.. _SynGen: ================================================================================ SynGen ================================================================================ Synchronous generator group. SynGen replaces StaticGen upon the initialization of dynamic studies. SynGen and inverter-based resources contain parameters ``gammap`` and ``gammaq`` for splitting the initial power of a StaticGen into multiple dynamic ones. ``gammap``, for example, is the active power ratio of the dynamic generator to the static one. If a StaticGen is supposed to be replaced by one SynGen, the ``gammap`` and ``gammaq`` should both be ``1``. It is critical to ensure that ``gammap`` and ``gammaq``, respectively, of all dynamic power sources sum up to 1.0. Otherwise, the initial power injections imposed by dynamic sources will differ from the static ones. The initialization will then fail with mismatches power injection equations corresponding to bus ``a`` and ``v``. Common Parameters: u, name, Sn, Vn, fn, bus, M, D, subidx Common Variables: omega, delta Available models: GENCLS_, GENROU_, PLBVFU1_ .. _GENCLS: -------------------------------------------------------------------------------- GENCLS -------------------------------------------------------------------------------- Classical generator model. Parameters ---------- +---------+------------------+-------------------------------------------------+---------+--------+-----------------------------+ | Name | Symbol | Description | Default | Unit | Properties | +=========+==================+=================================================+=========+========+=============================+ | idx | | unique device idx | | | | +---------+------------------+-------------------------------------------------+---------+--------+-----------------------------+ | u | :math:`u` | connection status | 1 | *bool* | | +---------+------------------+-------------------------------------------------+---------+--------+-----------------------------+ | name | | device name | | | | +---------+------------------+-------------------------------------------------+---------+--------+-----------------------------+ | bus | | interface bus id | | | mandatory | +---------+------------------+-------------------------------------------------+---------+--------+-----------------------------+ | gen | | static generator index | | | mandatory | +---------+------------------+-------------------------------------------------+---------+--------+-----------------------------+ | coi | | center of inertia index | | | | +---------+------------------+-------------------------------------------------+---------+--------+-----------------------------+ | coi2 | | center of inertia index | | | | +---------+------------------+-------------------------------------------------+---------+--------+-----------------------------+ | Sn | :math:`S_n` | Power rating | 100 | *MVA* | | +---------+------------------+-------------------------------------------------+---------+--------+-----------------------------+ | Vn | :math:`V_n` | AC voltage rating | 110 | | | +---------+------------------+-------------------------------------------------+---------+--------+-----------------------------+ | fn | :math:`f` | rated frequency | 60 | | | +---------+------------------+-------------------------------------------------+---------+--------+-----------------------------+ | D | :math:`D` | Damping coefficient | 0 | | power | +---------+------------------+-------------------------------------------------+---------+--------+-----------------------------+ | M | :math:`M` | machine start up time (2H) | 6 | | non_zero,non_negative,power | +---------+------------------+-------------------------------------------------+---------+--------+-----------------------------+ | ra | :math:`r_a` | armature resistance | 0 | | z | +---------+------------------+-------------------------------------------------+---------+--------+-----------------------------+ | xl | :math:`x_l` | leakage reactance | 0 | | z | +---------+------------------+-------------------------------------------------+---------+--------+-----------------------------+ | xd1 | :math:`x'_d` | d-axis transient reactance | 0.302 | | z | +---------+------------------+-------------------------------------------------+---------+--------+-----------------------------+ | kp | :math:`k_p` | active power feedback gain | 0 | | | +---------+------------------+-------------------------------------------------+---------+--------+-----------------------------+ | kw | :math:`k_w` | speed feedback gain | 0 | | | +---------+------------------+-------------------------------------------------+---------+--------+-----------------------------+ | S10 | :math:`S_{1.0}` | first saturation factor | 0 | | | +---------+------------------+-------------------------------------------------+---------+--------+-----------------------------+ | S12 | :math:`S_{1.2}` | second saturation factor | 1 | | | +---------+------------------+-------------------------------------------------+---------+--------+-----------------------------+ | gammap | :math:`\gamma_P` | P ratio of linked static gen | 1 | | | +---------+------------------+-------------------------------------------------+---------+--------+-----------------------------+ | gammaq | :math:`\gamma_Q` | Q ratio of linked static gen | 1 | | | +---------+------------------+-------------------------------------------------+---------+--------+-----------------------------+ | subidx | | Generator idx in plant; only used by PSS/E data | 0 | | | +---------+------------------+-------------------------------------------------+---------+--------+-----------------------------+ Variables --------- +---------+----------------+----------+------------------------------------+------------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +=========+================+==========+====================================+============+============+ | delta | :math:`\delta` | State | rotor angle | *rad* | v_str | +---------+----------------+----------+------------------------------------+------------+------------+ | omega | :math:`\omega` | State | rotor speed | *pu (Hz)* | v_str | +---------+----------------+----------+------------------------------------+------------+------------+ | Id | :math:`Id` | Algeb | d-axis current | | v_str | +---------+----------------+----------+------------------------------------+------------+------------+ | Iq | :math:`Iq` | Algeb | q-axis current | | v_str | +---------+----------------+----------+------------------------------------+------------+------------+ | vd | :math:`vd` | Algeb | d-axis voltage | | v_str | +---------+----------------+----------+------------------------------------+------------+------------+ | vq | :math:`vq` | Algeb | q-axis voltage | | v_str | +---------+----------------+----------+------------------------------------+------------+------------+ | tm | :math:`tm` | Algeb | mechanical torque | | v_str | +---------+----------------+----------+------------------------------------+------------+------------+ | te | :math:`te` | Algeb | electric torque | | v_str | +---------+----------------+----------+------------------------------------+------------+------------+ | vf | :math:`vf` | Algeb | excitation voltage | *pu* | v_str | +---------+----------------+----------+------------------------------------+------------+------------+ | XadIfd | :math:`XadIfd` | Algeb | d-axis armature excitation current | *p.u (kV)* | v_str | +---------+----------------+----------+------------------------------------+------------+------------+ | Pe | :math:`Pe` | Algeb | active power injection | | v_str | +---------+----------------+----------+------------------------------------+------------+------------+ | Qe | :math:`Qe` | Algeb | reactive power injection | | v_str | +---------+----------------+----------+------------------------------------+------------+------------+ | psid | :math:`psid` | Algeb | d-axis flux | | v_str | +---------+----------------+----------+------------------------------------+------------+------------+ | psiq | :math:`psiq` | Algeb | q-axis flux | | v_str | +---------+----------------+----------+------------------------------------+------------+------------+ | a | :math:`a` | ExtAlgeb | Bus voltage phase angle | | | +---------+----------------+----------+------------------------------------+------------+------------+ | v | :math:`v` | ExtAlgeb | Bus voltage magnitude | | | +---------+----------------+----------+------------------------------------+------------+------------+ Initialization Equations ------------------------ +---------+----------------+----------+------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+================+==========+======================================================+ | delta | :math:`\delta` | State | :math:`\delta_{0}` | +---------+----------------+----------+------------------------------------------------------+ | omega | :math:`\omega` | State | :math:`u` | +---------+----------------+----------+------------------------------------------------------+ | Id | :math:`Id` | Algeb | :math:`Id_{0} u` | +---------+----------------+----------+------------------------------------------------------+ | Iq | :math:`Iq` | Algeb | :math:`Iq_{0} u` | +---------+----------------+----------+------------------------------------------------------+ | vd | :math:`vd` | Algeb | :math:`u vd_{0}` | +---------+----------------+----------+------------------------------------------------------+ | vq | :math:`vq` | Algeb | :math:`u vq_{0}` | +---------+----------------+----------+------------------------------------------------------+ | tm | :math:`tm` | Algeb | :math:`tm_{0}` | +---------+----------------+----------+------------------------------------------------------+ | te | :math:`te` | Algeb | :math:`tm_{0} u` | +---------+----------------+----------+------------------------------------------------------+ | vf | :math:`vf` | Algeb | :math:`u vf_{0}` | +---------+----------------+----------+------------------------------------------------------+ | XadIfd | :math:`XadIfd` | Algeb | :math:`u vf_{0}` | +---------+----------------+----------+------------------------------------------------------+ | Pe | :math:`Pe` | Algeb | :math:`u \left(Id_{0} vd_{0} + Iq_{0} vq_{0}\right)` | +---------+----------------+----------+------------------------------------------------------+ | Qe | :math:`Qe` | Algeb | :math:`u \left(Id_{0} vq_{0} - Iq_{0} vd_{0}\right)` | +---------+----------------+----------+------------------------------------------------------+ | psid | :math:`psid` | Algeb | :math:`psid_{0} u` | +---------+----------------+----------+------------------------------------------------------+ | psiq | :math:`psiq` | Algeb | :math:`psiq_{0} u` | +---------+----------------+----------+------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | | +---------+----------------+----------+------------------------------------------------------+ | v | :math:`v` | ExtAlgeb | | +---------+----------------+----------+------------------------------------------------------+ Differential Equations ----------------------------- +--------+----------------+-------+--------------------------------------------------------------+-----------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+================+=======+==============================================================+===========+ | delta | :math:`\delta` | State | :math:`2 \pi fn u \left(\omega - 1\right)` | | +--------+----------------+-------+--------------------------------------------------------------+-----------+ | omega | :math:`\omega` | State | :math:`u \left(- D \left(\omega - 1\right) - te + tm\right)` | :math:`M` | +--------+----------------+-------+--------------------------------------------------------------+-----------+ Algebraic Equations ----------------------------- +---------+----------------+----------+---------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+================+==========+===================================================+ | Id | :math:`Id` | Algeb | :math:`Id xq + psid - vf` | +---------+----------------+----------+---------------------------------------------------+ | Iq | :math:`Iq` | Algeb | :math:`Iq xq + psiq` | +---------+----------------+----------+---------------------------------------------------+ | vd | :math:`vd` | Algeb | :math:`- u v \sin{\left(a - \delta \right)} - vd` | +---------+----------------+----------+---------------------------------------------------+ | vq | :math:`vq` | Algeb | :math:`u v \cos{\left(a - \delta \right)} - vq` | +---------+----------------+----------+---------------------------------------------------+ | tm | :math:`tm` | Algeb | :math:`- tm + tm_{0}` | +---------+----------------+----------+---------------------------------------------------+ | te | :math:`te` | Algeb | :math:`- te + u \left(- Id psiq + Iq psid\right)` | +---------+----------------+----------+---------------------------------------------------+ | vf | :math:`vf` | Algeb | :math:`u vf_{0} - vf` | +---------+----------------+----------+---------------------------------------------------+ | XadIfd | :math:`XadIfd` | Algeb | :math:`- XadIfd + u vf_{0}` | +---------+----------------+----------+---------------------------------------------------+ | Pe | :math:`Pe` | Algeb | :math:`- Pe + u \left(Id vd + Iq vq\right)` | +---------+----------------+----------+---------------------------------------------------+ | Qe | :math:`Qe` | Algeb | :math:`- Qe + u \left(Id vq - Iq vd\right)` | +---------+----------------+----------+---------------------------------------------------+ | psid | :math:`psid` | Algeb | :math:`- psid + u \left(Iq ra + vq\right)` | +---------+----------------+----------+---------------------------------------------------+ | psiq | :math:`psiq` | Algeb | :math:`psiq + u \left(Id ra + vd\right)` | +---------+----------------+----------+---------------------------------------------------+ | a | :math:`a` | ExtAlgeb | :math:`- u \left(Id vd + Iq vq\right)` | +---------+----------------+----------+---------------------------------------------------+ | v | :math:`v` | ExtAlgeb | :math:`- u \left(Id vq - Iq vd\right)` | +---------+----------------+----------+---------------------------------------------------+ Services ---------- +----------+-------------------+--------------------------------------------------------------------------------------------------------+--------------+ | Name | Symbol | Equation | Type | +==========+===================+========================================================================================================+==============+ | p0 | :math:`P_0` | :math:`gammap p0s` | ConstService | +----------+-------------------+--------------------------------------------------------------------------------------------------------+--------------+ | q0 | :math:`Q_0` | :math:`gammaq q0s` | ConstService | +----------+-------------------+--------------------------------------------------------------------------------------------------------+--------------+ | _V | :math:`V_c` | :math:`v e^{i a}` | ConstService | +----------+-------------------+--------------------------------------------------------------------------------------------------------+--------------+ | _S | :math:`S` | :math:`p_{0} - i q_{0}` | ConstService | +----------+-------------------+--------------------------------------------------------------------------------------------------------+--------------+ | _I | :math:`I_c` | :math:`\frac{_S}{\operatorname{conj}{\left(_V \right)}}` | ConstService | +----------+-------------------+--------------------------------------------------------------------------------------------------------+--------------+ | _E | :math:`E` | :math:`_I \left(ra + i xq\right) + _V` | ConstService | +----------+-------------------+--------------------------------------------------------------------------------------------------------+--------------+ | _deltac | :math:`\delta_c` | :math:`\log{\left(\frac{_E}{\left|{_E}\right|} \right)}` | ConstService | +----------+-------------------+--------------------------------------------------------------------------------------------------------+--------------+ | delta0 | :math:`\delta_0` | :math:`u \operatorname{im}{\left(_deltac\right)}` | ConstService | +----------+-------------------+--------------------------------------------------------------------------------------------------------+--------------+ | vdq | :math:`V_{dq}` | :math:`_V u e^{- _deltac + 0.5 i \pi}` | ConstService | +----------+-------------------+--------------------------------------------------------------------------------------------------------+--------------+ | Idq | :math:`I_{dq}` | :math:`_I u e^{- _deltac + 0.5 i \pi}` | ConstService | +----------+-------------------+--------------------------------------------------------------------------------------------------------+--------------+ | Id0 | :math:`I_{d0}` | :math:`\operatorname{re}{\left(Idq\right)}` | ConstService | +----------+-------------------+--------------------------------------------------------------------------------------------------------+--------------+ | Iq0 | :math:`I_{q0}` | :math:`\operatorname{im}{\left(Idq\right)}` | ConstService | +----------+-------------------+--------------------------------------------------------------------------------------------------------+--------------+ | vd0 | :math:`V_{d0}` | :math:`\operatorname{re}{\left(vdq\right)}` | ConstService | +----------+-------------------+--------------------------------------------------------------------------------------------------------+--------------+ | vq0 | :math:`V_{q0}` | :math:`\operatorname{im}{\left(vdq\right)}` | ConstService | +----------+-------------------+--------------------------------------------------------------------------------------------------------+--------------+ | tm0 | :math:`\tau_{m0}` | :math:`u \left(Id_{0} \left(Id_{0} ra + vd_{0}\right) + Iq_{0} \left(Iq_{0} ra + vq_{0}\right)\right)` | ConstService | +----------+-------------------+--------------------------------------------------------------------------------------------------------+--------------+ | psid0 | :math:`\psi_{d0}` | :math:`Iq_{0} ra u + vq_{0}` | ConstService | +----------+-------------------+--------------------------------------------------------------------------------------------------------+--------------+ | psiq0 | :math:`\psi_{q0}` | :math:`- Id_{0} ra u - vd_{0}` | ConstService | +----------+-------------------+--------------------------------------------------------------------------------------------------------+--------------+ | vf0 | :math:`v_{f0}` | :math:`Id_{0} xq + Iq_{0} ra + vq_{0}` | ConstService | +----------+-------------------+--------------------------------------------------------------------------------------------------------+--------------+ Config Fields in [GENCLS] +---------------+--------+-------+---------------------------------------+-----------------+ | 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) | +---------------+--------+-------+---------------------------------------+-----------------+ | vf_lower | | 1 | lower limit for vf warning | | +---------------+--------+-------+---------------------------------------+-----------------+ | vf_upper | | 5 | upper limit for vf warning | | +---------------+--------+-------+---------------------------------------+-----------------+ .. _GENROU: -------------------------------------------------------------------------------- GENROU -------------------------------------------------------------------------------- Round rotor generator with quadratic saturation. Notes ----- Parameters: - ``xd2`` and ``xq2`` must be equal to pass initialization. Parameters ---------- +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | Name | Symbol | Description | Default | Unit | Properties | +=========+====================+=================================================+=========+========+=============================+ | idx | | unique device idx | | | | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | u | :math:`u` | connection status | 1 | *bool* | | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | name | | device name | | | | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | bus | | interface bus id | | | mandatory | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | gen | | static generator index | | | mandatory | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | coi | | center of inertia index | | | | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | coi2 | | center of inertia index | | | | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | Sn | :math:`S_n` | Power