REECA

REECA is a WECC renewable energy electrical control model for inverter-coupled resources. In GridKit it is represented as a signal-control model that computes active- and reactive-current commands.

Warning

Post-dip reactive-current injection and active-current limit holds require timer/history states that are not modeled. \(T_{\mathrm{hld}}\) and \(T_{\mathrm{hld2}}\) must be zero: \(I_{\mathrm{qinj}}^{\mathrm{frz}}\) is unused, and \(I_{\mathrm{p}}^{\max}\) is recalculated from VDL2 and current-circle logic at each residual evaluation instead of held after voltage recovery.

Notes

• Internal electrical quantities and current commands are on model base unless otherwise stated.

• Optional signal inputs default to their documented constant values when omitted.

Block Diagram

Figure 1: REECA block diagram. Figure courtesy of PowerWorld

Model Parameters

Symbol	Units	JSON	Description	Typical Value	Note
\(S^{\mathrm{base}}\)	[MVA]	TBD	REECA model power base	TBD	Source label: MVABase
\(s_{\mathrm{pf}}\)	[binary]	TBD	Power-factor control flag	TBD	Source label: PfFlag; 1 = power-factor control, 0 = Q control
\(s_V\)	[binary]	TBD	Voltage-control mode flag	TBD	Source label: VFlag; 1 = Q control, 0 = voltage control
\(s_Q\)	[binary]	TBD	Reactive-power control flag	TBD	Source label: QFlag; 1 = voltage/Q control, 0 = constant pf or Q control
\(s_P\)	[binary]	TBD	Active-power reference speed-multiplier flag	TBD	Source label: Pflag; 1 = multiply by generator speed
\(s_\mathrm{PQ}\)	[binary]	TBD	P/Q priority flag for converter current limit	TBD	Source label: Pqflag; 0 = Q priority, 1 = P priority
\(T_{\mathrm{rv}}\)	[s]	TBD	Voltage-measurement filter time constant	TBD	Source label: Trv; if zero, \(V_{\mathrm{meas}}\) is algebraic
\(T_{\mathrm{p}}\)	[s]	TBD	Electrical-power measurement filter time constant	TBD	Source label: Tp; if zero, \(P_{\mathrm{meas}}\) is algebraic
\(V_{\mathrm{ref0}}\)	[p.u.]	TBD	Outer-loop voltage reference	TBD	Source label: Vref0; initialized to terminal voltage if omitted
\(V_{\mathrm{dip}}\)	[p.u.]	TBD	Low-voltage threshold for reactive-current injection logic	TBD	Source label: Vdip
\(V_{\mathrm{up}}\)	[p.u.]	TBD	High-voltage threshold for reactive-current injection logic	TBD	Source label: Vup
\(D_{\mathrm{bd1}}\)	[p.u.]	TBD	Overvoltage deadband for voltage-error response	TBD	Source label: dbd1
\(D_{\mathrm{bd2}}\)	[p.u.]	TBD	Undervoltage deadband for voltage-error response	TBD	Source label: dbd2
\(K_{\mathrm{qv}}\)	[p.u.]	TBD	Reactive-current injection gain during voltage dip/overvoltage logic	TBD	Source label: kqv
\(I_{\mathrm{qinj}}^{\min}\)	[p.u.]	TBD	Minimum reactive-current injection limit	TBD	Source label: Iql1
\(I_{\mathrm{qinj}}^{\max}\)	[p.u.]	TBD	Maximum reactive-current injection limit	TBD	Source label: Iqh1
\(I_{\mathrm{qinj}}^{\mathrm{frz}}\)	[p.u.]	TBD	Held reactive-current injection value after voltage dip	TBD	Source label: Iqfrz; unused when \(T_{\mathrm{hld}} = 0\)
