REPCA

REPCA is a WECC renewable energy plant control model for inverter-coupled resources.

Warning

GridKit does not yet apply the associated generator’s Governor Response Limits modes Down Only and Fixed to REPCA.

Notes

Note

freq is optional because the regulated bus does not yet expose a frequency signal. With frequency control and nonzero droop enabled, omitting it holds frequency at 1.0 p.u. and logs a warning. freq and freqref use absolute per-unit frequency.

Block Diagram

Figure 1: REPCA plant-control model. Figure courtesy of PowerWorld REPC_A model reference.

Model Parameters

All parameters are optional; omitted keys use the defaults below.

Symbol	Units	JSON	Description	Typical Value	Note
\(S^\mathrm{base}\)	[MVA]	mva	REPCA component power base	100.0	Set to the associated converter base
\(s_\mathrm{comp}\)	[boolean]	VcompFlag	Voltage-compensation selector	true	true = line-drop compensation, false = reactive droop
\(s_\mathrm{ref}\)	[boolean]	RefFlag	Reactive-loop reference selector	true	true = voltage control, false = reactive-power control
\(s_\mathrm{freq}\)	[boolean]	Freqflag	Active-power output selector	false	true = command enabled, false = zero output
\(T_\mathrm{fltr}\)	[s]	Tfltr	Voltage and reactive-power filter time constant	0.05
\(V^\mathrm{frz}\)	[p.u.]	Vfrz	Reactive-power PI freeze-voltage threshold	0.7
\(R_c\)	[p.u.]	Rc	Line-drop compensation resistance	0.0	Component base
\(X_c\)	[p.u.]	Xc	Line-drop compensation reactance	0.0	Component base
\(K_c\)	[p.u.]	Kc	Reactive-current compensation gain	1.0
\(D_\mathrm{bd1}\)	[p.u.]	dbdlow	Lower reactive-loop deadband threshold	0.0
\(D_\mathrm{bd2}\)	[p.u.]	dbdupper	Upper reactive-loop deadband threshold	0.0
\(e^{\max}\)	[p.u.]	emax	Upper limit on the signed reactive-loop error	1.0
\(e^{\min}\)	[p.u.]	emin	Lower limit on the signed reactive-loop error	-1.0
\(K_\mathrm{p}\)	[p.u.]	Kp	Reactive-power controller proportional gain	10.0
\(K_\mathrm{i}\)	[p.u./s]	Ki	Reactive-power controller integral gain	10.0
\(Q^{\max}\)	[p.u.]	Qmax	Maximum reactive-power command	1.0	Component base
\(Q^{\min}\)	[p.u.]	Qmin	Minimum reactive-power command	-1.0	Component base
\(T_\mathrm{ft}\)	[s]	Tft	Reactive-command lead time constant	0.0
\(T_\mathrm{fv}\)	[s]	Tfv	Reactive-command lag time constant	3.0
\(T_\mathrm{p}\)	[s]	Tp	Active-power measurement filter time constant	0.0
\(D_\mathrm{bd1}^{f}\)	[p.u.]	fdbd1	Lower frequency-error deadband threshold	0.0
\(D_\mathrm{bd2}^{f}\)	[p.u.]	fdbd2	Upper frequency-error deadband threshold	0.0
\(D_\mathrm{dn}\)	[p.u./p.u.]	Ddn	Down-regulation (overfrequency) gain	20.0
\(D_\mathrm{up}\)	[p.u./p.u.]	Dup	Up-regulation (underfrequency) gain	0.0
\(e_P^{\max}\)	[p.u.]	femax	Upper limit on the signed active-power error	1.0
\(e_P^{\min}\)	[p.u.]	femin	Lower limit on the signed active-power error	-1.0
\(K_\mathrm{pg}\)	[p.u.]	Kpg	Active-power controller proportional gain	10.0
\(K_\mathrm{ig}\)	[p.u./s]	Kig	Active-power controller integral gain	10.0
\(P^{\max}\)	[p.u.]	Pmax	Maximum active-power command	2.0	Component base
\(P^{\min}\)	[p.u.]	Pmin	Minimum active-power command	0.0	Component base
\(T_\mathrm{lag}\)	[s]	Tlag	Active-power command lag time constant	3.0

Parameter Validation

A valid REPCA parameter set must satisfy the following conditions:

\[\begin{split}\begin{aligned} S^\mathrm{base} &> 0 \\ T_\mathrm{fltr}, T_\mathrm{ft}, T_\mathrm{fv}, T_\mathrm{p}, T_\mathrm{lag} &\ge 0 \\ D_\mathrm{bd1} &\le 0 \le D_\mathrm{bd2} \\ e^{\min} &\le 0 \le e^{\max} \\ Q^{\min} &\le Q^{\max} \\ D_\mathrm{bd1}^{f} &\le 0 \le D_\mathrm{bd2}^{f} \\ D_\mathrm{dn},D_\mathrm{up} &\ge 0 \\ e_P^{\min} &\le 0 \le e_P^{\max} \\ P^{\min} &\le P^{\max} \end{aligned}\end{split}\]

All real parameters must be finite.

