1. ECE 576 POWER SYSTEM DYNAMICS AND STABILITY
Lecture 2
System Structures and Electromagnetic Transients
Professor Pete Sauer
Department of Electrical and Computer Engineering
© 2000 University of Illinois Board of Trustees, All Rights Reserved

2. System dynamic structure

3. Dynamic phenomena time scales

4. Two-time-scale system
Slow time scale t (sec)
Fast time scale

5.  = 0 in t scale
 = 0 in  scale

6. System organizational structure

7. Voltage-levels, control, stability Frequency-control, stability
Phenomena of interest
Voltage-levels, control, stability
Frequency-control, stability
Current-thermal limits
Relay action
Overall S.S. stability
Overall transient stability

8. Electromagnetic transients
Transmission line
Long, medium, short
Partial D.E.
Ordinary D.E.
Phasors

9. Electromagnetic fields

10. Transmission line segment

13. Special case #1
(neglect shunts)

14. Special case #2
The lossless line
wave equation

15. General solution

16. Terminal conditions
Receiving end m is x = 0
Use this to eliminate f1

17. Look at sending end at negative time
Use this to eliminate f2

18. Eliminating f1 and f2 gives:

19. Repeat this for the other end to get:

20. Sinusoidal steady state equivalent circuit

21. Numerical integration
EMTP solutions
Numerical integration
Find: y(t)

22. Euler’s forward (Explicit method)
Trapezoidal rule (Implicit method)

23. Example

24. Trapezoidal rule solution

25. For R = 200, L=0.3H, and the following voltage applied at time zero,
with
the exact time-domain solution for the current is:

26. Trapezoidal rule solution
Exact solution:

27. t = .0002 i(.0002) = 117.3A Exact solution i(.0002) = 117.3A
Solving for i(.0002)
i(.0002) = 117.3A
Exact solution
i(.0002) = 117.3A