ch 03 phasor

Chaper3. Phasors and Polarity

Protective Relaying Principles And Applications

디지털 보호제어 연구실2

Contents

3.1 Introduction

3.2 Phasors

3.3 Circuit and Phasor Diagrams for A Balanced Three-Phase Power System

3.4 Phasor and Phase Rotation

3.5 Polarity

3.6 Application of Polarity for Phase-fault Directional Sensing

3.7 Directional Sensing for Ground Faults : Voltage Polarization

3.8 Directional Sensing for Ground Faults : Current Polarization

3.9 Summary


3.1 Introduction

Phasor and Polarity are important and useful tools in power system protection

Understanding and analysis of the connections, operation, testing of relays and relay systems

Understanding power system performance during both normal and abnormal operation


3.2 Phasors

The IEEE Dictionary (IEEE 100-1984) definesa phasor as “A complex number”

Phasor : consist of the absolute value of the complex number and the phase to the phase angle at zero time

3.2.1. Phasor RepresentationThe common pictorial form for representing electrical and magnetic phasor quantities uses the cartesian coordinates with x and y


3.2 Phasors

3.2.1. Phasor Representation

c ) j ( c e c jy x c j φφφφ +∠=+==+= sincos

( * : conjugate form )

c ) j ( c e c jy x c j φφφφ −∠=−==−= −∗ sincos

The modulus of the phasor

22 yx c +=

► From, Eq. (3.1) and (3.2)

( ) 2 1 ∗+= cc x

( ) 2

1 ∗−= ccj

y

The several alternative forms

(3.1)

(3.2)

(3.3)

(3.4)

(3.5)


3.2 Phasors

3.2.2 Phasor Diagrams for Sinusoidal QuantitiesIn applying the notation above to sinusoidal voltage, currents, and fluxes, the axes are assumed fixed, with the phasor quantities rotating at constant angular velocityPhasors always rotate in the counterclockwise direction

Impedance and power phasors


3.2 Phasors

3.2.3 Combining PhasorsThe various laws for combining phasors

• Multiplication

• Division

• Powers

IV I V VI φφ +∠= (3.6)

IV I V VI φφ −∠=∗ (3.7)2 I II =∗ (3.8)

IV I V

IV φφ −∠=

(3.9)

( ) njnnjn e I e I I φφ )( == (3.10)

n jn

n e I I φ= (3.11)


3.2 Phasors

3.2.4 Phasor Diagrams Require a Circuit DiagramCircuit Diagram

• Identify the direction and the location for the current• Identify the polarity and the location for the voltage

Phasor Diagram• Provide the correct magnitudes and phase relations


3.2 Phasors

3.2.5 Nomenclature for Current and Voltage - In the circuit diagramsVoltage

• Vab , Vbc , Vcd or VX , VR , VC

Current and Flux• Is = Iab = Ibc = Icd• Direction : arrow indicator or arbitrary


3.2 Phasors

3.2.6 The Phasor Diagramcurrent, voltage magnitudes and phase relationsOpen Type

• All the phasors originate from a common originClose Type

• The phasors are summed together from left to right for the same series circuit


3.3 Circuit and Phasor Diagrams for A Balanced Three-Phase Power System

A four-wire three-phase systemG or g : the potential of the true earth

A symmetrical or balanced systemCurrents & Voltages :

• Equal in magnitude , 120° apart in phase

No current can flow in the neutralsof the two transformer banks

The delta voltages at fig. 3.3(b)

, , cgcnbgbnagan VVVVVV ===

ancncacnbnbcbnanab VVVVVVVVV - , - , - ===


3.4 Phasor and Phase Rotation

Phasor and Phasoe rotation are two entirely different terms

phasormagnitude and phase

phase rotation or phase sequence IEEE 100-1984 defines

• a,b,c or A,B,C or 1,2,3 or r,s,t


3.5 Polarity

polarity : important in transformer and in protection equipment

3.5.1 Transformer Polarityfundamental rules of transformer polarity

• Current flowing : polarity mark to mark• Voltage drop : polarity to nonpolarity

(a) subtractive polarity(b) additive polarity


3.5 Polarity

3.5.1 Transformer PolarityCT polarity marking

• Note : direction of secondary current isthe same independent of the polarity marks

ANSI/IEEE standard for transformer states • High-voltage should lead low-voltage by 30°

with Y-∆ or ∆-Y banks

Fig 3.6(a) : Y leads ∆ by 30 °• Van = VAB , Vbn = VBC , Vcn = VCA

• Van leads phase-A-to-neutral voltage

Fig 3.6(b) : ∆ leads Y by 30 °• Van = VAC , Vbn = VBA , Vcn = VCB

• phase-A-to-neutral leads Van voltage


3.5 Polarity

3.5.2 Relay PolarityPolarity of Relay interaction

• Relay involving interaction have the polarity making that is necessary for their correct operation

Directional Relay operation• If the current flow is in the desired operating direction (trip direction) and its magnitude is

greater than the fault sensor’s minimum operating current (pickup), the relay can operate• If the current is in the opposite direction (non trip), no operation can occur even though the

magnitude of the current is above the pickup threshold current

Phase position• Most system voltages do not change their phase positions during a fault • But, line current can shift around 180 ° during a fault

>> reverse their direction or flow

Reference quantity is Called the “polarizing” quantity

Fig 3.7 Typical directional relay characteristics : adjustments for • 1) the maximum torque angle , 2) the angle limits of operate zone


3.5 Polarity

3.5.2 Relay PolarityFig 3.7A : For phase fault protection

• max. operating torque or energy occurswhen current flow(Ipq) leads Vrs by 30°

• directional unit : operate for current from60° lagging Vrs to 120° leading

Fig 3.7B : For ground fault protection• max. operating torque or energy occurs

when current flow(Ipq) lags Vrs by 60°• directional unit : operate for current from

30° leading Vrs to 150° leading

Fig 3.7C : For power or var applications


3.6 Application of Polarity for Phase-fault Directional Sensing

Connections 4 & 5 have been used almost exclusively :Known as the “90º connection”Difference : the angle that system current lags the system voltage

for maximum-operating torque or energy


3.6.1 The 90º-60º Connection for Phase-Fault Protection

90º connectionVoltage lags current by 90º

• The maximum torque line : 30º leading Vbc , 60º lagging Ia→ The lowest pickup value

highest sensitivity

90º - 60º connection : • a 90º lagging voltage used• max. operation occurs when the phase

current lags in the system by 60º


3.7 Directional Sensing for Ground Faults : Voltage Polarization

Phase A-to-ground fault : A collapse of the faulted-phase voltage( Vag ) with an increase and lag of the faulted-phase current ( Ia )The unfaulted (b,c) phase currents are small and phase-to-ground voltages are uncollapsedIb = Ic = 0 , Ia = 3I0

For ground-fault protection : Used a directional 60º unit ( Fig. 3.7B )current lags in power system by 60ºIt will operate for current from 30ºleading to 150º lagging


3.8 Directional Sensing for Ground Faults : Current Polarization

Flowing the current in the grounded neutral of a wye-delta power :

• Used as a reference or polarizing quantityfor ground-fault protection

Fault Ia current from the CTson the line flows from nonpolarityto polarity on the relay coil

Primary fault In flows up to the neutral of Tr.

Current leads or lags by 90ºfrom the other


3.9 Summary

Phasors and Polarity are essential as useful aids in => the selection, connection, operation, performance

and testing of the protection for all power system

ch 03 phasor

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