\(T_{\mathrm{hld}}\)	[s]	TBD	Reactive-current injection hold time after voltage dip clears	TBD	Source label: Thld; required to be zero in this version
\(Q^{\max}\)	[p.u.]	TBD	Maximum reactive-power control limit	TBD	Source label: Qmax
\(Q^{\min}\)	[p.u.]	TBD	Minimum reactive-power control limit	TBD	Source label: Qmin
\(K_{\mathrm{qp}}\)	[p.u.]	TBD	Reactive-power control proportional gain	TBD	Source label: Kqp
\(K_{\mathrm{qi}}\)	[p.u./s]	TBD	Reactive-power control integral gain	TBD	Source label: Kqi
\(V^{\max}\)	[p.u.]	TBD	Maximum voltage-control limit	TBD	Source label: Vmax
\(V^{\min}\)	[p.u.]	TBD	Minimum voltage-control limit	TBD	Source label: Vmin
\(V_{\mathrm{ref1}}\)	[p.u.]	TBD	Inner-loop voltage-control reference/bias	0	Source label: Vref1
\(K_{\mathrm{vp}}\)	[p.u.]	TBD	Voltage-control proportional gain	TBD	Source label: Kvp
\(K_{\mathrm{vi}}\)	[p.u./s]	TBD	Voltage-control integral gain	TBD	Source label: Kvi
\(T_{\mathrm{iq}}\)	[s]	TBD	Reactive-current command lag time constant	TBD	Source label: Tiq
\(T_{\mathrm{pord}}\)	[s]	TBD	Active-power order filter time constant	TBD	Source label: Tpord
\(R_P^{\max}\)	[p.u./s]	TBD	Positive active-power order ramp-rate limit	TBD	Source label: dPmax
\(R_P^{\min}\)	[p.u./s]	TBD	Negative active-power order ramp-rate limit	TBD	Source label: dPmin
\(P^{\max}\)	[p.u.]	TBD	Maximum active-power order limit	TBD	Source label: Pmax
\(P^{\min}\)	[p.u.]	TBD	Minimum active-power order limit	TBD	Source label: Pmin
\(I^{\max}\)	[p.u.]	TBD	Maximum total converter current	TBD	Source label: Imax
\(V_{\mathrm{q},1}\)	[p.u.]	TBD	VDL1 voltage point 1	TBD	Source label: vq1
\(I_{\mathrm{q},1}^{\max}\)	[p.u.]	TBD	VDL1 reactive-current limit point 1	TBD	Source label: lq1
\(V_{\mathrm{q},2}\)	[p.u.]	TBD	VDL1 voltage point 2	TBD	Source label: vq2
\(I_{\mathrm{q},2}^{\max}\)	[p.u.]	TBD	VDL1 reactive-current limit point 2	TBD	Source label: lq2
\(V_{\mathrm{q},3}\)	[p.u.]	TBD	VDL1 voltage point 3	TBD	Source label: vq3
\(I_{\mathrm{q},3}^{\max}\)	[p.u.]	TBD	VDL1 reactive-current limit point 3	TBD	Source label: lq3
\(V_{\mathrm{q},4}\)	[p.u.]	TBD	VDL1 voltage point 4	TBD	Source label: vq4
\(I_{\mathrm{q},4}^{\max}\)	[p.u.]	TBD	VDL1 reactive-current limit point 4	TBD	Source label: lq4
\(V_{\mathrm{p},1}\)	[p.u.]	TBD	VDL2 voltage point 1	TBD	Source label: vp1
\(I_{\mathrm{p},1}^{\max}\)	[p.u.]	TBD	VDL2 active-current limit point 1	TBD	Source label: lp1
\(V_{\mathrm{p},2}\)	[p.u.]	TBD	VDL2 voltage point 2	TBD	Source label: vp2
\(I_{\mathrm{p},2}^{\max}\)	[p.u.]	TBD	VDL2 active-current limit point 2	TBD	Source label: lp2
\(V_{\mathrm{p},3}\)	[p.u.]	TBD	VDL2 voltage point 3	TBD	Source label: vp3
\(I_{\mathrm{p},3}^{\max}\)	[p.u.]	TBD	VDL2 active-current limit point 3	TBD	Source label: lp3
\(V_{\mathrm{p},4}\)	[p.u.]	TBD	VDL2 voltage point 4	TBD	Source label: vp4
\(I_{\mathrm{p},4}^{\max}\)	[p.u.]	TBD	VDL2 active-current limit point 4	TBD	Source label: lp4
\(T_{\mathrm{hld2}}\)	[s]	TBD	Active-current limit hold time after voltage dip clears	TBD	Source label: Thld2; required to be zero in this version

JSON parameter names are not yet specified.