The power bases and both conversion ratios must also be finite and positive; verify() also enforces Model Ports.

Model Derived Parameters

Let \(\epsilon_T=10^{-3}\ \mathrm{s}\). Smaller time constants are raised to that floor with a warning:

\[\begin{split}\begin{aligned} T_x &\leftarrow \max(T_x,\epsilon_T), \quad x\in\{\mathrm{fltr},\mathrm{fv},\mathrm{p},\mathrm{lag}\} \\ s_\mathrm{comp}^\mathrm{off} &= 1 - s_\mathrm{comp} \\ s_\mathrm{ref}^\mathrm{off} &= 1 - s_\mathrm{ref} \\ k_\mathrm{base} &= \dfrac{S^\mathrm{sys}}{S^\mathrm{base}} \\ I_r^\mathrm{comp} &= k_\mathrm{base}I_r, \quad I_i^\mathrm{comp} = k_\mathrm{base}I_i \end{aligned}\end{split}\]

\(S^\mathrm{sys}\) is the system power base; \(k_\mathrm{base}\) converts system-base power and current signals to component base. GridKit does not expose PUflag; these ports are always on system base.

Model Ports

Name	Port	Init	Description
bus	Bus	Known	Regulated-bus voltage
ir	Input	Known	Branch-current real component on system base
ii	Input	Known	Branch-current imaginary component on system base
p	Input	Known	Branch active power on system base
q	Input	Known	Branch reactive power on system base
freq	Input	Known	Optional absolute frequency; defaults to 1.0 p.u.[1]
vref	Input	Unknown	Voltage-control reference
pref	Input	Unknown	Plant active-power reference on system base
qref	Input	Unknown	Reactive-power reference on system base
freqref	Input	Unknown	Absolute per-unit frequency reference
qext	Output	Known	Reactive-power command on system base
pext	Output	Known	Active-power command on system base

The bus and measurement inputs are required; attached inputs must be linked. Optional references are published when attached and latched otherwise. The qext and pext assignments are optional; both remain monitorable. Initialization preserves qext and preserves pext only when \(s_\mathrm{freq}=1\); otherwise pext becomes zero.

Model Variables

Internal Variables

Differential

Symbol	Units	Description	Note
\(V^\mathrm{meas}\)	[p.u.]	Filtered regulated voltage	State 1 in Fig. 1; Source label: Vmeas
\(Q^\mathrm{meas}\)	[p.u.]	Filtered reactive-power signal	State 2 in Fig. 1; Source label: Qmeas; component base
\(x_Q^\mathrm{PI}\)	[p.u.]	Reactive-power PI controller state	State 3 in Fig. 1; Source label: Reactive PI; component base
\(x_Q^\mathrm{lag}\)	[p.u.]	Reactive-command lead–lag state	State 4 in Fig. 1; Source label: Qext; component base
\(P^\mathrm{meas}\)	[p.u.]	Filtered active-power signal	State 5 in Fig. 1; Source label: Pmeas; component base
\(x_P^\mathrm{PI}\)	[p.u.]	Active-power PI controller state	State 6 in Fig. 1; Source label: Power PI; component base
\(P^\mathrm{ref}\)	[p.u.]	Active-power command lag state	State 7 in Fig. 1; Source label: Pref; component base

Algebraic

Symbol	Units	Description	Note
\(V\)	[p.u.]	Regulated-bus voltage magnitude
\(V^\mathrm{ldc}\)	[p.u.]	Line-drop compensated voltage magnitude
\(V^\mathrm{droop}\)	[p.u.]	Reactive-droop-compensated voltage
\(V^\mathrm{ctrl}\)	[p.u.]	Selected voltage-measurement input
\(s_\mathrm{frz}\)	[-]	Smooth reactive-power PI voltage-enable gate
\(e_\mathrm{RQ}\)	[p.u.]	Selected reactive-loop error
\(e_\mathrm{RQ}^\mathrm{db}\)	[p.u.]	Deadbanded reactive-loop error
\(e_\mathrm{RQ}^\mathrm{lim}\)	[p.u.]	Limited reactive-loop error
\(Q^\mathrm{PI}\)	[p.u.]	Reactive-power PI output	Component base
\(Q^\mathrm{ext}\)	[p.u.]	Reactive-power command output	System base
\(e_f\)	[p.u.]	Frequency error after deadband
\(e_P\)	[p.u.]	Active-power control error	Component base
\(e_P^\mathrm{lim}\)	[p.u.]	Limited active-power control error	Component base
\(P^\mathrm{PI}\)	[p.u.]	Active-power PI output	Component base
\(P^\mathrm{ext}\)	[p.u.]	Active-power command output	System base

