.. _RenExciter: ================================================================================ RenExciter ================================================================================ Renewable electrical control (exciter) group. Common Parameters: u, name, reg Common Variables: Pref, Qref, wg, Pord Available models: REECA1_, REECA1E_, REECA1G_ .. _REECA1: -------------------------------------------------------------------------------- REECA1 -------------------------------------------------------------------------------- Renewable energy electrical control. There are two user-defined voltages: `Vref0` and `Vref1`. - The difference between the initial bus voltage and `Vref0` should be within the voltage deadbands `dbd1` and `dbd2`. - If `VFLAG=0`, the input to the second PI controller will be `Vref1`. Regarding the additional reactive current injection during voltage dip: - Exercise caution when coordinating the parameters ``dbd1``, ``dbd2``, ``Vdip``, and ``Vup`` to avoid unintended responses. - ``Kqv`` in ``pu current / pu voltage deviation`` controls the intensity of reactive power injection. The parameter needs to tuned properly to avoid voltage overshoot. - When multiple renewable generators are connected to the same bus, ``Kqv`` shall be reduced accordingly to avoid excessive reactive power injection. Parameters ---------- +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +=========+==================+========================================================================+=========+========+============+ | idx | | unique device idx | | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | name | | device name | | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | reg | | Renewable generator idx | | | mandatory | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | busr | | Optional remote bus for voltage control | | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | PFFLAG | | Power factor control flag; 1-PF control, 0-Q control | | *bool* | mandatory | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | VFLAG | | Voltage control flag; 1-Q control, 0-V control | | *bool* | mandatory | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | QFLAG | | Q control flag; 1-V or Q control, 0-const. PF or Q | | *bool* | mandatory | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | PFLAG | | P speed-dependency flag; 1-has speed dep., 0-no dep. | | *bool* | mandatory | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | PQFLAG | | P/Q priority flag for I limit; 0-Q priority, 1-P priority | | *bool* | mandatory | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vdip | :math:`V_{dip}` | Low V threshold to activate Iqinj logic | 0.800 | *p.u.* | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vup | :math:`V_{up}` | V threshold above which to activate Iqinj logic | 1.200 | *p.u.* | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Trv | :math:`T_{rv}` | Voltage filter time constant | 0.020 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | dbd1 | :math:`d_{bd1}` | Lower bound of the voltage deadband (<=0) | -0.020 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | dbd2 | :math:`d_{bd2}` | Upper bound of the voltage deadband (>=0) | 0.020 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Kqv | :math:`K_{qv}` | Gain to compute Iqinj from V error (caution!!) | 1 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Iqh1 | :math:`I_{qh1}` | Upper limit on Iqinj | 999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Iql1 | :math:`I_{ql1}` | Lower limit on Iqinj | -999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vref0 | :math:`V_{ref0}` | User defined Vref (if 0, use initial bus V) | 1 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Iqfrz | :math:`I_{qfrz}` | Hold Iqinj at the value for Thld (>0) seconds following a Vdip | 0 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Thld | :math:`T_{hld}` | Time for which Iqinj is held. Hold at Iqinj if>0; hold at State 1 if<0 | 0 | *s* | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Thld2 | :math:`T_{hld2}` | Time for which IPMAX is held after voltage dip ends | 0 | *s* | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Tp | :math:`T_p` | Filter time constant for Pe | 0.020 | *s* | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | QMax | :math:`Q_{max}` | Upper limit for reactive power regulator | 999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | QMin | :math:`Q_{min}` | Lower limit for reactive power regulator | -999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | VMAX | :math:`V_{max}` | Upper limit for voltage control | 999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | VMIN | :math:`V_{min}` | Lower limit for voltage control | -999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Kqp | :math:`K_{qp}` | Proportional gain for reactive power error | 1 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Kqi | :math:`K_{qi}` | Integral gain for reactive power error | 0.100 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Kvp | :math:`K_{vp}` | Proportional gain for voltage error | 1 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Kvi | :math:`K_{vi}` | Integral gain for voltage error | 0.100 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vref1 | :math:`V_{ref1}` | Voltage ref. if VFLAG=0 | 1 | | non_zero | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Tiq | :math:`T_{iq}` | Filter time constant for Iq | 0.020 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | dPmax | :math:`d_{Pmax}` | Power reference max. ramp rate (>0) | 999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | dPmin | :math:`d_{Pin}` | Power reference min. ramp rate (<0) | -999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | PMAX | :math:`P_{max}` | Max. active power limit > 0 | 999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | PMIN | :math:`P_{min}` | Min. active power limit | 0 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Imax | :math:`I_{max}` | Max. apparent current limit | 999 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Tpord | :math:`T_{pord}` | Filter time constant for power setpoint | 0.020 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vq1 | :math:`V_{q1}` | Reactive power V-I pair (point 1), voltage | 0.200 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Iq1 | :math:`I_{q1}` | Reactive power V-I pair (point 1), current | 2 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vq2 | :math:`V_{q2}` | Reactive power V-I pair (point 2), voltage | 0.400 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Iq2 | :math:`I_{q2}` | Reactive power V-I pair (point 2), current | 4 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vq3 | :math:`V_{q3}` | Reactive power V-I pair (point 3), voltage | 0.800 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Iq3 | :math:`I_{q3}` | Reactive power V-I pair (point 3), current | 8 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vq4 | :math:`V_{q4}` | Reactive power V-I pair (point 4), voltage | 1 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Iq4 | :math:`I_{q4}` | Reactive power V-I pair (point 4), current | 10 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vp1 | :math:`V_{p1}` | Active power V-I pair (point 1), voltage | 0.200 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Ip1 | :math:`I_{p1}` | Active power V-I pair (point 1), current | 2 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vp2 | :math:`V_{p2}` | Active power V-I pair (point 2), voltage | 0.400 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Ip2 | :math:`I_{p2}` | Active power V-I pair (point 2), current | 4 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vp3 | :math:`V_{p3}` | Active power V-I pair (point 3), voltage | 0.800 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Ip3 | :math:`I_{p3}` | Active power V-I pair (point 3), current | 8 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vp4 | :math:`V_{p4}` | Active power V-I pair (point 4), voltage | 1 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Ip4 | :math:`I_{p4}` | Active power V-I pair (point 4), current | 12 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | bus | | Retrieved bus idx | | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | gen | | Retrieved StaticGen idx | | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Sn | :math:`S_n` | | 0 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ Variables --------- +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +==========+======================+============+====================================================+========+============+ | s0_y | :math:`y_{s0}` | State | State in lag transfer function | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | S1_y | :math:`y_{S_1}` | State | State in lag transfer function | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | PIQ_xi | :math:`xi_{PIQ}` | State | Integrator output | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | s4_y | :math:`y_{s_4}` | State | State in lag transfer function | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | pfilt_y | :math:`y_{P_{filt}}` | State | State in lag TF | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | s5_y | :math:`y_{s5}` | State | State in lag TF | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | PIV_xi | :math:`xi_{PIV}` | State | Integrator output | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Pord | :math:`Pord` | AliasState | Alias of s5_y | | | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | vp | :math:`V_{p}` | Algeb | Sensed lower-capped voltage | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | pfaref | :math:`\Phi_{ref}` | Algeb | power factor angle ref | *rad* | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Qref | :math:`Q_{ref}` | Algeb | external Q ref | *p.u.* | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Qcpf | :math:`Q_{cpf}` | Algeb | Q calculated from P and power factor | *p.u.* | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | PFsel | :math:`PFsel` | Algeb | Output of PFFLAG selector | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Qerr | :math:`Q_{err}` | Algeb | Reactive power error | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | PIQ_ys | :math:`ys_{PIQ}` | Algeb | PI summation before limit | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | PIQ_y | :math:`y_{PIQ}` | Algeb | PI output | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Vsel_x | :math:`x_{Vsel}` | Algeb | Value before limiter | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Vsel_y | :math:`y_{Vsel}` | Algeb | Output after limiter and post gain | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Verr | :math:`V_{err}` | Algeb | Voltage error (Vref0) | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | dbV_y | :math:`y_{dbV}` | Algeb | Deadband type 1 output | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Iqinj | :math:`I_{qinj}` | Algeb | Additional Iq signal during under- or over-voltage | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | wg | :math:`\omega_{g}` | Algeb | Drive train generator speed | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Pref | :math:`P_{ref}` | Algeb | external P ref | *p.u.* | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Psel | :math:`P_{sel}` | Algeb | Output selection of PFLAG | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | VDL1_y | :math:`y_{V_{DL1}}` | Algeb | Output of piecewise | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | VDL2_y | :math:`y_{V_{DL2}}` | Algeb | Output of piecewise | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Ipmax | :math:`I_{pmax}` | Algeb | Upper limit on Ipcmd | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Iqmax | :math:`I_{qmax}` | Algeb | Upper limit on Iqcmd | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | PIV_ys | :math:`ys_{PIV}` | Algeb | PI summation before limit | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | PIV_y | :math:`y_{PIV}` | Algeb | PI output | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Qsel | :math:`Q_{sel}` | Algeb | Selection output of QFLAG | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | IpHL_x | :math:`x_{IpHL}` | Algeb | Value before limiter | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | IpHL_y | :math:`y_{IpHL}` | Algeb | Output after limiter and post gain | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | IqHL_x | :math:`x_{IqHL}` | Algeb | Value before limiter | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | IqHL_y | :math:`y_{IqHL}` | Algeb | Output after limiter and post gain | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | a | :math:`\theta` | ExtAlgeb | Bus voltage angle | | | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | v | :math:`V_{d}` | ExtAlgeb | d-axis bus voltage magnitude | | | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Pe | :math:`Pe` | ExtAlgeb | Retrieved Pe of RenGen | | | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Qe | :math:`Qe` | ExtAlgeb | Retrieved Qe of RenGen | | | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Ipcmd | :math:`Ipcmd` | ExtAlgeb | Retrieved Ipcmd of RenGen | | | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Iqcmd | :math:`Iqcmd` | ExtAlgeb | Retrieved Iqcmd of RenGen | | | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ Initialization Equations ------------------------ +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +==========+======================+============+=======================================================================================================================================================================================================================================================================================================================================================================================================+ | s0_y | :math:`y_{s0}` | State | :math:`V_{d}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | S1_y | :math:`y_{S_1}` | State | :math:`Pe` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_xi | :math:`xi_{PIQ}` | State | :math:`0.0` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | s4_y | :math:`y_{s_4}` | State | :math:`\frac{PFsel}{V_{p}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | pfilt_y | :math:`y_{P_{filt}}` | State | :math:`P_{ref}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | s5_y | :math:`y_{s5}` | State | :math:`P_{sel}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_xi | :math:`xi_{PIV}` | State | :math:`- Iqcmd_{0} s_1^{SW_{V}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pord | :math:`Pord` | AliasState | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vp | :math:`V_{p}` | Algeb | :math:`V_{d} z_i^{VLower} + 0.01 z_l^{VLower}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | pfaref | :math:`\Phi_{ref}` | Algeb | :math:`\Phi_{ref0}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qref | :math:`Q_{ref}` | Algeb | :math:`- q_{ref0}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qcpf | :math:`Q_{cpf}` | Algeb | :math:`Q_{0}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PFsel | :math:`PFsel` | Algeb | :math:`Q_{cpf} s_1^{SW_{PF}} + Q_{ref} s_0^{SW_{PF}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qerr | :math:`Q_{err}` | Algeb | :math:`PFsel z_i^{PFlim} + Q_{max} z_u^{PFlim} + Q_{min} z_l^{PFlim} - Qe` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_ys | :math:`ys_{PIQ}` | Algeb | :math:`K_{qp} Q_{err} s_1^{SW_{V}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_y | :math:`y_{PIQ}` | Algeb | :math:`V_{max} z_u^{lim_{PIQ}} + V_{min} z_l^{lim_{PIQ}} + ys_{PIQ} z_i^{lim_{PIQ}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vsel_x | :math:`x_{Vsel}` | Algeb | :math:`s_0^{SW_{V}} \left(Q_{cpf} s_1^{SW_{PF}} + Q_{ref} s_0^{SW_{PF}} + V_{ref1}\right) + s_1^{SW_{V}} y_{PIQ}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vsel_y | :math:`y_{Vsel}` | Algeb | :math:`V_{max} z_u^{lim_{Vsel}} + V_{min} z_l^{lim_{Vsel}} + x_{Vsel} z_i^{lim_{Vsel}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Verr | :math:`V_{err}` | Algeb | :math:`V_{ref0} - y_{s0}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | dbV_y | :math:`y_{dbV}` | Algeb | :math:`1.0 z_l^{db_{dbV}} \left(V_{err} - d_{bd1}\right) + 1.0 z_u^{db_{dbV}} \left(V_{err} - d_{bd2}\right)` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqinj | :math:`I_{qinj}` | Algeb | :math:`K_{qv} y_{dbV} z_{Vdip} + fThld \left(1 - z_{Vdip}\right) \left(I_{qfrz} p_{Thld} + K_{qv} n_{Thld} y_{dbV}\right)` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | wg | :math:`\omega_{g}` | Algeb | :math:`1.0` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pref | :math:`P_{ref}` | Algeb | :math:`\frac{P_{0}}{\omega_{g}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Psel | :math:`P_{sel}` | Algeb | :math:`\omega_{g} s_1^{SW_{P}} y_{P_{filt}} + s_0^{SW_{P}} y_{P_{filt}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VDL1_y | :math:`y_{V_{DL1}}` | Algeb | :math:`\operatorname{FixPiecewise}{\left(\left( I_{q1}, \ V_{q1} \geq y_{s0}\right),\left( I_{q1} + k_{Vq12} \left(- V_{q1} + y_{s0}\right), \ V_{q2} \geq y_{s0}\right),\left( I_{q2} + k_{Vq23} \left(- V_{q2} + y_{s0}\right), \ V_{q3} \geq y_{s0}\right),\left( I_{q3} + k_{Vq34} \left(- V_{q3} + y_{s0}\right), \ V_{q4} \geq y_{s0}\right),\left( I_{q4}, \ \text{True}\right) \right)}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VDL2_y | :math:`y_{V_{DL2}}` | Algeb | :math:`\operatorname{FixPiecewise}{\left(\left( I_{p1}, \ V_{p1} \geq y_{s0}\right),\left( I_{p1} + k_{Vp12} \left(- V_{p1} + y_{s0}\right), \ V_{p2} \geq y_{s0}\right),\left( I_{p2} + k_{Vp23} \left(- V_{p2} + y_{s0}\right), \ V_{p3} \geq y_{s0}\right),\left( I_{p3} + k_{Vp34} \left(- V_{p3} + y_{s0}\right), \ V_{p4} \geq y_{s0}\right),\left( I_{p4}, \ \text{True}\right) \right)}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Ipmax | :math:`I_{pmax}` | Algeb | :math:`\left(1 - fThld_{2}\right) \left(\sqrt{I_{pmax20,nn}^2} s_0^{SW_{PQ}} + s_1^{SW_{PQ}} \left(z_{VDL2} \left(I_{maxr} \left(1 - VDL2c\right) + VDL2c y_{V_{DL2}}\right) - 100000000.0 z_{VDL2} + 100000000.0\right)\right)` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqmax | :math:`I_{qmax}` | Algeb | :math:`\sqrt{I_{qmax,nn}^2} s_1^{SW_{PQ}} + s_0^{SW_{PQ}} \left(z_{VDL1} \left(I_{maxr} \left(1 - VDL1c\right) + VDL1c y_{V_{DL1}}\right) - 100000000.0 z_{VDL1} + 100000000.0\right)` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_ys | :math:`ys_{PIV}` | Algeb | :math:`- Iqcmd_{0} s_1^{SW_{V}} + K_{vp} s_1^{SW_{V}} \left(- s_0^{SW_{V}} y_{s0} + y_{Vsel}\right)` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_y | :math:`y_{PIV}` | Algeb | :math:`I_{qmax} z_u^{lim_{PIV}} + I_{qmin} z_l^{lim_{PIV}} + ys_{PIV} z_i^{lim_{PIV}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qsel | :math:`Q_{sel}` | Algeb | :math:`s_0^{SW_{V}} y_{s_4} + s_1^{SW_{V}} y_{PIV}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IpHL_x | :math:`x_{IpHL}` | Algeb | :math:`\frac{y_{s5}}{V_{p}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IpHL_y | :math:`y_{IpHL}` | Algeb | :math:`I_{pmax} z_u^{lim_{IpHL}} + I_{pmin} z_l^{lim_{IpHL}} + x_{IpHL} z_i^{lim_{IpHL}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IqHL_x | :math:`x_{IqHL}` | Algeb | :math:`I_{qinj} + Q_{sel}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IqHL_y | :math:`y_{IqHL}` | Algeb | :math:`I_{qmax} z_u^{lim_{IqHL}} + I_{qmin} z_l^{lim_{IqHL}} + x_{IqHL} z_i^{lim_{IqHL}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`V_{d}` | ExtAlgeb | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pe | :math:`Pe` | ExtAlgeb | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qe | :math:`Qe` | ExtAlgeb | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Ipcmd | :math:`Ipcmd` | ExtAlgeb | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqcmd | :math:`Iqcmd` | ExtAlgeb | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +==========+======================+============+===========================================================================================================================================+==================+ | s0_y | :math:`y_{s0}` | State | :math:`V_{d} - y_{s0}` | :math:`T_{rv}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | S1_y | :math:`y_{S_1}` | State | :math:`Pe - y_{S_1}` | :math:`T_p` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | PIQ_xi | :math:`xi_{PIQ}` | State | :math:`K_{qi} \left(1 - z_{Vdip}\right) \left(Q_{err} s_1^{SW_{V}} + 2 y_{PIQ} - 2 ys_{PIQ}\right)` | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | s4_y | :math:`y_{s_4}` | State | :math:`\left(1 - z_{Vdip}\right) \left(\frac{PFsel}{V_{p}} - y_{s_4}\right)` | :math:`T_{iq}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | pfilt_y | :math:`y_{P_{filt}}` | State | :math:`P_{ref} - y_{P_{filt}}` | :math:`0.02` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | s5_y | :math:`y_{s5}` | State | :math:`\left(1 - z_{Vdip}\right) \left(P_{sel} - y_{s5}\right)` | :math:`T_{pord}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | PIV_xi | :math:`xi_{PIV}` | State | :math:`K_{vi} \left(1 - z_{Vdip}\right) \left(s_1^{SW_{V}} \left(- s_0^{SW_{V}} y_{s0} + y_{Vsel}\right) + 2 y_{PIV} - 2 ys_{PIV}\right)` | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | Pord | :math:`Pord` | AliasState | :math:`0` | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ Algebraic Equations ----------------------------- +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+=====================+==========+=======================================================================================================================================================================================================================================================================================================================================================================================================================+ | vp | :math:`V_{p}` | Algeb | :math:`V_{d} z_i^{VLower} - V_{p} + 0.01 z_l^{VLower}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | pfaref | :math:`\Phi_{ref}` | Algeb | :math:`\Phi_{ref0} - \Phi_{ref}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qref | :math:`Q_{ref}` | Algeb | :math:`- Q_{ref} - q_{ref0}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qcpf | :math:`Q_{cpf}` | Algeb | :math:`\left(1 - z_1^{zp}\right) \left(- Q_{cpf} + y_{S_1} \tan{\left(\Phi_{ref} \right)}\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PFsel | :math:`PFsel` | Algeb | :math:`- PFsel + Q_{cpf} s_1^{SW_{PF}} + Q_{ref} s_0^{SW_{PF}}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qerr | :math:`Q_{err}` | Algeb | :math:`PFsel z_i^{PFlim} - Q_{err} + Q_{max} z_u^{PFlim} + Q_{min} z_l^{PFlim} - Qe` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_ys | :math:`ys_{PIQ}` | Algeb | :math:`\left(1 - z_{Vdip}\right) \left(K_{qp} Q_{err} s_1^{SW_{V}} + xi_{PIQ} - ys_{PIQ}\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_y | :math:`y_{PIQ}` | Algeb | :math:`\left(1 - z_{Vdip}\right) \left(V_{max} z_u^{lim_{PIQ}} + V_{min} z_l^{lim_{PIQ}} - y_{PIQ} + ys_{PIQ} z_i^{lim_{PIQ}}\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vsel_x | :math:`x_{Vsel}` | Algeb | :math:`s_0^{SW_{V}} \left(Q_{cpf} s_1^{SW_{PF}} + Q_{ref} s_0^{SW_{PF}} + V_{ref1}\right) + s_1^{SW_{V}} y_{PIQ} - x_{Vsel}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vsel_y | :math:`y_{Vsel}` | Algeb | :math:`V_{max} z_u^{lim_{Vsel}} + V_{min} z_l^{lim_{Vsel}} + x_{Vsel} z_i^{lim_{Vsel}} - y_{Vsel}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Verr | :math:`V_{err}` | Algeb | :math:`- V_{err} + V_{ref0} - y_{s0}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | dbV_y | :math:`y_{dbV}` | Algeb | :math:`- y_{dbV} + 1.0 z_l^{db_{dbV}} \left(V_{err} - d_{bd1}\right) + 1.0 z_u^{db_{dbV}} \left(V_{err} - d_{bd2}\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqinj | :math:`I_{qinj}` | Algeb | :math:`- I_{qinj} + K_{qv} y_{dbV} z_{Vdip} + fThld \left(1 - z_{Vdip}\right) \left(I_{qfrz} p_{Thld} + K_{qv} n_{Thld} y_{dbV}\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | wg | :math:`\omega_{g}` | Algeb | :math:`1.0 - \omega_{g}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pref | :math:`P_{ref}` | Algeb | :math:`\frac{P_{0}}{\omega_{g}} - P_{ref}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Psel | :math:`P_{sel}` | Algeb | :math:`- P_{sel} + \omega_{g} s_1^{SW_{P}} y_{P_{filt}} + s_0^{SW_{P}} y_{P_{filt}}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VDL1_y | :math:`y_{V_{DL1}}` | Algeb | :math:`- y_{V_{DL1}} + \operatorname{FixPiecewise}{\left(\left( I_{q1}, \ V_{q1} \geq y_{s0}\right),\left( I_{q1} + k_{Vq12} \left(- V_{q1} + y_{s0}\right), \ V_{q2} \geq y_{s0}\right),\left( I_{q2} + k_{Vq23} \left(- V_{q2} + y_{s0}\right), \ V_{q3} \geq y_{s0}\right),\left( I_{q3} + k_{Vq34} \left(- V_{q3} + y_{s0}\right), \ V_{q4} \geq y_{s0}\right),\left( I_{q4}, \ \text{True}\right) \right)}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VDL2_y | :math:`y_{V_{DL2}}` | Algeb | :math:`- y_{V_{DL2}} + \operatorname{FixPiecewise}{\left(\left( I_{p1}, \ V_{p1} \geq y_{s0}\right),\left( I_{p1} + k_{Vp12} \left(- V_{p1} + y_{s0}\right), \ V_{p2} \geq y_{s0}\right),\left( I_{p2} + k_{Vp23} \left(- V_{p2} + y_{s0}\right), \ V_{p3} \geq y_{s0}\right),\left( I_{p3} + k_{Vp34} \left(- V_{p3} + y_{s0}\right), \ V_{p4} \geq y_{s0}\right),\left( I_{p4}, \ \text{True}\right) \right)}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Ipmax | :math:`I_{pmax}` | Algeb | :math:`- I_{pmax} + Ipmaxh fThld_{2} + \left(1 - fThld_{2}\right) \left(\sqrt{I_{pmax2}^2} s_0^{SW_{PQ}} + s_1^{SW_{PQ}} \left(z_{VDL2} \left(I_{maxr} \left(1 - VDL2c\right) + VDL2c y_{V_{DL2}}\right) - 100000000.0 z_{VDL2} + 100000000.0\right)\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqmax | :math:`I_{qmax}` | Algeb | :math:`\sqrt{I_{qmax2}^2} s_1^{SW_{PQ}} - I_{qmax} + s_0^{SW_{PQ}} \left(z_{VDL1} \left(I_{maxr} \left(1 - VDL1c\right) + VDL1c y_{V_{DL1}}\right) - 100000000.0 z_{VDL1} + 100000000.0\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_ys | :math:`ys_{PIV}` | Algeb | :math:`\left(1 - z_{Vdip}\right) \left(K_{vp} s_1^{SW_{V}} \left(- s_0^{SW_{V}} y_{s0} + y_{Vsel}\right) + xi_{PIV} - ys_{PIV}\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_y | :math:`y_{PIV}` | Algeb | :math:`\left(1 - z_{Vdip}\right) \left(I_{qmax} z_u^{lim_{PIV}} + I_{qmin} z_l^{lim_{PIV}} - y_{PIV} + ys_{PIV} z_i^{lim_{PIV}}\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qsel | :math:`Q_{sel}` | Algeb | :math:`- Q_{sel} + s_0^{SW_{V}} y_{s_4} + s_1^{SW_{V}} y_{PIV}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IpHL_x | :math:`x_{IpHL}` | Algeb | :math:`- x_{IpHL} + \frac{y_{s5}}{V_{p}}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IpHL_y | :math:`y_{IpHL}` | Algeb | :math:`I_{pmax} z_u^{lim_{IpHL}} + I_{pmin} z_l^{lim_{IpHL}} + x_{IpHL} z_i^{lim_{IpHL}} - y_{IpHL}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IqHL_x | :math:`x_{IqHL}` | Algeb | :math:`I_{qinj} + Q_{sel} - x_{IqHL}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IqHL_y | :math:`y_{IqHL}` | Algeb | :math:`I_{qmax} z_u^{lim_{IqHL}} + I_{qmin} z_l^{lim_{IqHL}} + x_{IqHL} z_i^{lim_{IqHL}} - y_{IqHL}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | :math:`0` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`V_{d}` | ExtAlgeb | :math:`0` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pe | :math:`Pe` | ExtAlgeb | :math:`0` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qe | :math:`Qe` | ExtAlgeb | :math:`0` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Ipcmd | :math:`Ipcmd` | ExtAlgeb | :math:`- Ipcmd_{0} + y_{IpHL}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqcmd | :math:`Iqcmd` | ExtAlgeb | :math:`- Iqcmd_{0} - y_{IqHL}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Name | Symbol | Equation | Type | +============+=========================+=====================================================================================================================================================================+===============+ | Ipcmd0 | :math:`Ipcmd0` | :math:`\frac{P_{0}}{V_{d}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Iqcmd0 | :math:`Iqcmd0` | :math:`- \frac{Q_{0}}{V_{d}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | pfaref0 | :math:`\Phi_{ref0}` | :math:`\operatorname{atan}_{2}{\left(Q_{0},P_{0} \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Volt_dip | :math:`z_{Vdip}` | :math:`1 - z_i^{V_{cmp}}` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | qref0 | :math:`q_{ref0}` | :math:`Iqcmd_{0} s_0^{SW_{V}} \left(V_{d} z_i^{VLower} + 0.01 z_l^{VLower}\right) + s_1^{SW_{V}} \left(V_{d} - V_{ref1}\right)` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | PIQ_flag | :math:`z^{flag}_{PIQ}` | :math:`0` | EventFlag | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | s4_flag | :math:`z^{flag}_{s_4}` | :math:`0` | EventFlag | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | pThld | :math:`p_{Thld}` | :math:`\operatorname{Indicator}{\left(T_{hld} > 0 \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | nThld | :math:`n_{Thld}` | :math:`\operatorname{Indicator}{\left(T_{hld} < 0 \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Thld_abs | :math:`|Thld|` | :math:`\left|{T_{hld}}\right|` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | fThld | :math:`fThld` | :math:`0` | ExtendedEvent | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | s5_flag | :math:`z^{flag}_{s5}` | :math:`0` | EventFlag | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVq12 | :math:`k_{Vq12}` | :math:`\frac{- I_{q1} + I_{q2}}{- V_{q1} + V_{q2}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVq23 | :math:`k_{Vq23}` | :math:`\frac{- I_{q2} + I_{q3}}{- V_{q2} + V_{q3}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVq34 | :math:`k_{Vq34}` | :math:`\frac{- I_{q3} + I_{q4}}{- V_{q3} + V_{q4}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | zVDL1 | :math:`z_{VDL1}` | :math:`I_{q1} \leq I_{q2} \wedge I_{q2} \leq I_{q3} \wedge I_{q3} \leq I_{q4} \wedge V_{q1} \leq V_{q2} \wedge V_{q2} \leq V_{q3} \wedge V_{q3} \leq V_{q4}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVp12 | :math:`k_{Vp12}` | :math:`\frac{- I_{p1} + I_{p2}}{- V_{p1} + V_{p2}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVp23 | :math:`k_{Vp23}` | :math:`\frac{- I_{p2} + I_{p3}}{- V_{p2} + V_{p3}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVp34 | :math:`k_{Vp34}` | :math:`\frac{- I_{p3} + I_{p4}}{- V_{p3} + V_{p4}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | zVDL2 | :math:`z_{VDL2}` | :math:`I_{p1} \leq I_{p2} \wedge I_{p2} \leq I_{p3} \wedge I_{p3} \leq I_{p4} \wedge V_{p1} \leq V_{p2} \wedge V_{p2} \leq V_{p3} \wedge V_{p3} \leq V_{p4}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | fThld2 | :math:`fThld2` | :math:`0` | ExtendedEvent | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | VDL1c | :math:`VDL1c` | :math:`y_{V_{DL1}} < I_{maxr}` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | VDL2c | :math:`VDL2c` | :math:`y_{V_{DL2}} < I_{maxr}` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Ipmax2sq0 | :math:`I_{pmax20,nn}^2` | :math:`\operatorname{FixPiecewise}{\left(\left( 0, \ I_{max}^{2} - Iqcmd_{0}^{2} \leq 0\right),\left( I_{max}^{2} - Iqcmd_{0}^{2}, \ \text{True}\right) \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Ipmax2sq | :math:`I_{pmax2}^2` | :math:`\operatorname{FixPiecewise}{\left(\left( 0, \ I_{max}^{2} - y_{IqHL}^{2} \leq 0\right),\left( I_{max}^{2} - y_{IqHL}^{2}, \ \text{True}\right) \right)}` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Ipmaxh | :math:`Ipmaxh` | :math:`0` | VarHold | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Iqmax2sq0 | :math:`I_{qmax,nn}^2` | :math:`\operatorname{FixPiecewise}{\left(\left( 0, \ I_{max}^{2} - Ipcmd_{0}^{2} \leq 0\right),\left( I_{max}^{2} - Ipcmd_{0}^{2}, \ \text{True}\right) \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Iqmax2sq | :math:`I_{qmax2}^2` | :math:`\operatorname{FixPiecewise}{\left(\left( 0, \ I_{max}^{2} - y_{IpHL}^{2} \leq 0\right),\left( I_{max}^{2} - y_{IpHL}^{2}, \ \text{True}\right) \right)}` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Ipmin | :math:`I_{pmin}` | :math:`0.0` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | PIV_flag | :math:`z^{flag}_{PIV}` | :math:`0` | EventFlag | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ Discretes ----------- +------------+------------------------+-------------+-------------------------------+ | Name | Symbol | Type | Info | +============+========================+=============+===============================+ | SWPF | :math:`SW_{PF}` | Switcher | | +------------+------------------------+-------------+-------------------------------+ | SWV | :math:`SW_{V}` | Switcher | | +------------+------------------------+-------------+-------------------------------+ | SWQ | :math:`SW_{V}` | Switcher | | +------------+------------------------+-------------+-------------------------------+ | SWP | :math:`SW_{P}` | Switcher | | +------------+------------------------+-------------+-------------------------------+ | SWPQ | :math:`SW_{PQ}` | Switcher | | +------------+------------------------+-------------+-------------------------------+ | zp | :math:`zp` | IsEqual | | +------------+------------------------+-------------+-------------------------------+ | Vcmp | :math:`V_{cmp}` | Limiter | Voltage dip comparator | +------------+------------------------+-------------+-------------------------------+ | VLower | :math:`VLower` | Limiter | Limiter for lower voltage cap | +------------+------------------------+-------------+-------------------------------+ | PFlim | :math:`PFlim` | Limiter | | +------------+------------------------+-------------+-------------------------------+ | PIQ_lim | :math:`lim_{PIQ}` | HardLimiter | | +------------+------------------------+-------------+-------------------------------+ | Vsel_lim | :math:`lim_{Vsel}` | HardLimiter | | +------------+------------------------+-------------+-------------------------------+ | dbV_db | :math:`db_{dbV}` | DeadBand | | +------------+------------------------+-------------+-------------------------------+ | pfilt_lim | :math:`lim_{P_{filt}}` | RateLimiter | Rate limiter in Lag | +------------+------------------------+-------------+-------------------------------+ | s5_lim | :math:`lim_{s5}` | AntiWindup | Limiter in Lag | +------------+------------------------+-------------+-------------------------------+ | PIV_lim | :math:`lim_{PIV}` | HardLimiter | | +------------+------------------------+-------------+-------------------------------+ | IpHL_lim | :math:`lim_{IpHL}` | HardLimiter | | +------------+------------------------+-------------+-------------------------------+ | IqHL_lim | :math:`lim_{IqHL}` | HardLimiter | | +------------+------------------------+-------------+-------------------------------+ Blocks ------- +--------+------------------+-----------------+-------------------------------------------+ | Name | Symbol | Type | Info | +========+==================+=================+===========================================+ | s0 | :math:`s0` | Lag | Voltage filter | +--------+------------------+-----------------+-------------------------------------------+ | S1 | :math:`S_1` | Lag | Pe filter | +--------+------------------+-----------------+-------------------------------------------+ | PIQ | :math:`PIQ` | PITrackAWFreeze | | +--------+------------------+-----------------+-------------------------------------------+ | Vsel | :math:`Vsel` | GainLimiter | Selection output of VFLAG | +--------+------------------+-----------------+-------------------------------------------+ | s4 | :math:`s_4` | LagFreeze | Filter for calculated voltage with freeze | +--------+------------------+-----------------+-------------------------------------------+ | dbV | :math:`dbV` | DeadBand1 | Deadband for voltage error (ref0) | +--------+------------------+-----------------+-------------------------------------------+ | pfilt | :math:`P_{filt}` | LagRate | Active power filter with rate limits | +--------+------------------+-----------------+-------------------------------------------+ | s5 | :math:`s5` | LagAWFreeze | | +--------+------------------+-----------------+-------------------------------------------+ | VDL1 | :math:`V_{DL1}` | Piecewise | Piecewise linear characteristics of Vq-Iq | +--------+------------------+-----------------+-------------------------------------------+ | VDL2 | :math:`V_{DL2}` | Piecewise | Piecewise linear characteristics of Vp-Ip | +--------+------------------+-----------------+-------------------------------------------+ | PIV | :math:`PIV` | PITrackAWFreeze | | +--------+------------------+-----------------+-------------------------------------------+ | IpHL | :math:`IpHL` | GainLimiter | | +--------+------------------+-----------------+-------------------------------------------+ | IqHL | :math:`IqHL` | GainLimiter | | +--------+------------------+-----------------+-------------------------------------------+ Config Fields in [REECA1] +---------------+-------------------+-------+---------------------------------------+-----------------+ | 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) | +---------------+-------------------+-------+---------------------------------------+-----------------+ | kqs | :math:`K_{qs}` | 2 | Q PI controller tracking gain | | +---------------+-------------------+-------+---------------------------------------+-----------------+ | kvs | :math:`K_{vs}` | 2 | Voltage PI controller tracking gain | | +---------------+-------------------+-------+---------------------------------------+-----------------+ | tpfilt | :math:`T_{pfilt}` | 0.020 | Time const. for Pref filter | | +---------------+-------------------+-------+---------------------------------------+-----------------+ .. _REECA1E: -------------------------------------------------------------------------------- REECA1E -------------------------------------------------------------------------------- REGCA1 with inertia emulation and primary frequency droop. Measurements are based on frequency measurement model. Bus ROCOF obtained from ``BusROCOF`` devices. Parameters ---------- +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +=========+==================+========================================================================+=========+========+============+ | idx | | unique device idx | | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | name | | device name | | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | reg | | Renewable generator idx | | | mandatory | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | busr | | Optional remote bus for voltage control | | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | PFFLAG | | Power factor control flag; 1-PF control, 0-Q control | | *bool* | mandatory | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | VFLAG | | Voltage control flag; 1-Q control, 0-V control | | *bool* | mandatory | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | QFLAG | | Q control flag; 1-V or Q control, 0-const. PF or Q | | *bool* | mandatory | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | PFLAG | | P speed-dependency flag; 1-has speed dep., 0-no dep. | | *bool* | mandatory | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | PQFLAG | | P/Q priority flag for I limit; 0-Q priority, 1-P priority | | *bool* | mandatory | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vdip | :math:`V_{dip}` | Low V threshold to activate Iqinj logic | 0.800 | *p.u.* | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vup | :math:`V_{up}` | V threshold above which to activate Iqinj logic | 1.200 | *p.u.* | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Trv | :math:`T_{rv}` | Voltage filter time constant | 0.020 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | dbd1 | :math:`d_{bd1}` | Lower bound of the voltage deadband (<=0) | -0.020 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | dbd2 | :math:`d_{bd2}` | Upper bound of the voltage deadband (>=0) | 0.020 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Kqv | :math:`K_{qv}` | Gain to compute Iqinj from V error (caution!!) | 1 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Iqh1 | :math:`I_{qh1}` | Upper limit on Iqinj | 999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Iql1 | :math:`I_{ql1}` | Lower limit on Iqinj | -999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vref0 | :math:`V_{ref0}` | User defined Vref (if 0, use initial bus V) | 1 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Iqfrz | :math:`I_{qfrz}` | Hold Iqinj at the value for Thld (>0) seconds following a Vdip | 0 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Thld | :math:`T_{hld}` | Time for which Iqinj is held. Hold at Iqinj if>0; hold at State 1 if<0 | 0 | *s* | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Thld2 | :math:`T_{hld2}` | Time for which IPMAX is held after voltage dip ends | 0 | *s* | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Tp | :math:`T_p` | Filter time constant for Pe | 0.020 | *s* | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | QMax | :math:`Q_{max}` | Upper limit for reactive power regulator | 999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | QMin | :math:`Q_{min}` | Lower limit for reactive power regulator | -999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | VMAX | :math:`V_{max}` | Upper limit for voltage control | 999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | VMIN | :math:`V_{min}` | Lower limit for voltage control | -999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Kqp | :math:`K_{qp}` | Proportional gain for reactive power error | 1 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Kqi | :math:`K_{qi}` | Integral gain for reactive power error | 0.100 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Kvp | :math:`K_{vp}` | Proportional gain for voltage error | 1 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Kvi | :math:`K_{vi}` | Integral gain for voltage error | 0.100 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vref1 | :math:`V_{ref1}` | Voltage ref. if VFLAG=0 | 1 | | non_zero | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Tiq | :math:`T_{iq}` | Filter time constant for Iq | 0.020 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | dPmax | :math:`d_{Pmax}` | Power reference max. ramp rate (>0) | 999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | dPmin | :math:`d_{Pin}` | Power reference