Parameter Validation

A valid REECA parameter set must satisfy the following conditions:

\[\begin{split}\begin{aligned} &S^{\mathrm{base}} > 0 \\ &s_{\mathrm{pf}}, s_V, s_Q, s_P, s_\mathrm{PQ} \in \{0,1\} \\ &T_{\mathrm{rv}}, T_{\mathrm{p}} \ge 0 \\ &0 \le V_{\mathrm{dip}} < V_{\mathrm{up}} \\ &D_{\mathrm{bd1}} \le 0 \le D_{\mathrm{bd2}} \\ &I_{\mathrm{qinj}}^{\min} \le I_{\mathrm{qinj}}^{\max} \\ &T_{\mathrm{hld}} = T_{\mathrm{hld2}} = 0 \\ &Q^{\min} \le Q^{\max} \\ &V^{\min} \le V^{\max} \\ &T_{\mathrm{iq}}, T_{\mathrm{pord}} > 0 \\ &R_P^{\min} < 0 < R_P^{\max} \\ &P^{\min} \le P^{\max} \\ &I^{\max} \ge 0 \\ &0 \le V_{\mathrm{q},1} < V_{\mathrm{q},2} < V_{\mathrm{q},3} < V_{\mathrm{q},4} \\ &I_{\mathrm{q},k}^{\max} \ge 0\ \text{for } k=1,\ldots,4 \\ &0 \le V_{\mathrm{p},1} < V_{\mathrm{p},2} < V_{\mathrm{p},3} < V_{\mathrm{p},4} \\ &I_{\mathrm{p},k}^{\max} \ge 0\ \text{for } k=1,\ldots,4 \end{aligned}\end{split}\]

Model Derived Parameters

The off-mode flag complements are:

\[\begin{split}\begin{aligned} s_{\mathrm{pf}}^{\mathrm{off}} &= 1 - s_{\mathrm{pf}} \\ s_V^{\mathrm{off}} &= 1 - s_V \\ s_Q^{\mathrm{off}} &= 1 - s_Q \\ s_\mathrm{PQ}^{\mathrm{off}} &= 1 - s_\mathrm{PQ} \end{aligned}\end{split}\]

The VDL functions use GridKit’s smooth Linear Segment helper and provide flat extrapolation outside the first and fourth voltage points:

\[\begin{split}\begin{aligned} g_q(x) &= I_{\mathrm{q},1}^{\max} + \sum_{k=1}^{3} \text{linseg}\!( x;\, V_{\mathrm{q},k},\, V_{\mathrm{q},k+1},\, I_{\mathrm{q},k+1}^{\max} - I_{\mathrm{q},k}^{\max} ) \\ g_p(x) &= I_{\mathrm{p},1}^{\max} + \sum_{k=1}^{3} \text{linseg}\!( x;\, V_{\mathrm{p},k},\, V_{\mathrm{p},k+1},\, I_{\mathrm{p},k+1}^{\max} - I_{\mathrm{p},k}^{\max} ) \end{aligned}\end{split}\]

Model Ports

Name	Port	Init	Description
bus	Bus	TBD	Terminal-bus voltage
speed	Input	TBD	Generator speed deviation
pe	Input	TBD	Electrical active-power feedback
qgen	Input	TBD	Reactive-power feedback
qext	Input	TBD	External reactive-power command
pfaref	Input	TBD	Power-factor angle reference
pref	Input	TBD	Active-power reference
iqcmd	Output	TBD	Reactive-current command
ipcmd	Output	TBD	Active-current command

Model Variables

Internal Variables

Differential

Symbol	Units	Description	Note
\(V_{\mathrm{meas}}\)	[p.u.]	Filtered terminal voltage	State 1 in Fig. 1; Source label: Vmeas; algebraic when \(T_{\mathrm{rv}} = 0\)
\(P_{\mathrm{meas}}\)	[p.u.]	Filtered electrical power	State 2 in Fig. 1; Source label: Pmeas; algebraic when \(T_{\mathrm{p}} = 0\)
\(x_{\mathrm{PIQ}}\)	[p.u.]	Reactive-power PI controller state	State 3 in Fig. 1; Source label: PIQ
\(x_{\mathrm{PIV}}\)	[p.u.]	Voltage PI controller state	State 4 in Fig. 1; Source label: PIV
\(Q_V\)	[p.u.]	Reactive-current command lag state	State 5 in Fig. 1; Source label: Q_V
\(P_{\mathrm{ord}}\)	[p.u.]	Filtered active-power order	State 6 in Fig. 1; Source label: Pord

