1. ECE 576 POWER SYSTEM DYNAMICS AND STABILITY
Lecture 19
Multi-machine Dynamic Models
Professor Pete Sauer
Department of Electrical and Computer Engineering
© 2000 University of Illinois Board of Trustees, All Rights Reserved

2. Multi-machine dynamic models
m – synchronous machines
n – system nodes (buses)
(excluding reference)
b - branches

3. The center of inertia speed The synchronous rotating reference frame
Common Reference Frame
One of the machines
The center of inertia speed
The synchronous rotating reference frame

4. The synchronous rotating reference frame

6. To see the reason for this choice, consider:

8. Suppose we have VDi, VQi as time varying quantities with , then:

9. Define

10. Then:

11. If the steady-state values are:
then,

12. (keep Idi, Iqi in rest of model)

13. Transformation between reference frames

14. Balanced 3-phase line

16. Network transients

18. m=1 (one machine)
n=3 (three buses)
b=4 (four branches)

20. Branch-loop incidence matrix

22. Systematically create independent loops:
b-n independent loops
Systematically create independent loops:
Form a tree
Add b-n links to form b-n loops
This creates the “basic loop” matrix cb
(b x b-n)

23. A tree: all nodes, but no loops

24. Add one tree link (branch c) and orient the loop with the direction of link.

25. Add second tree link (branch d) and orient the loop with the direction of the link (new loop may not go through an old link).