.. _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:`s_{0 y}` | State | State in lag transfer function | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | S1_y | :math:`S_{1 y}` | State | State in lag transfer function | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | PIQ_xi | :math:`PIQ_{\xi}` | State | Integrator output | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | s4_y | :math:`s_{4 y}` | State | State in lag transfer function | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | pfilt_y | :math:`pfilt_{y}` | State | State in lag TF | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | s5_y | :math:`s_{5 y}` | State | State in lag TF | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | PIV_xi | :math:`PIV_{\xi}` | State | Integrator output | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Pord | :math:`Pord` | AliasState | Alias of s5_y | | | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | vp | :math:`vp` | Algeb | Sensed lower-capped voltage | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | pfaref | :math:`pfaref` | Algeb | power factor angle ref | *rad* | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Qref | :math:`Qref` | Algeb | external Q ref | *p.u.* | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Qcpf | :math:`Qcpf` | Algeb | Q calculated from P and power factor | *p.u.* | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | PFsel | :math:`PFsel` | Algeb | Output of PFFLAG selector | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Qerr | :math:`Qerr` | Algeb | Reactive power error | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | PIQ_ys | :math:`PIQ_{ys}` | Algeb | PI summation before limit | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | PIQ_y | :math:`PIQ_{y}` | Algeb | PI output | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Vsel_x | :math:`Vsel_{x}` | Algeb | Value before limiter | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Vsel_y | :math:`Vsel_{y}` | Algeb | Output after limiter and post gain | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Verr | :math:`Verr` | Algeb | Voltage error (Vref0) | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | dbV_y | :math:`dbV_{y}` | Algeb | Deadband type 1 output | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Iqinj | :math:`Iqinj` | Algeb | Additional Iq signal during under- or over-voltage | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | wg | :math:`wg` | Algeb | Drive train generator speed | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Pref | :math:`Pref` | Algeb | external P ref | *p.u.* | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Psel | :math:`Psel` | Algeb | Output selection of PFLAG | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | VDL1_y | :math:`VDL_{1 y}` | Algeb | Output of piecewise | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | VDL2_y | :math:`VDL_{2 y}` | Algeb | Output of piecewise | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Ipmax | :math:`Ipmax` | Algeb | Upper limit on Ipcmd | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Iqmax | :math:`Iqmax` | Algeb | Upper limit on Iqcmd | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | PIV_ys | :math:`PIV_{ys}` | Algeb | PI summation before limit | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | PIV_y | :math:`PIV_{y}` | Algeb | PI output | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Qsel | :math:`Qsel` | Algeb | Selection output of QFLAG | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | IpHL_x | :math:`IpHL_{x}` | Algeb | Value before limiter | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | IpHL_y | :math:`IpHL_{y}` | Algeb | Output after limiter and post gain | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | IqHL_x | :math:`IqHL_{x}` | Algeb | Value before limiter | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | IqHL_y | :math:`IqHL_{y}` | Algeb | Output after limiter and post gain | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | a | :math:`a` | ExtAlgeb | Bus voltage angle | | | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | v | :math:`v` | 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:`s_{0 y}` | State | :math:`v` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | S1_y | :math:`S_{1 y}` | State | :math:`Pe` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_xi | :math:`PIQ_{\xi}` | State | :math:`0.0` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | s4_y | :math:`s_{4 y}` | State | :math:`\frac{PFsel}{vp}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | pfilt_y | :math:`pfilt_{y}` | State | :math:`Pref` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | s5_y | :math:`s_{5 y}` | State | :math:`Psel` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_xi | :math:`PIV_{\xi}` | State | :math:`- Iqcmd_{0} SWQ_{s1}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pord | :math:`Pord` | AliasState | | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vp | :math:`vp` | Algeb | :math:`VLower_{zi} v + 0.01 VLower_{zl}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | pfaref | :math:`pfaref` | Algeb | :math:`pfaref_{0}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qref | :math:`Qref` | Algeb | :math:`- qref_{0}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qcpf | :math:`Qcpf` | Algeb | :math:`q_{0}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PFsel | :math:`PFsel` | Algeb | :math:`Qcpf SWPF_{s1} + Qref SWPF_{s0}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qerr | :math:`Qerr` | Algeb | :math:`PFlim_{zi} PFsel + PFlim_{zl} QMin + PFlim_{zu} QMax - Qe` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_ys | :math:`PIQ_{ys}` | Algeb | :math:`Kqp Qerr SWV_{s1}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_y | :math:`PIQ_{y}` | Algeb | :math:`PIQ_{lim zi} PIQ_{ys} + PIQ_{lim zl} VMIN + PIQ_{lim zu} VMAX` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vsel_x | :math:`Vsel_{x}` | Algeb | :math:`PIQ_{y} SWV_{s1} + SWV_{s0} \left(Qcpf SWPF_{s1} + Qref SWPF_{s0} + Vref_{1}\right)` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vsel_y | :math:`Vsel_{y}` | Algeb | :math:`VMAX Vsel_{lim zu} + VMIN Vsel_{lim zl} + Vsel_{lim zi} Vsel_{x}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Verr | :math:`Verr` | Algeb | :math:`Vref_{0} - s_{0 y}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | dbV_y | :math:`dbV_{y}` | Algeb | :math:`1.0 dbV_{db zl} \left(Verr - dbd_{1}\right) + 1.0 dbV_{db zu} \left(Verr - dbd_{2}\right)` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqinj | :math:`Iqinj` | Algeb | :math:`Kqv Volt_{dip} dbV_{y} + fThld \left(1 - Volt_{dip}\right) \left(Iqfrz pThld + Kqv dbV_{y} nThld\right)` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | wg | :math:`wg` | Algeb | :math:`1.0` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pref | :math:`Pref` | Algeb | :math:`\frac{p_{0}}{wg}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Psel | :math:`Psel` | Algeb | :math:`SWP_{s0} pfilt_{y} + SWP_{s1} pfilt_{y} wg` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VDL1_y | :math:`VDL_{1 y}` | Algeb | :math:`\operatorname{FixPiecewise}{\left(\left( Iq_{1}, \ Vq_{1} \geq s_{0 y}\right),\left( Iq_{1} + kVq_{12} \left(- Vq_{1} + s_{0 y}\right), \ Vq_{2} \geq s_{0 y}\right),\left( Iq_{2} + kVq_{23} \left(- Vq_{2} + s_{0 y}\right), \ Vq_{3} \geq s_{0 y}\right),\left( Iq_{3} + kVq_{34} \left(- Vq_{3} + s_{0 y}\right), \ Vq_{4} \geq s_{0 y}\right),\left( Iq_{4}, \ \text{True}\right) \right)}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VDL2_y | :math:`VDL_{2 y}` | Algeb | :math:`\operatorname{FixPiecewise}{\left(\left( Ip_{1}, \ Vp_{1} \geq s_{0 y}\right),\left( Ip_{1} + kVp_{12} \left(- Vp_{1} + s_{0 y}\right), \ Vp_{2} \geq s_{0 y}\right),\left( Ip_{2} + kVp_{23} \left(- Vp_{2} + s_{0 y}\right), \ Vp_{3} \geq s_{0 y}\right),\left( Ip_{3} + kVp_{34} \left(- Vp_{3} + s_{0 y}\right), \ Vp_{4} \geq s_{0 y}\right),\left( Ip_{4}, \ \text{True}\right) \right)}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Ipmax | :math:`Ipmax` | Algeb | :math:`\left(1 - fThld_{2}\right) \left(\sqrt{Ipmax2sq0} SWPQ_{s0} + SWPQ_{s1} \left(zVDL_{2} \left(Imaxr \left(1 - VDL2c\right) + VDL_{2 y} VDL2c\right) - 100000000.0 zVDL_{2} + 