0. ECE 476 POWER SYSTEM ANALYSIS
Lecture 21
Symmetrical Components, Unbalanced Fault Analysis
Professor Tom Overbye
Department of Electrical and Computer Engineering

1. Announcements Be reading Chapters 9 and 10 HW 8 is due now.
HW 9 is 8.4, 8.12, 9.1,9.2 (bus 2), 9.14; due Nov 10 in class
Start working on Design Project. Tentatively due Nov 17 in class
Second exam is on Nov 15 in class. Same format as first exam, except you can bring two note sheets (e.g., the one from the first exam and another)

2. Single Line-to-Ground (SLG) Faults
Unbalanced faults unbalance the network, but only at the fault location. This causes a coupling of the sequence networks. How the sequence networks are coupled depends upon the fault type. We’ll derive these relationships for several common faults.
With a SLG fault only one phase has non-zero fault current -- we’ll assume it is phase A.

3. SLG Faults, cont’d

4. SLG Faults, cont’d

5. SLG Faults, cont’d With the sequence networks in series we can
solve for the
fault currents
(assume Zf=0)

6. Example 9.3

7. Line-to-Line (LL) Faults
The second most common fault is line-to-line, which occurs when two of the conductors come in contact with each other. With out loss of generality we'll assume phases b and c.

8. LL Faults, cont'd

9. LL Faults, con'td

10. LL Faults, cont'd

11. LL Faults, cont'd

12. LL Faults, cont'd

13. Double Line-to-Ground Faults
With a double line-to-ground (DLG) fault two line conductors come in contact both with each other and ground. We'll assume these are phases b and c.

14. DLG Faults, cont'd

15. DLG Faults, cont'd

16. DLG Faults, cont'd

17. DLG Faults, cont'd The three sequence networks are joined as follows
Assuming Zf=0, then

18. DLG Faults, cont'd

19. Unbalanced Fault Summary
SLG: Sequence networks are connected in series, parallel to three times the fault impedance
LL: Positive and negative sequence networks are connected in parallel; zero sequence network is not included since there is no path to ground
DLG: Positive, negative and zero sequence networks are connected in parallel, with the zero sequence network including three times the fault impedance

20. Generalized System Solution
Assume we know the pre-fault voltages
The general procedure is then
Calculate Zbus for each sequence
For a fault at bus i, the Zii values are the thevenin equivalent impedances; the pre-fault voltage is the positive sequence thevenin voltage
Connect and solve the thevenin equivalent sequence networks to determine the fault current
Sequence voltages throughout the system are

21. Generalized System Solution, cont’d
Sequence voltages throughout the system are given by
This is solved
for each
sequence
network!
5. Phase values are determined from the sequence values

22. Unbalanced System Example
For the generators assume Z+ = Z = j0.2; Z0 = j0.05
For the transformers assume Z+ = Z =Z0 = j0.05
For the lines assume Z+ = Z = j0.1; Z0 = j0.3
Assume unloaded pre-fault, with voltages =1.0 p.u.

23. Positive/Negative Sequence Network
Negative sequence is identical to positive sequence

24. Zero Sequence Network

25. For a SLG Fault at Bus 3
The sequence networks are created using the pre-fault
voltage for the positive sequence thevenin voltage,
and the Zbus diagonals for the thevenin impedances
Positive Seq Negative Seq Zero Seq.
The fault type then determines how the networks are
interconnected

26. Bus 3 SLG Fault, cont’d

27. Bus 3 SLG Fault, cont’d

28. Faults on Lines
The previous analysis has assumed that the fault is at a bus. Most faults occur on transmission lines, not at the buses
For analysis these faults are treated by including a dummy bus at the fault location. How the impedance of the transmission line is then split depends upon the fault location

29. Line Fault Example Assume a SLG fault occurs on the previous system
on the line from bus 1 to bus 3, one third of the way
from bus 1 to bus 3. To solve the system we add a
dummy bus, bus 4, at the fault location

30. Line Fault Example, cont’d
The Ybus
now has
4 buses

31. Power System Protection
Main idea is to remove faults as quickly as possible while leaving as much of the system intact as possible
Fault sequence of events
Fault occurs somewhere on the system, changing the system currents and voltages
Current transformers (CTs) and potential transformers (PTs) sensors detect the change in currents/voltages
Relays use sensor input to determine whether a fault has occurred
If fault occurs relays open circuit breakers to isolate fault

32. Power System Protection
Protection systems must be designed with both primary protection and backup protection in case primary protection devices fail
In designing power system protection systems there are two main types of systems that need to be considered:
Radial: there is a single source of power, so power always flows in a single direction; this is the easiest from a protection point of view
Network: power can flow in either direction: protection is much more involved

33. Radial Power System Protection
Radial systems are primarily used in the lower voltage distribution systems. Protection actions usually result in loss of customer load, but the outages are usually quite local.
The figure shows
potential protection
schemes for a
radial system. The
bottom scheme is
preferred since it
results in less lost load

34. Radial Power System Protection
In radial power systems the amount of fault current is limited by the fault distance from the power source: faults further done the feeder have less fault current since the current is limited by feeder impedance
Radial power system protection systems usually use inverse-time overcurrent relays.
Coordination of relay current settings is needed to open the correct breakers

35. Inverse Time Overcurrent Relays
Inverse time overcurrent relays respond instan-taneously to a current above their maximum setting
They respond slower to currents below this value but above the pickup current value