1. ECE 576 POWER SYSTEM DYNAMICS AND STABILITY
Lecture 11
Integral Manifolds and Reduced-Order Models
Professor Pete Sauer
Department of Electrical and Computer Engineering
© 2000 University of Illinois Board of Trustees, All Rights Reserved

2. Manifolds

4. Integral manifolds
Suppose we could find

6. Linear systems – one-way coupling
Example

12. One solution h =0, c =1

13. If z =1 at time zero, then
z =1 for all time

14. Use z = 1
This is exact only if z(0) = 1

15. Linear systems – full coupling

17. Look for z = hx+c or

18. Substitute z = -1.3x into

19. Substitute z = -7.7x
Not good

20. Formal two-time-scale analysis
small

21. For

25. General two-time-scale linear system
nonsingular

26. (equilibrium manifold)

27. Example