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.

Warning

The damping, fuel-flow, PID, limiter, temperature, and transport-delay paths remain incomplete or unverified. The initialization below does not yet establish a consistent steady state for the smooth selector paths.

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.

• 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

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	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
\(T_\mathrm{pelec}\)	[s]	Tpelec	Electrical-power measurement time constant	0.0	State 1 in Fig. 1
\(e^{\max}\)	[p.u.]	Maxerr	Upper limit on the signed governor error	1.0	Source label: maxerr
\(e^{\min}\)	[p.u.]	Minerr	Lower limit on the signed governor error	-1.0	Source label: minerr
\(K_\mathrm{pgov}\)	[p.u.]	Kpgov	Governor proportional gain	10.0
\(K_\mathrm{igov}\)	[p.u./s]	Kigov	Governor integral gain	1.0	State 3
\(K_\mathrm{dgov}\)	[p.u.]	Kdgov	Governor differential gain	0.0	State 2
\(T_\mathrm{dgov}\)	[s]	Tdgov	Governor differential time constant	0.0
\(V^{\max}\)	[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
\(T_\mathrm{act}\)	[s]	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
\(R_\mathrm{close}\)	[p.u./s]	Rclose	Maximum actuator closing rate	-1.0
\(K_\mathrm{turb}\)	[p.u.]	Kturb	Turbine gain	1.0
\(W_\mathrm{fnl}\)	[p.u.]	Wfnl	No-load fuel flow	0.0
\(T_B\)	[s]	Tb	Turbine lead–lag denominator time constant	0.0	State 5 in Fig. 1
\(T_C\)	[s]	Tc	Turbine lead–lag numerator time constant	0.0
\(T_\mathrm{eng}\)	[s]	Teng	Engine transport lag	0.0	Source label: e^{-sTeng}; source transport delay is not represented as a differential state below
\(T_\mathrm{fload}\)	[s]	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	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
\(D_\mathrm{m}\)	[p.u.]	Dm	Diesel damping gain	0.0	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	Source label: KA
\(T_A\)	[s]	Ta	Acceleration-control time constant	0.0	State 9 in Fig. 1
\(T_\mathrm{sa}\)	[s]	Tsa	Temperature-detection numerator time constant	0.0	State 10 in Fig. 1
\(T_\mathrm{sb}\)	[s]	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

A valid GGOV1 parameter set must satisfy the following conditions:

\[\begin{split}\begin{aligned} P^{\mathrm{rate}} &\ge 0,\quad R \gt 0,\quad K_\mathrm{turb} \gt 0 \\ I_R &\in \{-2,-1,1\},\quad s_\mathrm{flag} \in \{0,1\} \end{aligned}\end{split}\]

\[\begin{split}\begin{aligned} T_\mathrm{pelec}, T_\mathrm{dgov}, T_\mathrm{eng}, T_\mathrm{fload} &\ge 0 \\ T_A, T_\mathrm{sa}, T_\mathrm{sb}, T_C &\ge 0 \\ T_\mathrm{act} &\gt 0 \\ T_B &\gt 0\quad\text{or}\quad T_B = T_C = 0 \end{aligned}\end{split}\]

\[\begin{split}\begin{aligned} e^{\min} &\le e^{\max} \\ V^{\min} &\le V^{\max} \\ R_\mathrm{close} &\lt 0 \lt R_\mathrm{open} \end{aligned}\end{split}\]

Model Derived Parameters

The component base and flag complements are:

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

\(S^{\mathrm{sys}}\) is the system power base.

Model Ports

Name	Port	Init	Description
pref	Input	TBD	Governor reference
paux	Input	TBD	Auxiliary power input
pmwset	Input	TBD	Supervisory MW setpoint
pelec	Input	TBD	Electrical active power
ldref	Input	TBD	Load reference
speed	Input	TBD	Machine speed deviation
pmech	Output	TBD	Mechanical-power output

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
\(P_\mathrm{m}\)	[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

Smooth functions: antiwindup, clamp, min.

Internal Equations

Differential

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

Algebraic

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

When \(T_B=T_C=0\), the turbine lead–lag block is bypassed before the turbine gain and no-load fuel-flow calculation.

External Equations

None.

Initialization

For a power-flow start, require \(\omega=0\) and initialize all internal derivatives to zero:

\[\begin{split}\begin{aligned} P_{\mathrm{aux}} &\leftarrow 0,\quad \text{if omitted} \\ P_{\mathrm{elec}}^{\mathrm{meas}} &\leftarrow P_{\mathrm{elec}} \\ x_{\mathrm{acc}} &\leftarrow 0 \\ P_{\mathrm{damp}} &\leftarrow 0 \end{aligned}\end{split}\]

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

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

Initialize the limiter and control states:

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

These assignments assume inactive low-value select alternatives, inactive actuator rate limits, \(V^{\min}\le f_{\mathrm{sr}}\le V^{\max}\), and \(K_\mathrm{turb}\ne 0\).

Monitors

Monitor	Units	Description	Note
pmech	[p.u.]	Mechanical-power output	\(P_\mathrm{m}\)
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