rating | 100 | *MVA* | | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | Vn | :math:`V_n` | AC voltage rating | 110 | | | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | fn | :math:`f` | rated frequency | 60 | | | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | D | :math:`D` | Damping coefficient | 0 | | power | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | M | :math:`M` | machine start up time (2H) | 6 | | non_zero,non_negative,power | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | ra | :math:`r_a` | armature resistance | 0 | | z | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | xl | :math:`x_l` | leakage reactance | 0 | | z | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | xd1 | :math:`x'_d` | d-axis transient reactance | 0.302 | | z | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | kp | :math:`k_p` | active power feedback gain | 0 | | | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | kw | :math:`k_w` | speed feedback gain | 0 | | | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | S10 | :math:`S_{1.0}` | first saturation factor | 0 | | | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | S12 | :math:`S_{1.2}` | second saturation factor | 1 | | | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | gammap | :math:`\gamma_P` | P ratio of linked static gen | 1 | | | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | gammaq | :math:`\gamma_Q` | Q ratio of linked static gen | 1 | | | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | xd | :math:`x_d` | d-axis synchronous reactance | 1.900 | | z | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | xq | :math:`x_q` | q-axis synchronous reactance | 1.700 | | z | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | xd2 | :math:`{x''_d}` | d-axis sub-transient reactance | 0.300 | | z | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | xq1 | :math:`{x'_q}` | q-axis transient reactance | 0.500 | | z | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | xq2 | :math:`{x''_q}` | q-axis sub-transient reactance | 0.300 | | z | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | Td10 | :math:`{T'_{d0}}` | d-axis transient time constant | 8 | | | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | Td20 | :math:`{T''_{d0}}` | d-axis sub-transient time constant | 0.040 | | | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | Tq10 | :math:`{T'_{q0}}` | q-axis transient time constant | 0.800 | | | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | Tq20 | :math:`{T''_{q0}}` | q-axis sub-transient time constant | 0.020 | | | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ | subidx | | Generator idx in plant; only used by PSS/E data | 0 | | | +---------+--------------------+-------------------------------------------------+---------+--------+-----------------------------+ Variables --------- +---------+------------------+----------+------------------------------------+------------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +=========+==================+==========+====================================+============+============+ | delta | :math:`\delta` | State | rotor angle | *rad* | v_str | +---------+------------------+----------+------------------------------------+------------+------------+ | omega | :math:`\omega` | State | rotor speed | *pu (Hz)* | v_str | +---------+------------------+----------+------------------------------------+------------+------------+ | e1q | :math:`e1q` | State | q-axis transient voltage | | v_str | +---------+------------------+----------+------------------------------------+------------+------------+ | e1d | :math:`e1d` | State | d-axis transient voltage | | v_str | +---------+------------------+----------+------------------------------------+------------+------------+ | e2d | :math:`e2d` | State | d-axis sub-transient voltage | | v_str | +---------+------------------+----------+------------------------------------+------------+------------+ | e2q | :math:`e2q` | State | q-axis sub-transient voltage | | v_str | +---------+------------------+----------+------------------------------------+------------+------------+ | Id | :math:`Id` | Algeb | d-axis current | | v_str | +---------+------------------+----------+------------------------------------+------------+------------+ | Iq | :math:`Iq` | Algeb | q-axis current | | v_str | +---------+------------------+----------+------------------------------------+------------+------------+ | vd | :math:`vd` | Algeb | d-axis voltage | | v_str | +---------+------------------+----------+------------------------------------+------------+------------+ | vq | :math:`vq` | Algeb | q-axis voltage | | v_str | +---------+------------------+----------+------------------------------------+------------+------------+ | tm | :math:`tm` | Algeb | mechanical torque | | v_str | +---------+------------------+----------+------------------------------------+------------+------------+ | te | :math:`te` | Algeb | electric torque | | v_str | +---------+------------------+----------+------------------------------------+------------+------------+ | vf | :math:`vf` | Algeb | excitation voltage | *pu* | v_str | +---------+------------------+----------+------------------------------------+------------+------------+ | XadIfd | :math:`XadIfd` | Algeb | d-axis armature excitation current | *p.u (kV)* | v_str | +---------+------------------+----------+------------------------------------+------------+------------+ | Pe | :math:`Pe` | Algeb | active power injection | | v_str | +---------+------------------+----------+------------------------------------+------------+------------+ | Qe | :math:`Qe` | Algeb | reactive power injection | | v_str | +---------+------------------+----------+------------------------------------+------------+------------+ | psid | :math:`psid` | Algeb | d-axis flux | | v_str | +---------+------------------+----------+------------------------------------+------------+------------+ | psiq | :math:`psiq` | Algeb | q-axis flux | | v_str | +---------+------------------+----------+------------------------------------+------------+------------+ | psi2q | :math:`psi2q` | Algeb | q-axis air gap flux | | v_str | +---------+------------------+----------+------------------------------------+------------+------------+ | psi2d | :math:`psi2d` | Algeb | d-axis air gap flux | | v_str | +---------+------------------+----------+------------------------------------+------------+------------+ | psi2 | :math:`\psi_{2}` | Algeb | air gap flux magnitude | | v_str | +---------+------------------+----------+------------------------------------+------------+------------+ | Se | :math:`Se` | Algeb | saturation output | | v_str | +---------+------------------+----------+------------------------------------+------------+------------+ | XaqI1q | :math:`XaqI1q` | Algeb | q-axis reaction | *p.u (kV)* | v_str | +---------+------------------+----------+------------------------------------+------------+------------+ | a | :math:`a` | ExtAlgeb | Bus voltage phase angle | | | +---------+------------------+----------+------------------------------------+------------+------------+ | v | :math:`v` | ExtAlgeb | Bus voltage magnitude | | | +---------+------------------+----------+------------------------------------+------------+------------+ Initialization Equations ------------------------ +---------+------------------+----------+------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=========+==================+==========+======================================================+ | delta | :math:`\delta` | State | :math:`\delta_{0}` | +---------+------------------+----------+------------------------------------------------------+ | omega | :math:`\omega` | State | :math:`u` | +---------+------------------+----------+------------------------------------------------------+ | e1q | :math:`e1q` | State | :math:`e1q0 u` | +---------+------------------+----------+------------------------------------------------------+ | e1d | :math:`e1d` | State | :math:`e1d0 u` | +---------+------------------+----------+------------------------------------------------------+ | e2d | :math:`e2d` | State | :math:`e2d0 u` | +---------+------------------+----------+------------------------------------------------------+ | e2q | :math:`e2q` | State | :math:`e2q0 u` | +---------+------------------+----------+------------------------------------------------------+ | Id | :math:`Id` | Algeb | :math:`Id_{0} u` | +---------+------------------+----------+------------------------------------------------------+ | Iq | :math:`Iq` | Algeb | :math:`Iq_{0} u` | +---------+------------------+----------+------------------------------------------------------+ | vd | :math:`vd` | Algeb | :math:`u vd_{0}` | +---------+------------------+----------+------------------------------------------------------+ | vq | :math:`vq` | Algeb | :math:`u vq_{0}` | +---------+------------------+----------+------------------------------------------------------+ | tm | :math:`tm` | Algeb | :math:`tm_{0}` | +---------+------------------+----------+------------------------------------------------------+ | te | :math:`te` | Algeb | :math:`tm_{0} u` | +---------+------------------+----------+------------------------------------------------------+ | vf | :math:`vf` | Algeb | :math:`u vf_{0}` | +---------+------------------+----------+------------------------------------------------------+ | XadIfd | :math:`XadIfd` | Algeb | :math:`u vf_{0}` | +---------+------------------+----------+------------------------------------------------------+ | Pe | :math:`Pe` | Algeb | :math:`u \left(Id_{0} vd_{0} + Iq_{0} vq_{0}\right)` | +---------+------------------+----------+------------------------------------------------------+ | Qe | :math:`Qe` | Algeb | :math:`u \left(Id_{0} vq_{0} - Iq_{0} vd_{0}\right)` | +---------+------------------+----------+------------------------------------------------------+ | psid | :math:`psid` | Algeb | :math:`psid_{0} u` | +---------+------------------+----------+------------------------------------------------------+ | psiq | :math:`psiq` | Algeb | :math:`psiq_{0} u` | +---------+------------------+----------+------------------------------------------------------+ | psi2q | :math:`psi2q` | Algeb | :math:`psi2q0 u` | +---------+------------------+----------+------------------------------------------------------+ | psi2d | :math:`psi2d` | Algeb | :math:`psi2d0 u` | +---------+------------------+----------+------------------------------------------------------+ | psi2 | :math:`\psi_{2}` | Algeb | :math:`u \left|{\psi_{20 dq}}\right|` | +---------+------------------+----------+------------------------------------------------------+ | Se | :math:`Se` | Algeb | :math:`Se_{0} u` | +---------+------------------+----------+------------------------------------------------------+ | XaqI1q | :math:`XaqI1q` | Algeb | :math:`0` | +---------+------------------+----------+------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | | +---------+------------------+----------+------------------------------------------------------+ | v | :math:`v` | ExtAlgeb | | +---------+------------------+----------+------------------------------------------------------+ Differential Equations ----------------------------- +--------+----------------+-------+--------------------------------------------------------------+--------------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+================+=======+==============================================================+====================+ | delta | :math:`\delta` | State | :math:`2 \pi fn u \left(\omega - 1\right)` | | +--------+----------------+-------+--------------------------------------------------------------+--------------------+ | omega | :math:`\omega` | State | :math:`u \left(- D \left(\omega - 1\right) - te + tm\right)` | :math:`M` | +--------+----------------+-------+--------------------------------------------------------------+--------------------+ | e1q | :math:`e1q` | State | :math:`- XadIfd + vf` | :math:`{T'_{d0}}` | +--------+----------------+-------+--------------------------------------------------------------+--------------------+ | e1d | :math:`e1d` | State | :math:`- XaqI1q` | :math:`{T'_{q0}}` | +--------+----------------+-------+--------------------------------------------------------------+--------------------+ | e2d | :math:`e2d` | State | :math:`- Id \left(xd_{1} - xl\right) + e1q - e2d` | :math:`{T''_{d0}}` | +--------+----------------+-------+--------------------------------------------------------------+--------------------+ | e2q | :math:`e2q` | State | :math:`Iq \left(- xl + xq_{1}\right) + e1d - e2q` | :math:`{T''_{q0}}` | +--------+----------------+-------+--------------------------------------------------------------+--------------------+ Algebraic Equations ----------------------------- +---------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+==================+==========+==============================================================================================================================+ | Id | :math:`Id` | Algeb | :math:`Id xd_{2} - psi2d + psid` | +---------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------+ | Iq | :math:`Iq` | Algeb | :math:`Iq xq_{2} + psi2q + psiq` | +---------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------+ | vd | :math:`vd` | Algeb | :math:`- u v \sin{\left(a - \delta \right)} - vd` | +---------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------+ | vq | :math:`vq` | Algeb | :math:`u v \cos{\left(a - \delta \right)} - vq` | +---------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------+ | tm | :math:`tm` | Algeb | :math:`- tm + tm_{0}` | +---------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------+ | te | :math:`te` | Algeb | :math:`- te + u \left(- Id psiq + Iq psid\right)` | +---------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------+ | vf | :math:`vf` | Algeb | :math:`u vf_{0} - vf` | +---------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------+ | XadIfd | :math:`XadIfd` | Algeb | :math:`- XadIfd + u \left(Se psi2d + e1q + \left(xd - xd_{1}\right) \left(Id gd_{1} + e1q gd_{2} - e2d gd_{2}\right)\right)` | +---------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------+ | Pe | :math:`Pe` | Algeb | :math:`- Pe + u \left(Id vd + Iq vq\right)` | +---------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------+ | Qe | :math:`Qe` | Algeb | :math:`- Qe + u \left(Id vq - Iq vd\right)` | +---------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------+ | psid | :math:`psid` | Algeb | :math:`- psid + u \left(Iq ra + vq\right)` | +---------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------+ | psiq | :math:`psiq` | Algeb | :math:`psiq + u \left(Id ra + vd\right)` | +---------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------+ | psi2q | :math:`psi2q` | Algeb | :math:`e1d gq_{1} + e2q \left(1 - gq_{1}\right) - psi2q` | +---------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------+ | psi2d | :math:`psi2d` | Algeb | :math:`e1q gd_{1} + e2d gd_{2} \left(xd_{1} - xl\right) - psi2d` | +---------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------+ | psi2 | :math:`\psi_{2}` | Algeb | :math:`- \psi_{2}^{2} + psi2d^{2} + psi2q^{2}` | +---------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------+ | Se | :math:`Se` | Algeb | :math:`SAT_{B} SL_{z0} \left(- SAT_{A} + \psi_{2}\right)^{2} - Se \psi_{2}` | +---------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------+ | XaqI1q | :math:`XaqI1q` | Algeb | :math:`Se gqd psi2q - XaqI1q + e1d + \left(xq - xq_{1}\right) \left(- Iq gq_{1} + e1d gq_{2} - e2q gq_{2}\right)` | +---------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | :math:`- u \left(Id vd + Iq vq\right)` | +---------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`v` | ExtAlgeb | :math:`- u \left(Id vq - Iq vd\right)` | +---------+------------------+----------+------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | Name | Symbol | Equation | Type | +================+============================+=============================================================================================================================================================================================================================+==============+ | p0 | :math:`P_0` | :math:`gammap p0s` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | q0 | :math:`Q_0` | :math:`gammaq q0s` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | gd1 | :math:`\gamma_{d1}` | :math:`\frac{xd_{2} - xl}{xd_{1} - xl}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | gq1 | :math:`\gamma_{q1}` | :math:`\frac{- xl + xq_{2}}{- xl + xq_{1}}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | gd2 | :math:`\gamma_{d2}` | :math:`\frac{xd_{1} - xd_{2}}{\left(xd_{1} - xl\right)^{2}}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | gq2 | :math:`\gamma_{q2}` | :math:`\frac{xq_{1} - xq_{2}}{\left(- xl + xq_{1}\right)^{2}}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | gqd | :math:`\gamma_{qd}` | :math:`\frac{- xl + xq}{xd - xl}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | _S12 | :math:`S_{1.2}` | :math:`S_{12} - _fS12 + 1` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | SAT_E1 | :math:`E^{1c}_{S_{AT}}` | :math:`1.0` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | SAT_E2 | :math:`E^{2c}_{S_{AT}}` | :math:`3.2 - 2 SAT_{zSE2}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | SAT_SE1 | :math:`SE^{1c}_{S_{AT}}` | :math:`S_{10}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | SAT_SE2 | :math:`SE^{2c}_{S_{AT}}` | :math:`S_{12} - 2 SAT_{zSE2} + 2` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | SAT_a | :math:`a_{S_{AT}}` | :math:`\sqrt{\frac{SAT_{E1} SAT_{SE1}}{SAT_{E2} SAT_{SE2}}} \left(\operatorname{Indicator}{\left(SAT_{SE2} > 0 \right)} + \operatorname{Indicator}{\left(SAT_{SE2} < 0 \right)}\right)` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | SAT_A | :math:`A^q_{S_{AT}}` | :math:`SAT_{E2} - \frac{SAT_{E1} - SAT_{E2}}{SAT_{a} - 1}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | SAT_B | :math:`B^q_{S_{AT}}` | :math:`\frac{SAT_{E2} SAT_{SE2} \left(SAT_{a} - 1\right)^{2} \left(\operatorname{Indicator}{\left(SAT_{a} > 0 \right)} + \operatorname{Indicator}{\left(SAT_{a} < 0 \right)}\right)}{\left(SAT_{E1} - SAT_{E2}\right)^{2}}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | _V | :math:`V_c` | :math:`v e^{i a}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | _S | :math:`S` | :math:`p_{0} - i q_{0}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | _Zs | :math:`Z_s` | :math:`ra + i xd_{2}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | _It | :math:`I_t` | :math:`\frac{_S}{\operatorname{conj}{\left(_V \right)}}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | _Is | :math:`I_s` | :math:`_It + \frac{_V}{_Zs}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | psi20 | :math:`{\psi''_0}` | :math:`_Is _Zs` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | psi20_arg | :math:`\theta_{\psi''0}` | :math:`\arg{\left(\psi_{20} \right)}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | psi20_abs | :math:`|{\psi''_0}|` | :math:`\left|{\psi_{20}}\right|` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | _It_arg | :math:`\theta_{It0}` | :math:`\arg{\left(_It \right)}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | _psi20_It_arg | :math:`\theta_{\psi a It}` | :math:`- _It_{arg} + \psi_{20 arg}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | Se0 | :math:`S_{e0}` | :math:`\frac{SAT_{B} \left(- SAT_{A} + \psi_{20 abs}\right)^{2} \operatorname{Indicator}{\left(\psi_{20 abs} \geq SAT_{A} \right)}}{\psi_{20 abs}}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | _a | :math:`{a'}` | :math:`\psi_{20 abs} \left(Se_{0} gqd + 1\right)` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | _b | :math:`{b'}` | :math:`\left(- xq + xq_{2}\right) \left|{_It}\right|` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | delta0 | :math:`\delta_0` | :math:`\psi_{20 arg} + \operatorname{atan}{\left(\frac{_b \cos{\left(_psi20_{It arg} \right)}}{- _a + _b \sin{\left(_psi20_{It arg} \right)}} \right)}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | _Tdq | :math:`T_{dq}` | :math:`- i \sin{\left(\delta_{0} \right)} + \cos{\left(\delta_{0} \right)}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | psi20_dq | :math:`{\psi''_{0,dq}}` | :math:`_Tdq \psi_{20}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | It_dq | :math:`I_{t,dq}` | :math:`\operatorname{conj}{\left(_It _Tdq \right)}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | psi2d0 | :math:`\psi_{ad0}` | :math:`\operatorname{re}{\left(\psi_{20 