GGOV1

Source: GridKit/Model/PhasorDynamics/Governor/GGOV1/README.md

GE General Governor-Turbine Model (GGOV1)

GGOV1 is a general governor-turbine model with electrical-power measurement, speed/load reference selection, proportional/integral/derivative governor control, load limiting, acceleration limiting, temperature limiting, actuator rate limits, turbine lag/lead dynamics, and optional diesel damping.

Notes:

• Internal control, valve-stroke, and turbine-power quantities are on the GGOV1 component base unless otherwise stated.

• The dashed speed deadband block and Db source field are only for GGOV1D. GGOV1 uses the speed input directly.

• Source governor-response settings may modify \(V^{\max}\) and \(V^{\min}\) before the equations are evaluated.

• The source diagram notes that Rup and Rdown inputs are not implemented in Simulator; the equations below do not use those source fields.

Block Diagram

Standard model of the GGOV1 Governor.

Figure 1: Governor GGOV1 model. Figure courtesy of PowerWorld

Model Parameters

Symbol	Units	JSON	Description	Typical Value	Note
\(P^{\mathrm{rate}}\)	[MW]	Trate	Optional turbine-rating power base	0.0	Trate > 0 defines the governor base
\(I_R\)	[integer]	Rselect	Droop feedback selector	1	Source label: Rselect; selects speed, electrical power, or valve feedback
\(s_\mathrm{flag}\)	[binary]	Flag	Turbine-speed multiplier selector	1	1 uses \(1+\omega\), 0 uses 1.0
\(R\)	[p.u.]	R	Permanent droop	0.05	Source label: r
\(T_\mathrm{pelec}\)	[sec]	Tpelec	Electrical-power measurement time constant	0.0	State 1 in Fig. 1
\(e^{\max}\)	[p.u.]	Maxerr	Maximum governor error	1.0	Source label: maxerr
\(e^{\min}\)	[p.u.]	Minerr	Minimum governor error	-1.0	Source label: minerr
\(K_\mathrm{pgov}\)	[p.u.]	Kpgov	Governor proportional gain	10.0	Block name: Kpgov
\(K_\mathrm{igov}\)	[p.u./s]	Kigov	Governor integral gain	1.0	Block name: Kigov; State 3
\(K_\mathrm{dgov}\)	[p.u.]	Kdgov	Governor differential gain	0.0	Block name: Kdgov; State 2
\(T_\mathrm{dgov}\)	[sec]	Tdgov	Governor differential time constant	0.0	Block name: Tdgov
\(V^{\max}\)	[p.u.]	Vmax	Maximum governor output before actuator	1.0	Governor response limits may adjust this value
\(V^{\min}\)	[p.u.]	Vmin	Minimum governor output before actuator	0.0	Governor response limits may adjust this value
\(T_\mathrm{act}\)	[sec]	Tact	Turbine actuator time constant	0.1	State 4 in Fig. 1
\(R_\mathrm{open}\)	[p.u./s]	Ropen	Maximum actuator opening rate	1.0	Source label: Ropen
\(R_\mathrm{close}\)	[p.u./s]	Rclose	Maximum actuator closing rate	-1.0	Source label: Rclose
\(K_\mathrm{turb}\)	[p.u.]	Kturb	Turbine gain	1.0	Block name: Kturb
\(W_\mathrm{fnl}\)	[p.u.]	Wfnl	No-load fuel flow	0.0	Source label: Wfnl
\(T_B\)	[sec]	Tb	Turbine lead-lag denominator time constant	0.0	State 5 in Fig. 1
\(T_C\)	[sec]	Tc	Turbine lead-lag numerator time constant	0.0	Block name: Tc
\(T_\mathrm{eng}\)	[sec]	Teng	Engine transport lag	0.0	Source label: e^{-sTeng}; source transport delay is not represented as a differential state below
\(T_\mathrm{fload}\)	[sec]	Tfload	Load-limiter lag time constant	0.0	State 6 in Fig. 1
\(K_\mathrm{pload}\)	[p.u.]	Kpload	Load-limiter proportional gain	0.0	Block name: Kpload; note path changes when zero
\(K_\mathrm{iload}\)	[p.u./s]	Kiload	Load-limiter integral gain	0.0	State 7 in Fig. 1
\(L_\mathrm{dref}\)	[p.u.]	Ldref	Load reference	1.0	Source label: Ldref
\(D_m\)	[p.u.]	Dm	Diesel damping gain	0.0	Source label: Dm; sign-dependent speed term in Fig. 1
\(K_\mathrm{imw}\)	[p.u./s]	Kimw	Supervisory load-control integral gain	0.0	State 8 in Fig. 1
\(A_\mathrm{set}\)	[p.u.]	Aset	Acceleration-control reference	0.0	Source label: aset
\(K_A\)	[p.u.]	Ka	Acceleration-control gain	0.0	Block name: KA
\(T_A\)	[sec]	Ta	Acceleration-control time constant	0.0	State 9 in Fig. 1
\(T_\mathrm{sa}\)	[sec]	Tsa	Temperature-detection numerator time constant	0.0	State 10 in Fig. 1
\(T_\mathrm{sb}\)	[sec]	Tsb	Temperature-detection denominator time constant	0.0	State 10 in Fig. 1
\(R_\mathrm{up}\)	[p.u./s]	Rup	Source upward ramp input	0.0	Source note says not implemented in Simulator
\(R_\mathrm{down}\)	[p.u./s]	Rdown	Source downward ramp input	0.0	Source note says not implemented in Simulator

