1. ECE 576 POWER SYSTEM DYNAMICS AND STABILITY
Lecture 13
Reduced-Order Synchronous Machine Models
Professor Pete Sauer
Department of Electrical and Computer Engineering
© 2000 University of Illinois Board of Trustees, All Rights Reserved

2. Two-axis model

8. Flux-decay model

12. Classical model
Or, go back to the two-axis model and assume:

13. Or, argue that an integral manifold exists for
such that

15. This is a pendulum model
Neglect resistance and assume TCH = ∞
This is a pendulum model

16. Summary of 5 Models ) Full model with stator transients
Sub-transient model
Two-axis model
One-axis model
Classical model (const. E behind )

17. All of these reduced-order models are valid for “long times” except the classical model.
The classical model is valid only for a brief period of time – i.e. 0.2seconds. This makes it acceptable for “first-swing” stability studies, but not much more.
The classical model will not give the correct steady-state solution for a “changed case”.

18. Damping torques
Friction and windage
Stator currents (load)
Field current (excitation)
Damper windings

19. Look for an integral manifold:

23. Substitute this into the torque equation
Substitute this into the torque equation. If the time constant is zero (zero-order integral manifold), you get the torque equation of the one-axis model. Since we are keeping the next term (first-order integral manifold), there is an additional torque term:

24. This can be approximated by a “constant D” damping torque term:
That is: using a zero-order integral manifold does not capture any of the effects of the damper winding. However, a first-order integral manifold does capture some of the damper winding effects.