Day 1 Part 1 Symmetrical Components

Symmetrical Components Power Transmission and Distribution

© Siemens

AG 2006

Symmetrical 3phase system

In a balanced 3 phase system it is possible to treat each phase as an independant single phase. The other phases follow with fixed 120°phase 120°phase displacement. © Siemens

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Mar 08

TLQ08 Symmetrical Components

Claus Wagner / Gustav Steynberg

AG 2006

Power Transmission and Distribution

Symmetrical Components History • Due to Charles LeGeyt Fortescue (1918): “a

set of n unbalanced phasors in an n-phase system can be resolved into n sets of balanced phasors by a linear transformation” The n sets of balanced phasors are called symmetrical components In the 3 phase system n = 3

© Siemens

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AG 2006


Symmetrical Components Example: Non-symmetrical 3 phase voltage Symmetrical Components

Unbalanced 3ph Voltage

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AG 2006


Symmetrical Components Equations (Example voltage) Calculation of phase voltage/current voltage/current from symmetrical symmetrical components:

V A

=

V 0 + V 1 + V 2

V B

=

V 0 + a V 1 + aV 2

2

2

V C = V 0 + aV 1 + a V 2

 V A    V P =  V B     V C 

V Sym

 V 0    =  V 1     V 2 

1 1  2 A = 1 a 1 a

V P

=

  a

1

2 a 

A ⋅ V Sym © Siemens

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AG 2006


Symmetrical Components Equations (Example voltage) Calculation of symmetrical components from phase voltage/current:

V 0

V 1

=

=

V A + V B

V A + aV B

=

1 1 1 A = 1 3 −

3 +

2

a V C

a

 2 a 

a

a

1

1

3 2

V 2

V C

+

V A + a V B

+

aV C

3

V Sym

=

A

V Sym −1

⋅

V P

 V 0    =  V 1     V 2 

 V A    V P =  V B     V C  © Siemens

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AG 2006


Single line diagram – symmetrical component circuits

Source

Transformer Line

Source

Trans ransfo form rmer er

Single Line

Line Line Positive se uence

Source

Trans ransfo form rmer er

Line Line Negative sequence

Source

Trans ransfo form rmer er delta

Line Line

star

Zero sequence

© Siemens

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AG 2006


Example: L1-E Fault Source

Transformer

Line

Single Line

L1-E

Source

Transformer

Line

Transformer

Line

Positive

Source Negative sequence

Source Zero sequence

IF

I2

Transformer delta

star

3ZF

Line I0

© Siemens

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AG 2006


Example: L2-L3 Fault Source

Transformer

Line

Single Line

L2-L3

Source

Transformer

Line I1

sequence

I Source

Transformer

Negative sequence

2 ZF

Line I2


Transformer delta

star

Line I0

© Siemens

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AG 2006


Example: L2-L3-E fault Source

Transformer

Line

Single Line

L2-L3-E

Source

ZF Transformer

ZF

ZF

Line

ZMF

Positive sequence

Source

Transformer

Negative sequence

Line

ZF

Line

ZF

I2


Transformer delta

star

I0

3ZMF

© Siemens

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AG 2006


Example: Infeed from 2 sides onto L1-E fault Source

Transformer Line

Single Line

Source

L1-E

Source

Tran Transf sfor orme merr

Line ine

Tran Transf sfor orme merr

Line ine

Source

Positive sequence

Source

I

Negative sequence

I2


Tran Transf sfor orme merr delta

star

Line ine

I0

© Siemens

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AG 2006


Day 1 Part 1 Symmetrical Components

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