------+----------+-------------------------------------------------------------------------------+ | IAW_y | :math:`IAW_{y}` | State | :math:`tm_{012}` | +--------+-----------------+----------+-------------------------------------------------------------------------------+ | L4_y | :math:`L_{4 y}` | State | :math:`IAW_{y}` | +--------+-----------------+----------+-------------------------------------------------------------------------------+ | L5_y | :math:`L_{5 y}` | State | :math:`L_{4 y}` | +--------+-----------------+----------+-------------------------------------------------------------------------------+ | L6_y | :math:`L_{6 y}` | State | :math:`L_{5 y}` | +--------+-----------------+----------+-------------------------------------------------------------------------------+ | L7_y | :math:`L_{7 y}` | State | :math:`L_{6 y}` | +--------+-----------------+----------+-------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +--------+-----------------+----------+-------------------------------------------------------------------------------+ | paux | :math:`paux` | Algeb | :math:`paux_{0}` | +--------+-----------------+----------+-------------------------------------------------------------------------------+ | pout | :math:`pout` | Algeb | :math:`tm_{0} ue` | +--------+-----------------+----------+-------------------------------------------------------------------------------+ | wref | :math:`wref` | Algeb | :math:`wref_{0}` | +--------+-----------------+----------+-------------------------------------------------------------------------------+ | wd | :math:`wd` | Algeb | :math:`0` | +--------+-----------------+----------+-------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`wd` | +--------+-----------------+----------+-------------------------------------------------------------------------------+ | vs | :math:`vs` | Algeb | :math:`0` | +--------+-----------------+----------+-------------------------------------------------------------------------------+ | vsl | :math:`vsl` | Algeb | :math:`HL_{zi} vs + HL_{zl} UC + HL_{zu} UO` | +--------+-----------------+----------+-------------------------------------------------------------------------------+ | PHP | :math:`PHP` | Algeb | :math:`ue \left(K1n L_{4 y} + K3n L_{5 y} + K5n L_{6 y} + K7n L_{7 y}\right)` | +--------+-----------------+----------+-------------------------------------------------------------------------------+ | PLP | :math:`PLP` | Algeb | :math:`ue \left(K2n L_{4 y} + K4n L_{5 y} + K6n L_{6 y} + K8n L_{7 y}\right)` | +--------+-----------------+----------+-------------------------------------------------------------------------------+ | tm | :math:`tm` | ExtAlgeb | | +--------+-----------------+----------+-------------------------------------------------------------------------------+ | tm2 | :math:`tm_{2}` | ExtAlgeb | | +--------+-----------------+----------+-------------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+----------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+==================================+=============+ | LL_x | :math:`LL_{x}` | State | :math:`- LL_{x} + wd` | :math:`T_1` | +--------+-----------------+----------+----------------------------------+-------------+ | IAW_y | :math:`IAW_{y}` | State | :math:`vsl` | :math:`1` | +--------+-----------------+----------+----------------------------------+-------------+ | L4_y | :math:`L_{4 y}` | State | :math:`IAW_{y} - L_{4 y}` | :math:`T_4` | +--------+-----------------+----------+----------------------------------+-------------+ | L5_y | :math:`L_{5 y}` | State | :math:`L_{4 y} - L_{5 y}` | :math:`T_5` | +--------+-----------------+----------+----------------------------------+-------------+ | L6_y | :math:`L_{6 y}` | State | :math:`L_{5 y} - L_{6 y}` | :math:`T_6` | +--------+-----------------+----------+----------------------------------+-------------+ | L7_y | :math:`L_{7 y}` | State | :math:`L_{6 y} - L_{7 y}` | :math:`T_7` | +--------+-----------------+----------+----------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+----------------------------------+-------------+ Algebraic Equations ----------------------------- +-------+----------------+----------+---------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=======+================+==========+=======================================================================================================================================+ | paux | :math:`paux` | Algeb | :math:`- paux + paux_{0}` | +-------+----------------+----------+---------------------------------------------------------------------------------------------------------------------------------------+ | pout | :math:`pout` | Algeb | :math:`PHP ue - pout` | +-------+----------------+----------+---------------------------------------------------------------------------------------------------------------------------------------+ | wref | :math:`wref` | Algeb | :math:`- wref + wref_{0}` | +-------+----------------+----------+---------------------------------------------------------------------------------------------------------------------------------------+ | wd | :math:`wd` | Algeb | :math:`ue \left(- \omega + wref\right) - wd` | +-------+----------------+----------+---------------------------------------------------------------------------------------------------------------------------------------+ | LL_y | :math:`LL_{y}` | Algeb | :math:`K LL_{x} T_{1} + K T_{2} \left(- LL_{x} + wd\right) + LL_{LT1 z1} LL_{LT2 z1} \left(- K LL_{x} + LL_{y}\right) - LL_{y} T_{1}` | +-------+----------------+----------+---------------------------------------------------------------------------------------------------------------------------------------+ | vs | :math:`vs` | Algeb | :math:`- vs + \frac{ue \left(- IAW_{y} + LL_{y} + paux + tm_{012}\right)}{T_{3}}` | +-------+----------------+----------+---------------------------------------------------------------------------------------------------------------------------------------+ | vsl | :math:`vsl` | Algeb | :math:`HL_{zi} vs + HL_{zl} UC + HL_{zu} UO - vsl` | +-------+----------------+----------+---------------------------------------------------------------------------------------------------------------------------------------+ | PHP | :math:`PHP` | Algeb | :math:`- PHP + ue \left(K1n L_{4 y} + K3n L_{5 y} + K5n L_{6 y} + K7n L_{7 y}\right)` | +-------+----------------+----------+---------------------------------------------------------------------------------------------------------------------------------------+ | PLP | :math:`PLP` | Algeb | :math:`- PLP + ue \left(K2n L_{4 y} + K4n L_{5 y} + K6n L_{6 y} + K8n L_{7 y}\right)` | +-------+----------------+----------+---------------------------------------------------------------------------------------------------------------------------------------+ | tm | :math:`tm` | ExtAlgeb | :math:`ue \left(pout - tm_{0}\right)` | +-------+----------------+----------+---------------------------------------------------------------------------------------------------------------------------------------+ | tm2 | :math:`tm_{2}` | ExtAlgeb | :math:`ue zsyn_{2} \left(PLP - tm_{02}\right)` | +-------+----------------+----------+---------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +----------+--------------------------+-----------------------------------------------------------------------+-----------------+ | Name | Symbol | Equation | Type | +==========+==========================+=======================================================================+=================+ | ue | :math:`u_{e}` | :math:`u ug` | ConstService | +----------+--------------------------+-----------------------------------------------------------------------+-----------------+ | pref0 | :math:`P_{ref0}` | :math:`tm_{0}` | 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}{_sumK18}` | ConstService | +----------+--------------------------+-----------------------------------------------------------------------+-----------------+ | K1n | :math:`K_{1n}` | :math:`K_{1} _Kcoeff` | ConstService | +----------+--------------------------+-----------------------------------------------------------------------+-----------------+ | K2n | :math:`K_{2n}` | :math:`K_{2} _Kcoeff` | ConstService | +----------+--------------------------+-----------------------------------------------------------------------+-----------------+ | K3n | :math:`K_{3n}` | :math:`K_{3} _Kcoeff` | ConstService | +----------+--------------------------+-----------------------------------------------------------------------+-----------------+ | K4n | :math:`K_{4n}` | :math:`K_{4} _Kcoeff` | ConstService | +----------+--------------------------+-----------------------------------------------------------------------+-----------------+ | K5n | :math:`K_{5n}` | :math:`K_{5} _Kcoeff` | ConstService | +----------+--------------------------+-----------------------------------------------------------------------+-----------------+ | K6n | :math:`K_{6n}` | :math:`K_{6} _Kcoeff` | ConstService | +----------+--------------------------+-----------------------------------------------------------------------+-----------------+ | K7n | :math:`K_{7n}` | :math:`K_{7} _Kcoeff` | ConstService | +----------+--------------------------+-----------------------------------------------------------------------+-----------------+ | K8n | :math:`K_{8n}` | :math:`K_{8} _Kcoeff` | ConstService | +----------+--------------------------+-----------------------------------------------------------------------+-----------------+ | _tm0K2 | :math:`_tm0K2` | :math:`tm_{0} zsyn_{2} \left(K2n + K4n + K6n + K8n\right)` | PostInitService | +----------+--------------------------+-----------------------------------------------------------------------+-----------------+ | _tm02K1 | :math:`_tm02K1` | :math:`tm_{02} \left(K1n + K3n + K5n + K7n\right)` | PostInitService | +----------+--------------------------+-----------------------------------------------------------------------+-----------------+ | tm012 | :math:`tm012` | :math:`tm_{0} + tm_{02}` | 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:`F_{1 y}` | State | State in lag transfer function | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | F2_x | :math:`F_{2 x}` | State | State in lead-lag | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | F3_y | :math:`F_{3 y}` | State | State in lag transfer function | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | F4_y | :math:`F_{4 y}` | State | State in lag transfer function | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | F5_y | :math:`F_{5 y}` | State | State in lag transfer function | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | *p.u.