Algebraic

Symbol	Units	Description	Note
\(V_T\)	[p.u.]	Terminal voltage magnitude
\(V_{\mathrm{meas}}^{\mathrm{safe}}\)	[p.u.]	Safe filtered terminal voltage for divider blocks	Lower bounded by 0.01
\(s_{\mathrm{dip}}\)	[binary]	Voltage-dip/overvoltage freeze indicator	1 when outside voltage thresholds
\(V_{\mathrm{err}}\)	[p.u.]	Deadbanded voltage error	Defined by CommonMath deadband2
\(I_{\mathrm{qv}}\)	[p.u.]	Reactive-current injection candidate	Converter base
\(Q_{\mathrm{ref}}\)	[p.u.]	Selected reactive-power reference	From power-factor or external reactive-power command
\(e_Q\)	[p.u.]	Reactive-power control error	Limited \(Q_{\mathrm{ref}}\) minus \(Q_{\mathrm{gen}}\)
\(V_{\mathrm{PIQ}}\)	[p.u.]	Reactive-power control PI output	Limited by \(V^{\min}\) and \(V^{\max}\)
\(e_{\mathrm{PIV}}\)	[p.u.]	Voltage-control PI error	Selected voltage-control signal minus \(V_{\mathrm{meas}}\)
\(f_{\mathrm{pord}}\)	[p.u./s]	Active-power order derivative before ramp-rate limiting	Feeds \(r_{\mathrm{pord}}\)
\(r_{\mathrm{pord}}\)	[p.u./s]	Ramp-rate-limited active-power order derivative	Feeds \(P_{\mathrm{ord}}\) anti-windup
\(I_{\mathrm{q}}^{\mathrm{circ}}\)	[p.u.]	Reactive-current limit from converter current circle	Converter base; nonnegative algebraic branch
\(I_{\mathrm{p}}^{\mathrm{circ}}\)	[p.u.]	Active-current limit from converter current circle	Converter base; nonnegative algebraic branch
\(I_{\mathrm{q}}^{\max}\)	[p.u.]	Final reactive-current upper limit	Converter base; updated by VDL1 and current-limit logic
\(I_{\mathrm{p}}^{\max}\)	[p.u.]	Final active-current upper limit	Converter base; updated by VDL2 and current-limit logic
\(I_{\mathrm{qbase}}\)	[p.u.]	Base reactive-current command	Converter base; before \(s_Q\) selection and reactive-current injection
\(I_{\mathrm{q}}^{\mathrm{raw}}\)	[p.u.]	Raw reactive-current command before final limit	Converter base
\(I_{\mathrm{q}}^{\mathrm{cmd}}\)	[p.u.]	Reactive-current command output	Converter base
\(I_{\mathrm{p}}^{\mathrm{cmd}}\)	[p.u.]	Active-current command output	Converter base

External Variables

Differential

Symbol	Units	Description	Note
\(\omega\)	[p.u.]	Generator speed deviation	Optional, defaults to zero; source diagram \(\omega_\mathrm{g} = 1 + \omega\)

Algebraic

Symbol	Units	Description	Note
\(V_r\)	[p.u.]	Terminal voltage, real component	Owned by bus object
\(V_i\)	[p.u.]	Terminal voltage, imaginary component	Owned by bus object
\(P_\mathrm{e}\)	[p.u.]	Electrical active power	Source label: Pe
\(Q_{\mathrm{gen}}\)	[p.u.]	Reactive-power feedback	Source label: Qgen
\(Q_{\mathrm{ext}}\)	[p.u.]	External reactive-power command	Optional, defaults to initialized constant
\(\phi_{\mathrm{pf}}^{\mathrm{ref}}\)	[rad]	Power-factor angle reference	Source label: pfaref; used through tangent block
\(P_{\mathrm{ref}}\)	[p.u.]	External active-power reference	Optional, defaults to initialized constant

Model Equations

Smooth functions: antiwindup, clamp, deadband2, max, min, outside.