Parameter Validation

Invalid GGOV1 parameter sets are rejected by the following checks. If source governor-response settings adjust limits, apply these checks to the effective values used by the equations.

\[\begin{split}\begin{aligned} &P^{\mathrm{rate}}\ge 0,\quad R\gt 0,\quad I_R\in\{-2,-1,1\},\quad s_\mathrm{flag}\in\{0,1\} \\ &T_\mathrm{pelec},T_\mathrm{dgov},T_B,T_C,T_\mathrm{eng},T_\mathrm{fload},T_A,T_\mathrm{sa},T_\mathrm{sb}\ge 0,\quad T_\mathrm{act}\gt 0 \\ &T_B \gt 0\quad\text{or}\quad(T_B = 0\ \text{and}\ T_C = 0) \\ &e^{\min}\le e^{\max},\quad V^{\min}\le V^{\max},\quad R_\mathrm{close}\lt 0\lt R_\mathrm{open} \\ &K_\mathrm{turb}\gt 0 \end{aligned}\end{split}\]

Model Derived Parameters

The component base and flag complements are:

\[\begin{split}\begin{aligned} S_\mathrm{gov}^{\mathrm{base}} &= \begin{cases} P^{\mathrm{rate}} & P^{\mathrm{rate}} \gt 0 \\ S^{\mathrm{machine}} & \text{otherwise} \end{cases} \\ s_\mathrm{flag}^{\mathrm{off}} &= 1 - s_\mathrm{flag} \end{aligned}\end{split}\]

Model Variables

Internal Variables

Differential

Symbol	Units	Description	Note
\(P_\mathrm{elec}^{\mathrm{meas}}\)	[p.u.]	Measured electrical power	State 1 in Fig. 1; source label: Pelec Measured
\(x_D\)	[p.u.]	Governor differential control state	State 2 in Fig. 1
\(x_I\)	[p.u.]	Governor integral control state	State 3 in Fig. 1
\(x_\mathrm{act}\)	[p.u.]	Turbine actuator or valve stroke	State 4 in Fig. 1
\(x_\mathrm{turb}\)	[p.u.]	Turbine lead-lag state	State 5 in Fig. 1; source label: Turbine LL
\(x_\mathrm{load}\)	[p.u.]	Turbine load-limiter lag state	State 6 in Fig. 1
\(x_\mathrm{ldint}\)	[p.u.]	Turbine load integral-control state	State 7 in Fig. 1
\(x_\mathrm{mw}\)	[p.u.]	Supervisory load-control state	State 8 in Fig. 1
\(x_\mathrm{acc}\)	[p.u.]	Acceleration-control state	State 9 in Fig. 1
\(x_\mathrm{temp}\)	[p.u.]	Temperature-detection lead-lag state	State 10 in Fig. 1

Algebraic

Symbol	Units	Description	Note
\(P_\mathrm{mwref}\)	[p.u.]	Supervisory load-control reference	From \(P_\mathrm{mwset}-P_\mathrm{elec}\)
\(y_R\)	[p.u.]	Selected droop feedback	Controlled by Rselect
\(e_G\)	[p.u.]	Limited governor error	After \(e^{\min}\) and \(e^{\max}\)
\(f_\mathrm{pid}\)	[p.u.]	Governor PID output	Forms fsrn
\(f_\mathrm{srn}\)	[p.u.]	Normal governor fuel/stroke request	Low-value select input
\(f_\mathrm{sra}\)	[p.u.]	Acceleration-control request	Low-value select input
\(f_\mathrm{srt}\)	[p.u.]	Temperature/load request	Low-value select input
\(f_\mathrm{srl}\)	[p.u.]	Acceleration/temperature low-value select	Lesser of \(f_\mathrm{sra}\) and \(f_\mathrm{srt}\)
\(f_\mathrm{sr}\)	[p.u.]	Low-value select output	Limited by \(V^{\min}\) and \(V^{\max}\)
\(r_\mathrm{act}\)	[p.u./s]	Actuator rate-limited derivative	Limited by \(R_\mathrm{close}\) and \(R_\mathrm{open}\)
\(P_\mathrm{turb}\)	[p.u.]	Turbine power before damping	After turbine lead-lag and transport lag
\(P_\mathrm{damp}\)	[p.u.]	Damping power term	Source label: Dm
\(P_m\)	[p.u.]	Mechanical-power output	Source label: Pmech

External Variables

Differential

None.

