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HV Power Seminar Nov 2009 1
Symmetrical Components
Power Transmission and Distribution
© Siemens AG 2006
HV Power Seminar Nov 2009 2
Symmetrical 3phase system
Page 2 TLQ08 Symmetrical Components
© Siemens AG 2006Power Transmission and DistributionClaus Wagner / Gustav Steynberg Mar 08
In a balanced 3 phase system it is possible to trea t each phase as an independant single phase. The othe r
phases follow with fixed 120°phase displacement.
HV Power Seminar Nov 2009 3
Symmetrical ComponentsHistory
• 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
Page 3 TLQ08 Symmetrical Components
© Siemens AG 2006Power Transmission and DistributionClaus Wagner / Gustav Steynberg Mar 08
The n sets of balanced phasors are called symmetrical components
In the 3 phase system n = 3
HV Power Seminar Nov 2009 4
Symmetrical ComponentsExample: Non-symmetrical 3 phase voltage
Symmetrical Components Unbalanced 3ph Voltage
Page 4 TLQ08 Symmetrical Components
© Siemens AG 2006Power Transmission and DistributionClaus Wagner / Gustav Steynberg Mar 08
HV Power Seminar Nov 2009 5
Symmetrical ComponentsEquations (Example voltage)
Calculation of phase voltage/current from symmetrical components:
210 VVVVA ++=
212
0 VaVaVVB ++=
= 21
111
aaA
Page 5 TLQ08 Symmetrical Components
© Siemens AG 2006Power Transmission and DistributionClaus Wagner / Gustav Steynberg Mar 08
22
10 VaVaVVC ++=
21 aa
SymP VAV ⋅=
=
C
B
A
P
V
V
V
V
=
2
1
0
V
V
V
VSym
HV Power Seminar Nov 2009 6
Symmetrical ComponentsEquations (Example voltage)
Calculation of symmetrical components from phase voltage/current:
30
CBA VVVV
++=
2VaVaV ++
=−
aa
aaA2
21
1
1
111
3
1
Page 6 TLQ08 Symmetrical Components
© Siemens AG 2006Power Transmission and DistributionClaus Wagner / Gustav Steynberg Mar 08
3
2
1
CBA VaVaVV
++=
aa213
PSym VAV ⋅= −1
=
C
B
A
P
V
V
V
V3
2
2
CBA VaVaVV
++=
=
2
1
0
V
V
V
VSym
HV Power Seminar Nov 2009 7
Single line diagram – symmetrical component circuits
Source TransformerLine
SourceTransformer Line
Single
Line
Positive
sequence
Page 7 TLQ08 Symmetrical Components
© Siemens AG 2006Power Transmission and DistributionClaus Wagner / Gustav Steynberg Mar 08
sequence
Source Transformer Line
Negative
sequence
Source Transformer Line
Zero
sequencedelta star
HV Power Seminar Nov 2009 8
Example: L1-E Fault
Source TransformerLine
Source Transformer Line
Single Line
Positive sequence
L1-E
I1
Page 8 TLQ08 Symmetrical Components
© Siemens AG 2006Power Transmission and DistributionClaus Wagner / Gustav Steynberg Mar 08
sequence
Source Transformer Line
Negative sequence
Source Transformer Line
Zero sequence
delta star
IF
I0
I2
I1
3ZF
HV Power Seminar Nov 2009 9
Example: L2-L3 Fault
Source TransformerLine
Source Transformer Line
Single Line
Positive
L2-L3
Page 9 TLQ08 Symmetrical Components
© Siemens AG 2006Power Transmission and DistributionClaus Wagner / Gustav Steynberg Mar 08
Positive sequence
Source Transformer Line
Negative sequence
Source Transformer Line
Zero sequence
delta star
I
I0
I2
I1
2 ZF
HV Power Seminar Nov 2009 10
Example: L2-L3-E fault
Source TransformerLine
Source Transformer Line
Single Line
Positive sequence
L2-L3-E
I1
ZF
ZF ZF
ZMF
Page 10 TLQ08 Symmetrical Components
© Siemens AG 2006Power Transmission and DistributionClaus Wagner / Gustav Steynberg Mar 08
sequence
Source Transformer Line
Negative sequence
Source Transformer Line
Zero sequence
delta star I0
I2
I1
ZF
ZF
3ZMF
HV Power Seminar Nov 2009 11
Example: Infeed from 2 sides onto L1-E fault
Source TransformerLine
SourceTransformer Line
Single
Line
Positive
L1-E
I1
Source
Source
Page 11 TLQ08 Symmetrical Components
© Siemens AG 2006Power Transmission and DistributionClaus Wagner / Gustav Steynberg Mar 08
sequence
Source Transformer Line
Negative
sequence
Source Transformer Line
Zero
sequencedelta star
I
I0
I2
I1
