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

1. 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

2. 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.

3. 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

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

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 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

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

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

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)

9. 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

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

11. 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

12. 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

13. Example of Transient Behavior

14. 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

15. Generator Mechanical Model
Generator Mechanical Block Diagram

16. Generator Mechanical Model, cont’d

17. Generator Mechanical Model, cont’d

18. Generator Mechanical Model, cont’d

19. Generator Swing Equation

20. 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

21. SMIB, cont’d

22. SMIB Equilibrium Points

23. 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

24. 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

25. 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.

26. SMIB Example, cont’d
Simplified prefault system

27. 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

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

29. SMIB Example, Dynamics

30. 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