ECE 476 POWER SYSTEM ANALYSIS

1. ECE 476POWER SYSTEM ANALYSIS Lecture 23 Power System Protection and Transient Stability Professor Tom Overbye Department of Electrical andComputer Engineering

2. Announcements • Design Project has firm due date of Dec 4 • Potentially useful article: T.J. Overbye, “Fostering Intuitive Minds for Power System Design,” IEEE Power and Energy Magazine, July-August 2003 • Be reading Chapter 13. • HW 10 is 8.3, 8.5, 9.1,9.2 (bus 3), 9.13, 9.53 is due on Thursday Dec 4. • Final is Tuesday Dec 16 from 7 to 10pm in EL 165 (note this is NOT what the web says). Final is comprehensive. One new note sheet, and your two old note sheets are allowed

3. Fault Calculation Example The zero, positive and negative sequence bus impedance matrixes for a three bus, three phase power system are given below. Determine the per unit fault current (sequence values only) for a double line to ground fault involving phases "B and C" at bus 2. The prefault voltage at all buses is 1.0 per unit. Assume the fault impedance is zero.

4. Directional Relays • Directional relays are commonly used to protect high voltage transmission lines • Voltage and current measurements are used to determine direction of current flow (into or out of line) • Relays on both ends of line communicate and will only trip the line if excessive current is flowing into the line from both ends • line carrier communication is popular in which a high frequency signal (30 kHz to 300 kHz) is used • microwave communication is sometimes used

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

6. 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 3f 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 3f fault gives very limited protection for LL faults

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

8. 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

9. 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)

10. Sequence of Events Recording • 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 sequence of events recording that provide time synchronization of at least 1 microsecond

11. 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

12. 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

13. 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

14. Example of Transient Behavior

15. 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. Generator Mechanical Model Generator Mechanical Block Diagram

17. Generator Mechanical Model, cont’d

18. Generator Mechanical Model, cont’d

19. Generator Mechanical Model, cont’d

20. Generator Swing Equation

21. 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 jXL

22. SMIB, cont’d

23. SMIB Equilibrium Points

24. 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

25. 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

26. 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.

27. SMIB Example, cont’d Simplified prefault system

28. 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

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

30. SMIB Example, Dynamics

31. 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