For readability, define:

\[\begin{split}\begin{aligned} f_{\mathrm{PIQ}} &= K_{\mathrm{qi}} e_Q \\ f_{\mathrm{PIV}} &= K_{\mathrm{vi}} e_{\mathrm{PIV}} \end{aligned}\end{split}\]

Internal Equations

Differential

\[\begin{split}\begin{aligned} 0 &= -T_{\mathrm{rv}}\dot V_{\mathrm{meas}} - V_{\mathrm{meas}} + V_T \\ 0 &= -T_{\mathrm{p}}\dot P_{\mathrm{meas}} - P_{\mathrm{meas}} + P_\mathrm{e} \\ 0 &= -\dot x_{\mathrm{PIQ}} + (1 - s_{\mathrm{dip}}) \text{antiwindup}\!( V_{\mathrm{PIQ}}, f_{\mathrm{PIQ}}; V^{\min}, V^{\max} ) \\ 0 &= -\dot x_{\mathrm{PIV}} + (1 - s_{\mathrm{dip}}) \text{antiwindup}\!( I_{\mathrm{qbase}}, f_{\mathrm{PIV}}; -I_{\mathrm{q}}^{\max}, I_{\mathrm{q}}^{\max} ) \\ 0 &= -T_{\mathrm{iq}}\dot Q_V - (1 - s_{\mathrm{dip}})Q_V + (1 - s_{\mathrm{dip}})Q_{\mathrm{ref}}/V_{\mathrm{meas}}^{\mathrm{safe}} \\ 0 &= -\dot P_{\mathrm{ord}} + (1 - s_{\mathrm{dip}}) \text{antiwindup}\!( P_{\mathrm{ord}}, r_{\mathrm{pord}}; P^{\min}, P^{\max} ) \end{aligned}\end{split}\]

Algebraic

\[\begin{split}\begin{aligned} 0 &= -V_T^2 + V_\mathrm r^2 + V_\mathrm i^2 \\ 0 &= -V_\mathrm{meas}^\mathrm{safe} + \max(V_\mathrm{meas}, 0.01) \\ 0 &= -s_\mathrm{dip} + \text{outside}(V_T; V_\mathrm{dip}, V_\mathrm{up}) \\ 0 &= -V_\mathrm{err} + \text{deadband2}(V_\mathrm{ref0} - V_\mathrm{meas}; D_\mathrm{bd1}, D_\mathrm{bd2}) \\ 0 &= -I_\mathrm{qv} + \text{clamp}(K_\mathrm{qv} V_\mathrm{err}; I_\mathrm{qinj}^{\min}, I_\mathrm{qinj}^{\max}) \\ 0 &= -Q_\mathrm{ref} + s_\mathrm{pf} P_\mathrm{meas}\tan(\phi_\mathrm{pf}^\mathrm{ref}) + s_\mathrm{pf}^\mathrm{off} Q_\mathrm{ext} \\ 0 &= -e_Q + \text{clamp}(Q_\mathrm{ref}; Q^{\min}, Q^{\max}) - Q_\mathrm{gen} \\ 0 &= -V_\mathrm{PIQ} + \text{clamp}(K_\mathrm{qp} e_Q + x_\mathrm{PIQ}; V^{\min}, V^{\max}) \\ 0 &= -e_\mathrm{PIV} + s_V V_\mathrm{PIQ} + s_V^\mathrm{off}(Q_\mathrm{ref} + V_\mathrm{ref1}) - V_\mathrm{meas} \\ 0 &= -T_\mathrm{pord} f_\mathrm{pord} + (1 + s_P\omega)P_\mathrm{ref} - P_\mathrm{ord} \\ 0 &= -r_\mathrm{pord} + \text{clamp}(f_\mathrm{pord}; R_P^{\min}, R_P^{\max}) \end{aligned}\end{split}\]

