.. _PSS: ================================================================================ PSS ================================================================================ Power system stabilizer group. Common Parameters: u, name Common Variables: vsout Available models: IEEEST_, ST2CUT_ .. _IEEEST: -------------------------------------------------------------------------------- IEEEST -------------------------------------------------------------------------------- IEEEST stabilizer model. Automatically adds frequency measurement devices if not provided. Input signals (MODE): 1. Rotor speed deviation (p.u.), 2. Bus frequency deviation (p.u.) (*), 3. Generator P electrical in Gen MVABase (p.u.), 4. Generator accelerating power (p.u.), 5. Bus voltage (p.u.), 6. Derivative of p.u. bus voltage. (*) Due to the frequency measurement implementation difference, mode 2 is likely to yield different results across software. .. note:: Blocks are named `F1`, `F2`, `LL1`, `LL2` and `WO` in sequence. Two limiters are named `VLIM` and `OLIM` in sequence. Parameters ---------- +--------+------------------+-----------------------------------+---------+--------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +========+==================+===================================+=========+========+============+ | idx | | unique device idx | | | | +--------+------------------+-----------------------------------+---------+--------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +--------+------------------+-----------------------------------+---------+--------+------------+ | name | | device name | | | | +--------+------------------+-----------------------------------+---------+--------+------------+ | avr | | Exciter idx | | | mandatory | +--------+------------------+-----------------------------------+---------+--------+------------+ | MODE | | Input signal | | | mandatory | +--------+------------------+-----------------------------------+---------+--------+------------+ | busr | | Optional remote bus idx | | | | +--------+------------------+-----------------------------------+---------+--------+------------+ | busf | | BusFreq idx for mode 2 | | | | +--------+------------------+-----------------------------------+---------+--------+------------+ | A1 | :math:`A_1` | filter time const. (pole) | 1 | | | +--------+------------------+-----------------------------------+---------+--------+------------+ | A2 | :math:`A_2` | filter time const. (pole) | 1 | | | +--------+------------------+-----------------------------------+---------+--------+------------+ | A3 | :math:`A_3` | filter time const. (pole) | 1 | | | +--------+------------------+-----------------------------------+---------+--------+------------+ | A4 | :math:`A_4` | filter time const. (pole) | 1 | | | +--------+------------------+-----------------------------------+---------+--------+------------+ | A5 | :math:`A_5` | filter time const. (zero) | 1 | | | +--------+------------------+-----------------------------------+---------+--------+------------+ | A6 | :math:`A_6` | filter time const. (zero) | 1 | | | +--------+------------------+-----------------------------------+---------+--------+------------+ | T1 | :math:`T_1` | first leadlag time const. (zero) | 1 | | | +--------+------------------+-----------------------------------+---------+--------+------------+ | T2 | :math:`T_2` | first leadlag time const. (pole) | 1 | | | +--------+------------------+-----------------------------------+---------+--------+------------+ | T3 | :math:`T_3` | second leadlag time const. (pole) | 1 | | | +--------+------------------+-----------------------------------+---------+--------+------------+ | T4 | :math:`T_4` | second leadlag time const. (pole) | 1 | | | +--------+------------------+-----------------------------------+---------+--------+------------+ | T5 | :math:`T_5` | washout time const. (zero) | 1 | | | +--------+------------------+-----------------------------------+---------+--------+------------+ | T6 | :math:`T_6` | washout time const. (pole) | 1 | | | +--------+------------------+-----------------------------------+---------+--------+------------+ | KS | :math:`K_S` | Gain before washout | 1 | | | +--------+------------------+-----------------------------------+---------+--------+------------+ | LSMAX | :math:`L_{SMAX}` | Max. output limit | 0.300 | | | +--------+------------------+-----------------------------------+---------+--------+------------+ | LSMIN | :math:`L_{SMIN}` | Min. output limit | -0.300 | | | +--------+------------------+-----------------------------------+---------+--------+------------+ | VCU | :math:`V_{CU}` | Upper enabling bus voltage | 999 | *p.u.* | | +--------+------------------+-----------------------------------+---------+--------+------------+ | VCL | :math:`V_{CL}` | Upper enabling bus voltage | -999 | *p.u.