min. ramp rate (<0) | -999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | PMAX | :math:`P_{max}` | Max. active power limit > 0 | 999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | PMIN | :math:`P_{min}` | Min. active power limit | 0 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Imax | :math:`I_{max}` | Max. apparent current limit | 999 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Tpord | :math:`T_{pord}` | Filter time constant for power setpoint | 0.020 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vq1 | :math:`V_{q1}` | Reactive power V-I pair (point 1), voltage | 0.200 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Iq1 | :math:`I_{q1}` | Reactive power V-I pair (point 1), current | 2 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vq2 | :math:`V_{q2}` | Reactive power V-I pair (point 2), voltage | 0.400 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Iq2 | :math:`I_{q2}` | Reactive power V-I pair (point 2), current | 4 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vq3 | :math:`V_{q3}` | Reactive power V-I pair (point 3), voltage | 0.800 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Iq3 | :math:`I_{q3}` | Reactive power V-I pair (point 3), current | 8 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vq4 | :math:`V_{q4}` | Reactive power V-I pair (point 4), voltage | 1 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Iq4 | :math:`I_{q4}` | Reactive power V-I pair (point 4), current | 10 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vp1 | :math:`V_{p1}` | Active power V-I pair (point 1), voltage | 0.200 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Ip1 | :math:`I_{p1}` | Active power V-I pair (point 1), current | 2 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vp2 | :math:`V_{p2}` | Active power V-I pair (point 2), voltage | 0.400 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Ip2 | :math:`I_{p2}` | Active power V-I pair (point 2), current | 4 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vp3 | :math:`V_{p3}` | Active power V-I pair (point 3), voltage | 0.800 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Ip3 | :math:`I_{p3}` | Active power V-I pair (point 3), current | 8 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vp4 | :math:`V_{p4}` | Active power V-I pair (point 4), voltage | 1 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Ip4 | :math:`I_{p4}` | Active power V-I pair (point 4), current | 12 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Kf | :math:`K_{df}` | gain for frequency deviation | 0 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Kdf | :math:`K_{df}` | gain for rate-of-change of frequency | 0 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | busroc | | Optional BusROCOF device idx | | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | bus | | Retrieved bus idx | | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | gen | | Retrieved StaticGen idx | | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Sn | :math:`S_n` | | 0 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ Variables --------- +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +==========+======================+============+====================================================+========+============+ | s0_y | :math:`y_{s0}` | State | State in lag transfer function | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | S1_y | :math:`y_{S_1}` | State | State in lag transfer function | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | PIQ_xi | :math:`xi_{PIQ}` | State | Integrator output | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | s4_y | :math:`y_{s_4}` | State | State in lag transfer function | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | pfilt_y | :math:`y_{P_{filt}}` | State | State in lag TF | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | s5_y | :math:`y_{s5}` | State | State in lag TF | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | PIV_xi | :math:`xi_{PIV}` | State | Integrator output | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Pord | :math:`Pord` | AliasState | Alias of s5_y | | | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | vp | :math:`V_{p}` | Algeb | Sensed lower-capped voltage | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | pfaref | :math:`\Phi_{ref}` | Algeb | power factor angle ref | *rad* | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Qref | :math:`Q_{ref}` | Algeb | external Q ref | *p.u.* | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Qcpf | :math:`Q_{cpf}` | Algeb | Q calculated from P and power factor | *p.u.* | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | PFsel | :math:`PFsel` | Algeb | Output of PFFLAG selector | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Qerr | :math:`Q_{err}` | Algeb | Reactive power error | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | PIQ_ys | :math:`ys_{PIQ}` | Algeb | PI summation before limit | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | PIQ_y | :math:`y_{PIQ}` | Algeb | PI output | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Vsel_x | :math:`x_{Vsel}` | Algeb | Value before limiter | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Vsel_y | :math:`y_{Vsel}` | Algeb | Output after limiter and post gain | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Verr | :math:`V_{err}` | Algeb | Voltage error (Vref0) | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | dbV_y | :math:`y_{dbV}` | Algeb | Deadband type 1 output | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Iqinj | :math:`I_{qinj}` | Algeb | Additional Iq signal during under- or over-voltage | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | wg | :math:`\omega_{g}` | Algeb | Drive train generator speed | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Pref | :math:`P_{ref}` | Algeb | external P ref | *p.u.* | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Psel | :math:`P_{sel}` | Algeb | Output selection of PFLAG | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | VDL1_y | :math:`y_{V_{DL1}}` | Algeb | Output of piecewise | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | VDL2_y | :math:`y_{V_{DL2}}` | Algeb | Output of piecewise | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Ipmax | :math:`I_{pmax}` | Algeb | Upper limit on Ipcmd | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Iqmax | :math:`I_{qmax}` | Algeb | Upper limit on Iqcmd | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | PIV_ys | :math:`ys_{PIV}` | Algeb | PI summation before limit | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | PIV_y | :math:`y_{PIV}` | Algeb | PI output | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Qsel | :math:`Q_{sel}` | Algeb | Selection output of QFLAG | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | IpHL_x | :math:`x_{IpHL}` | Algeb | Value before limiter | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | IpHL_y | :math:`y_{IpHL}` | Algeb | Output after limiter and post gain | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | IqHL_x | :math:`x_{IqHL}` | Algeb | Value before limiter | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | IqHL_y | :math:`y_{IqHL}` | Algeb | Output after limiter and post gain | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | a | :math:`\theta` | ExtAlgeb | Bus voltage angle | | | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | v | :math:`V_{d}` | ExtAlgeb | d-axis bus voltage magnitude | | | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Pe | :math:`Pe` | ExtAlgeb | Retrieved Pe of RenGen | | | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Qe | :math:`Qe` | ExtAlgeb | Retrieved Qe of RenGen | | | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Ipcmd | :math:`Ipcmd` | ExtAlgeb | Retrieved Ipcmd of RenGen | | | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Iqcmd | :math:`Iqcmd` | ExtAlgeb | Retrieved Iqcmd of RenGen | | | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | df | :math:`df` | ExtAlgeb | Bus frequency deviation | | | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | dfdt | :math:`dfdt` | ExtAlgeb | Bus ROCOF | *p.u.* | | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ Initialization Equations ------------------------ +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +==========+======================+============+=======================================================================================================================================================================================================================================================================================================================================================================================================+ | s0_y | :math:`y_{s0}` | State | :math:`V_{d}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | S1_y | :math:`y_{S_1}` | State | :math:`Pe` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_xi | :math:`xi_{PIQ}` | State | :math:`0.0` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | s4_y | :math:`y_{s_4}` | State | :math:`\frac{PFsel}{V_{p}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | pfilt_y | :math:`y_{P_{filt}}` | State | :math:`P_{ref}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | s5_y | :math:`y_{s5}` | State | :math:`P_{sel}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_xi | :math:`xi_{PIV}` | State | :math:`- Iqcmd_{0} s_1^{SW_{V}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pord | :math:`Pord` | AliasState | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vp | :math:`V_{p}` | Algeb | :math:`V_{d} z_i^{VLower} + 0.01 z_l^{VLower}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | pfaref | :math:`\Phi_{ref}` | Algeb | :math:`\Phi_{ref0}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qref | :math:`Q_{ref}` | Algeb | :math:`- q_{ref0}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qcpf | :math:`Q_{cpf}` | Algeb | :math:`Q_{0}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PFsel | :math:`PFsel` | Algeb | :math:`Q_{cpf} s_1^{SW_{PF}} + Q_{ref} s_0^{SW_{PF}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qerr | :math:`Q_{err}` | Algeb | :math:`PFsel z_i^{PFlim} + Q_{max} z_u^{PFlim} + Q_{min} z_l^{PFlim} - Qe` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_ys | :math:`ys_{PIQ}` | Algeb | :math:`K_{qp} Q_{err} s_1^{SW_{V}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_y | :math:`y_{PIQ}` | Algeb | :math:`V_{max} z_u^{lim_{PIQ}} + V_{min} z_l^{lim_{PIQ}} + ys_{PIQ} z_i^{lim_{PIQ}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vsel_x | :math:`x_{Vsel}` | Algeb | :math:`s_0^{SW_{V}} \left(Q_{cpf} s_1^{SW_{PF}} + Q_{ref} s_0^{SW_{PF}} + V_{ref1}\right) + s_1^{SW_{V}} y_{PIQ}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vsel_y | :math:`y_{Vsel}` | Algeb | :math:`V_{max} z_u^{lim_{Vsel}} + V_{min} z_l^{lim_{Vsel}} + x_{Vsel} z_i^{lim_{Vsel}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Verr | :math:`V_{err}` | Algeb | :math:`V_{ref0} - y_{s0}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | dbV_y | :math:`y_{dbV}` | Algeb | :math:`1.0 z_l^{db_{dbV}} \left(V_{err} - d_{bd1}\right) + 1.0 z_u^{db_{dbV}} \left(V_{err} - d_{bd2}\right)` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqinj | :math:`I_{qinj}` | Algeb | :math:`K_{qv} y_{dbV} z_{Vdip} + fThld \left(1 - z_{Vdip}\right) \left(I_{qfrz} p_{Thld} + K_{qv} n_{Thld} y_{dbV}\right)` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | wg | :math:`\omega_{g}` | Algeb | :math:`1.0` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pref | :math:`P_{ref}` | Algeb | :math:`\frac{P_{0}}{\omega_{g}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Psel | :math:`P_{sel}` | Algeb | :math:`\omega_{g} s_1^{SW_{P}} y_{P_{filt}} + s_0^{SW_{P}} y_{P_{filt}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VDL1_y | :math:`y_{V_{DL1}}` | Algeb | :math:`\operatorname{FixPiecewise}{\left(\left( I_{q1}, \ V_{q1} \geq y_{s0}\right),\left( I_{q1} + k_{Vq12} \left(- V_{q1} + y_{s0}\right), \ V_{q2} \geq y_{s0}\right),\left( I_{q2} + k_{Vq23} \left(- V_{q2} + y_{s0}\right), \ V_{q3} \geq y_{s0}\right),\left( I_{q3} + k_{Vq34} \left(- V_{q3} + y_{s0}\right), \ V_{q4} \geq y_{s0}\right),\left( I_{q4}, \ \text{True}\right) \right)}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VDL2_y | :math:`y_{V_{DL2}}` | Algeb | :math:`\operatorname{FixPiecewise}{\left(\left( I_{p1}, \ V_{p1} \geq y_{s0}\right),\left( I_{p1} + k_{Vp12} \left(- V_{p1} + y_{s0}\right), \ V_{p2} \geq y_{s0}\right),\left( I_{p2} + k_{Vp23} \left(- V_{p2} + y_{s0}\right), \ V_{p3} \geq y_{s0}\right),\left( I_{p3} + k_{Vp34} \left(- V_{p3} + y_{s0}\right), \ V_{p4} \geq y_{s0}\right),\left( I_{p4}, \ \text{True}\right) \right)}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Ipmax | :math:`I_{pmax}` | Algeb | :math:`\left(1 - fThld_{2}\right) \left(\sqrt{I_{pmax20,nn}^2} s_0^{SW_{PQ}} + s_1^{SW_{PQ}} \left(z_{VDL2} \left(I_{maxr} \left(1 - VDL2c\right) + VDL2c y_{V_{DL2}}\right) - 100000000.0 z_{VDL2} + 100000000.0\right)\right)` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqmax | :math:`I_{qmax}` | Algeb | :math:`\sqrt{I_{qmax,nn}^2} s_1^{SW_{PQ}} + s_0^{SW_{PQ}} \left(z_{VDL1} \left(I_{maxr} \left(1 - VDL1c\right) + VDL1c y_{V_{DL1}}\right) - 100000000.0 z_{VDL1} + 100000000.0\right)` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_ys | :math:`ys_{PIV}` | Algeb | :math:`- Iqcmd_{0} s_1^{SW_{V}} + K_{vp} s_1^{SW_{V}} \left(- s_0^{SW_{V}} y_{s0} + y_{Vsel}\right)` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_y | :math:`y_{PIV}` | Algeb | :math:`I_{qmax} z_u^{lim_{PIV}} + I_{qmin} z_l^{lim_{PIV}} + ys_{PIV} z_i^{lim_{PIV}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qsel | :math:`Q_{sel}` | Algeb | :math:`s_0^{SW_{V}} y_{s_4} + s_1^{SW_{V}} y_{PIV}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IpHL_x | :math:`x_{IpHL}` | Algeb | :math:`\frac{y_{s5}}{V_{p}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IpHL_y | :math:`y_{IpHL}` | Algeb | :math:`I_{pmax} z_u^{lim_{IpHL}} + I_{pmin} z_l^{lim_{IpHL}} + x_{IpHL} z_i^{lim_{IpHL}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IqHL_x | :math:`x_{IqHL}` | Algeb | :math:`I_{qinj} + Q_{sel}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IqHL_y | :math:`y_{IqHL}` | Algeb | :math:`I_{qmax} z_u^{lim_{IqHL}} + I_{qmin} z_l^{lim_{IqHL}} + x_{IqHL} z_i^{lim_{IqHL}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`V_{d}` | ExtAlgeb | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pe | :math:`Pe` | ExtAlgeb | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qe | :math:`Qe` | ExtAlgeb | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Ipcmd | :math:`Ipcmd` | ExtAlgeb | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqcmd | :math:`Iqcmd` | ExtAlgeb | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | df | :math:`df` | ExtAlgeb | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | dfdt | :math:`dfdt` | ExtAlgeb | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +==========+======================+============+===========================================================================================================================================+==================+ | s0_y | :math:`y_{s0}` | State | :math:`V_{d} - y_{s0}` | :math:`T_{rv}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | S1_y | :math:`y_{S_1}` | State | :math:`Pe - y_{S_1}` | :math:`T_p` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | PIQ_xi | :math:`xi_{PIQ}` | State | :math:`K_{qi} \left(1 - z_{Vdip}\right) \left(Q_{err} s_1^{SW_{V}} + 2 y_{PIQ} - 2 ys_{PIQ}\right)` | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | s4_y | :math:`y_{s_4}` | State | :math:`\left(1 - z_{Vdip}\right) \left(\frac{PFsel}{V_{p}} - y_{s_4}\right)` | :math:`T_{iq}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | pfilt_y | :math:`y_{P_{filt}}` | State | :math:`P_{ref} - y_{P_{filt}}` | :math:`0.02` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | s5_y | :math:`y_{s5}` | State | :math:`\left(1 - z_{Vdip}\right) \left(P_{sel} - y_{s5}\right)` | :math:`T_{pord}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | PIV_xi | :math:`xi_{PIV}` | State | :math:`K_{vi} \left(1 - z_{Vdip}\right) \left(s_1^{SW_{V}} \left(- s_0^{SW_{V}} y_{s0} + y_{Vsel}\right) + 2 y_{PIV} - 2 ys_{PIV}\right)` | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | Pord | :math:`Pord` | AliasState | :math:`0` | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ Algebraic Equations ----------------------------- +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+=====================+==========+=======================================================================================================================================================================================================================================================================================================================================================================================================================+ | vp | :math:`V_{p}` | Algeb | :math:`V_{d} z_i^{VLower} - V_{p} + 0.01 z_l^{VLower}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | pfaref | :math:`\Phi_{ref}` | Algeb | :math:`\Phi_{ref0} - \Phi_{ref}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qref | :math:`Q_{ref}` | Algeb | :math:`- Q_{ref} - q_{ref0}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qcpf | :math:`Q_{cpf}` | Algeb | :math:`\left(1 - z_1^{zp}\right) \left(- Q_{cpf} + y_{S_1} \tan{\left(\Phi_{ref} \right)}\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PFsel | :math:`PFsel` | Algeb | :math:`- PFsel + Q_{cpf} s_1^{SW_{PF}} + Q_{ref} s_0^{SW_{PF}}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qerr | :math:`Q_{err}` | Algeb | :math:`PFsel z_i^{PFlim} - Q_{err} + Q_{max} z_u^{PFlim} + Q_{min} z_l^{PFlim} - Qe` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_ys | :math:`ys_{PIQ}` | Algeb | :math:`\left(1 - z_{Vdip}\right) \left(K_{qp} Q_{err} s_1^{SW_{V}} + xi_{PIQ} - ys_{PIQ}\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_y | :math:`y_{PIQ}` | Algeb | :math:`\left(1 - z_{Vdip}\right) \left(V_{max} z_u^{lim_{PIQ}} + V_{min} z_l^{lim_{PIQ}} - y_{PIQ} + ys_{PIQ} z_i^{lim_{PIQ}}\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vsel_x | :math:`x_{Vsel}` | Algeb | :math:`s_0^{SW_{V}} \left(Q_{cpf} s_1^{SW_{PF}} + Q_{ref} s_0^{SW_{PF}} + V_{ref1}\right) + s_1^{SW_{V}} y_{PIQ} - x_{Vsel}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vsel_y | :math:`y_{Vsel}` | Algeb | :math:`V_{max} z_u^{lim_{Vsel}} + V_{min} z_l^{lim_{Vsel}} + x_{Vsel} z_i^{lim_{Vsel}} - y_{Vsel}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Verr | :math:`V_{err}` | Algeb | :math:`- V_{err} + V_{ref0} - y_{s0}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | dbV_y | :math:`y_{dbV}` | Algeb | :math:`- y_{dbV} + 1.0 z_l^{db_{dbV}} \left(V_{err} - d_{bd1}\right) + 1.0 z_u^{db_{dbV}} \left(V_{err} - d_{bd2}\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqinj | :math:`I_{qinj}` | Algeb | :math:`- I_{qinj} + K_{qv} y_{dbV} z_{Vdip} + fThld \left(1 - z_{Vdip}\right) \left(I_{qfrz} p_{Thld} + K_{qv} n_{Thld} y_{dbV}\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | wg | :math:`\omega_{g}` | Algeb | :math:`1.0 - \omega_{g}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pref | :math:`P_{ref}` | Algeb | :math:`- K_{df} df - K_{df} dfdt + \frac{P_{0}}{\omega_{g}} - P_{ref}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Psel | :math:`P_{sel}` | Algeb | :math:`- P_{sel} + \omega_{g} s_1^{SW_{P}} y_{P_{filt}} + s_0^{SW_{P}} y_{P_{filt}}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VDL1_y | :math:`y_{V_{DL1}}` | Algeb | :math:`- y_{V_{DL1}} + \operatorname{FixPiecewise}{\left(\left( I_{q1}, \ V_{q1} \geq y_{s0}\right),\left( I_{q1} + k_{Vq12} \left(- V_{q1} + y_{s0}\right), \ V_{q2} \geq y_{s0}\right),\left( I_{q2} + k_{Vq23} \left(- V_{q2} + y_{s0}\right), \ V_{q3} \geq y_{s0}\right),\left( I_{q3} + k_{Vq34} \left(- V_{q3} + y_{s0}\right), \ V_{q4} \geq y_{s0}\right),\left( I_{q4}, \ \text{True}\right) \right)}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VDL2_y | :math:`y_{V_{DL2}}` | Algeb | :math:`- y_{V_{DL2}} + \operatorname{FixPiecewise}{\left(\left( I_{p1}, \ V_{p1} \geq y_{s0}\right),\left( I_{p1} + k_{Vp12} \left(- V_{p1} + y_{s0}\right), \ V_{p2} \geq y_{s0}\right),\left( I_{p2} + k_{Vp23} \left(- V_{p2} + y_{s0}\right), \ V_{p3} \geq y_{s0}\right),\left( I_{p3} + k_{Vp34} \left(- V_{p3} + y_{s0}\right), \ V_{p4} \geq y_{s0}\right),\left( I_{p4}, \ \text{True}\right) \right)}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Ipmax | :math:`I_{pmax}` | Algeb | :math:`- I_{pmax} + Ipmaxh fThld_{2} + \left(1 - fThld_{2}\right) \left(\sqrt{I_{pmax2}^2} s_0^{SW_{PQ}} + s_1^{SW_{PQ}} \left(z_{VDL2} \left(I_{maxr} \left(1 - VDL2c\right) + VDL2c y_{V_{DL2}}\right) - 100000000.0 z_{VDL2} + 100000000.0\right)\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqmax | :math:`I_{qmax}` | Algeb | :math:`\sqrt{I_{qmax2}^2} s_1^{SW_{PQ}} - I_{qmax} + s_0^{SW_{PQ}} \left(z_{VDL1} \left(I_{maxr} \left(1 - VDL1c\right) + VDL1c y_{V_{DL1}}\right) - 100000000.0 z_{VDL1} + 100000000.0\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_ys | :math:`ys_{PIV}` | Algeb | :math:`\left(1 - z_{Vdip}\right) \left(K_{vp} s_1^{SW_{V}} \left(- s_0^{SW_{V}} y_{s0} + y_{Vsel}\right) + xi_{PIV} - ys_{PIV}\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_y | :math:`y_{PIV}` | Algeb | :math:`\left(1 - z_{Vdip}\right) \left(I_{qmax} z_u^{lim_{PIV}} + I_{qmin} z_l^{lim_{PIV}} - y_{PIV} + ys_{PIV} z_i^{lim_{PIV}}\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qsel | :math:`Q_{sel}` | Algeb | :math:`- Q_{sel} + s_0^{SW_{V}} y_{s_4} + s_1^{SW_{V}} y_{PIV}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IpHL_x | :math:`x_{IpHL}` | Algeb | :math:`- x_{IpHL} + \frac{y_{s5}}{V_{p}}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IpHL_y | :math:`y_{IpHL}` | Algeb | :math:`I_{pmax} z_u^{lim_{IpHL}} + I_{pmin} z_l^{lim_{IpHL}} + x_{IpHL} z_i^{lim_{IpHL}} - y_{IpHL}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IqHL_x | :math:`x_{IqHL}` | Algeb | :math:`I_{qinj} + Q_{sel} - x_{IqHL}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IqHL_y | :math:`y_{IqHL}` | Algeb | :math:`I_{qmax} z_u^{lim_{IqHL}} + I_{qmin} z_l^{lim_{IqHL}} + x_{IqHL} z_i^{lim_{IqHL}} - y_{IqHL}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | :math:`0` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`V_{d}` | ExtAlgeb | :math:`0` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pe | :math:`Pe` | ExtAlgeb | :math:`0` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qe | :math:`Qe` | ExtAlgeb | :math:`0` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Ipcmd | :math:`Ipcmd` | ExtAlgeb | :math:`- Ipcmd_{0} + y_{IpHL}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqcmd | :math:`Iqcmd` | ExtAlgeb | :math:`- Iqcmd_{0} - y_{IqHL}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | df | :math:`df` | ExtAlgeb | :math:`0` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | dfdt | :math:`dfdt` | ExtAlgeb | :math:`0` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Name | Symbol | Equation | Type | +============+=========================+=====================================================================================================================================================================+===============+ | Ipcmd0 | :math:`Ipcmd0` | :math:`\frac{P_{0}}{V_{d}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Iqcmd0 | :math:`Iqcmd0` | :math:`- \frac{Q_{0}}{V_{d}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | pfaref0 | :math:`\Phi_{ref0}` | :math:`\operatorname{atan}_{2}{\left(Q_{0},P_{0} \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Volt_dip | :math:`z_{Vdip}` | :math:`1 - z_i^{V_{cmp}}` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | qref0 | :math:`q_{ref0}` | :math:`Iqcmd_{0} s_0^{SW_{V}} \left(V_{d} z_i^{VLower} + 0.01 z_l^{VLower}\right) + s_1^{SW_{V}} \left(V_{d} - V_{ref1}\right)` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | PIQ_flag | :math:`z^{flag}_{PIQ}` | :math:`0` | EventFlag | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | s4_flag | :math:`z^{flag}_{s_4}` | :math:`0` | EventFlag | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | pThld | :math:`p_{Thld}` | :math:`\operatorname{Indicator}{\left(T_{hld} > 0 \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | nThld | :math:`n_{Thld}` | :math:`\operatorname{Indicator}{\left(T_{hld} < 0 \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Thld_abs | :math:`|Thld|` | :math:`\left|{T_{hld}}\right|` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | fThld | :math:`fThld` | :math:`0` | ExtendedEvent | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | s5_flag | :math:`z^{flag}_{s5}` | :math:`0` | EventFlag | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVq12 | :math:`k_{Vq12}` | :math:`\frac{- I_{q1} + I_{q2}}{- V_{q1} + V_{q2}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVq23 | :math:`k_{Vq23}` | :math:`\frac{- I_{q2} + I_{q3}}{- V_{q2} + V_{q3}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVq34 | :math:`k_{Vq34}` | :math:`\frac{- I_{q3} + I_{q4}}{- V_{q3} + V_{q4}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | zVDL1 | :math:`z_{VDL1}` | :math:`I_{q1} \leq I_{q2} \wedge I_{q2} \leq I_{q3} \wedge I_{q3} \leq I_{q4} \wedge V_{q1} \leq V_{q2} \wedge V_{q2} \leq V_{q3} \wedge V_{q3} \leq V_{q4}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVp12 | :math:`k_{Vp12}` | :math:`\frac{- I_{p1} + I_{p2}}{- V_{p1} + V_{p2}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVp23 | :math:`k_{Vp23}` | :math:`\frac{- I_{p2} + I_{p3}}{- V_{p2} + V_{p3}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVp34 | :math:`k_{Vp34}` | :math:`\frac{- I_{p3} + I_{p4}}{- V_{p3} + V_{p4}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | zVDL2 | :math:`z_{VDL2}` | :math:`I_{p1} \leq I_{p2} \wedge I_{p2} \leq I_{p3} \wedge I_{p3} \leq I_{p4} \wedge V_{p1} \leq V_{p2} \wedge V_{p2} \leq V_{p3} \wedge V_{p3} \leq V_{p4}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | fThld2 | :math:`fThld2` | :math:`0` | ExtendedEvent | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | VDL1c | :math:`VDL1c` | :math:`y_{V_{DL1}} < I_{maxr}` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | VDL2c | :math:`VDL2c` | :math:`y_{V_{DL2}} < I_{maxr}` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Ipmax2sq0 | :math:`I_{pmax20,nn}^2` | :math:`\operatorname{FixPiecewise}{\left(\left( 0, \ I_{max}^{2} - Iqcmd_{0}^{2} \leq 0\right),\left( I_{max}^{2} - Iqcmd_{0}^{2}, \ \text{True}\right) \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Ipmax2sq | :math:`I_{pmax2}^2` | :math:`\operatorname{FixPiecewise}{\left(\left( 0, \ I_{max}^{2} - y_{IqHL}^{2} \leq 0\right),\left( I_{max}^{2} - y_{IqHL}^{2}, \ \text{True}\right) \right)}` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Ipmaxh | :math:`Ipmaxh` | :math:`0` | VarHold | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Iqmax2sq0 | :math:`I_{qmax,nn}^2` | :math:`\operatorname{FixPiecewise}{\left(\left( 0, \ I_{max}^{2} - Ipcmd_{0}^{2} \leq 0\right),\left( I_{max}^{2} - Ipcmd_{0}^{2}, \ \text{True}\right) \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Iqmax2sq | :math:`I_{qmax2}^2` | :math:`\operatorname{FixPiecewise}{\left(\left( 0, \ I_{max}^{2} - y_{IpHL}^{2} \leq 0\right),\left( I_{max}^{2} - y_{IpHL}^{2}, \ \text{True}\right) \right)}` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Ipmin | :math:`I_{pmin}` | :math:`0.0` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | PIV_flag | :math:`z^{flag}_{PIV}` | :math:`0` | EventFlag | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ Discretes ----------- +------------+------------------------+-------------+-------------------------------+ | Name | Symbol | Type | Info | +============+========================+=============+===============================+ | SWPF | :math:`SW_{PF}` | Switcher | | +------------+------------------------+-------------+-------------------------------+ | SWV | :math:`SW_{V}` | Switcher | | +------------+------------------------+-------------+-------------------------------+ | SWQ | :math:`SW_{V}` | Switcher | | +------------+------------------------+-------------+-------------------------------+ | SWP | :math:`SW_{P}` | Switcher | | +------------+------------------------+-------------+-------------------------------+ | SWPQ | :math:`SW_{PQ}` | Switcher | | +------------+------------------------+-------------+-------------------------------+ | zp | :math:`zp` | IsEqual | | +------------+------------------------+-------------+-------------------------------+ | Vcmp | :math:`V_{cmp}` | Limiter | Voltage dip comparator | +------------+------------------------+-------------+-------------------------------+ | VLower | :math:`VLower` | Limiter | Limiter for lower voltage cap | +------------+------------------------+-------------+-------------------------------+ | PFlim | :math:`PFlim` | Limiter | | +------------+------------------------+-------------+-------------------------------+ | PIQ_lim | :math:`lim_{PIQ}` | HardLimiter | | +------------+------------------------+-------------+-------------------------------+ | Vsel_lim | :math:`lim_{Vsel}` | HardLimiter | | +------------+------------------------+-------------+-------------------------------+ | dbV_db | :math:`db_{dbV}` | DeadBand | | +------------+------------------------+-------------+-------------------------------+ | pfilt_lim | :math:`lim_{P_{filt}}` | RateLimiter | Rate limiter in Lag | +------------+------------------------+-------------+-------------------------------+ | s5_lim | :math:`lim_{s5}` | AntiWindup | Limiter in Lag | +------------+------------------------+-------------+-------------------------------+ | PIV_lim | :math:`lim_{PIV}` | HardLimiter | | +------------+------------------------+-------------+-------------------------------+ | IpHL_lim | :math:`lim_{IpHL}` | HardLimiter | | +------------+------------------------+-------------+-------------------------------+ | IqHL_lim | :math:`lim_{IqHL}` | HardLimiter | | +------------+------------------------+-------------+-------------------------------+ Blocks ------- +--------+------------------+-----------------+-------------------------------------------+ | Name | Symbol | Type | Info | +========+==================+=================+===========================================+ | s0 | :math:`s0` | Lag | Voltage filter | +--------+------------------+-----------------+-------------------------------------------+ | S1 | :math:`S_1` | Lag | Pe filter | +--------+------------------+-----------------+-------------------------------------------+ | PIQ | :math:`PIQ` | PITrackAWFreeze | | +--------+------------------+-----------------+-------------------------------------------+ | Vsel | :math:`Vsel` | GainLimiter | Selection output of VFLAG | +--------+------------------+-----------------+-------------------------------------------+ | s4 | :math:`s_4` | LagFreeze | Filter for calculated voltage with freeze | +--------+------------------+-----------------+-------------------------------------------+ | dbV | :math:`dbV` | DeadBand1 | Deadband for voltage error (ref0) | +--------+------------------+-----------------+-------------------------------------------+ | pfilt | :math:`P_{filt}` | LagRate | Active power filter with rate limits | +--------+------------------+-----------------+-------------------------------------------+ | s5 | :math:`s5` | LagAWFreeze | | +--------+------------------+-----------------+-------------------------------------------+ | VDL1 | :math:`V_{DL1}` | Piecewise | Piecewise linear characteristics of Vq-Iq | +--------+------------------+-----------------+-------------------------------------------+ | VDL2 | :math:`V_{DL2}` | Piecewise | Piecewise linear characteristics of Vp-Ip | +--------+------------------+-----------------+-------------------------------------------+ | PIV | :math:`PIV` | PITrackAWFreeze | | +--------+------------------+-----------------+-------------------------------------------+ | IpHL | :math:`IpHL` | GainLimiter | | +--------+------------------+-----------------+-------------------------------------------+ | IqHL | :math:`IqHL` | GainLimiter | | +--------+------------------+-----------------+-------------------------------------------+ Config Fields in [REECA1E] +---------------+-------------------+-------+---------------------------------------+-----------------+ | 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) | +---------------+-------------------+-------+---------------------------------------+-----------------+ | kqs | :math:`K_{qs}` | 2 | Q PI controller tracking gain | | +---------------+-------------------+-------+---------------------------------------+-----------------+ | kvs | :math:`K_{vs}` | 2 | Voltage PI controller tracking gain | | +---------------+-------------------+-------+---------------------------------------+-----------------+ | tpfilt | :math:`T_{pfilt}` | 0.020 | Time const. for Pref filter | | +---------------+-------------------+-------+---------------------------------------+-----------------+ .. _REECA1G: -------------------------------------------------------------------------------- REECA1G -------------------------------------------------------------------------------- REECA1G is a variant of REECA1E. REECA1G uses speed from synchronous generators. The application of this model is limited because it is uncommon to connect a SynGen on the same bus as a RenGen. Parameters ---------- +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +=========+==================+========================================================================+=========+========+============+ | idx | | unique device idx | | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | name | | device name | | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | reg | | Renewable generator idx | | | mandatory | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | busr | | Optional remote bus for voltage control | | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | PFFLAG | | Power factor control flag; 1-PF control, 0-Q control | | *bool* | mandatory | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | VFLAG | | Voltage control flag; 1-Q control, 0-V control | | *bool* | mandatory | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | QFLAG | | Q control flag; 1-V or Q control, 0-const. PF or Q | | *bool* | mandatory | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | PFLAG | | P speed-dependency flag; 1-has speed dep., 0-no dep. | | *bool* | mandatory | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | PQFLAG | | P/Q priority flag for I limit; 0-Q priority, 1-P priority | | *bool* | mandatory | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vdip | :math:`V_{dip}` | Low V threshold to activate Iqinj logic | 0.800 | *p.u.* | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vup | :math:`V_{up}` | V threshold above which to activate Iqinj logic | 1.200 | *p.u.* | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Trv | :math:`T_{rv}` | Voltage filter time constant | 0.020 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | dbd1 | :math:`d_{bd1}` | Lower bound of the voltage deadband (<=0) | -0.020 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | dbd2 | :math:`d_{bd2}` | Upper bound of the voltage deadband (>=0) | 0.020 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Kqv | :math:`K_{qv}` | Gain to compute Iqinj from V error (caution!!) | 1 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Iqh1 | :math:`I_{qh1}` | Upper limit on Iqinj | 999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Iql1 | :math:`I_{ql1}` | Lower limit on Iqinj | -999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vref0 | :math:`V_{ref0}` | User defined Vref (if 0, use initial bus V) | 1 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Iqfrz | :math:`I_{qfrz}` | Hold Iqinj at the value for Thld (>0) seconds following a Vdip | 0 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Thld | :math:`T_{hld}` | Time for which Iqinj is held. Hold at Iqinj if>0; hold at State 1 if<0 | 0 | *s* | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Thld2 | :math:`T_{hld2}` | Time for which IPMAX is held after voltage dip ends | 0 | *s* | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Tp | :math:`T_p` | Filter time constant for Pe | 0.020 | *s* | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | QMax | :math:`Q_{max}` | Upper limit for reactive power regulator | 999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | QMin | :math:`Q_{min}` | Lower limit for reactive power regulator | -999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | VMAX | :math:`V_{max}` | Upper limit for voltage control | 999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | VMIN | :math:`V_{min}` | Lower limit for voltage control | -999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Kqp | :math:`K_{qp}` | Proportional gain for reactive power error | 1 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Kqi | :math:`K_{qi}` | Integral gain for reactive power error | 0.100 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Kvp | :math:`K_{vp}` | Proportional gain for voltage error | 1 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Kvi | :math:`K_{vi}` | Integral gain for voltage error | 0.100 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vref1 | :math:`V_{ref1}` | Voltage ref. if VFLAG=0 | 1 | | non_zero | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Tiq | :math:`T_{iq}` | Filter time constant for Iq | 0.020 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | dPmax | :math:`d_{Pmax}` | Power reference max. ramp rate (>0) | 999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | dPmin | :math:`d_{Pin}` | Power reference min. ramp rate (<0) | -999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | PMAX | :math:`P_{max}` | Max. active power limit > 0 | 999 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | PMIN | :math:`P_{min}` | Min. active power limit | 0 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Imax | :math:`I_{max}` | Max. apparent current limit | 999 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Tpord | :math:`T_{pord}` | Filter time constant for power setpoint | 0.020 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vq1 | :math:`V_{q1}` | Reactive power V-I pair (point 1), voltage | 0.200 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Iq1 | :math:`I_{q1}` | Reactive power V-I pair (point 1), current | 2 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vq2 | :math:`V_{q2}` | Reactive power V-I pair (point 2), voltage | 0.400 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Iq2 | :math:`I_{q2}` | Reactive power V-I pair (point 2), current | 4 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vq3 | :math:`V_{q3}` | Reactive power V-I pair (point 3), voltage | 0.800 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Iq3 | :math:`I_{q3}` | Reactive power V-I pair (point 3), current | 8 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vq4 | :math:`V_{q4}` | Reactive power V-I pair (point 4), voltage | 1 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Iq4 | :math:`I_{q4}` | Reactive power V-I pair (point 4), current | 10 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vp1 | :math:`V_{p1}` | Active power V-I pair (point 1), voltage | 0.200 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Ip1 | :math:`I_{p1}` | Active power V-I pair (point 1), current | 2 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vp2 | :math:`V_{p2}` | Active power V-I pair (point 2), voltage | 0.400 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Ip2 | :math:`I_{p2}` | Active power V-I pair (point 2), current | 4 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vp3 | :math:`V_{p3}` | Active power V-I pair (point 3), voltage | 0.800 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Ip3 | :math:`I_{p3}` | Active power V-I pair (point 3), current | 8 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Vp4 | :math:`V_{p4}` | Active power V-I pair (point 4), voltage | 1 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Ip4 | :math:`I_{p4}` | Active power V-I pair (point 4), current | 12 | | current | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Kf | :math:`K_{df}` | gain for frequency deviation | 0 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | sg | | synchronous gen idx | | | mandatory | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | bus | | Retrieved bus idx | | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | gen | | Retrieved StaticGen idx | | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ | Sn | :math:`S_n` | | 0 | | | +---------+------------------+------------------------------------------------------------------------+---------+--------+------------+ Variables --------- +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +==========+======================+============+====================================================+========+============+ | s0_y | :math:`y_{s0}` | State | State in lag transfer function | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | S1_y | :math:`y_{S_1}` | State | State in lag transfer function | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | PIQ_xi | :math:`xi_{PIQ}` | State | Integrator output | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | s4_y | :math:`y_{s_4}` | State | State in lag transfer function | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | pfilt_y | :math:`y_{P_{filt}}` | State | State in lag TF | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | s5_y | :math:`y_{s5}` | State | State in lag TF | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | PIV_xi | :math:`xi_{PIV}` | State | Integrator output | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Pord | :math:`Pord` | AliasState | Alias of s5_y | | | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | generator speed | *pu* | | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | vp | :math:`V_{p}` | Algeb | Sensed lower-capped voltage | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | pfaref | :math:`\Phi_{ref}` | Algeb | power factor angle ref | *rad* | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Qref | :math:`Q_{ref}` | Algeb | external Q ref | *p.u.* | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Qcpf | :math:`Q_{cpf}` | Algeb | Q calculated from P and power factor | *p.u.* | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | PFsel | :math:`PFsel` | Algeb | Output of PFFLAG selector | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Qerr | :math:`Q_{err}` | Algeb | Reactive power error | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | PIQ_ys | :math:`ys_{PIQ}` | Algeb | PI summation before limit | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | PIQ_y | :math:`y_{PIQ}` | Algeb | PI output | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Vsel_x | :math:`x_{Vsel}` | Algeb | Value before limiter | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Vsel_y | :math:`y_{Vsel}` | Algeb | Output after limiter and post gain | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Verr | :math:`V_{err}` | Algeb | Voltage error (Vref0) | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | dbV_y | :math:`y_{dbV}` | Algeb | Deadband type 1 output | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Iqinj | :math:`I_{qinj}` | Algeb | Additional Iq signal during under- or over-voltage | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | wg | :math:`\omega_{g}` | Algeb | Drive train generator speed | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Pref | :math:`P_{ref}` | Algeb | external P ref | *p.u.* | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Psel | :math:`P_{sel}` | Algeb | Output selection of PFLAG | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | VDL1_y | :math:`y_{V_{DL1}}` | Algeb | Output of piecewise | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | VDL2_y | :math:`y_{V_{DL2}}` | Algeb | Output of piecewise | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Ipmax | :math:`I_{pmax}` | Algeb | Upper limit on Ipcmd | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Iqmax | :math:`I_{qmax}` | Algeb | Upper limit on Iqcmd | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | PIV_ys | :math:`ys_{PIV}` | Algeb | PI summation before limit | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | PIV_y | :math:`y_{PIV}` | Algeb | PI output | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Qsel | :math:`Q_{sel}` | Algeb | Selection output of QFLAG | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | IpHL_x | :math:`x_{IpHL}` | Algeb | Value before limiter | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | IpHL_y | :math:`y_{IpHL}` | Algeb | Output after limiter and post gain | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | IqHL_x | :math:`x_{IqHL}` | Algeb | Value before limiter | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | IqHL_y | :math:`y_{IqHL}` | Algeb | Output after limiter and post gain | | v_str | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | a | :math:`\theta` | ExtAlgeb | Bus voltage angle | | | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | v | :math:`V_{d}` | ExtAlgeb | d-axis bus voltage magnitude | | | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Pe | :math:`Pe` | ExtAlgeb | Retrieved Pe of RenGen | | | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Qe | :math:`Qe` | ExtAlgeb | Retrieved Qe of RenGen | | | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Ipcmd | :math:`Ipcmd` | ExtAlgeb | Retrieved Ipcmd of RenGen | | | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ | Iqcmd | :math:`Iqcmd` | ExtAlgeb | Retrieved Iqcmd of RenGen | | | +----------+----------------------+------------+----------------------------------------------------+--------+------------+ Initialization Equations ------------------------ +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +==========+======================+============+=======================================================================================================================================================================================================================================================================================================================================================================================================+ | s0_y | :math:`y_{s0}` | State | :math:`V_{d}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | S1_y | :math:`y_{S_1}` | State | :math:`Pe` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_xi | :math:`xi_{PIQ}` | State | :math:`0.0` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | s4_y | :math:`y_{s_4}` | State | :math:`\frac{PFsel}{V_{p}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | pfilt_y | :math:`y_{P_{filt}}` | State | :math:`P_{ref}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | s5_y | :math:`y_{s5}` | State | :math:`P_{sel}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_xi | :math:`xi_{PIV}` | State | :math:`- Iqcmd_{0} s_1^{SW_{V}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pord | :math:`Pord` | AliasState | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vp | :math:`V_{p}` | Algeb | :math:`V_{d} z_i^{VLower} + 0.01 z_l^{VLower}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | pfaref | :math:`\Phi_{ref}` | Algeb | :math:`\Phi_{ref0}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qref | :math:`Q_{ref}` | Algeb | :math:`- q_{ref0}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qcpf | :math:`Q_{cpf}` | Algeb | :math:`Q_{0}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PFsel | :math:`PFsel` | Algeb | :math:`Q_{cpf} s_1^{SW_{PF}} + Q_{ref} s_0^{SW_{PF}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qerr | :math:`Q_{err}` | Algeb | :math:`PFsel z_i^{PFlim} + Q_{max} z_u^{PFlim} + Q_{min} z_l^{PFlim} - Qe` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_ys | :math:`ys_{PIQ}` | Algeb | :math:`K_{qp} Q_{err} s_1^{SW_{V}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_y | :math:`y_{PIQ}` | Algeb | :math:`V_{max} z_u^{lim_{PIQ}} + V_{min} z_l^{lim_{PIQ}} + ys_{PIQ} z_i^{lim_{PIQ}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vsel_x | :math:`x_{Vsel}` | Algeb | :math:`s_0^{SW_{V}} \left(Q_{cpf} s_1^{SW_{PF}} + Q_{ref} s_0^{SW_{PF}} + V_{ref1}\right) + s_1^{SW_{V}} y_{PIQ}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vsel_y | :math:`y_{Vsel}` | Algeb | :math:`V_{max} z_u^{lim_{Vsel}} + V_{min} z_l^{lim_{Vsel}} + x_{Vsel} z_i^{lim_{Vsel}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Verr | :math:`V_{err}` | Algeb | :math:`V_{ref0} - y_{s0}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | dbV_y | :math:`y_{dbV}` | Algeb | :math:`1.0 z_l^{db_{dbV}} \left(V_{err} - d_{bd1}\right) + 1.0 z_u^{db_{dbV}} \left(V_{err} - d_{bd2}\right)` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqinj | :math:`I_{qinj}` | Algeb | :math:`K_{qv} y_{dbV} z_{Vdip} + fThld \left(1 - z_{Vdip}\right) \left(I_{qfrz} p_{Thld} + K_{qv} n_{Thld} y_{dbV}\right)` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | wg | :math:`\omega_{g}` | Algeb | :math:`1.0` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pref | :math:`P_{ref}` | Algeb | :math:`\frac{P_{0}}{\omega_{g}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Psel | :math:`P_{sel}` | Algeb | :math:`\omega_{g} s_1^{SW_{P}} y_{P_{filt}} + s_0^{SW_{P}} y_{P_{filt}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VDL1_y | :math:`y_{V_{DL1}}` | Algeb | :math:`\operatorname{FixPiecewise}{\left(\left( I_{q1}, \ V_{q1} \geq y_{s0}\right),\left( I_{q1} + k_{Vq12} \left(- V_{q1} + y_{s0}\right), \ V_{q2} \geq y_{s0}\right),\left( I_{q2} + k_{Vq23} \left(- V_{q2} + y_{s0}\right), \ V_{q3} \geq y_{s0}\right),\left( I_{q3} + k_{Vq34} \left(- V_{q3} + y_{s0}\right), \ V_{q4} \geq y_{s0}\right),\left( I_{q4}, \ \text{True}\right) \right)}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VDL2_y | :math:`y_{V_{DL2}}` | Algeb | :math:`\operatorname{FixPiecewise}{\left(\left( I_{p1}, \ V_{p1} \geq y_{s0}\right),\left( I_{p1} + k_{Vp12} \left(- V_{p1} + y_{s0}\right), \ V_{p2} \geq y_{s0}\right),\left( I_{p2} + k_{Vp23} \left(- V_{p2} + y_{s0}\right), \ V_{p3} \geq y_{s0}\right),\left( I_{p3} + k_{Vp34} \left(- V_{p3} + y_{s0}\right), \ V_{p4} \geq y_{s0}\right),\left( I_{p4}, \ \text{True}\right) \right)}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Ipmax | :math:`I_{pmax}` | Algeb | :math:`\left(1 - fThld_{2}\right) \left(\sqrt{I_{pmax20,nn}^2} s_0^{SW_{PQ}} + s_1^{SW_{PQ}} \left(z_{VDL2} \left(I_{maxr} \left(1 - VDL2c\right) + VDL2c y_{V_{DL2}}\right) - 100000000.0 z_{VDL2} + 100000000.0\right)\right)` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqmax | :math:`I_{qmax}` | Algeb | :math:`\sqrt{I_{qmax,nn}^2} s_1^{SW_{PQ}} + s_0^{SW_{PQ}} \left(z_{VDL1} \left(I_{maxr} \left(1 - VDL1c\right) + VDL1c y_{V_{DL1}}\right) - 100000000.0 z_{VDL1} + 100000000.0\right)` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_ys | :math:`ys_{PIV}` | Algeb | :math:`- Iqcmd_{0} s_1^{SW_{V}} + K_{vp} s_1^{SW_{V}} \left(- s_0^{SW_{V}} y_{s0} + y_{Vsel}\right)` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_y | :math:`y_{PIV}` | Algeb | :math:`I_{qmax} z_u^{lim_{PIV}} + I_{qmin} z_l^{lim_{PIV}} + ys_{PIV} z_i^{lim_{PIV}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qsel | :math:`Q_{sel}` | Algeb | :math:`s_0^{SW_{V}} y_{s_4} + s_1^{SW_{V}} y_{PIV}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IpHL_x | :math:`x_{IpHL}` | Algeb | :math:`\frac{y_{s5}}{V_{p}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IpHL_y | :math:`y_{IpHL}` | Algeb | :math:`I_{pmax} z_u^{lim_{IpHL}} + I_{pmin} z_l^{lim_{IpHL}} + x_{IpHL} z_i^{lim_{IpHL}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IqHL_x | :math:`x_{IqHL}` | Algeb | :math:`I_{qinj} + Q_{sel}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IqHL_y | :math:`y_{IqHL}` | Algeb | :math:`I_{qmax} z_u^{lim_{IqHL}} + I_{qmin} z_l^{lim_{IqHL}} + x_{IqHL} z_i^{lim_{IqHL}}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`V_{d}` | ExtAlgeb | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pe | :math:`Pe` | ExtAlgeb | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qe | :math:`Qe` | ExtAlgeb | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Ipcmd | :math:`Ipcmd` | ExtAlgeb | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqcmd | :math:`Iqcmd` | ExtAlgeb | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Differential Equations ----------------------------- +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +==========+======================+============+===========================================================================================================================================+==================+ | s0_y | :math:`y_{s0}` | State | :math:`V_{d} - y_{s0}` | :math:`T_{rv}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | S1_y | :math:`y_{S_1}` | State | :math:`Pe - y_{S_1}` | :math:`T_p` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | PIQ_xi | :math:`xi_{PIQ}` | State | :math:`K_{qi} \left(1 - z_{Vdip}\right) \left(Q_{err} s_1^{SW_{V}} + 2 y_{PIQ} - 2 ys_{PIQ}\right)` | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | s4_y | :math:`y_{s_4}` | State | :math:`\left(1 - z_{Vdip}\right) \left(\frac{PFsel}{V_{p}} - y_{s_4}\right)` | :math:`T_{iq}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | pfilt_y | :math:`y_{P_{filt}}` | State | :math:`P_{ref} - y_{P_{filt}}` | :math:`0.02` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | s5_y | :math:`y_{s5}` | State | :math:`\left(1 - z_{Vdip}\right) \left(P_{sel} - y_{s5}\right)` | :math:`T_{pord}` | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | PIV_xi | :math:`xi_{PIV}` | State | :math:`K_{vi} \left(1 - z_{Vdip}\right) \left(s_1^{SW_{V}} \left(- s_0^{SW_{V}} y_{s0} + y_{Vsel}\right) + 2 y_{PIV} - 2 ys_{PIV}\right)` | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | Pord | :math:`Pord` | AliasState | :math:`0` | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ | omega | :math:`\omega` | ExtState | :math:`0` | | +----------+----------------------+------------+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+ Algebraic Equations ----------------------------- +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+=====================+==========+=======================================================================================================================================================================================================================================================================================================================================================================================================================+ | vp | :math:`V_{p}` | Algeb | :math:`V_{d} z_i^{VLower} - V_{p} + 0.01 z_l^{VLower}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | pfaref | :math:`\Phi_{ref}` | Algeb | :math:`\Phi_{ref0} - \Phi_{ref}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qref | :math:`Q_{ref}` | Algeb | :math:`- Q_{ref} - q_{ref0}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qcpf | :math:`Q_{cpf}` | Algeb | :math:`\left(1 - z_1^{zp}\right) \left(- Q_{cpf} + y_{S_1} \tan{\left(\Phi_{ref} \right)}\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PFsel | :math:`PFsel` | Algeb | :math:`- PFsel + Q_{cpf} s_1^{SW_{PF}} + Q_{ref} s_0^{SW_{PF}}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qerr | :math:`Q_{err}` | Algeb | :math:`PFsel z_i^{PFlim} - Q_{err} + Q_{max} z_u^{PFlim} + Q_{min} z_l^{PFlim} - Qe` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_ys | :math:`ys_{PIQ}` | Algeb | :math:`\left(1 - z_{Vdip}\right) \left(K_{qp} Q_{err} s_1^{SW_{V}} + xi_{PIQ} - ys_{PIQ}\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_y | :math:`y_{PIQ}` | Algeb | :math:`\left(1 - z_{Vdip}\right) \left(V_{max} z_u^{lim_{PIQ}} + V_{min} z_l^{lim_{PIQ}} - y_{PIQ} + ys_{PIQ} z_i^{lim_{PIQ}}\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vsel_x | :math:`x_{Vsel}` | Algeb | :math:`s_0^{SW_{V}} \left(Q_{cpf} s_1^{SW_{PF}} + Q_{ref} s_0^{SW_{PF}} + V_{ref1}\right) + s_1^{SW_{V}} y_{PIQ} - x_{Vsel}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vsel_y | :math:`y_{Vsel}` | Algeb | :math:`V_{max} z_u^{lim_{Vsel}} + V_{min} z_l^{lim_{Vsel}} + x_{Vsel} z_i^{lim_{Vsel}} - y_{Vsel}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Verr | :math:`V_{err}` | Algeb | :math:`- V_{err} + V_{ref0} - y_{s0}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | dbV_y | :math:`y_{dbV}` | Algeb | :math:`- y_{dbV} + 1.0 z_l^{db_{dbV}} \left(V_{err} - d_{bd1}\right) + 