\[\begin{split}\begin{aligned} 0 &= -{I_\mathrm{q}^\mathrm{circ}}^2 + (I^{\max})^2 - s_\mathrm{PQ}(I_\mathrm{p}^\mathrm{cmd})^2 \\ 0 &= -{I_\mathrm{p}^\mathrm{circ}}^2 + (I^{\max})^2 - s_\mathrm{PQ}^\mathrm{off}(I_\mathrm{q}^\mathrm{cmd})^2 \\ 0 &= -I_\mathrm{q}^{\max} + \text{min}(g_q(V_\mathrm{meas}), I_\mathrm{q}^\mathrm{circ}) \\ 0 &= -I_\mathrm{p}^{\max} + \text{min}(g_p(V_\mathrm{meas}), I_\mathrm{p}^\mathrm{circ}) \\ 0 &= -I_\mathrm{qbase} + \text{clamp}(K_\mathrm{vp} e_\mathrm{PIV} + x_\mathrm{PIV}; -I_\mathrm{q}^{\max}, I_\mathrm{q}^{\max}) \\ 0 &= -I_\mathrm{q}^\mathrm{raw} + s_Q I_\mathrm{qbase} + s_Q^\mathrm{off} Q_V + s_\mathrm{dip} I_\mathrm{qv} \\ 0 &= -I_\mathrm{q}^\mathrm{cmd} + \text{clamp}(I_\mathrm{q}^\mathrm{raw}; -I_\mathrm{q}^{\max}, I_\mathrm{q}^{\max}) \\ 0 &= -I_\mathrm{p}^\mathrm{cmd} + \text{clamp}(P_\mathrm{ord}/V_\mathrm{meas}^\mathrm{safe}; 0, I_\mathrm{p}^{\max}) \end{aligned}\end{split}\]

The \(V_T\), \(I_{\mathrm{q}}^{\mathrm{circ}}\), and \(I_{\mathrm{p}}^{\mathrm{circ}}\) variables use nonnegative branches of squared algebraic residuals.

External Equations

None.

Initialization

All internal derivatives initialize to zero. Omitted optional signals use the following constants:

\[\begin{split}\begin{aligned} V_T &\leftarrow \sqrt{V_r^2 + V_i^2} \\ \omega &\leftarrow 0,\quad \text{if omitted} \\ Q_{\mathrm{ext}} &\leftarrow Q_{\mathrm{gen}},\quad \text{if omitted} \\ P_{\mathrm{ref}} &\leftarrow \dfrac{P_{\mathrm{e}}}{1+s_P\omega},\quad \text{if omitted} \end{aligned}\end{split}\]

Connected optional signals use their supplied initial values; if only some are omitted, compute the omitted constants with the connected initial values. Inconsistent supplied commands require a residual solve or initialization rejection.

If \(V_{\mathrm{ref0}}\) is omitted, set \(V_{\mathrm{ref0}}\leftarrow V_T\).

\[\begin{split}\begin{aligned} V_{\mathrm{meas}} &\leftarrow V_T \\ P_{\mathrm{meas}} &\leftarrow P_{\mathrm{e}} \end{aligned}\end{split}\]

Then evaluate the upstream algebraic chain:

\[\begin{split}\begin{aligned} V_{\mathrm{meas}}^{\mathrm{safe}} &\leftarrow \text{max}(V_{\mathrm{meas}}, 0.01) \\ s_{\mathrm{dip}} &\leftarrow \text{outside}(V_T; V_{\mathrm{dip}}, V_{\mathrm{up}}) \\ V_{\mathrm{err}} &\leftarrow \text{deadband2}(V_{\mathrm{ref0}} - V_{\mathrm{meas}}; D_{\mathrm{bd1}}, D_{\mathrm{bd2}}) \\ I_{\mathrm{qv}} &\leftarrow \text{clamp}(K_{\mathrm{qv}} V_{\mathrm{err}}; I_{\mathrm{qinj}}^{\min}, I_{\mathrm{qinj}}^{\max}) \\ Q_{\mathrm{ref}} &\leftarrow s_{\mathrm{pf}} P_{\mathrm{meas}}\tan(\phi_{\mathrm{pf}}^{\mathrm{ref}}) + s_{\mathrm{pf}}^{\mathrm{off}} Q_{\mathrm{ext}} \\ e_Q &\leftarrow \text{clamp}(Q_{\mathrm{ref}}; Q^{\min}, Q^{\max}) - Q_{\mathrm{gen}} \\ Q_V &\leftarrow \dfrac{Q_{\mathrm{ref}}}{V_{\mathrm{meas}}^{\mathrm{safe}}} \\ P_{\mathrm{ord}} &\leftarrow (1+s_P\omega)P_{\mathrm{ref}} \end{aligned}\end{split}\]

The PI states must satisfy:

\[\begin{split}\begin{aligned} 0 &= -V_{\mathrm{PIQ}} + \text{clamp}(K_{\mathrm{qp}} e_Q + x_{\mathrm{PIQ}}; V^{\min}, V^{\max}) \\ 0 &= -e_{\mathrm{PIV}} + s_V V_{\mathrm{PIQ}} + s_V^{\mathrm{off}}(Q_{\mathrm{ref}} + V_{\mathrm{ref1}}) - V_{\mathrm{meas}} \end{aligned}\end{split}\]

