1. ECE 476 Power System Analysis Lecture 22: System Protection, Transient Stability Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign overbye@illinois.edu

2. Announcements Read Chapters 10 and 11 Homework 10 is 9.1,9.2 (bus 3), 9.14, 9.16, 11.7. It should be turned in on Dec 3 (no quiz) Design project due date has been extended to Tuesday, December 8 – A useful paper associated with the design project is T. J. Overbye, "Fostering intuitive minds for power system design," IEEE Power and Energy Magazine, pp. 42-49, July- August 2003. – You can download it from campus computers at http://ieeexplore.ieee.org/xpl/abstractAuthors.jsp?arnumber= 1213526 1

3. In the News: UI Solar Farm The UI 21 acre "solar farm" has its official ribbon cutting today It is suppose to produce a maximum of 5.87 MW, with 7.86 thousand MWhs per year (about 2% of the campus total); capacity factor of 15.3% UI buys power for ten years then owns it, total of $15.5 million Cost per MWh (20 year life) is about $99 Source: www.news-gazette.com/news/local/2015-11-19/ribbon-cutting-uis-solar-farm-set-morning.html

4. Impedance Relays Impedance (distance) relays measure ratio of voltage to current to determine if a fault exists on a particular line 3

5. Impedance Relays Protection Zones To avoid inadvertent tripping for faults on other transmission lines, impedance relays usually have several zones of protection: – zone 1 may be 80% of line for a 3  fault; trip is instantaneous – zone 2 may cover 120% of line but with a delay to prevent tripping for faults on adjacent lines – zone 3 went further; most removed due to 8/14/03 events The key problem is that different fault types will present the relays with different apparent impedances; adequate protection for a 3  fault gives very limited protection for LL faults 4

6. Impedance Relay Trip Characteristics Source: August 14 th 2003 Blackout Final Report, p. 78 5

7. Differential Relays Main idea behind differential protection is that during normal operation the net current into a device should sum to zero for each phase – transformer turns ratios must, of course, be considered Differential protection is used with geographically local devices – buses – transformers – generators 6

8. Other Types of Relays In addition to providing fault protection, relays are used to protect the system against operational problems as well Being automatic devices, relays can respond much quicker than a human operator and therefore have an advantage when time is of the essence Other common types of relays include – under-frequency for load: e.g., 10% of system load must be shed if system frequency falls to 59.3 Hz – over-frequency on generators – under-voltage on loads (less common) 7

9. Digital Fault Recorders (DFRs) During major system disturbances numerous relays at a number of substations may operate Event reconstruction requires time synchronization between substations to figure out the sequence of events Most utilities now have digital fault recorders (DFRs) to provide a detailed recording of system events with time resolution of at least 1 microsecond Some of this functionality is now included in digital relays 8

10. Use of GPS for Fault Location Since power system lines may span hundreds of miles, a key difficulty in power system restoration is determining the location of the fault One newer technique is the use of the global positioning system (GPS). GPS can provide time synchronization of about 1 microsecond Since the traveling electromagnetic waves propagate at about the speed of light (300m per microsecond), the fault location can be found by comparing arrival times of the waves at each substation 9

11. Power System Time Scales and Transient Stability Image source: P.W. Sauer, M.A. Pai, Power System Dynamics and Stability, 1997, Fig 1.2, modified 10

12. Example of Frequency Variation Figure shows Eastern Interconnect frequency variation after loss of 2600 MWs 11

13. Example of Transient Behavior 12 Source: August 14 th 2003 Blackout Final Report

14. Power Grid Disturbance Example Time in Seconds Figures show the frequency change as a result of the sudden loss of a large amount of generation in the Southern WECC Frequency Contour

15. Power System Transient Stability In order to operate as an interconnected system all of the generators (and other synchronous machines) must remain in synchronism with one another – synchronism requires that (for two pole machines) the rotors turn at exactly the same speed Loss of synchronism results in a condition in which no net power can be transferred between the machines A system is said to be transiently unstable if following a disturbance one or more of the generators lose synchronism 14

16. Generator Transient Stability Models In order to study the transient response of a power system we need to develop models for the generator valid during the transient time frame of several seconds following a system disturbance We need to develop both electrical and mechanical models for the generators 15

17. Generator Electrical Model The simplest generator model, known as the classical model, treats the generator as a voltage source behind the direct-axis transient reactance; the voltage magnitude is fixed, but its angle changes according to the mechanical dynamics 16

18. Generator Mechanical Model Generator Mechanical Block Diagram 17

19. Generator Mechanical Model, cont’d 18

20. Generator Mechanical Model, cont’d 19

21. Generator Mechanical Model, cont’d 20

22. Generator Swing Equation 21

23. Single Machine Infinite Bus (SMIB) To understand the transient stability problem we’ll first consider the case of a single machine (generator) connected to a power system bus with a fixed voltage magnitude and angle (known as an infinite bus) through a transmission line with impedance jX L 22

24. SMIB, cont’d 23

25. SMIB Equilibrium Points 24