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

Manifolds

Integral manifolds Suppose we could find

Linear systems – one-way coupling Example

One solution h =0, c =1

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

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

Linear systems – full coupling

Look for z = hx+c or

Substitute z = -1.3x into

Substitute z = -7.7x Not good

Formal two-time-scale analysis small

For

General two-time-scale linear system nonsingular

(equilibrium manifold)

Example