* | | +--------+-----------------+----------+--------------------------------------+--------+------------+ | paux | :math:`paux` | Algeb | Auxiliary power input | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | pout | :math:`pout` | Algeb | Turbine final output power | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | wref | :math:`wref` | Algeb | Speed reference variable | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | F2_y | :math:`F_{2 y}` | Algeb | Output of lead-lag | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | HL_x | :math:`HL_{x}` | Algeb | Value before limiter | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | HL_y | :math:`HL_{y}` | Algeb | Output after limiter and post gain | | v_str | +--------+-----------------+----------+--------------------------------------+--------+------------+ | tm | :math:`tm` | ExtAlgeb | Mechanical power interface to SynGen | | | +--------+-----------------+----------+--------------------------------------+--------+------------+ Initialization Equations ------------------------ +--------+-----------------+----------+------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +========+=================+==========+==============================================================================+ | F1_y | :math:`F_{1 y}` | State | :math:`K_{1} ue \left(\omega - wref\right)` | +--------+-----------------+----------+------------------------------------------------------------------------------+ | F2_x | :math:`F_{2 x}` | State | :math:`F_{1 y}` | +--------+-----------------+----------+------------------------------------------------------------------------------+ | F3_y | :math:`F_{3 y}` | State | :math:`1.0 HL_{y}` | +--------+-----------------+----------+------------------------------------------------------------------------------+ | F4_y | :math:`F_{4 y}` | State | :math:`F_{3 y} K_{2}` | +--------+-----------------+----------+------------------------------------------------------------------------------+ | F5_y | :math:`F_{5 y}` | State | :math:`F_{4 y} K_{3}` | +--------+-----------------+----------+------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +--------+-----------------+----------+------------------------------------------------------------------------------+ | paux | :math:`paux` | Algeb | :math:`paux_{0}` | +--------+-----------------+----------+------------------------------------------------------------------------------+ | pout | :math:`pout` | Algeb | :math:`tm_{0} ue` | +--------+-----------------+----------+------------------------------------------------------------------------------+ | wref | :math:`wref` | Algeb | :math:`wref_{0}` | +--------+-----------------+----------+------------------------------------------------------------------------------+ | F2_y | :math:`F_{2 y}` | Algeb | :math:`F_{1 y}` | +--------+-----------------+----------+------------------------------------------------------------------------------+ | HL_x | :math:`HL_{x}` | Algeb | :math:`1.0 ue \left(- F_{2 y} + paux + pref_{0}\right)` | +--------+-----------------+----------+------------------------------------------------------------------------------+ | HL_y | :math:`HL_{y}` | Algeb | :math:`1.0 HL_{lim zi} HL_{x} + 1.0 HL_{lim zl} PMIN + 1.0 HL_{lim zu} PMAX` | +--------+-----------------+----------+------------------------------------------------------------------------------+ | tm | :math:`tm` | ExtAlgeb | | +--------+-----------------+----------+------------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+-----------------+----------+---------------------------------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+=================+==========+=========================================================+=============+ | F1_y | :math:`F_{1 y}` | State | :math:`- F_{1 y} + K_{1} ue \left(\omega - wref\right)` | :math:`T_1` | +--------+-----------------+----------+---------------------------------------------------------+-------------+ | F2_x | :math:`F_{2 x}` | State | :math:`F_{1 y} - F_{2 x}` | :math:`T_3` | +--------+-----------------+----------+---------------------------------------------------------+-------------+ | F3_y | :math:`F_{3 y}` | State | :math:`- F_{3 y} + 1.0 HL_{y}` | :math:`T_4` | +--------+-----------------+----------+---------------------------------------------------------+-------------+ | F4_y | :math:`F_{4 y}` | State | :math:`F_{3 y} K_{2} - F_{4 y}` | :math:`T_5` | +--------+-----------------+----------+---------------------------------------------------------+-------------+ | F5_y | :math:`F_{5 y}` | State | :math:`F_{4 y} K_{3} - F_{5 y}` | :math:`T_6` | +--------+-----------------+----------+---------------------------------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+-----------------+----------+---------------------------------------------------------+-------------+ Algebraic Equations ----------------------------- +-------+-----------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=======+=================+==========+=======================================================================================================================================================+ | paux | :math:`paux` | Algeb | :math:`- paux + paux_{0}` | +-------+-----------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------+ | pout | :math:`pout` | Algeb | :math:`- pout + ue \left(F_{3 y} \left(1 - K_{2}\right) + F_{4 y} \left(1 - K_{3}\right) + F_{5 y}\right)` | +-------+-----------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------+ | wref | :math:`wref` | Algeb | :math:`- wref + wref_{0}` | +-------+-----------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------+ | F2_y | :math:`F_{2 y}` | Algeb | :math:`F_{2 LT1 z1} F_{2 LT2 z1} \left(- 1.0 F_{2 x} + F_{2 y}\right) + 1.0 F_{2 x} T_{3} - F_{2 y} T_{3} + 1.0 T_{2} \left(F_{1 y} - F_{2 x}\right)` | +-------+-----------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------+ | HL_x | :math:`HL_{x}` | Algeb | :math:`- HL_{x} + 1.0 ue \left(- F_{2 y} + paux + pref_{0}\right)` | +-------+-----------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------+ | HL_y | :math:`HL_{y}` | Algeb | :math:`1.0 HL_{lim zi} HL_{x} + 1.0 HL_{lim zl} PMIN + 1.0 HL_{lim zu} PMAX - HL_{y}` | +-------+-----------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------+ | tm | :math:`tm` | ExtAlgeb | :math:`ue \left(pout - tm_{0}\right)` | +-------+-----------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +--------+------------------+----------------+--------------+ | Name | Symbol | Equation | Type | +========+==================+================+==============+ | ue | :math:`u_{e}` | :math:`u ug` | ConstService | +--------+------------------+----------------+--------------+ | pref0 | :math:`P_{ref0}` | :math:`tm_{0}` | 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:`LAG_{y}` | State | State in lag TF | | v_str | +--------+------------------+----------+--------------------------------------+--------+------------+ | LG2_y | :math:`LG_{2 y}` | State | State in lag transfer function | | v_str | +--------+------------------+----------+--------------------------------------+--------+------------+ | LG3_y | :math:`LG_{3 y}` | State | State in lag transfer function | | v_str | +--------+------------------+----------+--------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | *p.u.* | | +--------+------------------+----------+--------------------------------------+--------+------------+ | paux | :math:`paux` | Algeb | Auxiliary power input | | v_str | +--------+------------------+----------+--------------------------------------+--------+------------+ | pout | :math:`pout` | Algeb | Turbine final output power | | v_str | +--------+------------------+----------+--------------------------------------+--------+------------+ | wref | :math:`wref` | Algeb | Speed reference variable | | v_str | +--------+------------------+----------+--------------------------------------+--------+------------+ | pref | :math:`pref` | Algeb | Reference power input | | v_str | +--------+------------------+----------+--------------------------------------+--------+------------+ | wd | :math:`wd` | Algeb | Generator under speed | *p.u.* | v_str | +--------+------------------+----------+--------------------------------------+--------+------------+ | pd | :math:`pd` | 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:`LVG_{y}` | Algeb | LVGate output | | v_str | +--------+------------------+----------+--------------------------------------+--------+------------+ | tm | :math:`tm` | ExtAlgeb | Mechanical power interface to SynGen | | | +--------+------------------+----------+--------------------------------------+--------+------------+ Initialization Equations ------------------------ +--------+------------------+----------+----------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +========+==================+==========+==========================================================+ | LAG_y | :math:`LAG_{y}` | State | :math:`LVG_{y}` | +--------+------------------+----------+----------------------------------------------------------+ | LG2_y | :math:`LG_{2 y}` | State | :math:`LAG_{y}` | +--------+------------------+----------+----------------------------------------------------------+ | LG3_y | :math:`LG_{3 y}` | State | :math:`LG_{2 