TGOV1

Steam turbine-governor model.

Block Diagram

Figure 1: Governor TGOV1 model. Figure courtesy of PowerWorld

Model Parameters

Symbol	Units	JSON	Description	Typical Value	Note
\(T_{\mathrm{rate}}\)	[MVA]	Trate	Governor component power base	100.0
\(R\)	[p.u.]	R	Permanent droop	0.05
\(T_1\)	[s]	T1	Steam-bowl time constant	0.5
\(T_2\)	[s]	T2	Turbine numerator time constant	2.5
\(T_3\)	[s]	T3	Reheater time constant	7.5
\(P_\mathrm{v}^{\max}\)	[p.u.]	Pvmax	Maximum valve position	1
\(P_\mathrm{v}^{\min}\)	[p.u.]	Pvmin	Minimum valve position	0
\(D_\mathrm{t}\)	[p.u.]	Dt	Turbine damping coefficient	0

Parameter Validation

A valid TGOV1 parameter set must satisfy the following conditions:

\[T_\mathrm{rate},S_\mathrm{sys}>0,\qquad R\ne0,\qquad P_\mathrm{v}^{\min}\le P_\mathrm{v}^{\max}\]

Set \(T_{\mathrm{rate}}\) equal to the connected machine MVA base. A zero component power base is not supported.

Model Derived Parameters

Let \(\epsilon_T=10^{-3}\ \mathrm{s}\). A time constant below \(\epsilon_T\) is raised to that floor in place, so every equation below uses the raised value:

\[\begin{aligned} T_x &\leftarrow \max\!(T_x,\epsilon_T), \quad x\in\{1,3\} \end{aligned}\]

Model Ports

Name	Port	Init	Description
speed	Input	Known	Machine speed deviation; optional, defaults to zero
pref	Input	Unknown	Governor reference; optional
pmech	Output	Known	Mechanical-power signal seeded by the machine

Model Variables

Internal Variables

Differential

Symbol	Units	Description	Note
\(P_\mathrm{v}\)	[p.u.]	Valve position	Component base
\(P_\mathrm{t}\)	[p.u.]	Turbine-block output	Component base

Algebraic

Symbol	Units	Description	Note
\(P_\mathrm{m}\)	[p.u.]	Mechanical-power output	System base; read by the machine model

External Variables

Differential

Symbol	Units	Description	Note
\(\omega\)	[p.u.]	Machine speed deviation	Optional speed input; defaults to zero

Algebraic

Symbol	Units	Description	Note
\(P_\mathrm{ref}\)	[p.u.]	Governor reference	Component base; optional pref input, otherwise held internally

Model Equations

Smooth functions: antiwindup.

For readability, define:

\[g_v=-P_\mathrm{v}+\dfrac{P_\mathrm{ref}-\omega}{R}\]

Internal Equations

Differential

\[\begin{split}\begin{aligned} 0 &= -\dot P_\mathrm{v} + \dfrac{1}{T_1}\text{antiwindup} (P_\mathrm{v},g_v;P_\mathrm{v}^{\min},P_\mathrm{v}^{\max}) \\ 0 &= -\dot P_\mathrm{t}-\dfrac{P_\mathrm{t}-P_\mathrm{v}-T_2\dot P_\mathrm{v}}{T_3} \end{aligned}\end{split}\]

Algebraic

\[0=-\dfrac{S_\mathrm{sys}}{T_\mathrm{rate}}P_\mathrm{m} +P_\mathrm{t}-D_\mathrm{t}\omega\]

External Equations

None.

Initialization

The machine provides \(P_\mathrm{m}\) on system base:

\[\begin{split}\begin{aligned} P_\mathrm{v} &\leftarrow \dfrac{S_\mathrm{sys}}{T_\mathrm{rate}}P_\mathrm{m}+D_\mathrm{t}\omega \\ P_\mathrm{t} &\leftarrow P_\mathrm{v} \\ P_\mathrm{ref} &\leftarrow \omega+RP_\mathrm{v} \\ \dot P_\mathrm{v},\dot P_\mathrm{t} &\leftarrow 0 \end{aligned}\end{split}\]

Initialization rejects \(P_\mathrm{v}\) outside the configured valve limits.

Monitors

None.