ECE 576 POWER SYSTEM DYNAMICS AND STABILITY Lecture 10 Synchronous Machine Controls – Turbine/Governor Professor Pete Sauer Department of Electrical and Computer Engineering © 2000 University of Illinois Board of Trustees, All Rights Reserved

Speed and voltage control

Possible prime movers gas engine diesel engine jet engine water wheel steam turbine

model shaft “squishiness” as a spring Turbine models model shaft “squishiness” as a spring High-pressure turbine shaft dynamics

Steam chest time delay High-pressure turbine shaft dynamics

For rigid shaft (no twist)

Speed governor model

Steam valve control Steam valve limits R = .05 (5% droop)

Example – no load to full load by governor action only (not be commanded power). (5% drop in speed)

A complete dynamic model Stator transients

d-axis rotor transients

q-axis rotor transients

Rotor shaft dynamics

Magnetic circuit algebraic equations (linear)

Excitation system (Exciter + Automatic Voltage Regulator)

Turbine/Governor

3 stator 1 field 3 dampers 2 shaft 1 exciter 2 VR 1 turbine 1 governor 14 14th order model

Terminal constraints How are Vd, Vq, Vo and Id, Iq, Io related? Open circuit: Id = Iq = Io = 0 Short circuit: Vd = Vq = Vo = 0

Balanced 3 resistive load: Substitute for Vd, Vq, Vo and eliminate Id, Iq, Io using the 3 magnetic circuit algebraic equations

Infinite bus

Substitute for Vd, Vq, Vo and eliminate Id, Iq, Io using the 3 magnetic circuit algebraic equations

Line impedance plus infinite bus Note: These flux linkages are not independent states. They are in “series” with the synchronous machine flux linkages. They do not increase the order of the model.

An infinite bus By definition, an infinite bus has:

How can we create one from our synchronous machine model? Infinitely slow field Infinitely slow 1q damper No 1d damper No 2q damper Infinite inertia No stator resistance Negligible transient reactances