1.0 z_u^{db_{dbV}} \left(V_{err} - d_{bd2}\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqinj | :math:`I_{qinj}` | Algeb | :math:`- I_{qinj} + K_{qv} y_{dbV} z_{Vdip} + fThld \left(1 - z_{Vdip}\right) \left(I_{qfrz} p_{Thld} + K_{qv} n_{Thld} y_{dbV}\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | wg | :math:`\omega_{g}` | Algeb | :math:`1.0 - \omega_{g}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pref | :math:`P_{ref}` | Algeb | :math:`- K_{df} \left(\omega - 1\right) + \frac{P_{0}}{\omega_{g}} - P_{ref}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Psel | :math:`P_{sel}` | Algeb | :math:`- P_{sel} + \omega_{g} s_1^{SW_{P}} y_{P_{filt}} + s_0^{SW_{P}} y_{P_{filt}}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VDL1_y | :math:`y_{V_{DL1}}` | Algeb | :math:`- y_{V_{DL1}} + \operatorname{FixPiecewise}{\left(\left( I_{q1}, \ V_{q1} \geq y_{s0}\right),\left( I_{q1} + k_{Vq12} \left(- V_{q1} + y_{s0}\right), \ V_{q2} \geq y_{s0}\right),\left( I_{q2} + k_{Vq23} \left(- V_{q2} + y_{s0}\right), \ V_{q3} \geq y_{s0}\right),\left( I_{q3} + k_{Vq34} \left(- V_{q3} + y_{s0}\right), \ V_{q4} \geq y_{s0}\right),\left( I_{q4}, \ \text{True}\right) \right)}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VDL2_y | :math:`y_{V_{DL2}}` | Algeb | :math:`- y_{V_{DL2}} + \operatorname{FixPiecewise}{\left(\left( I_{p1}, \ V_{p1} \geq y_{s0}\right),\left( I_{p1} + k_{Vp12} \left(- V_{p1} + y_{s0}\right), \ V_{p2} \geq y_{s0}\right),\left( I_{p2} + k_{Vp23} \left(- V_{p2} + y_{s0}\right), \ V_{p3} \geq y_{s0}\right),\left( I_{p3} + k_{Vp34} \left(- V_{p3} + y_{s0}\right), \ V_{p4} \geq y_{s0}\right),\left( I_{p4}, \ \text{True}\right) \right)}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Ipmax | :math:`I_{pmax}` | Algeb | :math:`- I_{pmax} + Ipmaxh fThld_{2} + \left(1 - fThld_{2}\right) \left(\sqrt{I_{pmax2}^2} s_0^{SW_{PQ}} + s_1^{SW_{PQ}} \left(z_{VDL2} \left(I_{maxr} \left(1 - VDL2c\right) + VDL2c y_{V_{DL2}}\right) - 100000000.0 z_{VDL2} + 100000000.0\right)\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqmax | :math:`I_{qmax}` | Algeb | :math:`\sqrt{I_{qmax2}^2} s_1^{SW_{PQ}} - I_{qmax} + s_0^{SW_{PQ}} \left(z_{VDL1} \left(I_{maxr} \left(1 - VDL1c\right) + VDL1c y_{V_{DL1}}\right) - 100000000.0 z_{VDL1} + 100000000.0\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_ys | :math:`ys_{PIV}` | Algeb | :math:`\left(1 - z_{Vdip}\right) \left(K_{vp} s_1^{SW_{V}} \left(- s_0^{SW_{V}} y_{s0} + y_{Vsel}\right) + xi_{PIV} - ys_{PIV}\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_y | :math:`y_{PIV}` | Algeb | :math:`\left(1 - z_{Vdip}\right) \left(I_{qmax} z_u^{lim_{PIV}} + I_{qmin} z_l^{lim_{PIV}} - y_{PIV} + ys_{PIV} z_i^{lim_{PIV}}\right)` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qsel | :math:`Q_{sel}` | Algeb | :math:`- Q_{sel} + s_0^{SW_{V}} y_{s_4} + s_1^{SW_{V}} y_{PIV}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IpHL_x | :math:`x_{IpHL}` | Algeb | :math:`- x_{IpHL} + \frac{y_{s5}}{V_{p}}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IpHL_y | :math:`y_{IpHL}` | Algeb | :math:`I_{pmax} z_u^{lim_{IpHL}} + I_{pmin} z_l^{lim_{IpHL}} + x_{IpHL} z_i^{lim_{IpHL}} - y_{IpHL}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IqHL_x | :math:`x_{IqHL}` | Algeb | :math:`I_{qinj} + Q_{sel} - x_{IqHL}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IqHL_y | :math:`y_{IqHL}` | Algeb | :math:`I_{qmax} z_u^{lim_{IqHL}} + I_{qmin} z_l^{lim_{IqHL}} + x_{IqHL} z_i^{lim_{IqHL}} - y_{IqHL}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | :math:`0` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`V_{d}` | ExtAlgeb | :math:`0` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pe | :math:`Pe` | ExtAlgeb | :math:`0` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qe | :math:`Qe` | ExtAlgeb | :math:`0` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Ipcmd | :math:`Ipcmd` | ExtAlgeb | :math:`- Ipcmd_{0} + y_{IpHL}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqcmd | :math:`Iqcmd` | ExtAlgeb | :math:`- Iqcmd_{0} - y_{IqHL}` | +---------+---------------------+----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Name | Symbol | Equation | Type | +============+=========================+=====================================================================================================================================================================+===============+ | Ipcmd0 | :math:`Ipcmd0` | :math:`\frac{P_{0}}{V_{d}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Iqcmd0 | :math:`Iqcmd0` | :math:`- \frac{Q_{0}}{V_{d}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | pfaref0 | :math:`\Phi_{ref0}` | :math:`\operatorname{atan}_{2}{\left(Q_{0},P_{0} \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Volt_dip | :math:`z_{Vdip}` | :math:`1 - z_i^{V_{cmp}}` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | qref0 | :math:`q_{ref0}` | :math:`Iqcmd_{0} s_0^{SW_{V}} \left(V_{d} z_i^{VLower} + 0.01 z_l^{VLower}\right) + s_1^{SW_{V}} \left(V_{d} - V_{ref1}\right)` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | PIQ_flag | :math:`z^{flag}_{PIQ}` | :math:`0` | EventFlag | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | s4_flag | :math:`z^{flag}_{s_4}` | :math:`0` | EventFlag | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | pThld | :math:`p_{Thld}` | :math:`\operatorname{Indicator}{\left(T_{hld} > 0 \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | nThld | :math:`n_{Thld}` | :math:`\operatorname{Indicator}{\left(T_{hld} < 0 \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Thld_abs | :math:`|Thld|` | :math:`\left|{T_{hld}}\right|` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | fThld | :math:`fThld` | :math:`0` | ExtendedEvent | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | s5_flag | :math:`z^{flag}_{s5}` | :math:`0` | EventFlag | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVq12 | :math:`k_{Vq12}` | :math:`\frac{- I_{q1} + I_{q2}}{- V_{q1} + V_{q2}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVq23 | :math:`k_{Vq23}` | :math:`\frac{- I_{q2} + I_{q3}}{- V_{q2} + V_{q3}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVq34 | :math:`k_{Vq34}` | :math:`\frac{- I_{q3} + I_{q4}}{- V_{q3} + V_{q4}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | zVDL1 | :math:`z_{VDL1}` | :math:`I_{q1} \leq I_{q2} \wedge I_{q2} \leq I_{q3} \wedge I_{q3} \leq I_{q4} \wedge V_{q1} \leq V_{q2} \wedge V_{q2} \leq V_{q3} \wedge V_{q3} \leq V_{q4}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVp12 | :math:`k_{Vp12}` | :math:`\frac{- I_{p1} + I_{p2}}{- V_{p1} + V_{p2}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVp23 | :math:`k_{Vp23}` | :math:`\frac{- I_{p2} + I_{p3}}{- V_{p2} + V_{p3}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVp34 | :math:`k_{Vp34}` | :math:`\frac{- I_{p3} + I_{p4}}{- V_{p3} + V_{p4}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | zVDL2 | :math:`z_{VDL2}` | :math:`I_{p1} \leq I_{p2} \wedge I_{p2} \leq I_{p3} \wedge I_{p3} \leq I_{p4} \wedge V_{p1} \leq V_{p2} \wedge V_{p2} \leq V_{p3} \wedge V_{p3} \leq V_{p4}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | fThld2 | :math:`fThld2` | :math:`0` | ExtendedEvent | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | VDL1c | :math:`VDL1c` | :math:`y_{V_{DL1}} < I_{maxr}` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | VDL2c | :math:`VDL2c` | :math:`y_{V_{DL2}} < I_{maxr}` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Ipmax2sq0 | :math:`I_{pmax20,nn}^2` | :math:`\operatorname{FixPiecewise}{\left(\left( 0, \ I_{max}^{2} - Iqcmd_{0}^{2} \leq 0\right),\left( I_{max}^{2} - Iqcmd_{0}^{2}, \ \text{True}\right) \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Ipmax2sq | :math:`I_{pmax2}^2` | :math:`\operatorname{FixPiecewise}{\left(\left( 0, \ I_{max}^{2} - y_{IqHL}^{2} \leq 0\right),\left( I_{max}^{2} - y_{IqHL}^{2}, \ \text{True}\right) \right)}` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Ipmaxh | :math:`Ipmaxh` | :math:`0` | VarHold | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Iqmax2sq0 | :math:`I_{qmax,nn}^2` | :math:`\operatorname{FixPiecewise}{\left(\left( 0, \ I_{max}^{2} - Ipcmd_{0}^{2} \leq 0\right),\left( I_{max}^{2} - Ipcmd_{0}^{2}, \ \text{True}\right) \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Iqmax2sq | :math:`I_{qmax2}^2` | :math:`\operatorname{FixPiecewise}{\left(\left( 0, \ I_{max}^{2} - y_{IpHL}^{2} \leq 0\right),\left( I_{max}^{2} - y_{IpHL}^{2}, \ \text{True}\right) \right)}` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Ipmin | :math:`I_{pmin}` | :math:`0.0` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | PIV_flag | :math:`z^{flag}_{PIV}` | :math:`0` | EventFlag | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ Discretes ----------- +------------+------------------------+-------------+-------------------------------+ | Name | Symbol | Type | Info | +============+========================+=============+===============================+ | SWPF | :math:`SW_{PF}` | Switcher | | +------------+------------------------+-------------+-------------------------------+ | SWV | :math:`SW_{V}` | Switcher | | +------------+------------------------+-------------+-------------------------------+ | SWQ | :math:`SW_{V}` | Switcher | | +------------+------------------------+-------------+-------------------------------+ | SWP | :math:`SW_{P}` | Switcher | | +------------+------------------------+-------------+-------------------------------+ | SWPQ | :math:`SW_{PQ}` | Switcher | | +------------+------------------------+-------------+-------------------------------+ | zp | :math:`zp` | IsEqual | | +------------+------------------------+-------------+-------------------------------+ | Vcmp | :math:`V_{cmp}` | Limiter | Voltage dip comparator | +------------+------------------------+-------------+-------------------------------+ | VLower | :math:`VLower` | Limiter | Limiter for lower voltage cap | +------------+------------------------+-------------+-------------------------------+ | PFlim | :math:`PFlim` | Limiter | | +------------+------------------------+-------------+-------------------------------+ | PIQ_lim | :math:`lim_{PIQ}` | HardLimiter | | +------------+------------------------+-------------+-------------------------------+ | Vsel_lim | :math:`lim_{Vsel}` | HardLimiter | | +------------+------------------------+-------------+-------------------------------+ | dbV_db | :math:`db_{dbV}` | DeadBand | | +------------+------------------------+-------------+-------------------------------+ | pfilt_lim | :math:`lim_{P_{filt}}` | RateLimiter | Rate limiter in Lag | +------------+------------------------+-------------+-------------------------------+ | s5_lim | :math:`lim_{s5}` | AntiWindup | Limiter in Lag | +------------+------------------------+-------------+-------------------------------+ | PIV_lim | :math:`lim_{PIV}` | HardLimiter | | +------------+------------------------+-------------+-------------------------------+ | IpHL_lim | :math:`lim_{IpHL}` | HardLimiter | | +------------+------------------------+-------------+-------------------------------+ | IqHL_lim | :math:`lim_{IqHL}` | HardLimiter | | +------------+------------------------+-------------+-------------------------------+ Blocks ------- +--------+------------------+-----------------+-------------------------------------------+ | Name | Symbol | Type | Info | +========+==================+=================+===========================================+ | s0 | :math:`s0` | Lag | Voltage filter | +--------+------------------+-----------------+-------------------------------------------+ | S1 | :math:`S_1` | Lag | Pe filter | +--------+------------------+-----------------+-------------------------------------------+ | PIQ | :math:`PIQ` | PITrackAWFreeze | | +--------+------------------+-----------------+-------------------------------------------+ | Vsel | :math:`Vsel` | GainLimiter | Selection output of VFLAG | +--------+------------------+-----------------+-------------------------------------------+ | s4 | :math:`s_4` | LagFreeze | Filter for calculated voltage with freeze | +--------+------------------+-----------------+-------------------------------------------+ | dbV | :math:`dbV` | DeadBand1 | Deadband for voltage error (ref0) | +--------+------------------+-----------------+-------------------------------------------+ | pfilt | :math:`P_{filt}` | LagRate | Active power filter with rate limits | +--------+------------------+-----------------+-------------------------------------------+ | s5 | :math:`s5` | LagAWFreeze | | +--------+------------------+-----------------+-------------------------------------------+ | VDL1 | :math:`V_{DL1}` | Piecewise | Piecewise linear characteristics of Vq-Iq | +--------+------------------+-----------------+-------------------------------------------+ | VDL2 | :math:`V_{DL2}` | Piecewise | Piecewise linear characteristics of Vp-Ip | +--------+------------------+-----------------+-------------------------------------------+ | PIV | :math:`PIV` | PITrackAWFreeze | | +--------+------------------+-----------------+-------------------------------------------+ | IpHL | :math:`IpHL` | GainLimiter | | +--------+------------------+-----------------+-------------------------------------------+ | IqHL | :math:`IqHL` | GainLimiter | | +--------+------------------+-----------------+-------------------------------------------+ Config Fields in [REECA1G] +---------------+-------------------+-------+---------------------------------------+-----------------+ | 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) | +---------------+-------------------+-------+---------------------------------------+-----------------+ | kqs | :math:`K_{qs}` | 2 | Q PI controller tracking gain | | +---------------+-------------------+-------+---------------------------------------+-----------------+ | kvs | :math:`K_{vs}` | 2 | Voltage PI controller tracking gain | | +---------------+-------------------+-------+---------------------------------------+-----------------+ | tpfilt | :math:`T_{pfilt}` | 0.020 | Time const. for Pref filter | | +---------------+-------------------+-------+---------------------------------------+-----------------+