Fault Analysis SC 2012

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Fault Analysis

Symmetrical Components

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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 thewires.

salt spray or pollution on insulators.2


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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 well

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


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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


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Fault Analysis Solution Techniques

Circuit models used during the fault allow the network to berepresented 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.

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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 systemoperation due to faults is through the use ofSymmetrical

Components6


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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 weve been using).

negative sequence.

zero sequence.

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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.

Weve been studying

positive sequence sets.Positive sequence sets

have zero neutral current

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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


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Zero Sequence Sets

Zero sequence sets have three

values with equal magnitude and

angle.

Zero sequence sets have neutralcurrent

Zero Sequence vectors with

Zero phase shift.


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Sequence Set Representation

Any arbitrary set of three phasors, say Ia, Ib, Ic can berepresented as a sum of the three sequence sets

0

0

0

0 0 0

where

, , is the zero sequence set

, , is the positive sequence set

, , is the negative sequence set

a a a a

b b b b

c c c c

a b c

a b c

a b c

I I I I

I I I I

I I I I

I I I

I I I

I I I

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Conversion from Sequence to Phase

0a

2 3 3

0 0 0a b c

2

Only three of the sequence values are unique,I , , ; the others are determined as follows:

1 120 0 1

I I I (since by definition they are all equal)

a a

b a c a b a c

I I

I I I I I I I

2

0

0 + 2 2a a

2 2

1 1 1 11 1I 1 I 1

1 1

a

aa

b a a

c a

I

III I I

I I

=

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Conversion Sequence to Phase

2

2

0 0

Define the symmetrical components transformationmatrix

1 1 1

11

Then

aa

b a s

c a

I II

I I I

I I I

A

I A A A I

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Conversion Phase to Sequence

1

1 2

2

By taking the inverse we can convert from thephase values to the sequence values

1 1 11

with 13

1

Sequence sets can be used with voltages as well

as with currents

s

I A I

A

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Example

1 2s

2

0

Let

Then

1 1 1 0 01

13

6.121

a

b

c

V

V

V

V

V A V

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Example

0

2

2

10 0

Let 10

Then

1 1 1 10 0

1 101

s

s

I

I

I

I

I AI

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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.

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Use of Symmetrical Components

Consider the following wye-connected load:

( )

( )

( )

n a b c

ag a y n n

ag Y n a n b n c

bg n a Y n b n c

cg n a n b Y n c

I I I I

V I Z I Z

V Z Z I Z I Z I

V Z I Z Z I Z I

V Z I Z I Z Z I

ag y n n n a

bg n y n n b

ccg n n y n

V Z Z Z Z I

V Z Z Z Z I

IV Z Z Z Z

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Use of Symmetrical Components

1

1

3 0 0

0 0

0 0

ag y n n na

bg n y n n b

ccg n n y n

s s

s s s s

y n

y

y

V Z Z Z Z I

V Z Z Z Z I

IV Z Z Z Z

Z Z

Z

Z

V Z I V A V I A I

A V Z A I V A Z A I

A Z A

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Networks are Now Decoupled

0 0

0 0

3 0 0

0 0

0 0

Systems are decoupled

( 3 )

y n

y

y

y n y

y

V IZ Z

V Z I

ZV I

V Z Z I V Z I

V Z I

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Grounding

When studying unbalanced system operation how asystem 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):

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Grounding, contd

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


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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+ ZXd. The zero sequence impedance is

usually substantially smaller. The value of Zn depends on

whether the generator is grounded.

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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

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Transformer Sequence Diagrams

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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 lets develop the

sequence networks.

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Sequence Diagrams

Positive Sequence Network

Negative Sequence Network

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Negative Sequence Network

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Zero Sequence Network

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Documents

Fault Analysis SC 2012