Algebraic

Symbol	Units	Description	Note
\(P_\mathrm{ref}\)	[p.u.]	Governor reference	Source label: Pref
\(P_\mathrm{aux}\)	[p.u.]	Auxiliary power input	Source label: Paux; optional, defaults to zero
\(P_\mathrm{mwset}\)	[p.u.]	Supervisory MW setpoint	Source label: Pmwset
\(P_\mathrm{elec}\)	[p.u.]	Electrical active power	Source label: Pelec
\(L_\mathrm{dref}\)	[p.u.]	Load reference input	Source label: Ldref
\(\omega\)	[p.u.]	Machine speed deviation	Source label: Speed

Model Equations

Differential Equations

\[\begin{split}\begin{aligned} 0 &= -T_\mathrm{pelec}\dot P_\mathrm{elec}^{\mathrm{meas}} - P_\mathrm{elec}^{\mathrm{meas}} + P_\mathrm{elec} \\ 0 &= -T_\mathrm{dgov}\dot x_D - x_D + e_G \\ 0 &= -\dot x_I + \text{antiwindup}\left( f_\mathrm{pid}, K_\mathrm{igov}e_G, V^{\min}, V^{\max} \right) \\ 0 &= -T_\mathrm{act}\dot x_\mathrm{act} + r_\mathrm{act} \\ 0 &= -T_B\dot x_\mathrm{turb} - x_\mathrm{turb} + x_\mathrm{act} \\ 0 &= -T_\mathrm{fload}\dot x_\mathrm{load} - x_\mathrm{load} + f_\mathrm{srt} \\ 0 &= -\dot x_\mathrm{ldint} + K_\mathrm{iload}\left(L_\mathrm{dref}-x_\mathrm{load}\right) \\ 0 &= -\dot x_\mathrm{mw} + K_\mathrm{imw}\left(P_\mathrm{mwset}-P_\mathrm{elec}\right) \\ 0 &= -T_A\dot x_\mathrm{acc} - x_\mathrm{acc} + \omega \\ 0 &= -T_\mathrm{sb}\dot x_\mathrm{temp} - x_\mathrm{temp} + f_\mathrm{sr} \end{aligned}\end{split}\]

CommonMath defines the Anti-Windup target and smooth approximation.

Algebraic Equations

\[\begin{split}\begin{aligned} 0 &= -P_\mathrm{mwref} + x_\mathrm{mw} + P_\mathrm{ref} + P_\mathrm{aux} \\ 0 &= -R y_R + \begin{cases} \omega & I_R = 1 \\ P_\mathrm{elec}^{\mathrm{meas}} & I_R = -1 \\ x_\mathrm{act} & I_R = -2 \end{cases} \\ 0 &= -e_G + \text{clamp}(P_\mathrm{mwref} - y_R,\ e^{\min},\ e^{\max}) \\ 0 &= -f_\mathrm{pid} + K_\mathrm{pgov}e_G + K_\mathrm{dgov}(e_G - x_D) + x_I \\ 0 &= -f_\mathrm{srn} + \text{clamp}(f_\mathrm{pid}, V^{\min}, V^{\max}) \\ 0 &= -f_\mathrm{sra} + \text{clamp}\left(A_\mathrm{set} - K_A x_\mathrm{acc}, V^{\min}, V^{\max}\right) \\ 0 &= -f_\mathrm{srt} + \text{clamp}\left(\dfrac{L_\mathrm{dref} + P_\mathrm{aux}}{K_\mathrm{turb}} + W_\mathrm{fnl} + x_\mathrm{ldint}, V^{\min}, V^{\max}\right) \\ 0 &= -f_\mathrm{srl} + \min\left(f_\mathrm{sra}, f_\mathrm{srt}\right) \\ 0 &= -f_\mathrm{sr} + \min\left(f_\mathrm{srn}, f_\mathrm{srl}\right) \\ 0 &= -r_\mathrm{act} + \text{clamp}\left(\dfrac{f_\mathrm{sr}-x_\mathrm{act}}{T_\mathrm{act}}, R_\mathrm{close}, R_\mathrm{open}\right) \\ 0 &= -P_\mathrm{turb} + K_\mathrm{turb} \begin{cases} x_\mathrm{act} - W_\mathrm{fnl} & T_B = T_C = 0 \\ x_\mathrm{turb} + \dfrac{T_C}{T_B}(x_\mathrm{act}-x_\mathrm{turb}) - W_\mathrm{fnl} & T_B \gt 0 \end{cases} \\ 0 &= -P_\mathrm{damp} + D_m \begin{cases} \omega & D_m \ge 0 \\ (1+\omega)^{D_m} & D_m \lt 0 \end{cases} \\ 0 &= -P_m + P_\mathrm{turb} + P_\mathrm{damp} \end{aligned}\end{split}\]