* | | +--------+------------------+-----------------------------------+---------+--------+------------+ | syn | | Retrieved generator idx | 0 | | | +--------+------------------+-----------------------------------+---------+--------+------------+ | bus | | Retrieved bus idx | | | | +--------+------------------+-----------------------------------+---------+--------+------------+ | Sn | :math:`S_n` | Generator power base | 0 | | | +--------+------------------+-----------------------------------+---------+--------+------------+ Variables --------- +--------+------------------+----------+------------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +========+==================+==========+==========================================+========+============+ | F1_x | :math:`x'_{F1}` | State | State in 2nd order LPF | | v_str | +--------+------------------+----------+------------------------------------------+--------+------------+ | F1_y | :math:`y_{F1}` | State | Output of 2nd order LPF | | v_str | +--------+------------------+----------+------------------------------------------+--------+------------+ | F2_x1 | :math:`x'_{F2}` | State | State #1 in 2nd order lead-lag | | v_str | +--------+------------------+----------+------------------------------------------+--------+------------+ | F2_x2 | :math:`x''_{F2}` | State | State #2 in 2nd order lead-lag | | v_str | +--------+------------------+----------+------------------------------------------+--------+------------+ | LL1_x | :math:`x'_{LL1}` | State | State in lead-lag | | v_str | +--------+------------------+----------+------------------------------------------+--------+------------+ | LL2_x | :math:`x'_{LL2}` | State | State in lead-lag | | v_str | +--------+------------------+----------+------------------------------------------+--------+------------+ | WO_x | :math:`x'_{WO}` | State | State in washout filter | | v_str | +--------+------------------+----------+------------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | *p.u.* | | +--------+------------------+----------+------------------------------------------+--------+------------+ | vsout | :math:`v_{sout}` | Algeb | PSS output voltage to exciter | | | +--------+------------------+----------+------------------------------------------+--------+------------+ | sig | :math:`S_{ig}` | Algeb | Input signal | | v_str | +--------+------------------+----------+------------------------------------------+--------+------------+ | F2_y | :math:`y_{F2}` | Algeb | Output of 2nd order lead-lag | | v_str | +--------+------------------+----------+------------------------------------------+--------+------------+ | LL1_y | :math:`y_{LL1}` | Algeb | Output of lead-lag | | v_str | +--------+------------------+----------+------------------------------------------+--------+------------+ | LL2_y | :math:`y_{LL2}` | Algeb | Output of lead-lag | | v_str | +--------+------------------+----------+------------------------------------------+--------+------------+ | Vks_y | :math:`y_{Vks}` | Algeb | Gain output | | v_str | +--------+------------------+----------+------------------------------------------+--------+------------+ | WO_y | :math:`y_{WO}` | Algeb | Output of washout filter | | v_str | +--------+------------------+----------+------------------------------------------+--------+------------+ | Vss | :math:`V_{ss}` | Algeb | Voltage output before output limiter | | | +--------+------------------+----------+------------------------------------------+--------+------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | Generator mechanical input | | | +--------+------------------+----------+------------------------------------------+--------+------------+ | te | :math:`\tau_{e}` | ExtAlgeb | Generator electrical output | | | +--------+------------------+----------+------------------------------------------+--------+------------+ | v | :math:`V` | ExtAlgeb | Bus (or busr, if given) terminal voltage | | | +--------+------------------+----------+------------------------------------------+--------+------------+ | f | :math:`f` | ExtAlgeb | Bus frequency | | | +--------+------------------+----------+------------------------------------------+--------+------------+ | vi | :math:`v_{i}` | ExtAlgeb | Exciter input voltage | | | +--------+------------------+----------+------------------------------------------+--------+------------+ Initialization Equations ------------------------ +--------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +========+==================+==========+============================================================================================================================================================+ | F1_x | :math:`x'_{F1}` | State | :math:`0` | +--------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------+ | F1_y | :math:`y_{F1}` | State | :math:`S_{ig}` | +--------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------+ | F2_x1 | :math:`x'_{F2}` | State | :math:`0` | +--------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------+ | F2_x2 | :math:`x''_{F2}` | State | :math:`y_{F1}` | +--------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL1_x | :math:`x'_{LL1}` | State | :math:`y_{F2}` | +--------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL2_x | :math:`x'_{LL2}` | State | :math:`y_{LL1}` | +--------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WO_x | :math:`x'_{WO}` | State | :math:`y_{Vks}` | +--------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +--------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vsout | :math:`v_{sout}` | Algeb | | +--------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------+ | sig | :math:`S_{ig}` | Algeb | :math:`u_{e} \left(V s_5^{SW} + s_1^{SW} \left(\omega - 1\right) + s_4^{SW} \left(\tau_{m} - \tau_{m0}\right) + \frac{\tau_{m0} s_3^{SW}}{(Sb/Sn)}\right)` | +--------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------+ | F2_y | :math:`y_{F2}` | Algeb | :math:`y_{F1}` | +--------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL1_y | :math:`y_{LL1}` | Algeb | :math:`y_{F2}` | +--------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL2_y | :math:`y_{LL2}` | Algeb | :math:`y_{LL1}` | +--------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vks_y | :math:`y_{Vks}` | Algeb | :math:`K_{S} y_{LL2}` | +--------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WO_y | :math:`y_{WO}` | Algeb | :math:`x'_{WO} z_1^{LT_{WO}}` | +--------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vss | :math:`V_{ss}` | Algeb | | +--------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | | +--------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------+ | te | :math:`\tau_{e}` | ExtAlgeb | | +--------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`V` | ExtAlgeb | | +--------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------+ | f | :math:`f` | ExtAlgeb | | +--------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`v_{i}` | ExtAlgeb | | +--------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+------------------+----------+---------------------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+==================+==========+=============================================+=============+ | F1_x | :math:`x'_{F1}` | State | :math:`- A_{1} x'_{F1} + S_{ig} - y_{F1}` | :math:`A_2` | +--------+------------------+----------+---------------------------------------------+-------------+ | F1_y | :math:`y_{F1}` | State | :math:`x'_{F1}` | | +--------+------------------+----------+---------------------------------------------+-------------+ | F2_x1 | :math:`x'_{F2}` | State | :math:`- A_{3} x'_{F2} - x''_{F2} + y_{F1}` | :math:`A_4` | +--------+------------------+----------+---------------------------------------------+-------------+ | F2_x2 | :math:`x''_{F2}` | State | :math:`x'_{F2}` | | +--------+------------------+----------+---------------------------------------------+-------------+ | LL1_x | :math:`x'_{LL1}` | State | :math:`- x'_{LL1} + y_{F2}` | :math:`T_2` | +--------+------------------+----------+---------------------------------------------+-------------+ | LL2_x | :math:`x'_{LL2}` | State | :math:`- x'_{LL2} + y_{LL1}` | :math:`T_4` | +--------+------------------+----------+---------------------------------------------+-------------+ | WO_x | :math:`x'_{WO}` | State | :math:`- x'_{WO} + y_{Vks}` | :math:`T_6` | +--------+------------------+----------+---------------------------------------------+-------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+------------------+----------+---------------------------------------------+-------------+ Algebraic Equations ----------------------------- +--------+------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +========+==================+==========+=========================================================================================================================================================================================================================+ | vsout | :math:`v_{sout}` | Algeb | :math:`V_{ss} u_{e} z_i^{OLIM} - v_{sout}` | +--------+------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | sig | :math:`S_{ig}` | Algeb | :math:`- S_{ig} + u_{e} \left(V s_5^{SW} + s_1^{SW} \left(\omega - 1\right) + s_2^{SW} \left(f - 1\right) + s_4^{SW} \left(\tau_{m} - \tau_{m0}\right) + s_6^{SW} v^{dV/dt} + \frac{\tau_{e} s_3^{SW}}{(Sb/Sn)}\right)` | +--------+------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | F2_y | :math:`y_{F2}` | Algeb | :math:`A_{4} A_{5} x'_{F2} + A_{4} x''_{F2} - A_{4} y_{F2} + A_{6} \left(- A_{3} x'_{F2} - x''_{F2} + y_{F1}\right) + \left(z_1^{LT_{F2}}\right)^{4} \left(- x''_{F2} + y_{F2}\right)` | +--------+------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL1_y | :math:`y_{LL1}` | Algeb | :math:`T_{1} \left(- x'_{LL1} + y_{F2}\right) + T_{2} x'_{LL1} - T_{2} y_{LL1} + \left(z_1^{LT_{LL1}}\right)^{2} \left(- x'_{LL1} + y_{LL1}\right)` | +--------+------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL2_y | :math:`y_{LL2}` | Algeb | :math:`T_{3} \left(- x'_{LL2} + y_{LL1}\right) + T_{4} x'_{LL2} - T_{4} y_{LL2} + \left(z_1^{LT_{LL2}}\right)^{2} \left(- x'_{LL2} + y_{LL2}\right)` | +--------+------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vks_y | :math:`y_{Vks}` | Algeb | :math:`K_{S} y_{LL2} - y_{Vks}` | +--------+------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WO_y | :math:`y_{WO}` | Algeb | :math:`T_{5} z_0^{LT_{WO}} \left(- x'_{WO} + y_{Vks}\right) + T_{6} x'_{WO} z_1^{LT_{WO}} - T_{6} y_{WO}` | +--------+------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vss | :math:`V_{ss}` | Algeb | :math:`L_{SMAX} z_u^{VLIM} + L_{SMIN} z_l^{VLIM} - V_{ss} + y_{WO} z_i^{VLIM}` | +--------+------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | :math:`0` | +--------+------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | te | :math:`\tau_{e}` | ExtAlgeb | :math:`0` | +--------+------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`V` | ExtAlgeb | :math:`0` | +--------+------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | f | :math:`f` | ExtAlgeb | :math:`0` | +--------+------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`v_{i}` | ExtAlgeb | :math:`u_{e} v_{sout}` | +--------+------------------+----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +------+---------------+------------------+--------------+ | Name | Symbol | Equation | Type | +======+===============+==================+==============+ | ue | :math:`u_{e}` | :math:`u u_{ee}` | ConstService | +------+---------------+------------------+--------------+ Discretes ----------- +----------+------------------+------------+----------------------------------+ | Name | Symbol | Type | Info | +==========+==================+============+==================================+ | dv | :math:`dV/dt` | Derivative | Finite difference of bus voltage | +----------+------------------+------------+----------------------------------+ | SW | :math:`SW` | Switcher | | +----------+------------------+------------+----------------------------------+ | F2_LT1 | :math:`LT_{F2}` | LessThan | | +----------+------------------+------------+----------------------------------+ | F2_LT2 | :math:`LT_{F2}` | LessThan | | +----------+------------------+------------+----------------------------------+ | F2_LT3 | :math:`LT_{F2}` | LessThan | | +----------+------------------+------------+----------------------------------+ | F2_LT4 | :math:`LT_{F2}` | LessThan | | +----------+------------------+------------+----------------------------------+ | LL1_LT1 | :math:`LT_{LL1}` | LessThan | | +----------+------------------+------------+----------------------------------+ | LL1_LT2 | :math:`LT_{LL1}` | LessThan | | +----------+------------------+------------+----------------------------------+ | LL2_LT1 | :math:`LT_{LL2}` | LessThan | | +----------+------------------+------------+----------------------------------+ | LL2_LT2 | :math:`LT_{LL2}` | LessThan | | +----------+------------------+------------+----------------------------------+ | WO_LT | :math:`LT_{WO}` | LessThan | | +----------+------------------+------------+----------------------------------+ | VLIM | :math:`VLIM` | Limiter | Vss limiter | +----------+------------------+------------+----------------------------------+ | OLIM | :math:`OLIM` | Limiter | output limiter | +----------+------------------+------------+----------------------------------+ Blocks ------- +------+-------------+---------------+------+ | Name | Symbol | Type | Info | +======+=============+===============+======+ | F1 | :math:`F1` | Lag2ndOrd | | +------+-------------+---------------+------+ | F2 | :math:`F2` | LeadLag2ndOrd | | +------+-------------+---------------+------+ | LL1 | :math:`LL1` | LeadLag | | +------+-------------+---------------+------+ | LL2 | :math:`LL2` | LeadLag | | +------+-------------+---------------+------+ | Vks | :math:`Vks` | Gain | | +------+-------------+---------------+------+ | WO | :math:`WO` | WashoutOrLag | | +------+-------------+---------------+------+ Config Fields in [IEEEST] +---------------+--------+---------+---------------------------------------+-----------------+ | 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) | +---------------+--------+---------+---------------------------------------+-----------------+ | freq_model | | BusFreq | default freq. measurement model | ('BusFreq',) | +---------------+--------+---------+---------------------------------------+-----------------+ .. _ST2CUT: -------------------------------------------------------------------------------- ST2CUT -------------------------------------------------------------------------------- ST2CUT stabilizer model. Automatically adds frequency measurement devices if not provided. Input signals (MODE and MODE2): 0 - Disable input signal 1 (s1) - Rotor speed deviation (p.u.), 2 (s2) - Bus frequency deviation (*) (p.u.), 3 (s3) - Generator P electrical in Gen MVABase (p.u.), 4 (s4) - Generator accelerating power (p.u.), 5 (s5) - Bus voltage (p.u.), 6 (s6) - Derivative of p.u. bus voltage. (*) Due to the frequency measurement implementation difference, mode 2 is likely to yield different results across software. Blocks are named `LL1`, `LL2`, `LL3`, `LL4` in sequence. Two limiters are named `VSS_lim` and `OLIM` in sequence. Parameters ---------- +--------+------------------+---------------------------------+---------+--------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +========+==================+=================================+=========+========+============+ | idx | | unique device idx | | | | +--------+------------------+---------------------------------+---------+--------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +--------+------------------+---------------------------------+---------+--------+------------+ | name | | device name | | | | +--------+------------------+---------------------------------+---------+--------+------------+ | avr | | Exciter idx | | | mandatory | +--------+------------------+---------------------------------+---------+--------+------------+ | MODE | | Input signal 1 | | | mandatory | +--------+------------------+---------------------------------+---------+--------+------------+ | busr | | Remote bus 1 | | | | +--------+------------------+---------------------------------+---------+--------+------------+ | busf | | BusFreq idx for signal 1 mode 2 | | | | +--------+------------------+---------------------------------+---------+--------+------------+ | MODE2 | | Input signal 2 | | | | +--------+------------------+---------------------------------+---------+--------+------------+ | busr2 | | Remote bus 2 | | | | +--------+------------------+---------------------------------+---------+--------+------------+ | busf2 | | BusFreq idx for signal 2 mode 2 | | | | +--------+------------------+---------------------------------+---------+--------+------------+ | K1 | :math:`K_1` | Transducer 1 gain | 1 | | | +--------+------------------+---------------------------------+---------+--------+------------+ | K2 | :math:`K_2` | Transducer 2 gain | 1 | | | +--------+------------------+---------------------------------+---------+--------+------------+ | T1 | :math:`T_1` | Transducer 1 time const. | 1 | | | +--------+------------------+---------------------------------+---------+--------+------------+ | T2 | :math:`T_2` | Transducer 2 time const. | 1 | | | +--------+------------------+---------------------------------+---------+--------+------------+ | T3 | :math:`T_3` | Washout int. time const. | 1 | | | +--------+------------------+---------------------------------+---------+--------+------------+ | T4 | :math:`T_4` | Washout delay time const. | 0.200 | | | +--------+------------------+---------------------------------+---------+--------+------------+ | T5 | :math:`T_5` | Leadlag 1 time const. (1) | 1 | | | +--------+------------------+---------------------------------+---------+--------+------------+ | T6 | :math:`T_6` | Leadlag 1 time const. (2) | 0.500 | | | +--------+------------------+---------------------------------+---------+--------+------------+ | T7 | :math:`T_7` | Leadlag 2 time const. (1) | 1 | | | +--------+------------------+---------------------------------+---------+--------+------------+ | T8 | :math:`T_8` | Leadlag 2 time const. (2) | 1 | | | +--------+------------------+---------------------------------+---------+--------+------------+ | T9 | :math:`T_9` | Leadlag 3 time const. (1) | 1 | | | +--------+------------------+---------------------------------+---------+--------+------------+ | T10 | :math:`T_{10}` | Leadlag 3 time const. (2) | 0.200 | | | +--------+------------------+---------------------------------+---------+--------+------------+ | LSMAX | :math:`L_{SMAX}` | Max. output limit | 0.300 | | | +--------+------------------+---------------------------------+---------+--------+------------+ | LSMIN | :math:`L_{SMIN}` | Min. output limit | -0.300 | | | +--------+------------------+---------------------------------+---------+--------+------------+ | VCU | :math:`V_{CU}` | Upper enabling bus voltage | 999 | *p.u.* | | +--------+------------------+---------------------------------+---------+--------+------------+ | VCL | :math:`V_{CL}` | Upper enabling bus voltage | -999 | *p.u.