An unsaturated start requires \(e_Q=0\) and \(e_{\mathrm{PIV}}=0\). When \(s_V=1\), set \(V_{\mathrm{PIQ}}\leftarrow V_{\mathrm{meas}}\); when \(s_V=0\), the supplied \(Q_{\mathrm{ref}}+V_{\mathrm{ref1}}\) must equal \(V_{\mathrm{meas}}\). Then \(x_{\mathrm{PIQ}}\leftarrow V_{\mathrm{PIQ}}-K_{\mathrm{qp}}e_Q\). Saturated starts require a solve against the anti-windup residuals.

Finish by evaluating \(g_q(V_{\mathrm{meas}})\), \(g_p(V_{\mathrm{meas}})\), and the current-limit and current-command algebraic residuals in priority order. At the command steps, use the power-flow current targets before final limiting:

\[\begin{split}\begin{aligned} I_{\mathrm{qbase}}^{\star} &\leftarrow \dfrac{Q_{\mathrm{gen}}}{V_{\mathrm{meas}}^{\mathrm{safe}}} \\ I_{\mathrm{p}}^{\star} &\leftarrow \dfrac{P_{\mathrm{ord}}}{V_{\mathrm{meas}}^{\mathrm{safe}}} \end{aligned}\end{split}\]

Evaluate current limits and commands in this order:

• \(s_\mathrm{PQ}=0\): \(I_{\mathrm{q}}^{\mathrm{circ}}\), \(I_{\mathrm{q}}^{\max}\), \(I_{\mathrm{qbase}}\), \(I_{\mathrm{q}}^{\mathrm{raw}}\), \(I_{\mathrm{q}}^{\mathrm{cmd}}\), \(I_{\mathrm{p}}^{\mathrm{circ}}\), \(I_{\mathrm{p}}^{\max}\), \(I_{\mathrm{p}}^{\mathrm{cmd}}\).

• \(s_\mathrm{PQ}=1\): \(I_{\mathrm{p}}^{\mathrm{circ}}\), \(I_{\mathrm{p}}^{\max}\), \(I_{\mathrm{p}}^{\mathrm{cmd}}\), \(I_{\mathrm{q}}^{\mathrm{circ}}\), \(I_{\mathrm{q}}^{\max}\), \(I_{\mathrm{qbase}}\), \(I_{\mathrm{q}}^{\mathrm{raw}}\), \(I_{\mathrm{q}}^{\mathrm{cmd}}\).

After \(I_{\mathrm{q}}^{\max}\) and \(I_{\mathrm{qbase}}\) are known, initialize the voltage PI state:

\[x_{\mathrm{PIV}} \leftarrow I_{\mathrm{qbase}} - K_{\mathrm{vp}} e_{\mathrm{PIV}}\]

The current-circle variables use the nonnegative branch of the squared algebraic residuals; initialization must reject negative radicands. A standard steady-state initialization assumes \(s_{\mathrm{dip}}=0\). If initialized during voltage-dip or overvoltage logic, \(Q_V\), \(P_{\mathrm{ord}}\), and the PI histories are not uniquely determined without the unsupported hold-timer histories, so the implementation should solve a saturation-consistent state or reject the start.

Monitors

Monitor	Units	Description	Note
iqcmd	[p.u.]	Reactive-current command output	Converter base
ipcmd	[p.u.]	Active-current command output	Converter base
vmeas	[p.u.]	Filtered terminal voltage
pmeas	[p.u.]	Filtered electrical power
piq	[p.u.]	Reactive-power PI controller state
piv	[p.u.]	Voltage PI controller state
qv	[p.u.]	Reactive-current command lag state
pord	[p.u.]	Filtered active-power order
qref	[p.u.]	Selected reactive-power reference
sdip	[binary]	Voltage-dip/overvoltage freeze indicator
iqmax	[p.u.]	Final reactive-current upper limit	Converter base
ipmax	[p.u.]	Final active-current upper limit	Converter base
iqv	[p.u.]	Reactive-current injection candidate	Converter base
vqctrl	[p.u.]	Reactive-power control PI output
iqbase	[p.u.]	Base reactive-current command	Converter base