1. ECE 476 POWER SYSTEM ANALYSIS
Lecture 19
Fault Analysis, Grounding, Symmetrical Components
Professor Tom Overbye
Department of Electrical and Computer Engineering

2. Announcements Homework 8 is 7.1, 7.17, 7.20, 7.24, 7.27
Should be done before second exam; not turned in
Be reading Chapter 7
Design Project has firm due date of Dec 4.
Exam 2 is Thursday Nov 13 in class.
Closed book, closed notes, except you can bring one new note sheet as well as your first exam note sheet.

3. Network Fault Example For the following network assume a fault on the
terminal of the generator; all data is per unit
except for the transmission line reactance
generator has 1.05
terminal voltage &
supplies 100 MVA
with 0.95 lag pf

4. Network Fault Example, cont'd
Faulted network per unit diagram

5. Network Fault Example, cont'd

6. Fault Analysis Solution Techniques
Circuit models used during the fault allow the network to be represented as a linear circuit
There are two main methods for solving for fault currents:
Direct method: Use prefault conditions to solve for the internal machine voltages; then apply fault and solve directly
Superposition: Fault is represented by two opposing voltage sources; solve system by superposition
first voltage just represents the prefault operating point
second system only has a single voltage source

7. Superposition Approach
Faulted Condition
Exact Equivalent to Faulted Condition
Fault is represented
by two equal and
opposite voltage
sources, each with
a magnitude equal
to the pre-fault voltage

8. Superposition Approach, cont’d
Since this is now a linear network, the faulted voltages
and currents are just the sum of the pre-fault conditions
[the (1) component] and the conditions with just a single
voltage source at the fault location [the (2) component]
Pre-fault (1) component equal to the pre-fault power flow solution
Obvious the
pre-fault
“fault current”
is zero!

9. Superposition Approach, cont’d
Fault (1) component due to a single voltage source
at the fault location, with a magnitude equal to the
negative of the pre-fault voltage at the fault location.

10. Two Bus Superposition Solution
This matches
what we
calculated
earlier

11. Determination of Fault Current

12. Determination of Fault Current

13. Three Gen System Fault Example

14. Three Gen Example, cont’d

15. Three Gen Example, cont’d

16. Three Gen Example, cont’d

17. PowerWorld Example 7.5: Bus 2 Fault

18. Problem 7.28

19. Grounding
When studying unbalanced system operation how a system is grounded can have a major impact on the fault flows
Ground current only impacts zero sequence system
In previous example if load was ungrounded the zero sequence network is (with Zn equal infinity):

20. Grounding, cont’d
Voltages are always defined as a voltage difference. The ground is used to establish the zero voltage reference point
ground need not be the actual ground (e.g., an airplane)
During balanced system operation we can ignore the ground since there is no neutral current
There are two primary reasons for grounding electrical systems
safety
protect equipment

21. How good a conductor is dirt?
There is nothing magical about an earth ground. All the electrical laws, such as Ohm’s law, still apply.
Therefore to determine the resistance of the ground we can treat it like any other resistive material:

22. How good a conductor is dirt?

23. How good a conductor is dirt?

24. Calculation of grounding resistance
Because of its large cross sectional area the earth is actually a pretty good conductor.
Devices are physically grounded by having a conductor in physical contact with the ground; having a fairly large area of contact is important.
Most of the resistance associated with establishing an earth ground comes within a short distance of the grounding point.

25. Calculation of grounding R, cont’d
Example: Calculate the resistance from a grounding rod out to a radial distance x from the rod, assuming the rod has a radius of r:

26. Calculation of grounding R, cont’d
The actual values will be
substantially less since
we’ve assumed no current
flowing downward into
the ground

27. Analysis of Unsymmetric Systems
Except for the balanced three-phase fault, faults result in an unbalanced system.
The most common types of faults are single line-ground (SLG) and line-line (LL). Other types are double line-ground (DLG), open conductor, and balanced three phase.
System is only unbalanced at point of fault!
The easiest method to analyze unbalanced system operation due to faults is through the use of symmetrical components

28. Symmetric Components
The key idea of symmetrical component analysis is to decompose the system into three sequence networks. The networks are then coupled only at the point of the unbalance (i.e., the fault)
The three sequence networks are known as the
positive sequence (this is the one we’ve been using)
negative sequence
zero sequence

29. Positive Sequence Sets
The positive sequence sets have three phase currents/voltages with equal magnitude, with phase b lagging phase a by 120°, and phase c lagging phase b by 120°.
We’ve been studying positive sequence sets
Positive sequence
sets have zero
neutral current

30. Negative Sequence Sets
The negative sequence sets have three phase currents/voltages with equal magnitude, with phase b leading phase a by 120°, and phase c leading phase b by 120°.
Negative sequence sets are similar to positive sequence, except the phase order is reversed
Negative sequence
sets have zero
neutral current

31. Zero Sequence Sets
Zero sequence sets have three values with equal magnitude and angle.
Zero sequence sets have neutral current

32. Sequence Set Representation
Any arbitrary set of three phasors, say Ia, Ib, Ic can be represented as a sum of the three sequence sets

33. Conversion from Sequence to Phase

34. Conversion Sequence to Phase

35. Conversion Phase to Sequence

36. Symmetrical Component Example 1

37. Symmetrical Component Example 2

38. Symmetrical Component Example 3

39. Use of Symmetrical Components
Consider the following wye-connected load:

40. Use of Symmetrical Components

41. Networks are Now Decoupled