Governors

The turbine-governor strategy is plugged onto a machine with the governor keyword, for example governor = "TGOV1". It reads the rotor speed and produces the mechanical power \(p_m\) for the shaft.

governor =	Class	Description
"Droop"	Droop	Pure speed-droop governor: primary frequency response with no turbine lag dynamics, the \(T_{ch}, T_{sv} \to 0\) limit of TGOV1.
"GOVCONST"	GOVCONST	Constant mechanical power: no turbine or governor dynamics, the zero-response limit of Droop (\(R_d \to \infty\)).
"TGOV1"	TGOV1	TGOV1 steam turbine-governor: droop-controlled valve and steam-chest lag (P.
"TGTypeII"	TGTypeII	Type II speed governor: a droop on the frequency deviation through one lead-lag, added to the constant reference power (F.

TGOV1: droop, servo and reheater lags (GOVCONST holds \(p_m\) constant; Droop keeps only the droop).

class hermess.devices.governor.GOVCONST

Constant mechanical power: no turbine or governor dynamics, the zero-response limit of Droop (\(R_d \to \infty\)).

Selected on a machine line with governor = "GOVCONST".

Model.

\[0 = -p_m + P_{ref}\]

Used by benchmarks that deliberately exclude prime-mover dynamics, such as the 14-generator South East Australian system (Gibbard and Vowles 2014), whose small- and large-signal models have no turbine or governor representation.

Symbols.

Code	Symbol	Meaning	Default
pm	\(p_m\)	mechanical power (private algebraic) [p.u.]
Pref	\(P_{ref}\)	mechanical-power setpoint (set by the initialization)

class hermess.devices.governor.Droop

Pure speed-droop governor: primary frequency response with no turbine lag dynamics, the \(T_{ch}, T_{sv} \to 0\) limit of TGOV1.

Selected on a machine line with governor = "Droop".

Model. The mechanical power follows the speed deviation instantaneously and is therefore a device-private algebraic variable (no states):

\[0 = -p_m + P_{ref} - \frac{\omega - \omega_{net}}{R_d}\]

with \(\omega\) the absolute per-unit rotor speed and \(\omega_{net} = 1\) p.u., so that \(p_m = P_{ref}\) at steady state. pm rides the device-private-algebraic mechanism and the swing equation reads it through Synchronous.var_sym('pm').

Symbols.

Code	Symbol	Meaning	Default
Rd	\(R_d\)	speed droop constant	0.05
pm	\(p_m\)	mechanical power (private algebraic) [p.u.]
Pref	\(P_{ref}\)	mechanical-power setpoint (set by the initialization)

class hermess.devices.governor.TGOV1

TGOV1 steam turbine-governor: droop-controlled valve and steam-chest lag (P. W. Sauer and M. A. Pai, Power System Dynamics and Stability, p. 100). The framework default.

Selected on a machine line with governor = "TGOV1".

Model.

\[\begin{split}T_{sv} \, \dot{p}_{sv} &= -p_{sv} + P_{ref} - \frac{\omega - \omega_{net}}{R_d} \\ T_{ch} \, \dot{p}_m &= p_{sv} - p_m\end{split}\]

with \(\omega\) the absolute per-unit rotor speed and \(\omega_{net} = 1\) p.u., so that \(p_{sv} = p_m = P_{ref}\) at steady state. With incl_lim the valve equation is multiplied by the anti-windup switch that freezes the valve at \(p_{sv}^{max,min}\).

Symbols.

Code	Symbol	Meaning	Default
Rd	\(R_d\)	speed droop constant	0.05
Tch	\(T_{ch}\)	steam chest time constant [s]	0.05
Tsv	\(T_{sv}\)	steam valve time constant [s]	1.5
psv_max / psv_min	\(p_{sv}^{max,min}\)	valve limits (with incl_lim)	10 / -10
psv	\(p_{sv}\)	steam valve position (state) [p.u.]
pm	\(p_m\)	mechanical power (state) [p.u.]
Pref	\(P_{ref}\)	mechanical-power setpoint (set by the initialization)

Type II governor: the frequency deviation acts through the droop and one lead-lag, added to the constant reference power.

class hermess.devices.governor.TGTypeII

Type II speed governor: a droop on the frequency deviation through one lead-lag, added to the constant reference power (F. Milano, Power System Modelling and Scripting, 2010; the PSID TGTypeII).

Selected on a machine line with governor = "TGTypeII".

Model. The lead-lag is realized as one lag state plus feedthrough, so the mechanical power is a device-private algebraic:

\[\begin{split}u &= \frac{1}{R_d} \left( \omega_{net} - \omega \right) \\ T_2 \, \dot{x}_g &= u - x_g \\ 0 &= -p_m + \frac{T_1}{T_2} \left( u - x_g \right) + x_g + P_{ref}\end{split}\]

with \(\omega\) the absolute per-unit rotor speed. At steady state \(x_g = u = 0\) and \(p_m = P_{ref}\). Like the PSID reference (which publishes this output as the mechanical torque without a \(1/\omega\) factor), the output feeds the swing equation unmodified.

Symbols.

Code	Symbol	Meaning	Default
Rd	\(R_d\)	speed droop constant	0.05
T1	\(T_1\)	lead (transient droop) time constant [s]	1
T2	\(T_2\)	lag time constant [s]	2
xg	\(x_g\)	lead-lag lag state [p.u.]
pm	\(p_m\)	mechanical power (private algebraic) [p.u.]
Pref	\(P_{ref}\)	mechanical-power setpoint (set by the initialization)