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Lecture II
Objective:
 Representation of sequence components
 Equation to find unbalanced vectors from
symmetrical components and vice versa.
 Definition: Sequence Impedance and sequence
Network
 Sequence Networks for Power system
Components
 Zero sequence network for transformer
connections.
Classification of Symmetrical
Components for 3Φ System
Three Types – Positive Sequence , Negative Sequence and Zero Sequence
- Magnitude, Displacement and Phase Sequence
Positive
Sequence
Negative
Sequence
• 3 vectors
• equal
magnitude
• 120° displaced
• Phase sequence
similar to
Original Vectors
• 3 Vectors
• equal
magnitude
• 120° displaced
• Phase sequence
Opposite to
Original Vectors
Zero Sequence
• 3 Vectors
• equal in
magnitude
• No phase
Difference
Representation of Positive Sequence
Components
Vc1
Va1
120°
120°
Va1
120°
Vb1
Vc1= a Va1
Vb1=a2Va1
Representation of Negative Sequence
Components
Vb2
Va2
Vb2= a Va2
Vc2=a2Va2
120°
120°
Va2
120°
Vc2
Representation of Zero Sequence
Components
Va0
Vb0
Vc0
Va0 = Vb0 = Vc0
Equation for Phase Voltage from Symmetrical
Components
Positive Sequence
Va1
Vc1= a Va1
Vb1=a2Va1
Negative Sequence Zero Sequence
Va2
Vb2= a Va2
Va0 = Vb0 = Vc0
2
Vc2=a Va2
Phase Voltage in terms of Symmetrical Components
Va= Va1 + Va2 + Va0 ………………………………. 1
Vb= Vb1 + Vb2 + Vb0
Vb= a2Va1 + a Va2 + Va0 ……………………………. 2
Vc= Vc1 + Vc2 + Vc0
Vc= a Va1 + a2Va2 + Va0 ………………………………. 3
Cond…
Equation in Matrix Form for phase Voltage and phase current in terms of
symmetrical components of voltage and current is,
Vph= T Vsym
where T is Symmetrical Component Transformation Matrix,
----------------------- 4
----------------------- 5
Equation for Symmetrical Components from Phase
Voltage
Symmetrical components of Voltage and
currents from phase Voltages and phase
currents
----------------- 6
----------------- 7
----------------- 8
Sequence Impedance
Definition:
The impedance offered by the circuit
elements for sequence current is called as
sequence Impedance.
 Positive sequence Impedance
 Negative Sequence Impedance
 Zero sequence Impedance
Definition sequence Impedances
1.Positive sequence Impedance:
The impedance offered by circuit elements for
positive sequence currents is called as positive
sequence impedance.
2. Negative Sequence Impedance:
The impedance offered by circuit elements for
negative sequence currents is called as negative
sequence impedance.
3. Zero Sequence Impedance:
The impedance offered by circuit elements for zero
sequence currents is called as zero sequence
impedance.
Sequence Networks
Definition:
The single phase equivalent circuit of power
system formed using the impedance of any one
sequence only is called as sequence network.
 Positive sequence Network (or) Per unit
reactance
Negative sequence Network
Zero sequence Network
Positive, Negative and Zero Sequence Networks
for Power System Components
•
•
•
•
Generator
Transmission Line
Transformer
Load
Positive, Negative Sequence Networks for Generator
with neutral is not Grounded
Positive Sequence
Ia1
Network
Va1=Ea-Ia1Z1
Ref. bus
Negative Sequence
Network
Va0= -Ia0Z0
Va2= -Ia2Z2
Ref. bus
Ref. bus
Zero Sequence
Network
Zero Sequence Network for Generator with
Neutral is Grounded
Va0= -Ia0Z0
Zn
Ref. bus
Zero Sequence
Network
Transmission Line
Ia1
Positive Sequence Network
Z1
Negative Sequence Network
Ia2
Va1
Z2
Va2
Ref. bus
Zero Sequence Network
Ia0
Z0
Va0
Ref. bus
Ref. bus
Transformer
Positive Sequence Network
Ia1
Negative Sequence Network
Z1
Ia2
Z2
Va2
Va1
Ref. bus
Ref. bus
Zero sequence Network of Transformer
Z0
S2
S1
D1
D2
Ref. bus
S – Indicates Star Connection
D – Indicates Delta Connection
1 – Indicates Primary Side
2 – Indicates Secondary Side
For Delta connections in primary and secondary side, switches D1 and D2 will be closed
otherwise in open condition.
For Star connection with neutral grounded, switches S1 and S2 will be closed otherwise in
open condition.
Zero sequence Network of Transformer
• Y–Y
Z0
S1
S2
Ref. bus
Z0
S1
D2
• Y–Δ
Z0
• Δ-Δ
S2
S1
D1
S2
D2