y}` | +--------+------------------+----------+----------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +--------+------------------+----------+----------------------------------------------------------+ | paux | :math:`paux` | Algeb | :math:`paux_{0}` | +--------+------------------+----------+----------------------------------------------------------+ | pout | :math:`pout` | Algeb | :math:`tm_{0} ue` | +--------+------------------+----------+----------------------------------------------------------+ | wref | :math:`wref` | Algeb | :math:`wref_{0}` | +--------+------------------+----------+----------------------------------------------------------+ | pref | :math:`pref` | Algeb | :math:`R tm_{0}` | +--------+------------------+----------+----------------------------------------------------------+ | wd | :math:`wd` | Algeb | :math:`0` | +--------+------------------+----------+----------------------------------------------------------+ | pd | :math:`pd` | Algeb | :math:`tm_{0} ue` | +--------+------------------+----------+----------------------------------------------------------+ | v9 | :math:`v_{9}` | Algeb | :math:`ue \left(AT + KT \left(AT - tm_{0}\right)\right)` | +--------+------------------+----------+----------------------------------------------------------+ | LVG_y | :math:`LVG_{y}` | Algeb | :math:`LVG_{lt z0} v_{9} + LVG_{lt z1} pd` | +--------+------------------+----------+----------------------------------------------------------+ | tm | :math:`tm` | ExtAlgeb | | +--------+------------------+----------+----------------------------------------------------------+ Differential Equations ----------------------------- +--------+------------------+----------+----------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+==================+==========+==================================+=============+ | LAG_y | :math:`LAG_{y}` | State | :math:`- LAG_{y} + LVG_{y}` | :math:`T_1` | +--------+------------------+----------+----------------------------------+-------------+ | LG2_y | :math:`LG_{2 y}` | State | :math:`LAG_{y} - LG_{2 y}` | :math:`T_2` | +--------+------------------+----------+----------------------------------+-------------+ | LG3_y | :math:`LG_{3 y}` | State | :math:`LG_{2 y} - LG_{3 y}` | :math:`T_3` | +--------+------------------+----------+----------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+------------------+----------+----------------------------------+-------------+ Algebraic Equations ----------------------------- +--------+-----------------+----------+--------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +========+=================+==========+====================================================================+ | paux | :math:`paux` | Algeb | :math:`- paux + paux_{0}` | +--------+-----------------+----------+--------------------------------------------------------------------+ | pout | :math:`pout` | Algeb | :math:`- pout + ue \left(- Dt wd + LG_{2 y}\right)` | +--------+-----------------+----------+--------------------------------------------------------------------+ | wref | :math:`wref` | Algeb | :math:`- wref + wref_{0}` | +--------+-----------------+----------+--------------------------------------------------------------------+ | pref | :math:`pref` | Algeb | :math:`R pref_{0} - pref` | +--------+-----------------+----------+--------------------------------------------------------------------+ | wd | :math:`wd` | Algeb | :math:`ue \left(\omega - wref\right) - wd` | +--------+-----------------+----------+--------------------------------------------------------------------+ | pd | :math:`pd` | Algeb | :math:`gain ue \left(paux + pref - wd\right) - pd` | +--------+-----------------+----------+--------------------------------------------------------------------+ | v9 | :math:`v_{9}` | Algeb | :math:`ue \left(AT + KT \left(AT - LG_{3 y}\right)\right) - v_{9}` | +--------+-----------------+----------+--------------------------------------------------------------------+ | LVG_y | :math:`LVG_{y}` | Algeb | :math:`LVG_{lt z0} v_{9} + LVG_{lt z1} pd - LVG_{y}` | +--------+-----------------+----------+--------------------------------------------------------------------+ | tm | :math:`tm` | ExtAlgeb | :math:`ue \left(pout - tm_{0}\right)` | +--------+-----------------+----------+--------------------------------------------------------------------+ Services ---------- +--------+------------------+----------------------+--------------+ | Name | Symbol | Equation | Type | +========+==================+======================+==============+ | ue | :math:`u_{e}` | :math:`u ug` | ConstService | +--------+------------------+----------------------+--------------+ | pref0 | :math:`P_{ref0}` | :math:`tm_{0}` | ConstService | +--------+------------------+----------------------+--------------+ | paux0 | :math:`P_{aux0}` | :math:`0` | ConstService | +--------+------------------+----------------------+--------------+ | gain | :math:`G` | :math:`\frac{ue}{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