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 3 vectors equal magnitude 120° displaced Phase sequence similar to Original Vectors Negative Sequence 3 Vectors Phase sequence Opposite to Original Vectors Zero Sequence equal in magnitude No phase Difference

Representation of Positive Sequence Components Vc1 Va1 120° Vc1= a Va1 120° Va1 Vb1=a2Va1 120° Vb1

Representation of Negative Sequence Components Vb2 Va2 Vb2= a Va2 Vc2=a2Va2 120° 120° Va2 120° Vc2

Representation of Zero Sequence Components Va0 Va0 = Vb0 = Vc0 Vb0 Vc0

Equation for Phase Voltage from Symmetrical Components Positive Sequence Va1 Vc1= a Va1 Vb1=a2Va1 Negative Sequence Va2 Vb2= a Va2 Vc2=a2Va2 Zero Sequence Va0 = Vb0 = Vc0 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 Network Ia1 Va1=Ea-Ia1Z1 Ref. bus Negative Sequence Network Va0= -Ia0Z0 Va2= -Ia2Z2 Ref. bus Zero Sequence Network Ref. bus

Zero Sequence Network for Generator with Neutral is Grounded Va0= -Ia0Z0 Zn Ref. bus Zero Sequence Network

Transmission Line Positive Sequence Network Ia2 Z2 Va2 Ref. bus Negative Sequence Network Ia1 Z1 Va1 Ref. bus Ia0 Z0 Va0 Ref. bus Zero Sequence Network

Transformer Positive Sequence Network Negative Sequence Network Z2 Z1 Ia2 Z2 Va2 Ref. bus Negative Sequence Network Ia1 Z1 Va1 Ref. bus

Zero sequence Network of Transformer 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 Y – Δ Δ - Δ Ref. bus Z0 S1 S2 D2 Z0 S1 S2 D2 D1