1. ECE 576 POWER SYSTEM DYNAMICS AND STABILITY
Lecture 1
Introduction and Overview
Professor Pete Sauer
Department of Electrical and Computer Engineering
© 2018 University of Illinois Board of Trustees, All Rights Reserved

2. Spring 2018 Instructors Pete Sauer
University of Illinois at Urbana-Champaign
Department of Electrical and Computer Eng.
4046 ECEB, 306 N. Wright St., Urbana, IL 61801
(217)
Periodic substitution by:
Karl Reinhard
4054 ECEB, 306 N. Wright St., Urbana, IL

3. Power Systems
Aircraft
Automobiles
Standby power sources
Electric utilities
Mechanical prime movers
Electrical generators
Electrical network
Electrical loads

4. Dynamics and Stability
Engineering analysis
static – steady state
dynamic – transients
Stability – study of system response
to disturbance

5. Course Topics Structures EMTP Synchronous machine Controls
Single machine
Simulation
Multi-machine
Steady-state stability
Transient Stability

6. Example (linear: spring/mass)
Newton’s 2nd Law

7. Equilibrium
Set time derivatives to zero
Solve for dynamic states

8. Stability Suppose mass is displaced from xe. Will it return?
Look at the D.E.
(v goes negative)
so x decreases
(Tends to return to xe)

9. (v goes positive) so x increases (Tends to return to xe)
Intuitive conclusion: system is stable at xe

10. c) Response K = 20 N/m C = 0.1 m M = 0.1 kg G = 9.8 m/sec2
Suppose fext = 0 N
This gives ve = 0 xe = m
What happens if x = m (at rest) and
fext is changed to 0.5 N at t = 0?

11. Solve:

12. What if we had gotten
____________
This says x can become negative!
Hard surface?

13. Example (nonlinear: pendulum)
Newton’s 2nd Law

14. Equilibrium
Set time derivatives to zero
(multiple values)

15. Stability ( goes negative) ( decreases) (Tends to go back to e)
Suppose mass is displaced.
Will it return to e?
Look at D.E.
Consider e = 0
( goes negative)
( decreases)
(Tends to go back to e)

16. ( goes positive)
( increases)
(Tends to go back to e)
Intuitive conclusion:
e = 0 is a stable equilibrium point

17. Now try:
( goes positive)
 increases
(Tends to go away from e)

18. ( goes negative)
 decreases
(Tends to go away from e)
Intuitive conclusion:
is an unstable equil. pt.

19. c) Response
Suppose  is at e = 0
(e = 0) and Text is changed. What will
happen?
M = 0.1 kg l = 1 m G = 9.8 m/sec2
Add Text = 0.5 NM at t = 0

20. Solve:
________________________________

21. Numerical Integration
Basic Idea: Taylor Series
t small

22. Euler’s Forward method:
t small

23. Choose t = .01 sec

25. Tutorial demo
The following demonstration software was created for a tutorial on nonlinear dynamics given for Union Electric (Ameren) with funding
provided by EPRI in 1993