1. ECE 476 POWER SYSTEM ANALYSIS
Lecture 24
Transient Stability
Professor Tom Overbye
Department of Electrical and Computer Engineering

2. Announcements Be reading Chapter 10 and 13
Including CH 10 article about zone 3 relays, CH 13 DSA and blackout articles
HW 11 is not turned in but should be done before final. HW 11 is 13.1, 13.7, 13.8, 13.18, and SP1
Final is Wednesday Dec 12 from 1:30 to 4:30pm in EL 269 (note room change). Final is comprehensive. One new note sheet, and your two old note sheets are allowed

3. In the News: Dallman Accident
Cause of CWLP (Springfield, IL) Dallman generator accident is still under investigation, but after the generator tripped the main turbine steam stop valve did not close. With the generator’s electrical output at zero (i.e., it was disconnected) the turbine/rotor continued to accelerate up to over 5000 rpm (3600 normal). Then it suddenly stopped.
95 MW unit, $60 million to repair damage/replace unit
On a more positive note for CWLP their Dallman 4 plant is on schedule for a January 2010 start.

4. After the Dallman Accident

5. Outside of Dallman

6. 2007 Energy Bill
Congress and President Bush are currently discussing an energy bill, with a key sticking point being whether to require investor owned utilities to provide 15% of their electricity from renewables by 2020.
There is a big difference between 15% of capacity versus 15% of energy from renewables
A major issue is lack of wind capacity in the southeast U.S.

7. US Wind Resource Map

8. Transient Stability Analysis
For transient stability analysis we need to consider three systems
Prefault - before the fault occurs the system is assumed to be at an equilibrium point
Faulted - the fault changes the system equations, moving the system away from its equilibrium point
Postfault - after fault is cleared the system hopefully returns to a new operating point

9. Transient Stability Solution Methods
There are two methods for solving the transient stability problem
Numerical integration
this is by far the most common technique, particularly for large systems; during the fault and after the fault the power system differential equations are solved using numerical methods
Direct or energy methods; for a two bus system this method is known as the equal area criteria
mostly used to provide an intuitive insight into the transient stability problem

10. SMIB Example
Assume a generator is supplying power to an infinite bus through two parallel transmission lines. Then a balanced three phase fault occurs at the terminal of one of the lines. The fault is cleared by the opening of this line’s circuit breakers.

11. SMIB Example, cont’d
Simplified prefault system

12. SMIB Example, Faulted System
During the fault the system changes
The equivalent system during the fault is then
During this fault no
power can be transferred
from the generator to
the system

13. SMIB Example, Post Fault System
After the fault the system again changes
The equivalent system after the fault is then

14. SMIB Example, Dynamics

15. Transient Stability Solution Methods
There are two methods for solving the transient stability problem
Numerical integration
this is by far the most common technique, particularly for large systems; during the fault and after the fault the power system differential equations are solved using numerical methods
Direct or energy methods; for a two bus system this method is known as the equal area criteria
mostly used to provide an intuitive insight into the transient stability problem

16. Numerical Integration of DEs

17. Examples

18. Euler’s Method

19. Euler’s Method Algorithm

20. Euler’s Method Example 1

21. Euler’s Method Example 1, cont’d
xactual(t)
x(t) Dt=0.1
x(t) Dt=0.05 10
0.1
9.048 9
9.02
0.2
8.187
8.10
8.15
0.3
7.408
7.29
7.35 …
1.0
3.678
3.49
3.58
2.0
1.353
1.22
1.29

22. Euler’s Method Example 2

23. Euler's Method Example 2, cont'd

24. Euler's Method Example 2, cont'd
x1actual(t)
x1(t) Dt=0.25 1
0.25
0.9689
0.50
0.8776
0.9375
0.75
0.7317
0.8125
1.00
0.5403
0.6289 …
10.0
-3.129
100.0
0.8623
-151,983

25. Euler's Method Example 2, cont'd
Below is a comparison of the solution values for x1(t)
at time t = 10 seconds Dt
x1(10)
actual
0.25
-3.129
0.10
0.01
0.001

26. Transient Stability Example
A 60 Hz generator is supplying 550 MW to an infinite bus (with 1.0 per unit voltage) through two parallel transmission lines. Determine initial angle change for a fault midway down one of the lines. H = 20 seconds, D = Use Dt=0.01 second. Ea

27. Transient Stability Example, cont'd

28. Transient Stability Example, cont'd

29. Transient Stability Example, cont'd

30. Transient Stability Example, cont'd

31. Equal Area Criteria
The goal of the equal area criteria is to try to determine whether a system is stable or not without having to completely integrate the system response.
System will
be stable after
the fault if
the Decel Area is greater
than the
Accel. Area