* | | +--------+------------------+---------------------------------+---------+--------+------------+ | syn | | Retrieved generator idx | 0 | | | +--------+------------------+---------------------------------+---------+--------+------------+ | bus | | Retrieved bus idx | | | | +--------+------------------+---------------------------------+---------+--------+------------+ | Sn | :math:`S_n` | Generator power base | 0 | | | +--------+------------------+---------------------------------+---------+--------+------------+ Variables --------- +--------+------------------+----------+-------------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +========+==================+==========+===========================================+========+============+ | L1_y | :math:`y_{L1}` | State | State in lag transfer function | | v_str | +--------+------------------+----------+-------------------------------------------+--------+------------+ | L2_y | :math:`y_{L2}` | State | State in lag transfer function | | v_str | +--------+------------------+----------+-------------------------------------------+--------+------------+ | WO_x | :math:`x'_{WO}` | State | State in washout filter | | v_str | +--------+------------------+----------+-------------------------------------------+--------+------------+ | LL1_x | :math:`x'_{LL1}` | State | State in lead-lag | | v_str | +--------+------------------+----------+-------------------------------------------+--------+------------+ | LL2_x | :math:`x'_{LL2}` | State | State in lead-lag | | v_str | +--------+------------------+----------+-------------------------------------------+--------+------------+ | LL3_x | :math:`x'_{LL3}` | State | State in lead-lag | | v_str | +--------+------------------+----------+-------------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | Generator speed | *p.u.* | | +--------+------------------+----------+-------------------------------------------+--------+------------+ | vsout | :math:`v_{sout}` | Algeb | PSS output voltage to exciter | | | +--------+------------------+----------+-------------------------------------------+--------+------------+ | sig | :math:`S_{ig}` | Algeb | Input signal | | v_str | +--------+------------------+----------+-------------------------------------------+--------+------------+ | sig2 | :math:`S_{ig2}` | Algeb | Input signal 2 | | v_str | +--------+------------------+----------+-------------------------------------------+--------+------------+ | IN | :math:`I_{N}` | Algeb | Sum of inputs | | v_str | +--------+------------------+----------+-------------------------------------------+--------+------------+ | WO_y | :math:`y_{WO}` | Algeb | Output of washout filter | | v_str | +--------+------------------+----------+-------------------------------------------+--------+------------+ | LL1_y | :math:`y_{LL1}` | Algeb | Output of lead-lag | | v_str | +--------+------------------+----------+-------------------------------------------+--------+------------+ | LL2_y | :math:`y_{LL2}` | Algeb | Output of lead-lag | | v_str | +--------+------------------+----------+-------------------------------------------+--------+------------+ | LL3_y | :math:`y_{LL3}` | Algeb | Output of lead-lag | | v_str | +--------+------------------+----------+-------------------------------------------+--------+------------+ | VSS_x | :math:`x_{VSS}` | Algeb | Value before limiter | | v_str | +--------+------------------+----------+-------------------------------------------+--------+------------+ | VSS_y | :math:`y_{VSS}` | Algeb | Output after limiter and post gain | | v_str | +--------+------------------+----------+-------------------------------------------+--------+------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | Generator mechanical input | | | +--------+------------------+----------+-------------------------------------------+--------+------------+ | te | :math:`\tau_{e}` | ExtAlgeb | Generator electrical output | | | +--------+------------------+----------+-------------------------------------------+--------+------------+ | v | :math:`V` | ExtAlgeb | Bus (or busr, if given) terminal voltage | | | +--------+------------------+----------+-------------------------------------------+--------+------------+ | f | :math:`f` | ExtAlgeb | Bus frequency | | | +--------+------------------+----------+-------------------------------------------+--------+------------+ | vi | :math:`v_{i}` | ExtAlgeb | Exciter input voltage | | | +--------+------------------+----------+-------------------------------------------+--------+------------+ | v2 | :math:`V` | ExtAlgeb | Bus (or busr2, if given) terminal voltage | | | +--------+------------------+----------+-------------------------------------------+--------+------------+ | f2 | :math:`f_{2}` | ExtAlgeb | Bus frequency 2 | | | +--------+------------------+----------+-------------------------------------------+--------+------------+ Initialization Equations ------------------------ +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +========+==================+==========+=============================================================================================================================================+ | L1_y | :math:`y_{L1}` | State | :math:`K_{1} S_{ig}` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ | L2_y | :math:`y_{L2}` | State | :math:`K_{2} S_{ig2}` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ | WO_x | :math:`x'_{WO}` | State | :math:`I_{N}` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ | LL1_x | :math:`x'_{LL1}` | State | :math:`y_{WO}` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ | LL2_x | :math:`x'_{LL2}` | State | :math:`y_{LL1}` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ | LL3_x | :math:`x'_{LL3}` | State | :math:`y_{LL2}` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ | vsout | :math:`v_{sout}` | Algeb | | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ | sig | :math:`S_{ig}` | Algeb | :math:`V s_5^{SW} + s_1^{SW} \left(\omega - 1\right) + s_4^{SW} \left(\tau_{m} - \tau_{m0}\right) + \frac{\tau_{m0} s_3^{SW}}{(Sb/Sn)}` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ | sig2 | :math:`S_{ig2}` | Algeb | :math:`V s_5^{SW2} + s_1^{SW2} \left(\omega - 1\right) + s_4^{SW2} \left(\tau_{m} - \tau_{m0}\right) + \frac{\tau_{m0} s_3^{SW2}}{(Sb/Sn)}` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`I_{N}` | Algeb | :math:`u_{e} \left(y_{L1} + y_{L2}\right)` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ | WO_y | :math:`y_{WO}` | Algeb | :math:`x'_{WO} z_1^{LT_{WO}}` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ | LL1_y | :math:`y_{LL1}` | Algeb | :math:`y_{WO}` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ | LL2_y | :math:`y_{LL2}` | Algeb | :math:`y_{LL1}` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ | LL3_y | :math:`y_{LL3}` | Algeb | :math:`y_{LL2}` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ | VSS_x | :math:`x_{VSS}` | Algeb | :math:`y_{LL3}` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ | VSS_y | :math:`y_{VSS}` | Algeb | :math:`L_{SMAX} z_u^{lim_{VSS}} + L_{SMIN} z_l^{lim_{VSS}} + x_{VSS} z_i^{lim_{VSS}}` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ | te | :math:`\tau_{e}` | ExtAlgeb | | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`V` | ExtAlgeb | | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ | f | :math:`f` | ExtAlgeb | | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`v_{i}` | ExtAlgeb | | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ | v2 | :math:`V` | ExtAlgeb | | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ | f2 | :math:`f_{2}` | ExtAlgeb | | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +--------+------------------+----------+----------------------------------+----------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+==================+==========+==================================+================+ | L1_y | :math:`y_{L1}` | State | :math:`K_{1} S_{ig} - y_{L1}` | :math:`T_1` | +--------+------------------+----------+----------------------------------+----------------+ | L2_y | :math:`y_{L2}` | State | :math:`K_{2} S_{ig2} - y_{L2}` | :math:`T_2` | +--------+------------------+----------+----------------------------------+----------------+ | WO_x | :math:`x'_{WO}` | State | :math:`I_{N} - x'_{WO}` | :math:`T_4` | +--------+------------------+----------+----------------------------------+----------------+ | LL1_x | :math:`x'_{LL1}` | State | :math:`- x'_{LL1} + y_{WO}` | :math:`T_6` | +--------+------------------+----------+----------------------------------+----------------+ | LL2_x | :math:`x'_{LL2}` | State | :math:`- x'_{LL2} + y_{LL1}` | :math:`T_8` | +--------+------------------+----------+----------------------------------+----------------+ | LL3_x | :math:`x'_{LL3}` | State | :math:`- x'_{LL3} + y_{LL2}` | :math:`T_{10}` | +--------+------------------+----------+----------------------------------+----------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +--------+------------------+----------+----------------------------------+----------------+ Algebraic Equations ----------------------------- +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +========+==================+==========+===============================================================================================================================================================================================================+ | vsout | :math:`v_{sout}` | Algeb | :math:`u_{e} y_{VSS} z_i^{OLIM} - v_{sout}` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | sig | :math:`S_{ig}` | Algeb | :math:`- S_{ig} + V s_5^{SW} + s_1^{SW} \left(\omega - 1\right) + s_2^{SW} \left(f - 1\right) + s_4^{SW} \left(\tau_{m} - \tau_{m0}\right) + s_6^{SW} v^{dv} + \frac{\tau_{e} s_3^{SW}}{(Sb/Sn)}` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | sig2 | :math:`S_{ig2}` | Algeb | :math:`- S_{ig2} + V s_5^{SW2} + s_1^{SW2} \left(\omega - 1\right) + s_2^{SW2} \left(f_{2} - 1\right) + s_4^{SW2} \left(\tau_{m} - \tau_{m0}\right) + s_6^{SW2} v^{dv2} + \frac{\tau_{e} s_3^{SW2}}{(Sb/Sn)}` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IN | :math:`I_{N}` | Algeb | :math:`- I_{N} + u_{e} \left(y_{L1} + y_{L2}\right)` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | WO_y | :math:`y_{WO}` | Algeb | :math:`T_{3} z_0^{LT_{WO}} \left(I_{N} - x'_{WO}\right) + T_{4} x'_{WO} z_1^{LT_{WO}} - T_{4} y_{WO}` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL1_y | :math:`y_{LL1}` | Algeb | :math:`T_{5} \left(- x'_{LL1} + y_{WO}\right) + T_{6} x'_{LL1} - T_{6} y_{LL1} + \left(z_1^{LT_{LL1}}\right)^{2} \left(- x'_{LL1} + y_{LL1}\right)` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL2_y | :math:`y_{LL2}` | Algeb | :math:`T_{7} \left(- x'_{LL2} + y_{LL1}\right) + T_{8} x'_{LL2} - T_{8} y_{LL2} + \left(z_1^{LT_{LL2}}\right)^{2} \left(- x'_{LL2} + y_{LL2}\right)` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | LL3_y | :math:`y_{LL3}` | Algeb | :math:`T_{9} \left(- x'_{LL3} + y_{LL2}\right) + T_{10} x'_{LL3} - T_{10} y_{LL3} + \left(z_1^{LT_{LL3}}\right)^{2} \left(- x'_{LL3} + y_{LL3}\right)` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VSS_x | :math:`x_{VSS}` | Algeb | :math:`- x_{VSS} + y_{LL3}` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VSS_y | :math:`y_{VSS}` | Algeb | :math:`L_{SMAX} z_u^{lim_{VSS}} + L_{SMIN} z_l^{lim_{VSS}} + x_{VSS} z_i^{lim_{VSS}} - y_{VSS}` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | tm | :math:`\tau_{m}` | ExtAlgeb | :math:`0` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | te | :math:`\tau_{e}` | ExtAlgeb | :math:`0` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`V` | ExtAlgeb | :math:`0` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | f | :math:`f` | ExtAlgeb | :math:`0` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vi | :math:`v_{i}` | ExtAlgeb | :math:`u_{e} v_{sout}` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v2 | :math:`V` | ExtAlgeb | :math:`0` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | f2 | :math:`f_{2}` | ExtAlgeb | :math:`0` | +--------+------------------+----------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +------+---------------+----------------------+--------------+ | Name | Symbol | Equation | Type | +======+===============+======================+==============+ | ue | :math:`u_{e}` | :math:`u u_{ee}` | ConstService | +------+---------------+----------------------+--------------+ | VOU | :math:`VOU` | :math:`VCUr + V_{0}` | ConstService | +------+---------------+----------------------+--------------+ | VOL | :math:`VOL` | :math:`VCLr + V_{0}` | ConstService | +------+---------------+----------------------+--------------+ Discretes ----------- +----------+-------------------+-------------+----------------+ | Name | Symbol | Type | Info | +==========+===================+=============+================+ | dv | :math:`dv` | Derivative | | +----------+-------------------+-------------+----------------+ | dv2 | :math:`dv2` | Derivative | | +----------+-------------------+-------------+----------------+ | SW | :math:`SW` | Switcher | | +----------+-------------------+-------------+----------------+ | SW2 | :math:`SW2` | Switcher | | +----------+-------------------+-------------+----------------+ | WO_LT | :math:`LT_{WO}` | LessThan | | +----------+-------------------+-------------+----------------+ | LL1_LT1 | :math:`LT_{LL1}` | LessThan | | +----------+-------------------+-------------+----------------+ | LL1_LT2 | :math:`LT_{LL1}` | LessThan | | +----------+-------------------+-------------+----------------+ | LL2_LT1 | :math:`LT_{LL2}` | LessThan | | +----------+-------------------+-------------+----------------+ | LL2_LT2 | :math:`LT_{LL2}` | LessThan | | +----------+-------------------+-------------+----------------+ | LL3_LT1 | :math:`LT_{LL3}` | LessThan | | +----------+-------------------+-------------+----------------+ | LL3_LT2 | :math:`LT_{LL3}` | LessThan | | +----------+-------------------+-------------+----------------+ | VSS_lim | :math:`lim_{VSS}` | HardLimiter | | +----------+-------------------+-------------+----------------+ | OLIM | :math:`OLIM` | Limiter | output limiter | +----------+-------------------+-------------+----------------+ Blocks ------- +------+-------------+--------------+--------------+ | Name | Symbol | Type | Info | +======+=============+==============+==============+ | L1 | :math:`L1` | Lag | Transducer 1 | +------+-------------+--------------+--------------+ | L2 | :math:`L2` | Lag | Transducer 2 | +------+-------------+--------------+--------------+ | WO | :math:`WO` | WashoutOrLag | | +------+-------------+--------------+--------------+ | LL1 | :math:`LL1` | LeadLag | | +------+-------------+--------------+--------------+ | LL2 | :math:`LL2` | LeadLag | | +------+-------------+--------------+--------------+ | LL3 | :math:`LL3` | LeadLag | | +------+-------------+--------------+--------------+ | VSS | :math:`VSS` | GainLimiter | | +------+-------------+--------------+--------------+ Config Fields in [ST2CUT] +---------------+--------+---------+---------------------------------------+-----------------+ | 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) | +---------------+--------+---------+---------------------------------------+-----------------+ | freq_model | | BusFreq | default freq. measurement model | ('BusFreq',) | +---------------+--------+---------+---------------------------------------+-----------------+