100000000.0\right)\right)` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqmax | :math:`Iqmax` | Algeb | :math:`\sqrt{Iqmax2sq0} SWPQ_{s1} + SWPQ_{s0} \left(zVDL_{1} \left(Imaxr \left(1 - VDL1c\right) + VDL_{1 y} VDL1c\right) - 100000000.0 zVDL_{1} + 100000000.0\right)` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_ys | :math:`PIV_{ys}` | Algeb | :math:`- Iqcmd_{0} SWQ_{s1} + Kvp SWQ_{s1} \left(- SWV_{s0} s_{0 y} + Vsel_{y}\right)` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_y | :math:`PIV_{y}` | Algeb | :math:`Iqmax PIV_{lim zu} + Iqmin PIV_{lim zl} + PIV_{lim zi} PIV_{ys}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qsel | :math:`Qsel` | Algeb | :math:`PIV_{y} SWQ_{s1} + SWQ_{s0} s_{4 y}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IpHL_x | :math:`IpHL_{x}` | Algeb | :math:`\frac{s_{5 y}}{vp}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IpHL_y | :math:`IpHL_{y}` | Algeb | :math:`IpHL_{lim zi} IpHL_{x} + IpHL_{lim zl} Ipmin + IpHL_{lim zu} Ipmax` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IqHL_x | :math:`IqHL_{x}` | Algeb | :math:`Iqinj + Qsel` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IqHL_y | :math:`IqHL_{y}` | Algeb | :math:`IqHL_{lim zi} IqHL_{x} + IqHL_{lim zl} Iqmin + IqHL_{lim zu} Iqmax` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`v` | 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:`s_{0 y}` | State | :math:`- s_{0 y} + v` | :math:`T_{rv}` | +----------+-------------------+------------+-----------------------------------------------------------------------------------------------------------------------------------+------------------+ | S1_y | :math:`S_{1 y}` | State | :math:`Pe - S_{1 y}` | :math:`T_p` | +----------+-------------------+------------+-----------------------------------------------------------------------------------------------------------------------------------+------------------+ | PIQ_xi | :math:`PIQ_{\xi}` | State | :math:`Kqi \left(1 - Volt_{dip}\right) \left(2 PIQ_{y} - 2 PIQ_{ys} + Qerr SWV_{s1}\right)` | | +----------+-------------------+------------+-----------------------------------------------------------------------------------------------------------------------------------+------------------+ | s4_y | :math:`s_{4 y}` | State | :math:`\left(1 - Volt_{dip}\right) \left(\frac{PFsel}{vp} - s_{4 y}\right)` | :math:`T_{iq}` | +----------+-------------------+------------+-----------------------------------------------------------------------------------------------------------------------------------+------------------+ | pfilt_y | :math:`pfilt_{y}` | State | :math:`Pref - pfilt_{y}` | :math:`0.02` | +----------+-------------------+------------+-----------------------------------------------------------------------------------------------------------------------------------+------------------+ | s5_y | :math:`s_{5 y}` | State | :math:`\left(1 - Volt_{dip}\right) \left(Psel - s_{5 y}\right)` | :math:`T_{pord}` | +----------+-------------------+------------+-----------------------------------------------------------------------------------------------------------------------------------+------------------+ | PIV_xi | :math:`PIV_{\xi}` | State | :math:`Kvi \left(1 - Volt_{dip}\right) \left(2 PIV_{y} - 2 PIV_{ys} + SWQ_{s1} \left(- SWV_{s0} s_{0 y} + Vsel_{y}\right)\right)` | | +----------+-------------------+------------+-----------------------------------------------------------------------------------------------------------------------------------+------------------+ | Pord | :math:`Pord` | AliasState | :math:`0` | | +----------+-------------------+------------+-----------------------------------------------------------------------------------------------------------------------------------+------------------+ Algebraic Equations ----------------------------- +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+===================+==========+============================================================================================================================================================================================================================================================================================================================================================================================================================+ | vp | :math:`vp` | Algeb | :math:`VLower_{zi} v + 0.01 VLower_{zl} - vp` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | pfaref | :math:`pfaref` | Algeb | :math:`- pfaref + pfaref_{0}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qref | :math:`Qref` | Algeb | :math:`- Qref - qref_{0}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qcpf | :math:`Qcpf` | Algeb | :math:`\left(1 - zp_{z1}\right) \left(- Qcpf + S_{1 y} \tan{\left(pfaref \right)}\right)` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PFsel | :math:`PFsel` | Algeb | :math:`- PFsel + Qcpf SWPF_{s1} + Qref SWPF_{s0}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qerr | :math:`Qerr` | Algeb | :math:`PFlim_{zi} PFsel + PFlim_{zl} QMin + PFlim_{zu} QMax - Qe - Qerr` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_ys | :math:`PIQ_{ys}` | Algeb | :math:`\left(1 - Volt_{dip}\right) \left(Kqp Qerr SWV_{s1} + PIQ_{\xi} - PIQ_{ys}\right)` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_y | :math:`PIQ_{y}` | Algeb | :math:`\left(1 - Volt_{dip}\right) \left(PIQ_{lim zi} PIQ_{ys} + PIQ_{lim zl} VMIN + PIQ_{lim zu} VMAX - PIQ_{y}\right)` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vsel_x | :math:`Vsel_{x}` | Algeb | :math:`PIQ_{y} SWV_{s1} + SWV_{s0} \left(Qcpf SWPF_{s1} + Qref SWPF_{s0} + Vref_{1}\right) - Vsel_{x}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vsel_y | :math:`Vsel_{y}` | Algeb | :math:`VMAX Vsel_{lim zu} + VMIN Vsel_{lim zl} + Vsel_{lim zi} Vsel_{x} - Vsel_{y}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Verr | :math:`Verr` | Algeb | :math:`- Verr + Vref_{0} - s_{0 y}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | dbV_y | :math:`dbV_{y}` | Algeb | :math:`1.0 dbV_{db zl} \left(Verr - dbd_{1}\right) + 1.0 dbV_{db zu} \left(Verr - dbd_{2}\right) - dbV_{y}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqinj | :math:`Iqinj` | Algeb | :math:`- Iqinj + Kqv Volt_{dip} dbV_{y} + fThld \left(1 - Volt_{dip}\right) \left(Iqfrz pThld + Kqv dbV_{y} nThld\right)` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | wg | :math:`wg` | Algeb | :math:`1.0 - wg` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pref | :math:`Pref` | Algeb | :math:`- Pref + \frac{p_{0}}{wg}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Psel | :math:`Psel` | Algeb | :math:`- Psel + SWP_{s0} pfilt_{y} + SWP_{s1} pfilt_{y} wg` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VDL1_y | :math:`VDL_{1 y}` | Algeb | :math:`- VDL_{1 y} + \operatorname{FixPiecewise}{\left(\left( Iq_{1}, \ Vq_{1} \geq s_{0 y}\right),\left( Iq_{1} + kVq_{12} \left(- Vq_{1} + s_{0 y}\right), \ Vq_{2} \geq s_{0 y}\right),\left( Iq_{2} + kVq_{23} \left(- Vq_{2} + s_{0 y}\right), \ Vq_{3} \geq s_{0 y}\right),\left( Iq_{3} + kVq_{34} \left(- Vq_{3} + s_{0 y}\right), \ Vq_{4} \geq s_{0 y}\right),\left( Iq_{4}, \ \text{True}\right) \right)}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VDL2_y | :math:`VDL_{2 y}` | Algeb | :math:`- VDL_{2 y} + \operatorname{FixPiecewise}{\left(\left( Ip_{1}, \ Vp_{1} \geq s_{0 y}\right),\left( Ip_{1} + kVp_{12} \left(- Vp_{1} + s_{0 y}\right), \ Vp_{2} \geq s_{0 y}\right),\left( Ip_{2} + kVp_{23} \left(- Vp_{2} + s_{0 y}\right), \ Vp_{3} \geq s_{0 y}\right),\left( Ip_{3} + kVp_{34} \left(- Vp_{3} + s_{0 y}\right), \ Vp_{4} \geq s_{0 y}\right),\left( Ip_{4}, \ \text{True}\right) \right)}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Ipmax | :math:`Ipmax` | Algeb | :math:`- Ipmax + Ipmaxh fThld_{2} + \left(1 - fThld_{2}\right) \left(\sqrt{Ipmax2sq} SWPQ_{s0} + SWPQ_{s1} \left(zVDL_{2} \left(Imaxr \left(1 - VDL2c\right) + VDL_{2 y} VDL2c\right) - 100000000.0 zVDL_{2} + 100000000.0\right)\right)` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqmax | :math:`Iqmax` | Algeb | :math:`- Iqmax + \sqrt{Iqmax2sq} SWPQ_{s1} + SWPQ_{s0} \left(zVDL_{1} \left(Imaxr \left(1 - VDL1c\right) + VDL_{1 y} VDL1c\right) - 100000000.0 zVDL_{1} + 