CommonMath defines helper targets and smooth approximations for clamp and min. When \(T_B=T_C=0\), the turbine lead-lag block is bypassed before the turbine gain and no-load fuel-flow calculation. If Kpgov = 0, the source diagram routes the integral path in parallel with the derivative control; document that effective structure before changing the equations. If Kpload = 0, the source diagram feeds Kiload/s from the Kpload input and avoids the fsrn feedback path.

Initialization

Initialization is performed by evaluating the steady-state residuals in dependency order. Let subscript \(0\) denote initial values and set all internal derivatives to zero:

\[\begin{split}\begin{aligned} \omega_0 &= 0 \\ P_{\mathrm{aux},0} &= 0 \\ P_{\mathrm{elec},0}^{\mathrm{meas}} &= P_{\mathrm{elec},0} \\ x_{\mathrm{acc},0} &= 0 \\ P_{\mathrm{damp},0} &= 0 \end{aligned}\end{split}\]

Given initialized machine mechanical power, solve the actuator and turbine path:

\[\begin{split}\begin{aligned} P_{\mathrm{turb},0} &= P_{m,0} - P_{\mathrm{damp},0} \\ x_{\mathrm{act},0} &= W_\mathrm{fnl} + \dfrac{P_{\mathrm{turb},0}}{K_\mathrm{turb}} \\ x_{\mathrm{turb},0} &= x_{\mathrm{act},0} \\ f_{\mathrm{sr},0} &= x_{\mathrm{act},0} \\ f_{\mathrm{srn},0} &= f_{\mathrm{sra},0} = f_{\mathrm{srt},0} = f_{\mathrm{srl},0} = f_{\mathrm{sr},0} \end{aligned}\end{split}\]

Then seed the limiter and control states consistently:

\[\begin{split}\begin{aligned} x_{\mathrm{load},0} &= f_{\mathrm{srt},0} \\ x_{\mathrm{ldint},0} &= f_{\mathrm{srt},0} - \dfrac{L_{\mathrm{dref},0}+P_{\mathrm{aux},0}}{K_\mathrm{turb}} - W_\mathrm{fnl} \\ x_{\mathrm{mw},0} &= 0 \\ 0 &= \begin{cases} -R y_{R,0} + \omega_0 & I_R = 1 \\ -R y_{R,0} + P_{\mathrm{elec},0}^{\mathrm{meas}} & I_R = -1 \\ -R y_{R,0} + x_{\mathrm{act},0} & I_R = -2 \end{cases} \\ P_{\mathrm{mwref},0} &= f_{\mathrm{pid},0} + y_{R,0} \\ P_{\mathrm{ref},0} &= P_{\mathrm{mwref},0} - P_{\mathrm{aux},0} - x_{\mathrm{mw},0} \end{aligned}\end{split}\]

This closed-form start requires inactive low-value select alternatives, inactive actuator rate limits, \(V^{\min}\le f_{\mathrm{sr},0}\le V^{\max}\), and \(K_\mathrm{turb}\ne 0\). Starts where governor response settings fix \(V^{\min}\) or \(V^{\max}\) to the initial condition must document those effective limits before applying the residuals.

Model Outputs

Output	Units	Description	Note
pmech	[p.u.]	Mechanical-power output	\(P_m\)
pelec_meas	[p.u.]	Measured electrical power	State 1
xd	[p.u.]	Governor differential-control state	State 2
xi	[p.u.]	Governor integral-control state	State 3
valve	[p.u.]	Turbine actuator or valve stroke	State 4
turbine_ll	[p.u.]	Turbine lead-lag state	State 5
load_limiter	[p.u.]	Turbine load-limiter state	State 6
load_int	[p.u.]	Turbine load integral-control state	State 7
mw_control	[p.u.]	Supervisory load-control state	State 8
accel_control	[p.u.]	Acceleration-control state	State 9
temp_ll	[p.u.]	Temperature-detection lead-lag state	State 10
fsrn	[p.u.]	Normal governor request	Low-value select input
fsra	[p.u.]	Acceleration-control request	Low-value select input
fsrt	[p.u.]	Temperature/load request	Low-value select input
fsr	[p.u.]	Selected governor request	Low-value select output