External Variables

Differential

None.

Algebraic

Symbol	Units	Description	Note
\(V_r\)	[p.u.]	Regulated-bus voltage, real component	Bus input
\(V_i\)	[p.u.]	Regulated-bus voltage, imaginary component	Bus input
\(I_r\)	[p.u.]	Branch-current real component	Signal port ir; system base
\(I_i\)	[p.u.]	Branch-current imaginary component	Signal port ii; system base
\(P\)	[p.u.]	Branch active power	Signal port p; system base
\(Q\)	[p.u.]	Branch reactive power	Signal port q; system base
\(f\)	[p.u.]	Frequency input	Signal port freq
\(V^\mathrm{ref}\)	[p.u.]	Voltage-control reference	Optional signal port vref
\(P_\mathrm{plant}^\mathrm{ref}\)	[p.u.]	Plant active-power reference	Optional signal port pref; system base
\(Q^\mathrm{ref}\)	[p.u.]	Reactive-power reference	Optional signal port qref; system base
\(f^\mathrm{ref}\)	[p.u.]	Frequency reference	Optional signal port freqref

Model Equations

Smooth functions: above, antiwindup, clamp, deadband2.

Internal Equations

Differential

\[\begin{split}\begin{aligned} 0 &= -\dot{V}^\mathrm{meas} + \dfrac{1}{T_\mathrm{fltr}} (V^\mathrm{ctrl} - V^\mathrm{meas}) \\ 0 &= -\dot{Q}^\mathrm{meas} + \dfrac{1}{T_\mathrm{fltr}} (k_\mathrm{base}Q - Q^\mathrm{meas}) \\ 0 &= -\dot{x}_Q^\mathrm{PI} + s_\mathrm{frz}\, \text{antiwindup}(Q^\mathrm{PI}, K_\mathrm{i}e_\mathrm{RQ}^\mathrm{lim};\,Q^{\min}, Q^{\max}) \\ 0 &= -\dot{x}_Q^\mathrm{lag} + \dfrac{1}{T_\mathrm{fv}} (Q^\mathrm{PI} - x_Q^\mathrm{lag}) \\ 0 &= -\dot{P}^\mathrm{meas} + \dfrac{1}{T_\mathrm{p}} (k_\mathrm{base}P - P^\mathrm{meas}) \\ 0 &= -\dot{x}_P^\mathrm{PI} + \text{antiwindup}(P^\mathrm{PI}, K_\mathrm{ig}e_P^\mathrm{lim};\,P^{\min}, P^{\max}) \\ 0 &= -\dot{P}^\mathrm{ref} + \dfrac{1}{T_\mathrm{lag}} (P^\mathrm{PI} - P^\mathrm{ref}) \end{aligned}\end{split}\]

