TGOV1

Block Diagram

Standard model of the stream turbine

Figure 1: Governor TGOV1 model. Figure courtesy of PowerWorld

Model Parameters

Symbol	Units	Description	Typical Value
\(T_{\mathrm{rate}}\)	[MW]	Turbine rating	100.0
\(R\)	[p.u.]	Droop Constant	0.05
\(T_1\)	[sec]	Valve Time Delay	0.5
\(T_2\)	[sec]	Turbine Numerator Time Constant	2.5
\(T_3\)	[sec]	Turbine Delay	7.5
\(P_v^{\max}\)	[p.u.]	Max Valve Position	1
\(P_v^{\min}\)	[p.u.]	Min Valve Position	0
\(D_t\)	[p.u.]	Turbine Damping Coefficient	0

Model Variables

Internal Variables

Differential

Symbol	Units	Description	Note
\(P_{tx}\)	[p.u.]	Turbine Power (State 1 in Fig. 1)
\(P_v\)	[p.u.]	Valve Position (State 2 in Fig. 1)

Algebraic

Symbol	Units	Description	Note
\(P_m\)	[p.u.]	Mechnical Power to Generator	Read by a Machine Model

External Variables

Differential

Symbol	Units	Description	Note
\(\omega\)	[p.u.]	Machine Speed Deviation	Read from a Machine Model

Algebraic

Symbol	Units	Description	Note
\(P_{ref}\)	[p.u.]	Reference Power	Either a constant parameter or external variable

Model Equations

For readability, define:

\[f = -P_v + \dfrac{1}{R}(P_{ref} - \omega)\]

Differential Equations

The TGOV1 differential equations, as derived from the model diagram.

\[\begin{split}\begin{aligned} 0 &= -T_3 \dot P_{tx} - P_{tx} + (T_3 - T_2)P_v \\ 0 &= -T_1 \dot P_v + \text{antiwindup}( P_v, f, P_v^{\min}, P_v^{\max} ) \end{aligned}\end{split}\]

CommonMath defines the Anti-Windup target and smooth approximation.

Algebraic Equations

The algebraic equation dictating the mechnical power output.

\[\begin{split}\begin{aligned} 0 &= -\dfrac{S_{\mathrm{sys}}}{T_{\mathrm{rate}}} P_m + \dfrac{1}{T_3}(P_{tx}+T_2P_v) - D_t \omega \\ \end{aligned}\end{split}\]

Initialization

At steady state we assume that \(P_v\) is at or within its limits. This implies the initial conditions are a function of the initial mechanical power converted to the TGOV1 component base.

\[\begin{split}\begin{aligned} P^{\mathrm{tgov1}}_{m,0} &= \dfrac{S_{\mathrm{sys}}}{T_{\mathrm{rate}}}P_{m,0} \\ P_{tx,0} &= (T_3 - T_2)P^{\mathrm{tgov1}}_{m,0} \\ P_{v,0} &= P^{\mathrm{tgov1}}_{m,0} \\ \dot P_{tx,0} &= 0 \\ \dot P_{v,0} &= 0 \end{aligned}\end{split}\]

And if the reference power is a constant parameter, we can determine the value by solving the steady state equations.

\[\begin{aligned} P_{ref,0} &= R P^{\mathrm{tgov1}}_{m,0} \end{aligned}\]