1. ECEN 460 Power System Operation and Control
Lecture 22: Transient Stability
Prof. Tom Overbye
Dept. of Electrical and Computer Engineering
Texas A&M University

2. Announcements Read Chapters 11 and 12
Design project is due on Dec 5; details on the website
Homework 8 is 11.12, (part a only), 11.19, 11.21, 11.25, 11.26; due on Thursday Nov 30
Lab 10 is on Nov 27/28, both in WEB 115; no lab week of Dec 4

3. Lab 9 Results: Marginal Prices2

4. Lab 9 Results: Profit 3

5. Earlier Experiment Results: Group A, LAO4

6. Earlier Experiment Results: Group B, LAO5

7. Earlier Experiment Results: Group A, PAO6

8. Earlier Experiment Results: Group B, PAO7

9. Earlier Experiment Results: Offer Movies8

10. Back to Transient Stability Example 11.10
Determine the initial conditions for the Example 11.3 case with the classical generator replaced by a two-axis model with H = 3.0 per unit-seconds, D = 0, = 2.1, = 2.0, = 0.3, = 0.5, all per unit using the 100 MVA system base
First determine the current out of the generator from the initial conditions, then the terminal voltage
Gen is delivering S=1+j to bus 2 9

11. Example 11.10, cont.
We can then get the initial angle, and initial d and q values 10

12. Example 11.10, cont.
The initial state variable are determined by solving with the differential equations equal to zero.
The transient stability solution is then solved by numerically integrating the differential equations, coupled with solving the algebraic equations 11

13. PowerWorld Solution of 11.1012

14. Generator Exciters and Governors
The two-axis synchronous model takes as an input the field voltage and the mechanical power. The next section discusses how these values are controlled 13

15. Generator Exciters
The purpose of the exciter is to maintain the generator terminal voltage (or other close by voltage) at a specified value.
Input is the sensed voltage
Output is the field voltage to the machine, Efd
Physically several technologies are used.
Older generators used dc machines with brushes transferring the power
With the newer brushless (or static) exciters power is obtained from an “inverted” synchronous generator whose field voltage is on the stator and armature windings are on rotor; output is rectified to create dc. 14

16. ABB UNICITER Example
Image source: www02.abb.com, Brushless Excitation Systems Upgrade, 15

17. Exciter Block Diagrams
Block diagrams are used to setup the transient stability models. The common IEEE Type 1 exciter is shown below (neglecting saturation); this is a dc type exciter. Initial state values are determined by knowing Efd and the terminal voltage Vt. 16

18. Exciter Block Diagram Example
Consider again the Example case, with an IEEE T1 exciter with Tr = 0, Ka = 100, Ta = 0.05, Vrmax = 5, Vrmin = -5, Ke = 1, Te = 0.26, Kf = 0.01 and Tf = 1.0. Determine the initial states. Initial value of Efd = and Vt = 17

19. PowerWorld Example 12.1 Solution18

20. Generator Governors
The other key generator control system is the governor, which changes the mechanical power into the generator to maintain a desired speed and hence frequency.
Historically centrifugal “flyball” governors have been used to regulate the speed of devices such as steam engines
The centrifugal force varies with speed, opening or closing the throttle valve
Photo source: en.wikipedia.org/wiki/Centrifugal_governor 19

21. Isochronous Governors
Ideally we would like the governor to maintain the frequency at a constant value of 60 Hz (in North America)
This can be accomplished using an isochronous governor.
A flyball governor is not an isochronous governor since the control action is proportional to the speed error
An isochronous governor requires an integration of the speed error
Isochronous governors are used on stand alone generators but cannot be used on interconnected generators because of “hunting” 20

22. Generator “Hunting”
Control system “hunting” is oscillation around an equilibrium point
Trying to interconnect multiple isochronous generators will cause hunting because the frequency setpoints of the two generators are never exactly equal
One will be accumulating a frequency error trying to speed up the system, whereas the other will be trying to slow it down
The generators will NOT share the power load proportionally. 21

23. Droop Control
The solution is to use what is known as droop control, in which the desired set point frequency is dependent upon the generator’s output
R is known as the regulation constant or droop; a typical value is 4 or 5%. 22

24. Governor Block Diagrams
The block diagram for a simple stream unit, the TGOV1 model, is shown below. The T1 block models the governor delays, whereas the second block models the turbine response. 23

25. Example 12.4 System Response24

26. Problem 12.11 25

27. Restoring Frequency to 60 Hz
In an interconnected power system the governors to not automatically restore the frequency to 60 Hz
Rather this is done via the ACE (area control area calculation). Previously we defined ACE as the difference between the actual real power exports from an area and the scheduled exports. But it has an additional term ACE = Pactual - Psched – 10b(freqact - freqsched)
b is the balancing authority frequency bias in MW/0.1 Hz with a negative sign. It is about 0.8% of peak load/generation 26

28. 2600 MW Loss Frequency Recovery
Frequency recovers in about ten minutes 27

29. Lab 10 Intro: Running Transient Stability and Critical Clearing Time28

30. Lab 10 Intro: Changing Transient Stability Model Parameters29

31. Lab 10 Intro: TSGC Frequency Response
Use to retire generators 30

32. In the News: Luminant Coal Plant Closings Eliminate 600 Texas Jobs
Dallas-based electricity generator Luminant is cutting about 600 jobs as it closes three coal-fired power plants and a mine in Texas
Texas Workforce Commission said Nov 20, 2017 that Luminant plans to make the layoffs in January
Previously announced closing are at Monticello, Big Brown and Sandow power plants
Closings are due to cheap natural gas, low wholesale power grids and increase in renewable generation
Monticello is 1880 MW by Mount Pleasant, Big Brown is 1150 MW by Fairfield, Sandow is 1137 MW by Rockdale
Source; DallasNews.com, Nov 21, 2017 31

33. Our Fictitious Texas Grid Company Generator Plant Locations
Red is nuclear, black is coal, brown is natural gas, green is wind, yellow is solar 32

34. Lab 10 Intro: PowerWorld DS33