Algebraic

\[\begin{split}\begin{aligned} 0 &= -V^2 + V_r^2 + V_i^2 \\ 0 &= -(V^\mathrm{ldc})^2 + (V_r - R_c I_r^\mathrm{comp} + X_c I_i^\mathrm{comp})^2 + (V_i - R_c I_i^\mathrm{comp} - X_c I_r^\mathrm{comp})^2 \\ 0 &= -V^\mathrm{droop} + V + K_c k_\mathrm{base}Q \\ 0 &= -V^\mathrm{ctrl} + s_\mathrm{comp}V^\mathrm{ldc} + s_\mathrm{comp}^\mathrm{off}V^\mathrm{droop} \\ 0 &= -s_\mathrm{frz} + \text{above}(V;\,V^\mathrm{frz}) \\ 0 &= -e_\mathrm{RQ} + s_\mathrm{ref}(V^\mathrm{ref} - V^\mathrm{meas}) + s_\mathrm{ref}^\mathrm{off} (k_\mathrm{base}Q^\mathrm{ref} - Q^\mathrm{meas}) \\ 0 &= -e_\mathrm{RQ}^\mathrm{db} + \text{deadband2}(e_\mathrm{RQ};\,D_\mathrm{bd1},D_\mathrm{bd2}) \\ 0 &= -e_\mathrm{RQ}^\mathrm{lim} + \text{clamp}(e_\mathrm{RQ}^\mathrm{db};\,e^{\min},e^{\max}) \\ 0 &= -Q^\mathrm{PI} + \text{clamp}(K_\mathrm{p}e_\mathrm{RQ}^\mathrm{lim}+x_Q^\mathrm{PI};\,Q^{\min},Q^{\max}) \\ 0 &= -T_\mathrm{fv} (k_\mathrm{base}Q^\mathrm{ext}-x_Q^\mathrm{lag}) + T_\mathrm{ft} (Q^\mathrm{PI}-x_Q^\mathrm{lag}) \\ 0 &= -e_f + \text{deadband2}(f^\mathrm{ref}-f;\,D_\mathrm{bd1}^{f},D_\mathrm{bd2}^{f}) \\ 0 &= -e_P + k_\mathrm{base}P_\mathrm{plant}^\mathrm{ref} - P^\mathrm{meas} + \text{droop}(e_f;D_\mathrm{dn},D_\mathrm{up}) \\ 0 &= -e_P^\mathrm{lim} + \text{clamp}(e_P;\,e_P^{\min},e_P^{\max}) \\ 0 &= -P^\mathrm{PI} + \text{clamp}(K_\mathrm{pg}e_P^\mathrm{lim}+x_P^\mathrm{PI};\,P^{\min},P^{\max}) \\ 0 &= -k_\mathrm{base}P^\mathrm{ext} + s_\mathrm{freq}P^\mathrm{ref} \end{aligned}\end{split}\]

Appendix A defines droop.

External Equations

None.

Initialization

REPCA reconstructs a steady operating point; arbitrary-state restart is unsupported.

Input Initialization

\[\begin{split}\begin{aligned} V_r, V_i &\leftarrow \text{regulated-bus voltage} \\ I_r, I_i &\leftarrow \text{branch current} \\ P, Q &\leftarrow \text{branch power} \\ f &\leftarrow \text{frequency input} \\ Q^\mathrm{ext} &\leftarrow \text{known reactive-power command on system base} \\ P^\mathrm{ext} &\leftarrow \text{known active-power command on system base}, \quad s_\mathrm{freq}=1 \end{aligned}\end{split}\]

Internal Initialization

iclamp and ideadband2 denote the initialization helpers invertClamp and invertDeadband, which recover inputs for the smooth CommonMath clamp and Type II deadband functions. Within \(10^{-12}\) of a clamp bound, REPCA uses that bound moved outward by \(0.1\); intervals of width at most \(10^{-12}\) return \(\ell\). Deadband outputs within \(10^{-12}\) of zero use the midpoint; other values are inverted by bisection.