100000000.0\right)` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_ys | :math:`PIV_{ys}` | Algeb | :math:`\left(1 - Volt_{dip}\right) \left(Kvp SWQ_{s1} \left(- SWV_{s0} s_{0 y} + Vsel_{y}\right) + PIV_{\xi} - PIV_{ys}\right)` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_y | :math:`PIV_{y}` | Algeb | :math:`\left(1 - Volt_{dip}\right) \left(Iqmax PIV_{lim zu} + Iqmin PIV_{lim zl} + PIV_{lim zi} PIV_{ys} - PIV_{y}\right)` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qsel | :math:`Qsel` | Algeb | :math:`PIV_{y} SWQ_{s1} - Qsel + SWQ_{s0} s_{4 y}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IpHL_x | :math:`IpHL_{x}` | Algeb | :math:`- IpHL_{x} + \frac{s_{5 y}}{vp}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IpHL_y | :math:`IpHL_{y}` | Algeb | :math:`IpHL_{lim zi} IpHL_{x} + IpHL_{lim zl} Ipmin + IpHL_{lim zu} Ipmax - IpHL_{y}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IqHL_x | :math:`IqHL_{x}` | Algeb | :math:`- IqHL_{x} + Iqinj + Qsel` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IqHL_y | :math:`IqHL_{y}` | Algeb | :math:`IqHL_{lim zi} IqHL_{x} + IqHL_{lim zl} Iqmin + IqHL_{lim zu} Iqmax - IqHL_{y}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | :math:`0` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`v` | ExtAlgeb | :math:`0` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pe | :math:`Pe` | ExtAlgeb | :math:`0` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qe | :math:`Qe` | ExtAlgeb | :math:`0` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Ipcmd | :math:`Ipcmd` | ExtAlgeb | :math:`IpHL_{y} - Ipcmd_{0}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqcmd | :math:`Iqcmd` | ExtAlgeb | :math:`- IqHL_{y} - Iqcmd_{0}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Name | Symbol | Equation | Type | +============+=========================+===============================================================================================================================================================+===============+ | Ipcmd0 | :math:`Ipcmd0` | :math:`\frac{p_{0}}{v}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Iqcmd0 | :math:`Iqcmd0` | :math:`- \frac{q_{0}}{v}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | pfaref0 | :math:`\Phi_{ref0}` | :math:`\operatorname{atan}_{2}{\left(q_{0},p_{0} \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Volt_dip | :math:`z_{Vdip}` | :math:`1 - Vcmp_{zi}` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | qref0 | :math:`q_{ref0}` | :math:`Iqcmd_{0} SWQ_{s0} \left(VLower_{zi} v + 0.01 VLower_{zl}\right) + SWQ_{s1} \left(- Vref_{1} + v\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(Thld > 0 \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | nThld | :math:`n_{Thld}` | :math:`\operatorname{Indicator}{\left(Thld < 0 \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Thld_abs | :math:`|Thld|` | :math:`\left|{Thld}\right|` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | fThld | :math:`fThld` | :math:`0` | ExtendedEvent | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | s5_flag | :math:`z^{flag}_{s5}` | :math:`0` | EventFlag | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVq12 | :math:`k_{Vq12}` | :math:`\frac{- Iq_{1} + Iq_{2}}{- Vq_{1} + Vq_{2}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVq23 | :math:`k_{Vq23}` | :math:`\frac{- Iq_{2} + Iq_{3}}{- Vq_{2} + Vq_{3}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVq34 | :math:`k_{Vq34}` | :math:`\frac{- Iq_{3} + Iq_{4}}{- Vq_{3} + Vq_{4}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | zVDL1 | :math:`z_{VDL1}` | :math:`Iq_{1} \leq Iq_{2} \wedge Iq_{2} \leq Iq_{3} \wedge Iq_{3} \leq Iq_{4} \wedge Vq_{1} \leq Vq_{2} \wedge Vq_{2} \leq Vq_{3} \wedge Vq_{3} \leq Vq_{4}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVp12 | :math:`k_{Vp12}` | :math:`\frac{- Ip_{1} + Ip_{2}}{- Vp_{1} + Vp_{2}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVp23 | :math:`k_{Vp23}` | :math:`\frac{- Ip_{2} + Ip_{3}}{- Vp_{2} + Vp_{3}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVp34 | :math:`k_{Vp34}` | :math:`\frac{- Ip_{3} + Ip_{4}}{- Vp_{3} + Vp_{4}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | zVDL2 | :math:`z_{VDL2}` | :math:`Ip_{1} \leq Ip_{2} \wedge Ip_{2} \leq Ip_{3} \wedge Ip_{3} \leq Ip_{4} \wedge Vp_{1} \leq Vp_{2} \wedge Vp_{2} \leq Vp_{3} \wedge Vp_{3} \leq Vp_{4}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | fThld2 | :math:`fThld2` | :math:`0` | ExtendedEvent | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | VDL1c | :math:`VDL1c` | :math:`VDL_{1 y} < Imaxr` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | VDL2c | :math:`VDL2c` | :math:`VDL_{2 y} < Imaxr` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Ipmax2sq0 | :math:`I_{pmax20,nn}^2` | :math:`\operatorname{FixPiecewise}{\left(\left( 0, \ Imax^{2} - Iqcmd_{0}^{2} \leq 0\right),\left( Imax^{2} - Iqcmd_{0}^{2}, \ \text{True}\right) \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Ipmax2sq | :math:`I_{pmax2}^2` | :math:`\operatorname{FixPiecewise}{\left(\left( 0, \ Imax^{2} - IqHL_{y}^{2} \leq 0\right),\left( Imax^{2} - IqHL_{y}^{2}, \ \text{True}\right) \right)}` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Ipmaxh | :math:`Ipmaxh` | :math:`0` | VarHold | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Iqmax2sq0 | :math:`I_{qmax,nn}^2` | :math:`\operatorname{FixPiecewise}{\left(\left( 0, \ Imax^{2} - Ipcmd_{0}^{2} \leq 0\right),\left( Imax^{2} - Ipcmd_{0}^{2}, \ \text{True}\right) \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Iqmax2sq | :math:`I_{qmax2}^2` | :math:`\operatorname{FixPiecewise}{\left(\left( 0, \ Imax^{2} - IpHL_{y}^{2} \leq 0\right),\left( Imax^{2} - IpHL_{y}^{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:`s_{0 y}` | State | State in lag transfer function | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | S1_y | :math:`S_{1 y}` | State | State in lag transfer function | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | PIQ_xi | :math:`PIQ_{\xi}` | State | Integrator output | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | s4_y | :math:`s_{4 y}` | State | State in lag transfer function | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | pfilt_y | :math:`pfilt_{y}` | State | State in lag TF | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | s5_y | :math:`s_{5 y}` | State | State in lag TF | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | PIV_xi | :math:`PIV_{\xi}` | State | Integrator output | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Pord | :math:`Pord` | AliasState | Alias of s5_y | | | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | vp | :math:`vp` | Algeb | Sensed lower-capped voltage | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | pfaref | :math:`pfaref` | Algeb | power factor angle ref | *rad* | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Qref | :math:`Qref` | Algeb | external Q ref | *p.u.* | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Qcpf | :math:`Qcpf` | Algeb | Q calculated from P and power factor | *p.u.* | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | PFsel | :math:`PFsel` | Algeb | Output of PFFLAG selector | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Qerr | :math:`Qerr` | Algeb | Reactive power error | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | PIQ_ys | :math:`PIQ_{ys}` | Algeb | PI summation before limit | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | PIQ_y | :math:`PIQ_{y}` | Algeb | PI output | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Vsel_x | :math:`Vsel_{x}` | Algeb | Value before limiter | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Vsel_y | :math:`Vsel_{y}` | Algeb | Output after limiter and post gain | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Verr | :math:`Verr` | Algeb | Voltage error (Vref0) | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | dbV_y | :math:`dbV_{y}` | Algeb | Deadband type 1 output | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Iqinj | :math:`Iqinj` | Algeb | Additional Iq signal during under- or over-voltage | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | wg | :math:`wg` | Algeb | Drive train generator speed | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Pref | :math:`Pref` | Algeb | external P ref | *p.u.* | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Psel | :math:`Psel` | Algeb | Output selection of PFLAG | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | VDL1_y | :math:`VDL_{1 y}` | Algeb | Output of piecewise | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | VDL2_y | :math:`VDL_{2 y}` | Algeb | Output of piecewise | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Ipmax | :math:`Ipmax` | Algeb | Upper limit on Ipcmd | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Iqmax | :math:`Iqmax` | Algeb | Upper limit on Iqcmd | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | PIV_ys | :math:`PIV_{ys}` | Algeb | PI summation before limit | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | PIV_y | :math:`PIV_{y}` | Algeb | PI output | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Qsel | :math:`Qsel` | Algeb | Selection output of QFLAG | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | IpHL_x | :math:`IpHL_{x}` | Algeb | Value before limiter | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | IpHL_y | :math:`IpHL_{y}` | Algeb | Output after limiter and post gain | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | IqHL_x | :math:`IqHL_{x}` | Algeb | Value before limiter | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | IqHL_y | :math:`IqHL_{y}` | Algeb | Output after limiter and post gain | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | a | :math:`a` | ExtAlgeb | Bus voltage angle | | | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | v | :math:`v` | 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:`s_{0 y}` | State | :math:`v` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | S1_y | :math:`S_{1 y}` | State | :math:`Pe` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_xi | :math:`PIQ_{\xi}` | State | :math:`0.0` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | s4_y | :math:`s_{4 y}` | State | :math:`\frac{PFsel}{vp}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | pfilt_y | :math:`pfilt_{y}` | State | :math:`Pref` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | s5_y | :math:`s_{5 y}` | State | :math:`Psel` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_xi | :math:`PIV_{\xi}` | State | :math:`- Iqcmd_{0} SWQ_{s1}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pord | :math:`Pord` | AliasState | | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vp | :math:`vp` | Algeb | :math:`VLower_{zi} v + 0.01 VLower_{zl}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | pfaref | :math:`pfaref` | Algeb | :math:`pfaref_{0}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qref | :math:`Qref` | Algeb | :math:`- qref_{0}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qcpf | :math:`Qcpf` | Algeb | :math:`q_{0}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PFsel | :math:`PFsel` | Algeb | :math:`Qcpf SWPF_{s1} + Qref SWPF_{s0}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qerr | :math:`Qerr` | Algeb | :math:`PFlim_{zi} PFsel + PFlim_{zl} QMin + PFlim_{zu} QMax - Qe` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_ys | :math:`PIQ_{ys}` | Algeb | :math:`Kqp Qerr SWV_{s1}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_y | :math:`PIQ_{y}` | Algeb | :math:`PIQ_{lim zi} PIQ_{ys} + PIQ_{lim zl} VMIN + PIQ_{lim zu} VMAX` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vsel_x | :math:`Vsel_{x}` | Algeb | :math:`PIQ_{y} SWV_{s1} + SWV_{s0} \left(Qcpf SWPF_{s1} + Qref SWPF_{s0} + Vref_{1}\right)` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vsel_y | :math:`Vsel_{y}` | Algeb | :math:`VMAX Vsel_{lim zu} + VMIN Vsel_{lim zl} + Vsel_{lim zi} Vsel_{x}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Verr | :math:`Verr` | Algeb | :math:`Vref_{0} - s_{0 y}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | dbV_y | :math:`dbV_{y}` | Algeb | :math:`1.0 dbV_{db zl} \left(Verr - dbd_{1}\right) + 1.0 dbV_{db zu} \left(Verr - dbd_{2}\right)` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqinj | :math:`Iqinj` | Algeb | :math:`Kqv Volt_{dip} dbV_{y} + fThld \left(1 - Volt_{dip}\right) \left(Iqfrz pThld + Kqv dbV_{y} nThld\right)` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | wg | :math:`wg` | Algeb | :math:`1.0` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pref | :math:`Pref` | Algeb | :math:`\frac{p_{0}}{wg}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Psel | :math:`Psel` | Algeb | :math:`SWP_{s0} pfilt_{y} + SWP_{s1} pfilt_{y} wg` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VDL1_y | :math:`VDL_{1 y}` | Algeb | :math:`\operatorname{FixPiecewise}{\left(\left( Iq_{1}, \ Vq_{1} \geq s_{0 y}\right),\left( Iq_{1} + kVq_{12} \left(- Vq_{1} + s_{0 y}\right), \ Vq_{2} \geq s_{0 y}\right),\left( Iq_{2} + kVq_{23} \left(- Vq_{2} + s_{0 y}\right), \ Vq_{3} \geq s_{0 y}\right),\left( Iq_{3} + kVq_{34} \left(- Vq_{3} + s_{0 y}\right), \ Vq_{4} \geq s_{0 y}\right),\left( Iq_{4}, \ \text{True}\right) \right)}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VDL2_y | :math:`VDL_{2 y}` | Algeb | :math:`\operatorname{FixPiecewise}{\left(\left( Ip_{1}, \ Vp_{1} \geq s_{0 y}\right),\left( Ip_{1} + kVp_{12} \left(- Vp_{1} + s_{0 y}\right), \ Vp_{2} \geq s_{0 y}\right),\left( Ip_{2} + kVp_{23} \left(- Vp_{2} + s_{0 y}\right), \ Vp_{3} \geq s_{0 y}\right),\left( Ip_{3} + kVp_{34} \left(- Vp_{3} + s_{0 y}\right), \ Vp_{4} \geq s_{0 y}\right),\left( Ip_{4}, \ \text{True}\right) \right)}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Ipmax | :math:`Ipmax` | Algeb | :math:`\left(1 - fThld_{2}\right) \left(\sqrt{Ipmax2sq0} SWPQ_{s0} + SWPQ_{s1} \left(zVDL_{2} \left(Imaxr \left(1 - VDL2c\right) + VDL_{2 y} VDL2c\right) - 100000000.0 zVDL_{2} + 100000000.0\right)\right)` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqmax | :math:`Iqmax` | Algeb | :math:`\sqrt{Iqmax2sq0} SWPQ_{s1} + SWPQ_{s0} \left(zVDL_{1} \left(Imaxr \left(1 - VDL1c\right) + VDL_{1 y} VDL1c\right) - 100000000.0 zVDL_{1} + 100000000.0\right)` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_ys | :math:`PIV_{ys}` | Algeb | :math:`- Iqcmd_{0} SWQ_{s1} + Kvp SWQ_{s1} \left(- SWV_{s0} s_{0 y} + Vsel_{y}\right)` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_y | :math:`PIV_{y}` | Algeb | :math:`Iqmax PIV_{lim zu} + Iqmin PIV_{lim zl} + PIV_{lim zi} PIV_{ys}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qsel | :math:`Qsel` | Algeb | :math:`PIV_{y} SWQ_{s1} + SWQ_{s0} s_{4 y}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IpHL_x | :math:`IpHL_{x}` | Algeb | :math:`\frac{s_{5 y}}{vp}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IpHL_y | :math:`IpHL_{y}` | Algeb | :math:`IpHL_{lim zi} IpHL_{x} + IpHL_{lim zl} Ipmin + IpHL_{lim zu} Ipmax` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IqHL_x | :math:`IqHL_{x}` | Algeb | :math:`Iqinj + Qsel` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IqHL_y | :math:`IqHL_{y}` | Algeb | :math:`IqHL_{lim zi} IqHL_{x} + IqHL_{lim zl} Iqmin + IqHL_{lim zu} Iqmax` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`v` | 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:`s_{0 y}` | State | :math:`- s_{0 y} + v` | :math:`T_{rv}` | +----------+-------------------+------------+-----------------------------------------------------------------------------------------------------------------------------------+------------------+ | S1_y | :math:`S_{1 y}` | State | :math:`Pe - S_{1 y}` | :math:`T_p` | +----------+-------------------+------------+-----------------------------------------------------------------------------------------------------------------------------------+------------------+ | PIQ_xi | :math:`PIQ_{\xi}` | State | :math:`Kqi \left(1 - Volt_{dip}\right) \left(2 PIQ_{y} - 2 PIQ_{ys} + Qerr SWV_{s1}\right)` | | +----------+-------------------+------------+-----------------------------------------------------------------------------------------------------------------------------------+------------------+ | s4_y | :math:`s_{4 y}` | State | :math:`\left(1 - Volt_{dip}\right) \left(\frac{PFsel}{vp} - s_{4 y}\right)` | :math:`T_{iq}` | +----------+-------------------+------------+-----------------------------------------------------------------------------------------------------------------------------------+------------------+ | pfilt_y | :math:`pfilt_{y}` | State | :math:`Pref - pfilt_{y}` | :math:`0.02` | +----------+-------------------+------------+-----------------------------------------------------------------------------------------------------------------------------------+------------------+ | s5_y | :math:`s_{5 y}` | State | :math:`\left(1 - Volt_{dip}\right) \left(Psel - s_{5 y}\right)` | :math:`T_{pord}` | +----------+-------------------+------------+-----------------------------------------------------------------------------------------------------------------------------------+------------------+ | PIV_xi | :math:`PIV_{\xi}` | State | :math:`Kvi \left(1 - Volt_{dip}\right) \left(2 PIV_{y} - 2 PIV_{ys} + SWQ_{s1} \left(- SWV_{s0} s_{0 y} + Vsel_{y}\right)\right)` | | +----------+-------------------+------------+-----------------------------------------------------------------------------------------------------------------------------------+------------------+ | Pord | :math:`Pord` | AliasState | :math:`0` | | +----------+-------------------+------------+-----------------------------------------------------------------------------------------------------------------------------------+------------------+ Algebraic Equations ----------------------------- +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +=========+===================+==========+============================================================================================================================================================================================================================================================================================================================================================================================================================+ | vp | :math:`vp` | Algeb | :math:`VLower_{zi} v + 0.01 VLower_{zl} - vp` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | pfaref | :math:`pfaref` | Algeb | :math:`- pfaref + pfaref_{0}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qref | :math:`Qref` | Algeb | :math:`- Qref - qref_{0}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qcpf | :math:`Qcpf` | Algeb | :math:`\left(1 - zp_{z1}\right) \left(- Qcpf + S_{1 y} \tan{\left(pfaref \right)}\right)` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PFsel | :math:`PFsel` | Algeb | :math:`- PFsel + Qcpf SWPF_{s1} + Qref SWPF_{s0}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qerr | :math:`Qerr` | Algeb | :math:`PFlim_{zi} PFsel + PFlim_{zl} QMin + PFlim_{zu} QMax - Qe - Qerr` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_ys | :math:`PIQ_{ys}` | Algeb | :math:`\left(1 - Volt_{dip}\right) \left(Kqp Qerr SWV_{s1} + PIQ_{\xi} - PIQ_{ys}\right)` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_y | :math:`PIQ_{y}` | Algeb | :math:`\left(1 - Volt_{dip}\right) \left(PIQ_{lim zi} PIQ_{ys} + PIQ_{lim zl} VMIN + PIQ_{lim zu} VMAX - PIQ_{y}\right)` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vsel_x | :math:`Vsel_{x}` | Algeb | :math:`PIQ_{y} SWV_{s1} + SWV_{s0} \left(Qcpf SWPF_{s1} + Qref SWPF_{s0} + Vref_{1}\right) - Vsel_{x}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vsel_y | :math:`Vsel_{y}` | Algeb | :math:`VMAX Vsel_{lim zu} + VMIN Vsel_{lim zl} + Vsel_{lim zi} Vsel_{x} - Vsel_{y}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Verr | :math:`Verr` | Algeb | :math:`- Verr + Vref_{0} - s_{0 y}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | dbV_y | :math:`dbV_{y}` | Algeb | :math:`1.0 dbV_{db zl} \left(Verr - dbd_{1}\right) + 1.0 dbV_{db zu} \left(Verr - dbd_{2}\right) - dbV_{y}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqinj | :math:`Iqinj` | Algeb | :math:`- Iqinj + Kqv Volt_{dip} dbV_{y} + fThld \left(1 - Volt_{dip}\right) \left(Iqfrz pThld + Kqv dbV_{y} nThld\right)` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | wg | :math:`wg` | Algeb | :math:`1.0 - wg` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pref | :math:`Pref` | Algeb | :math:`- Kdf dfdt - Kf df - Pref + \frac{p_{0}}{wg}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Psel | :math:`Psel` | Algeb | :math:`- Psel + SWP_{s0} pfilt_{y} + SWP_{s1} pfilt_{y} wg` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VDL1_y | :math:`VDL_{1 y}` | Algeb | :math:`- VDL_{1 y} + \operatorname{FixPiecewise}{\left(\left( Iq_{1}, \ Vq_{1} \geq s_{0 y}\right),\left( Iq_{1} + kVq_{12} \left(- Vq_{1} + s_{0 y}\right), \ Vq_{2} \geq s_{0 y}\right),\left( Iq_{2} + kVq_{23} \left(- Vq_{2} + s_{0 y}\right), \ Vq_{3} \geq s_{0 y}\right),\left( Iq_{3} + kVq_{34} \left(- Vq_{3} + s_{0 y}\right), \ Vq_{4} \geq s_{0 y}\right),\left( Iq_{4}, \ \text{True}\right) \right)}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VDL2_y | :math:`VDL_{2 y}` | Algeb | :math:`- VDL_{2 y} + \operatorname{FixPiecewise}{\left(\left( Ip_{1}, \ Vp_{1} \geq s_{0 y}\right),\left( Ip_{1} + kVp_{12} \left(- Vp_{1} + s_{0 y}\right), \ Vp_{2} \geq s_{0 y}\right),\left( Ip_{2} + kVp_{23} \left(- Vp_{2} + s_{0 y}\right), \ Vp_{3} \geq s_{0 y}\right),\left( Ip_{3} + kVp_{34} \left(- Vp_{3} + s_{0 y}\right), \ Vp_{4} \geq s_{0 y}\right),\left( Ip_{4}, \ \text{True}\right) \right)}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Ipmax | :math:`Ipmax` | Algeb | :math:`- Ipmax + Ipmaxh fThld_{2} + \left(1 - fThld_{2}\right) \left(\sqrt{Ipmax2sq} SWPQ_{s0} + SWPQ_{s1} \left(zVDL_{2} \left(Imaxr \left(1 - VDL2c\right) + VDL_{2 y} VDL2c\right) - 100000000.0 zVDL_{2} + 100000000.0\right)\right)` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqmax | :math:`Iqmax` | Algeb | :math:`- Iqmax + \sqrt{Iqmax2sq} SWPQ_{s1} + SWPQ_{s0} \left(zVDL_{1} \left(Imaxr \left(1 - VDL1c\right) + VDL_{1 y} VDL1c\right) - 100000000.0 zVDL_{1} + 100000000.0\right)` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_ys | :math:`PIV_{ys}` | Algeb | :math:`\left(1 - Volt_{dip}\right) \left(Kvp SWQ_{s1} \left(- SWV_{s0} s_{0 y} + Vsel_{y}\right) + PIV_{\xi} - PIV_{ys}\right)` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_y | :math:`PIV_{y}` | Algeb | :math:`\left(1 - Volt_{dip}\right) \left(Iqmax PIV_{lim zu} + Iqmin PIV_{lim zl} + PIV_{lim zi} PIV_{ys} - PIV_{y}\right)` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qsel | :math:`Qsel` | Algeb | :math:`PIV_{y} SWQ_{s1} - Qsel + SWQ_{s0} s_{4 y}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IpHL_x | :math:`IpHL_{x}` | Algeb | :math:`- IpHL_{x} + \frac{s_{5 y}}{vp}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IpHL_y | :math:`IpHL_{y}` | Algeb | :math:`IpHL_{lim zi} IpHL_{x} + IpHL_{lim zl} Ipmin + IpHL_{lim zu} Ipmax - IpHL_{y}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IqHL_x | :math:`IqHL_{x}` | Algeb | :math:`- IqHL_{x} + Iqinj + Qsel` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IqHL_y | :math:`IqHL_{y}` | Algeb | :math:`IqHL_{lim zi} IqHL_{x} + IqHL_{lim zl} Iqmin + IqHL_{lim zu} Iqmax - IqHL_{y}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | :math:`0` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`v` | ExtAlgeb | :math:`0` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pe | :math:`Pe` | ExtAlgeb | :math:`0` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qe | :math:`Qe` | ExtAlgeb | :math:`0` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Ipcmd | :math:`Ipcmd` | ExtAlgeb | :math:`IpHL_{y} - Ipcmd_{0}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqcmd | :math:`Iqcmd` | ExtAlgeb | :math:`- IqHL_{y} - Iqcmd_{0}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | 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}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Iqcmd0 | :math:`Iqcmd0` | :math:`- \frac{q_{0}}{v}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | pfaref0 | :math:`\Phi_{ref0}` | :math:`\operatorname{atan}_{2}{\left(q_{0},p_{0} \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Volt_dip | :math:`z_{Vdip}` | :math:`1 - Vcmp_{zi}` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | qref0 | :math:`q_{ref0}` | :math:`Iqcmd_{0} SWQ_{s0} \left(VLower_{zi} v + 0.01 VLower_{zl}\right) + SWQ_{s1} \left(- Vref_{1} + v\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(Thld > 0 \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | nThld | :math:`n_{Thld}` | :math:`\operatorname{Indicator}{\left(Thld < 0 \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Thld_abs | :math:`|Thld|` | :math:`\left|{Thld}\right|` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | fThld | :math:`fThld` | :math:`0` | ExtendedEvent | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | s5_flag | :math:`z^{flag}_{s5}` | :math:`0` | EventFlag | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVq12 | :math:`k_{Vq12}` | :math:`\frac{- Iq_{1} + Iq_{2}}{- Vq_{1} + Vq_{2}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVq23 | :math:`k_{Vq23}` | :math:`\frac{- Iq_{2} + Iq_{3}}{- Vq_{2} + Vq_{3}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVq34 | :math:`k_{Vq34}` | :math:`\frac{- Iq_{3} + Iq_{4}}{- Vq_{3} + Vq_{4}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | zVDL1 | :math:`z_{VDL1}` | :math:`Iq_{1} \leq Iq_{2} \wedge Iq_{2} \leq Iq_{3} \wedge Iq_{3} \leq Iq_{4} \wedge Vq_{1} \leq Vq_{2} \wedge Vq_{2} \leq Vq_{3} \wedge Vq_{3} \leq Vq_{4}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVp12 | :math:`k_{Vp12}` | :math:`\frac{- Ip_{1} + Ip_{2}}{- Vp_{1} + Vp_{2}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVp23 | :math:`k_{Vp23}` | :math:`\frac{- Ip_{2} + Ip_{3}}{- Vp_{2} + Vp_{3}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVp34 | :math:`k_{Vp34}` | :math:`\frac{- Ip_{3} + Ip_{4}}{- Vp_{3} + Vp_{4}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | zVDL2 | :math:`z_{VDL2}` | :math:`Ip_{1} \leq Ip_{2} \wedge Ip_{2} \leq Ip_{3} \wedge Ip_{3} \leq Ip_{4} \wedge Vp_{1} \leq Vp_{2} \wedge Vp_{2} \leq Vp_{3} \wedge Vp_{3} \leq Vp_{4}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | fThld2 | :math:`fThld2` | :math:`0` | ExtendedEvent | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | VDL1c | :math:`VDL1c` | :math:`VDL_{1 y} < Imaxr` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | VDL2c | :math:`VDL2c` | :math:`VDL_{2 y} < Imaxr` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Ipmax2sq0 | :math:`I_{pmax20,nn}^2` | :math:`\operatorname{FixPiecewise}{\left(\left( 0, \ Imax^{2} - Iqcmd_{0}^{2} \leq 0\right),\left( Imax^{2} - Iqcmd_{0}^{2}, \ \text{True}\right) \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Ipmax2sq | :math:`I_{pmax2}^2` | :math:`\operatorname{FixPiecewise}{\left(\left( 0, \ Imax^{2} - IqHL_{y}^{2} \leq 0\right),\left( Imax^{2} - IqHL_{y}^{2}, \ \text{True}\right) \right)}` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Ipmaxh | :math:`Ipmaxh` | :math:`0` | VarHold | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Iqmax2sq0 | :math:`I_{qmax,nn}^2` | :math:`\operatorname{FixPiecewise}{\left(\left( 0, \ Imax^{2} - Ipcmd_{0}^{2} \leq 0\right),\left( Imax^{2} - Ipcmd_{0}^{2}, \ \text{True}\right) \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Iqmax2sq | :math:`I_{qmax2}^2` | :math:`\operatorname{FixPiecewise}{\left(\left( 0, \ Imax^{2} - IpHL_{y}^{2} \leq 0\right),\left( Imax^{2} - IpHL_{y}^{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:`s_{0 y}` | State | State in lag transfer function | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | S1_y | :math:`S_{1 y}` | State | State in lag transfer function | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | PIQ_xi | :math:`PIQ_{\xi}` | State | Integrator output | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | s4_y | :math:`s_{4 y}` | State | State in lag transfer function | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | pfilt_y | :math:`pfilt_{y}` | State | State in lag TF | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | s5_y | :math:`s_{5 y}` | State | State in lag TF | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | PIV_xi | :math:`PIV_{\xi}` | State | Integrator output | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Pord | :math:`Pord` | AliasState | Alias of s5_y | | | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | omega | :math:`\omega` | ExtState | generator speed | *pu* | | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | vp | :math:`vp` | Algeb | Sensed lower-capped voltage | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | pfaref | :math:`pfaref` | Algeb | power factor angle ref | *rad* | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Qref | :math:`Qref` | Algeb | external Q ref | *p.u.* | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Qcpf | :math:`Qcpf` | Algeb | Q calculated from P and power factor | *p.u.* | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | PFsel | :math:`PFsel` | Algeb | Output of PFFLAG selector | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Qerr | :math:`Qerr` | Algeb | Reactive power error | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | PIQ_ys | :math:`PIQ_{ys}` | Algeb | PI summation before limit | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | PIQ_y | :math:`PIQ_{y}` | Algeb | PI output | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Vsel_x | :math:`Vsel_{x}` | Algeb | Value before limiter | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Vsel_y | :math:`Vsel_{y}` | Algeb | Output after limiter and post gain | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Verr | :math:`Verr` | Algeb | Voltage error (Vref0) | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | dbV_y | :math:`dbV_{y}` | Algeb | Deadband type 1 output | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Iqinj | :math:`Iqinj` | Algeb | Additional Iq signal during under- or over-voltage | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | wg | :math:`wg` | Algeb | Drive train generator speed | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Pref | :math:`Pref` | Algeb | external P ref | *p.u.* | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Psel | :math:`Psel` | Algeb | Output selection of PFLAG | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | VDL1_y | :math:`VDL_{1 y}` | Algeb | Output of piecewise | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | VDL2_y | :math:`VDL_{2 y}` | Algeb | Output of piecewise | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Ipmax | :math:`Ipmax` | Algeb | Upper limit on Ipcmd | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Iqmax | :math:`Iqmax` | Algeb | Upper limit on Iqcmd | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | PIV_ys | :math:`PIV_{ys}` | Algeb | PI summation before limit | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | PIV_y | :math:`PIV_{y}` | Algeb | PI output | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | Qsel | :math:`Qsel` | Algeb | Selection output of QFLAG | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | IpHL_x | :math:`IpHL_{x}` | Algeb | Value before limiter | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | IpHL_y | :math:`IpHL_{y}` | Algeb | Output after limiter and post gain | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | IqHL_x | :math:`IqHL_{x}` | Algeb | Value before limiter | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | IqHL_y | :math:`IqHL_{y}` | Algeb | Output after limiter and post gain | | v_str | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | a | :math:`a` | ExtAlgeb | Bus voltage angle | | | +----------+-------------------+------------+----------------------------------------------------+--------+------------+ | v | :math:`v` | 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:`s_{0 y}` | State | :math:`v` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | S1_y | :math:`S_{1 y}` | State | :math:`Pe` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_xi | :math:`PIQ_{\xi}` | State | :math:`0.0` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | s4_y | :math:`s_{4 y}` | State | :math:`\frac{PFsel}{vp}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | pfilt_y | :math:`pfilt_{y}` | State | :math:`Pref` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | s5_y | :math:`s_{5 y}` | State | :math:`Psel` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_xi | :math:`PIV_{\xi}` | State | :math:`- Iqcmd_{0} SWQ_{s1}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pord | :math:`Pord` | AliasState | | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | omega | :math:`\omega` | ExtState | | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vp | :math:`vp` | Algeb | :math:`VLower_{zi} v + 0.01 VLower_{zl}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | pfaref | :math:`pfaref` | Algeb | :math:`pfaref_{0}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qref | :math:`Qref` | Algeb | :math:`- qref_{0}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qcpf | :math:`Qcpf` | Algeb | :math:`q_{0}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PFsel | :math:`PFsel` | Algeb | :math:`Qcpf SWPF_{s1} + Qref SWPF_{s0}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qerr | :math:`Qerr` | Algeb | :math:`PFlim_{zi} PFsel + PFlim_{zl} QMin + PFlim_{zu} QMax - Qe` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_ys | :math:`PIQ_{ys}` | Algeb | :math:`Kqp Qerr SWV_{s1}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_y | :math:`PIQ_{y}` | Algeb | :math:`PIQ_{lim zi} PIQ_{ys} + PIQ_{lim zl} VMIN + PIQ_{lim zu} VMAX` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vsel_x | :math:`Vsel_{x}` | Algeb | :math:`PIQ_{y} SWV_{s1} + SWV_{s0} \left(Qcpf SWPF_{s1} + Qref SWPF_{s0} + Vref_{1}\right)` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vsel_y | :math:`Vsel_{y}` | Algeb | :math:`VMAX Vsel_{lim zu} + VMIN Vsel_{lim zl} + Vsel_{lim zi} Vsel_{x}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Verr | :math:`Verr` | Algeb | :math:`Vref_{0} - s_{0 y}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | dbV_y | :math:`dbV_{y}` | Algeb | :math:`1.0 dbV_{db zl} \left(Verr - dbd_{1}\right) + 1.0 dbV_{db zu} \left(Verr - dbd_{2}\right)` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqinj | :math:`Iqinj` | Algeb | :math:`Kqv Volt_{dip} dbV_{y} + fThld \left(1 - Volt_{dip}\right) \left(Iqfrz pThld + Kqv dbV_{y} nThld\right)` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | wg | :math:`wg` | Algeb | :math:`1.0` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pref | :math:`Pref` | Algeb | :math:`\frac{p_{0}}{wg}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Psel | :math:`Psel` | Algeb | :math:`SWP_{s0} pfilt_{y} + SWP_{s1} pfilt_{y} wg` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VDL1_y | :math:`VDL_{1 y}` | Algeb | :math:`\operatorname{FixPiecewise}{\left(\left( Iq_{1}, \ Vq_{1} \geq s_{0 y}\right),\left( Iq_{1} + kVq_{12} \left(- Vq_{1} + s_{0 y}\right), \ Vq_{2} \geq s_{0 y}\right),\left( Iq_{2} + kVq_{23} \left(- Vq_{2} + s_{0 y}\right), \ Vq_{3} \geq s_{0 y}\right),\left( Iq_{3} + kVq_{34} \left(- Vq_{3} + s_{0 y}\right), \ Vq_{4} \geq s_{0 y}\right),\left( Iq_{4}, \ \text{True}\right) \right)}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VDL2_y | :math:`VDL_{2 y}` | Algeb | :math:`\operatorname{FixPiecewise}{\left(\left( Ip_{1}, \ Vp_{1} \geq s_{0 y}\right),\left( Ip_{1} + kVp_{12} \left(- Vp_{1} + s_{0 y}\right), \ Vp_{2} \geq s_{0 y}\right),\left( Ip_{2} + kVp_{23} \left(- Vp_{2} + s_{0 y}\right), \ Vp_{3} \geq s_{0 y}\right),\left( Ip_{3} + kVp_{34} \left(- Vp_{3} + s_{0 y}\right), \ Vp_{4} \geq s_{0 y}\right),\left( Ip_{4}, \ \text{True}\right) \right)}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Ipmax | :math:`Ipmax` | Algeb | :math:`\left(1 - fThld_{2}\right) \left(\sqrt{Ipmax2sq0} SWPQ_{s0} + SWPQ_{s1} \left(zVDL_{2} \left(Imaxr \left(1 - VDL2c\right) + VDL_{2 y} VDL2c\right) - 100000000.0 zVDL_{2} + 100000000.0\right)\right)` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqmax | :math:`Iqmax` | Algeb | :math:`\sqrt{Iqmax2sq0} SWPQ_{s1} + SWPQ_{s0} \left(zVDL_{1} \left(Imaxr \left(1 - VDL1c\right) + VDL_{1 y} VDL1c\right) - 100000000.0 zVDL_{1} + 100000000.0\right)` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_ys | :math:`PIV_{ys}` | Algeb | :math:`- Iqcmd_{0} SWQ_{s1} + Kvp SWQ_{s1} \left(- SWV_{s0} s_{0 y} + Vsel_{y}\right)` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_y | :math:`PIV_{y}` | Algeb | :math:`Iqmax PIV_{lim zu} + Iqmin PIV_{lim zl} + PIV_{lim zi} PIV_{ys}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qsel | :math:`Qsel` | Algeb | :math:`PIV_{y} SWQ_{s1} + SWQ_{s0} s_{4 y}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IpHL_x | :math:`IpHL_{x}` | Algeb | :math:`\frac{s_{5 y}}{vp}` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IpHL_y | :math:`IpHL_{y}` | Algeb | :math:`IpHL_{lim zi} IpHL_{x} + IpHL_{lim zl} Ipmin + IpHL_{lim zu} Ipmax` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IqHL_x | :math:`IqHL_{x}` | Algeb | :math:`Iqinj + Qsel` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IqHL_y | :math:`IqHL_{y}` | Algeb | :math:`IqHL_{lim zi} IqHL_{x} + IqHL_{lim zl} Iqmin + IqHL_{lim zu} Iqmax` | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | | +----------+-------------------+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`v` | 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:`s_{0 y}` | State | :math:`- s_{0 y} + v` | :math:`T_{rv}` | +----------+-------------------+------------+-----------------------------------------------------------------------------------------------------------------------------------+------------------+ | S1_y | :math:`S_{1 y}` | State | :math:`Pe - S_{1 y}` | :math:`T_p` | +----------+-------------------+------------+-----------------------------------------------------------------------------------------------------------------------------------+------------------+ | PIQ_xi | :math:`PIQ_{\xi}` | State | :math:`Kqi \left(1 - Volt_{dip}\right) \left(2 PIQ_{y} - 2 PIQ_{ys} + Qerr SWV_{s1}\right)` | | +----------+-------------------+------------+-----------------------------------------------------------------------------------------------------------------------------------+------------------+ | s4_y | :math:`s_{4 y}` | State | :math:`\left(1 - Volt_{dip}\right) \left(\frac{PFsel}{vp} - s_{4 y}\right)` | :math:`T_{iq}` | +----------+-------------------+------------+-----------------------------------------------------------------------------------------------------------------------------------+------------------+ | pfilt_y | :math:`pfilt_{y}` | State | :math:`Pref - pfilt_{y}` | :math:`0.02` | +----------+-------------------+------------+-----------------------------------------------------------------------------------------------------------------------------------+------------------+ | s5_y | :math:`s_{5 y}` | State | :math:`\left(1 - Volt_{dip}\right) \left(Psel - s_{5 y}\right)` | :math:`T_{pord}` | +----------+-------------------+------------+-----------------------------------------------------------------------------------------------------------------------------------+------------------+ | PIV_xi | :math:`PIV_{\xi}` | State | :math:`Kvi \left(1 - Volt_{dip}\right) \left(2 PIV_{y} - 2 PIV_{ys} + SWQ_{s1} \left(- SWV_{s0} s_{0 y} + Vsel_{y}\right)\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:`vp` | Algeb | :math:`VLower_{zi} v + 0.01 VLower_{zl} - vp` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | pfaref | :math:`pfaref` | Algeb | :math:`- pfaref + pfaref_{0}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qref | :math:`Qref` | Algeb | :math:`- Qref - qref_{0}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qcpf | :math:`Qcpf` | Algeb | :math:`\left(1 - zp_{z1}\right) \left(- Qcpf + S_{1 y} \tan{\left(pfaref \right)}\right)` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PFsel | :math:`PFsel` | Algeb | :math:`- PFsel + Qcpf SWPF_{s1} + Qref SWPF_{s0}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qerr | :math:`Qerr` | Algeb | :math:`PFlim_{zi} PFsel + PFlim_{zl} QMin + PFlim_{zu} QMax - Qe - Qerr` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_ys | :math:`PIQ_{ys}` | Algeb | :math:`\left(1 - Volt_{dip}\right) \left(Kqp Qerr SWV_{s1} + PIQ_{\xi} - PIQ_{ys}\right)` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIQ_y | :math:`PIQ_{y}` | Algeb | :math:`\left(1 - Volt_{dip}\right) \left(PIQ_{lim zi} PIQ_{ys} + PIQ_{lim zl} VMIN + PIQ_{lim zu} VMAX - PIQ_{y}\right)` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vsel_x | :math:`Vsel_{x}` | Algeb | :math:`PIQ_{y} SWV_{s1} + SWV_{s0} \left(Qcpf SWPF_{s1} + Qref SWPF_{s0} + Vref_{1}\right) - Vsel_{x}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Vsel_y | :math:`Vsel_{y}` | Algeb | :math:`VMAX Vsel_{lim zu} + VMIN Vsel_{lim zl} + Vsel_{lim zi} Vsel_{x} - Vsel_{y}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Verr | :math:`Verr` | Algeb | :math:`- Verr + Vref_{0} - s_{0 y}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | dbV_y | :math:`dbV_{y}` | Algeb | :math:`1.0 dbV_{db zl} \left(Verr - dbd_{1}\right) + 1.0 dbV_{db zu} \left(Verr - dbd_{2}\right) - dbV_{y}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqinj | :math:`Iqinj` | Algeb | :math:`- Iqinj + Kqv Volt_{dip} dbV_{y} + fThld \left(1 - Volt_{dip}\right) \left(Iqfrz pThld + Kqv dbV_{y} nThld\right)` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | wg | :math:`wg` | Algeb | :math:`1.0 - wg` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pref | :math:`Pref` | Algeb | :math:`- Kf \left(\omega - 1\right) - Pref + \frac{p_{0}}{wg}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Psel | :math:`Psel` | Algeb | :math:`- Psel + SWP_{s0} pfilt_{y} + SWP_{s1} pfilt_{y} wg` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VDL1_y | :math:`VDL_{1 y}` | Algeb | :math:`- VDL_{1 y} + \operatorname{FixPiecewise}{\left(\left( Iq_{1}, \ Vq_{1} \geq s_{0 y}\right),\left( Iq_{1} + kVq_{12} \left(- Vq_{1} + s_{0 y}\right), \ Vq_{2} \geq s_{0 y}\right),\left( Iq_{2} + kVq_{23} \left(- Vq_{2} + s_{0 y}\right), \ Vq_{3} \geq s_{0 y}\right),\left( Iq_{3} + kVq_{34} \left(- Vq_{3} + s_{0 y}\right), \ Vq_{4} \geq s_{0 y}\right),\left( Iq_{4}, \ \text{True}\right) \right)}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | VDL2_y | :math:`VDL_{2 y}` | Algeb | :math:`- VDL_{2 y} + \operatorname{FixPiecewise}{\left(\left( Ip_{1}, \ Vp_{1} \geq s_{0 y}\right),\left( Ip_{1} + kVp_{12} \left(- Vp_{1} + s_{0 y}\right), \ Vp_{2} \geq s_{0 y}\right),\left( Ip_{2} + kVp_{23} \left(- Vp_{2} + s_{0 y}\right), \ Vp_{3} \geq s_{0 y}\right),\left( Ip_{3} + kVp_{34} \left(- Vp_{3} + s_{0 y}\right), \ Vp_{4} \geq s_{0 y}\right),\left( Ip_{4}, \ \text{True}\right) \right)}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Ipmax | :math:`Ipmax` | Algeb | :math:`- Ipmax + Ipmaxh fThld_{2} + \left(1 - fThld_{2}\right) \left(\sqrt{Ipmax2sq} SWPQ_{s0} + SWPQ_{s1} \left(zVDL_{2} \left(Imaxr \left(1 - VDL2c\right) + VDL_{2 y} VDL2c\right) - 100000000.0 zVDL_{2} + 100000000.0\right)\right)` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqmax | :math:`Iqmax` | Algeb | :math:`- Iqmax + \sqrt{Iqmax2sq} SWPQ_{s1} + SWPQ_{s0} \left(zVDL_{1} \left(Imaxr \left(1 - VDL1c\right) + VDL_{1 y} VDL1c\right) - 100000000.0 zVDL_{1} + 100000000.0\right)` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_ys | :math:`PIV_{ys}` | Algeb | :math:`\left(1 - Volt_{dip}\right) \left(Kvp SWQ_{s1} \left(- SWV_{s0} s_{0 y} + Vsel_{y}\right) + PIV_{\xi} - PIV_{ys}\right)` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | PIV_y | :math:`PIV_{y}` | Algeb | :math:`\left(1 - Volt_{dip}\right) \left(Iqmax PIV_{lim zu} + Iqmin PIV_{lim zl} + PIV_{lim zi} PIV_{ys} - PIV_{y}\right)` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qsel | :math:`Qsel` | Algeb | :math:`PIV_{y} SWQ_{s1} - Qsel + SWQ_{s0} s_{4 y}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IpHL_x | :math:`IpHL_{x}` | Algeb | :math:`- IpHL_{x} + \frac{s_{5 y}}{vp}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IpHL_y | :math:`IpHL_{y}` | Algeb | :math:`IpHL_{lim zi} IpHL_{x} + IpHL_{lim zl} Ipmin + IpHL_{lim zu} Ipmax - IpHL_{y}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IqHL_x | :math:`IqHL_{x}` | Algeb | :math:`- IqHL_{x} + Iqinj + Qsel` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | IqHL_y | :math:`IqHL_{y}` | Algeb | :math:`IqHL_{lim zi} IqHL_{x} + IqHL_{lim zl} Iqmin + IqHL_{lim zu} Iqmax - IqHL_{y}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | :math:`0` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`v` | ExtAlgeb | :math:`0` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Pe | :math:`Pe` | ExtAlgeb | :math:`0` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Qe | :math:`Qe` | ExtAlgeb | :math:`0` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Ipcmd | :math:`Ipcmd` | ExtAlgeb | :math:`IpHL_{y} - Ipcmd_{0}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Iqcmd | :math:`Iqcmd` | ExtAlgeb | :math:`- IqHL_{y} - Iqcmd_{0}` | +---------+-------------------+----------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Name | Symbol | Equation | Type | +============+=========================+===============================================================================================================================================================+===============+ | Ipcmd0 | :math:`Ipcmd0` | :math:`\frac{p_{0}}{v}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Iqcmd0 | :math:`Iqcmd0` | :math:`- \frac{q_{0}}{v}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | pfaref0 | :math:`\Phi_{ref0}` | :math:`\operatorname{atan}_{2}{\left(q_{0},p_{0} \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Volt_dip | :math:`z_{Vdip}` | :math:`1 - Vcmp_{zi}` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | qref0 | :math:`q_{ref0}` | :math:`Iqcmd_{0} SWQ_{s0} \left(VLower_{zi} v + 0.01 VLower_{zl}\right) + SWQ_{s1} \left(- Vref_{1} + v\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(Thld > 0 \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | nThld | :math:`n_{Thld}` | :math:`\operatorname{Indicator}{\left(Thld < 0 \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Thld_abs | :math:`|Thld|` | :math:`\left|{Thld}\right|` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | fThld | :math:`fThld` | :math:`0` | ExtendedEvent | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | s5_flag | :math:`z^{flag}_{s5}` | :math:`0` | EventFlag | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVq12 | :math:`k_{Vq12}` | :math:`\frac{- Iq_{1} + Iq_{2}}{- Vq_{1} + Vq_{2}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVq23 | :math:`k_{Vq23}` | :math:`\frac{- Iq_{2} + Iq_{3}}{- Vq_{2} + Vq_{3}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVq34 | :math:`k_{Vq34}` | :math:`\frac{- Iq_{3} + Iq_{4}}{- Vq_{3} + Vq_{4}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | zVDL1 | :math:`z_{VDL1}` | :math:`Iq_{1} \leq Iq_{2} \wedge Iq_{2} \leq Iq_{3} \wedge Iq_{3} \leq Iq_{4} \wedge Vq_{1} \leq Vq_{2} \wedge Vq_{2} \leq Vq_{3} \wedge Vq_{3} \leq Vq_{4}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVp12 | :math:`k_{Vp12}` | :math:`\frac{- Ip_{1} + Ip_{2}}{- Vp_{1} + Vp_{2}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVp23 | :math:`k_{Vp23}` | :math:`\frac{- Ip_{2} + Ip_{3}}{- Vp_{2} + Vp_{3}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | kVp34 | :math:`k_{Vp34}` | :math:`\frac{- Ip_{3} + Ip_{4}}{- Vp_{3} + Vp_{4}}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | zVDL2 | :math:`z_{VDL2}` | :math:`Ip_{1} \leq Ip_{2} \wedge Ip_{2} \leq Ip_{3} \wedge Ip_{3} \leq Ip_{4} \wedge Vp_{1} \leq Vp_{2} \wedge Vp_{2} \leq Vp_{3} \wedge Vp_{3} \leq Vp_{4}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | fThld2 | :math:`fThld2` | :math:`0` | ExtendedEvent | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | VDL1c | :math:`VDL1c` | :math:`VDL_{1 y} < Imaxr` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | VDL2c | :math:`VDL2c` | :math:`VDL_{2 y} < Imaxr` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Ipmax2sq0 | :math:`I_{pmax20,nn}^2` | :math:`\operatorname{FixPiecewise}{\left(\left( 0, \ Imax^{2} - Iqcmd_{0}^{2} \leq 0\right),\left( Imax^{2} - Iqcmd_{0}^{2}, \ \text{True}\right) \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Ipmax2sq | :math:`I_{pmax2}^2` | :math:`\operatorname{FixPiecewise}{\left(\left( 0, \ Imax^{2} - IqHL_{y}^{2} \leq 0\right),\left( Imax^{2} - IqHL_{y}^{2}, \ \text{True}\right) \right)}` | VarService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Ipmaxh | :math:`Ipmaxh` | :math:`0` | VarHold | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Iqmax2sq0 | :math:`I_{qmax,nn}^2` | :math:`\operatorname{FixPiecewise}{\left(\left( 0, \ Imax^{2} - Ipcmd_{0}^{2} \leq 0\right),\left( Imax^{2} - Ipcmd_{0}^{2}, \ \text{True}\right) \right)}` | ConstService | +------------+-------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------+ | Iqmax2sq | :math:`I_{qmax2}^2` | :math:`\operatorname{FixPiecewise}{\left(\left( 0, \ Imax^{2} - IpHL_{y}^{2} \leq 0\right),\left( Imax^{2} - IpHL_{y}^{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 | | +---------------+-------------------+-------+---------------------------------------+-----------------+