# Fault Analysis Symmetrical Components

Electronics - Devices

Oct 13, 2013 (4 years and 6 months ago)

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Fault Analysis

Symmetrical Components

1

Fault Analysis

The cause of electric power system faults is
insulation breakdown

This breakdown can be due to a variety of
different factors:

Lightning.

wires blowing together in the wind.

animals or plants coming in contact with the
wires.

salt spray or pollution on insulators.

2

Fault Types

There are two main types of faults

Symmetric faults: system remains balanced; these faults
are relatively rare, but are the easiest to analyze so we’ll
consider them first.

Un
-
symmetric faults: system is no longer balanced; very
common, but more difficult to analyze.

The most common type of fault on a three phase system by
far is the single line
-
to
-
ground (SLG), followed by the line
-
to
-
line faults (LL), double line
-
to
-
ground (DLG) faults, and
balanced three phase faults.

3

Fault Analysis

Fault currents cause equipment damage due to both
thermal and mechanical processes.

Goal of fault analysis is to determine the magnitudes
of the currents present during the fault.

need to determine the maximum current to insure
devices can survive the fault.

need to determine the maximum current the circuit
breakers (CBs) need to interrupt to correctly size the
CBs.

4

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:

1.
Direct method: Use pre
-
fault conditions to solve for the
internal machine voltages; then apply fault and solve
directly.

2.
Superposition: Fault is represented by two opposing
voltage sources; solve system by superposition.

5

Analysis of Un
-
Symmetric 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

6

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.

7

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

8

Negative Sequence Sets

The negative sequence sets
have three phase
currents/voltages with
equal magnitude, with
phase b

phase a by
120
°
, and phase c

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

Zero Sequence Sets

Zero sequence sets have three
values with equal magnitude and
angle.

Zero sequence sets have neutral
current

Zero Sequence vectors with

Zero phase shift.

Sequence Set Representation

Any

arbitrary set of three phasors, say I
a
, I
b
, I
c

can be
represented as a sum of the three sequence sets

11

Conversion from Sequence to Phase

=

12

Conversion Sequence to Phase

13

Conversion Phase to Sequence

14

Example

15

Example

16

Power in Symmetrical Components

The total power in a three
-
phase network is given in
terms of phase variables by

where the asterisk denotes complex conjugation. We can show that the

corresponding expression in terms of sequence variables is given by

The total power is three times the sum of powers in individual
sequence networks.

17

Use of Symmetrical Components

Consider the following wye
-

18

Use of Symmetrical Components

19

Networks are Now Decoupled

20

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 Z
n
equal infinity):

21

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

1.
safety

2.
protect equipment

22

Sequence diagrams for generators

Key point: generators only produce positive sequence voltages; therefore
only the positive sequence has a voltage source.

During a fault Z+

Z

Xd”. The zero sequence impedance is
usually substantially smaller. The value of Zn depends on
whether the generator is grounded.

23

Sequence diagrams for Transformers

The positive and negative sequence diagrams for transformers are similar to those for
transmission lines.

The zero sequence network depends upon both how the transformer is grounded and
its type of connection. The easiest to understand is a double grounded wye
-
wye

24

Transformer Sequence Diagrams

25

Unbalanced Fault Analysis

The first step in the analysis of unbalanced faults is to assemble
the three sequence networks.

For example, for the following power system let’s develop the
sequence networks.

26

Sequence Diagrams

Positive Sequence Network

Negative Sequence Network

27

Negative Sequence Network

28

Zero Sequence Network

29