\[\begin{split}\begin{aligned} V &\leftarrow \sqrt{V_r^2 + V_i^2} \\ V^\mathrm{ldc} &\leftarrow \sqrt{(V_r-R_c I_r^\mathrm{comp}+X_c I_i^\mathrm{comp})^2 + (V_i-R_c I_i^\mathrm{comp}-X_c I_r^\mathrm{comp})^2} \\ V^\mathrm{droop} &\leftarrow V + K_c k_\mathrm{base}Q \\ V^\mathrm{ctrl} &\leftarrow s_\mathrm{comp}V^\mathrm{ldc} + s_\mathrm{comp}^\mathrm{off}V^\mathrm{droop} \\ V^\mathrm{meas} &\leftarrow V^\mathrm{ctrl} \\ Q^\mathrm{meas} &\leftarrow k_\mathrm{base}Q \\ P^\mathrm{meas} &\leftarrow k_\mathrm{base}P \\ s_\mathrm{frz} &\leftarrow \text{above}(V;\,V^\mathrm{frz}) \\ e_\mathrm{RQ}^\mathrm{db} &\leftarrow \text{iclamp}(0;\,e^{\min},e^{\max}) \\ e_\mathrm{RQ} &\leftarrow \text{ideadband2}(e_\mathrm{RQ}^\mathrm{db};\,D_\mathrm{bd1},D_\mathrm{bd2}) \\ e_\mathrm{RQ}^\mathrm{lim} &\leftarrow 0 \\ Q^\mathrm{PI} &\leftarrow k_\mathrm{base}Q^\mathrm{ext} \\ Q^{\min} &\leftarrow \min(Q^{\min},Q^\mathrm{PI}),\quad Q^{\max}\leftarrow \max(Q^{\max},Q^\mathrm{PI}) \\ x_Q^\mathrm{lag} &\leftarrow Q^\mathrm{PI} \\ u_Q^\mathrm{PI} &\leftarrow \text{iclamp}(Q^\mathrm{PI};\,Q^{\min},Q^{\max}) \\ x_Q^\mathrm{PI} &\leftarrow u_Q^\mathrm{PI} - K_\mathrm{p}e_\mathrm{RQ}^\mathrm{lim} \\ e_f &\leftarrow 0 \\ P^\mathrm{freq} &\leftarrow \text{droop}(e_f;D_\mathrm{dn},D_\mathrm{up}) \\ e_P &\leftarrow \text{iclamp}(0;\,e_P^{\min},e_P^{\max}) \\ e_P^\mathrm{lim} &\leftarrow 0 \\ P^\mathrm{ref} &\leftarrow \begin{cases} k_\mathrm{base}P^\mathrm{ext} & s_\mathrm{freq}=1 \\ P^\mathrm{meas} & s_\mathrm{freq}=0 \end{cases} \\ P^\mathrm{PI} &\leftarrow P^\mathrm{ref} \\ P^{\min} &\leftarrow \min(P^{\min},P^\mathrm{PI}),\quad P^{\max}\leftarrow \max(P^{\max},P^\mathrm{PI}) \\ u_P^\mathrm{PI} &\leftarrow \text{iclamp}(P^\mathrm{PI};\,P^{\min},P^{\max}) \\ x_P^\mathrm{PI} &\leftarrow u_P^\mathrm{PI} - K_\mathrm{pg}e_P^\mathrm{lim} \\ P^\mathrm{ext} &\leftarrow \dfrac{s_\mathrm{freq}}{k_\mathrm{base}}P^\mathrm{ref} \\ \dot{V}^\mathrm{meas},\dot{Q}^\mathrm{meas}, \dot{x}_Q^\mathrm{PI},\dot{x}_Q^\mathrm{lag}, \dot{P}^\mathrm{meas},\dot{x}_P^\mathrm{PI},\dot{P}^\mathrm{ref} &\leftarrow 0 \end{aligned}\end{split}\]

If an initial PI output falls outside its configured limits, REPCA expands the limits to include it and logs a warning. This matches PowerWorld’s default Modify Limits and Run treatment of initial limit violations.

Initialization rejects an operating point if:

• a required input or derived value is not finite;

• the gated reactive-power or active-power PI state rate is nonfinite or does not vanish within the implementation tolerance.

Initialization is atomic; candidates are validated before state or signal writes.

Output Initialization

\[\begin{split}\begin{aligned} V^\mathrm{ref} &\leftarrow V^\mathrm{meas} + s_\mathrm{ref}e_\mathrm{RQ} \\ Q^\mathrm{ref} &\leftarrow Q + \dfrac{s_\mathrm{ref}^\mathrm{off}e_\mathrm{RQ}}{k_\mathrm{base}} \\ P_\mathrm{plant}^\mathrm{ref} &\leftarrow P + \dfrac{e_P-P^\mathrm{freq}}{k_\mathrm{base}} \\ f^\mathrm{ref} &\leftarrow f + \text{ideadband2}(0;\,D_\mathrm{bd1}^{f},D_\mathrm{bd2}^{f}) \end{aligned}\end{split}\]

Monitors

Monitor	Units	Description	Note
qext	[p.u.]	Reactive-power command output	\(Q^\mathrm{ext}\); system base
pext	[p.u.]	Active-power command output	\(P^\mathrm{ext}\); system base
vmeas	[p.u.]	Filtered regulated voltage	\(V^\mathrm{meas}\)
qmeas	[p.u.]	Filtered reactive-power signal	\(Q^\mathrm{meas}\); component base
pmeas	[p.u.]	Filtered active-power signal	\(P^\mathrm{meas}\); component base

Appendix A: droop

\[\text{droop}(e;D_\mathrm{dn},D_\mathrm{up}) =e\left[D_\mathrm{dn}+(D_\mathrm{up}-D_\mathrm{dn})\sigma(e)\right]\]

where \(\sigma\) is GridKit’s smooth sigmoid. The response preserves \(\text{droop}(0;D_\mathrm{dn},D_\mathrm{up})=0\).

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[1]

Background for phase-derived, filtered frequency measurement: PSCAD Frequency/Phase/Magnitude Meter and Ting et al., Evaluating Methods for Measuring Grid Frequency in Low-Inertia Power Systems.