dq}\right)}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | psi2q0 | :math:`\psi_{aq0}` | :math:`- \operatorname{im}{\left(\psi_{20 dq}\right)}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | Id0 | :math:`I_{d0}` | :math:`\operatorname{im}{\left(It_{dq}\right)}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | Iq0 | :math:`I_{q0}` | :math:`\operatorname{re}{\left(It_{dq}\right)}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | vd0 | :math:`V_{d0}` | :math:`- Id_{0} ra + Iq_{0} xq_{2} + psi2q0` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | vq0 | :math:`V_{q0}` | :math:`- Id_{0} xd_{2} - Iq_{0} ra + psi2d0` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | tm0 | :math:`\tau_{m0}` | :math:`u \left(Id_{0} \left(Id_{0} ra + vd_{0}\right) + Iq_{0} \left(Iq_{0} ra + vq_{0}\right)\right)` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | vf0 | :math:`v_{f0}` | :math:`Id_{0} \left(xd - xd_{2}\right) + psi2d0 \left(Se_{0} + 1\right)` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | psid0 | :math:`\psi_{d0}` | :math:`Iq_{0} ra u + vq_{0}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | psiq0 | :math:`\psi_{q0}` | :math:`- Id_{0} ra u - vd_{0}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | e1q0 | :math:`{e'_{q0}}` | :math:`Id_{0} \left(- xd + xd_{1}\right) - Se_{0} psi2d0 + vf_{0}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | e1d0 | :math:`{e'_{d0}}` | :math:`Iq_{0} \left(xq - xq_{1}\right) - Se_{0} gqd psi2q0` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | e2d0 | :math:`{e''_{d0}}` | :math:`Id_{0} \left(- xd + xl\right) - Se_{0} psi2d0 + vf_{0}` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ | e2q0 | :math:`{e''_{q0}}` | :math:`- Iq_{0} \left(xl - xq\right) - Se_{0} gqd psi2q0` | ConstService | +----------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+ Discretes ----------- +------+------------+----------+------+ | Name | Symbol | Type | Info | +======+============+==========+======+ | SL | :math:`SL` | LessThan | | +------+------------+----------+------+ Blocks ------- +------+----------------+------------+------+ | Name | Symbol | Type | Info | +======+================+============+======+ | SAT | :math:`S_{AT}` | ExcQuadSat | | +------+----------------+------------+------+ Config Fields in [GENROU] +---------------+--------+-------+---------------------------------------+-----------------+ | 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) | +---------------+--------+-------+---------------------------------------+-----------------+ | vf_lower | | 1 | lower limit for vf warning | | +---------------+--------+-------+---------------------------------------+-----------------+ | vf_upper | | 5 | upper limit for vf warning | | +---------------+--------+-------+---------------------------------------+-----------------+ .. _PLBVFU1: -------------------------------------------------------------------------------- PLBVFU1 -------------------------------------------------------------------------------- PLBVFU1 model: playback of voltage and frequency as a generator. The internal voltage and frequency are named ``Vflt`` and ``omega``. Rotor angle is named ``delta``. The current implementation relies on a ``TimeSeries`` device to provide the voltage and frequency signals. See ``ieee14_plbvfu1.xlsx`` and ``plbvf.xlsx`` in ``andes/cases/ieee14`` for an example. Voltage and frequeny data needs to be specified in per unit. Nominal values are not yet supported. Parameters ---------- +-----------+-------------------+-------------------------------------------------+---------+----------+--------------+ | Name | Symbol | Description | Default | Unit | Properties | +===========+===================+=================================================+=========+==========+==============+ | idx | | unique device idx | | | | +-----------+-------------------+-------------------------------------------------+---------+----------+--------------+ | u | :math:`u` | connection status | 1 | *bool* | | +-----------+-------------------+-------------------------------------------------+---------+----------+--------------+ | name | | device name | | | | +-----------+-------------------+-------------------------------------------------+---------+----------+--------------+ | bus | | interface bus id | | | mandatory | +-----------+-------------------+-------------------------------------------------+---------+----------+--------------+ | gen | | static generator index | | | mandatory | +-----------+-------------------+-------------------------------------------------+---------+----------+--------------+ | Sn | :math:`S_n` | Power rating | 100 | *MVA* | | +-----------+-------------------+-------------------------------------------------+---------+----------+--------------+ | Vn | :math:`V_n` | AC voltage rating | 110 | | | +-----------+-------------------+-------------------------------------------------+---------+----------+--------------+ | ra | :math:`r_a` | armature resistance | 0 | | z | +-----------+-------------------+-------------------------------------------------+---------+----------+--------------+ | xs | :math:`x_s` | generator transient reactance | 0.200 | | non_zero,z | +-----------+-------------------+-------------------------------------------------+---------+----------+--------------+ | fn | :math:`f_n` | rated frequency | 60 | | | +-----------+-------------------+-------------------------------------------------+---------+----------+--------------+ | Vflag | | playback voltage signal | 1 | *bool* | | +-----------+-------------------+-------------------------------------------------+---------+----------+--------------+ | fflag | | playback frequency signal | 1 | *bool* | | +-----------+-------------------+-------------------------------------------------+---------+----------+--------------+ | filename | | playback file name | | *string* | mandatory | +-----------+-------------------+-------------------------------------------------+---------+----------+--------------+ | Vscale | :math:`V_{scale}` | playback voltage scale | 1 | *pu* | non_negative | +-----------+-------------------+-------------------------------------------------+---------+----------+--------------+ | fscale | :math:`f_{scale}` | playback frequency scale | 1 | *pu* | non_negative | +-----------+-------------------+-------------------------------------------------+---------+----------+--------------+ | Tv | :math:`T_v` | filtering time constant for voltage | 0.200 | *s* | non_negative | +-----------+-------------------+-------------------------------------------------+---------+----------+--------------+ | Tf | :math:`T_f` | filtering time constant for frequency | 0.200 | *s* | non_negative | +-----------+-------------------+-------------------------------------------------+---------+----------+--------------+ | subidx | | Generator idx in plant; only used by PSS/E data | 0 | | | +-----------+-------------------+-------------------------------------------------+---------+----------+--------------+ Variables --------- +--------+----------------+----------+-------------------------+-------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +========+================+==========+=========================+=======+============+ | Vflt | :math:`Vflt` | State | filtered voltage | *pu* | v_str | +--------+----------------+----------+-------------------------+-------+------------+ | omega | :math:`\omega` | State | filtered frequency | *pu* | v_str | +--------+----------------+----------+-------------------------+-------+------------+ | delta | :math:`\delta` | State | rotor angle | *rad* | v_str | +--------+----------------+----------+-------------------------+-------+------------+ | a | :math:`a` | ExtAlgeb | Bus voltage phase angle | | | +--------+----------------+----------+-------------------------+-------+------------+ | v | :math:`v` | ExtAlgeb | Bus voltage magnitude | | | +--------+----------------+----------+-------------------------+-------+------------+ Initialization Equations ------------------------ +--------+----------------+----------+-------------------------------+ | Name | Symbol | Type | Initial Value | +========+================+==========+===============================+ | Vflt | :math:`Vflt` | State | :math:`- Voffs + Vts iVscale` | +--------+----------------+----------+-------------------------------+ | omega | :math:`\omega` | State | :math:`- foffs + fts ifscale` | +--------+----------------+----------+-------------------------------+ | delta | :math:`\delta` | State | :math:`\delta_{0}` | +--------+----------------+----------+-------------------------------+ | a | :math:`a` | ExtAlgeb | | +--------+----------------+----------+-------------------------------+ | v | :math:`v` | ExtAlgeb | | +--------+----------------+----------+-------------------------------+ Differential Equations ----------------------------- +--------+----------------+-------+--------------------------------------------+-------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +========+================+=======+============================================+=============+ | Vflt | :math:`Vflt` | State | :math:`- Vflt - Voffs + Vts iVscale` | :math:`T_v` | +--------+----------------+-------+--------------------------------------------+-------------+ | omega | :math:`\omega` | State | :math:`- foffs + fts ifscale - \omega` | :math:`T_f` | +--------+----------------+-------+--------------------------------------------+-------------+ | delta | :math:`\delta` | State | :math:`2 \pi fn u \left(\omega - 1\right)` | | +--------+----------------+-------+--------------------------------------------+-------------+ Algebraic Equations ----------------------------- +------+-----------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +======+===========+==========+==================================================================================================================================================================+ | a | :math:`a` | ExtAlgeb | :math:`\frac{Vflt v xs \sin{\left(a - \delta \right)}}{ra^{2} + xs^{2}} + \frac{ra v \left(- Vflt \cos{\left(a - \delta \right)} + v\right)}{ra^{2} + xs^{2}}` | +------+-----------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`v` | ExtAlgeb | :math:`- \frac{Vflt ra v \sin{\left(a - \delta \right)}}{ra^{2} + xs^{2}} + \frac{v xs \left(- Vflt \cos{\left(a - \delta \right)} + v\right)}{ra^{2} + xs^{2}}` | +------+-----------+----------+------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +----------+---------------------+------------------------------------------------------------------------------------------------------------------------+--------------+ | Name | Symbol | Equation | Type | +==========+=====================+========================================================================================================================+==============+ | zs | :math:`zs` | :math:`ra + i xs` | ConstService | +----------+---------------------+------------------------------------------------------------------------------------------------------------------------+--------------+ | zs2n | :math:`zs2n` | :math:`ra^{2} - xs^{2}` | ConstService | +----------+---------------------+------------------------------------------------------------------------------------------------------------------------+--------------+ | Ec | :math:`E_c` | :math:`v e^{i a} + \left(ra + i xs\right) \operatorname{conj}{\left(\frac{\left(p + i q\right) e^{- i a}}{v} \right)}` | ConstService | +----------+---------------------+------------------------------------------------------------------------------------------------------------------------+--------------+ | E0 | :math:`E_0` | :math:`\left|{Ec}\right|` | ConstService | +----------+---------------------+------------------------------------------------------------------------------------------------------------------------+--------------+ | delta0 | :math:`\delta_0` | :math:`\arg{\left(Ec \right)}` | ConstService | +----------+---------------------+------------------------------------------------------------------------------------------------------------------------+--------------+ | Vts | :math:`Vts` | :math:`0` | ConstService | +----------+---------------------+------------------------------------------------------------------------------------------------------------------------+--------------+ | fts | :math:`fts` | :math:`0` | ConstService | +----------+---------------------+------------------------------------------------------------------------------------------------------------------------+--------------+ | ifscale | :math:`1/f_{scale}` | :math:`\frac{1}{fscale}` | ConstService | +----------+---------------------+------------------------------------------------------------------------------------------------------------------------+--------------+ | iVscale | :math:`1/V_{scale}` | :math:`\frac{1}{Vscale}` | ConstService | +----------+---------------------+------------------------------------------------------------------------------------------------------------------------+--------------+ | foffs | :math:`f_{offs}` | :math:`fts ifscale - 1` | ConstService | +----------+---------------------+------------------------------------------------------------------------------------------------------------------------+--------------+ | Voffs | :math:`V_{offs}` | :math:`- E_{0} + Vts iVscale` | ConstService | +----------+---------------------+------------------------------------------------------------------------------------------------------------------------+--------------+ Config Fields in [PLBVFU1] +---------------+--------+-------+---------------------------------------+-----------------+ | 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) | +---------------+--------+-------+---------------------------------------+-----------------+