Balanced Three Phase System

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Balanced Three-Phase System

EE 103 CIRCUITS 3

by:Cesar G. Manalo, Jr.

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Objectives

Construct the circuit and phasor diagram of a three-

phase system with a balanced wye- and/or delta-

connected load.

Solve for the phase and line current/voltage of a three-phase system with balanced wye- and/or delta-

connected load.

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Balanced Three-Phase Load

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Balanced 3-Phase Loads

A 3-phase load is said to bebalanced, if all phase impedances

(load) are equal, otherwise, they

are unbalanced.

In a Y-connected load, the phaseimpedances or loads are

connected to a common point.

Za

Zc

Zb

3-phase Y-connected

Balanced Load, ZA= ZB= ZC

3-phaserectifier

3-phase induction motor

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Balanced 3-Phase Loads

Za

Zc

Zb

3-phase Y-connectedBalanced Load, Za= Zb= Zc

Va

VbVc

A

B

C

VAB

VBC

VCAn

3-phase Y-connected sourceor generator

Balanced 3-phase 3-wire Y-Y Circuit with Balanced 3-phase source

ZT

ZT

ZT

Transmission line

Za

Zc

Zb

3-phase Y-connected

Balanced Load, Za= Zb= Zc

Va

VbVc

A

B

C

VAB

VBC

VCAn

3-phase Y-connected source

or generatorTransmission line

+-

+

-

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Balanced 3-Phase Loads

Za

Zc

Zb

3-phase Y-connected

Balanced Load, Za= Zb= Zc

Va=VAn

Vb=VBnVc=VCn

A

B

C

VAB

VBCVCA

n

3-phase Y-connected source

or generatorTransmission line

Ia

IbIc

IA

IB

IC

IN Ia

IbIc

Va

Vb Vc

Balanced 3-phase 4-wire Y-Y Circuit with Balanced 3-phase source

+

-

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Illustrative Problem 1

A 3-phase Y-connected load with phase impedance Z = 150 + j270

is connected to the secondary of a Y-connected transformer with a110-V phase voltage. Find,

a) The line voltages

b) Line currents IA, IB, ICassuming V2a= 110

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Illustrative Problem 1

a) Repeat a) if neutral of load is connected to neutral of source.

Za

Zc

Zb

3-phase Y-connected

Balanced Load, Za= Zb= Zc

A

B

C

VAB

VBC

VCA

IA

IB

IC

Ia

Ib Ic

Va

Vb Vc

3-phase transformer

IN

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Per Phase Analysis

Za

ZcZb

3-phase Y-connected

Balanced Load, Za= Zb= Zc

IA

IB

IC

IN = 0 Ia

IbIc

Va

Vb Vc

VAB

VBC

VCA

A

B

C

NZ

a

IA

IN = 0Ia Va

Va=VAB/1.73

A

NPer phase analysis using phase A

Zb

IB Vb

IN = 0

B

N

Vb=VBC/1.73

Ib

Per phase analysis using phase

B

Zc

C

N

VC=VCA/1.73IC

Ic

Vc

Per phase analysis using phase C

n

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Per Phase Analysis

Za

ZcZb

3-phase Y-connected

Balanced Load, Za= Zb= Zc

IA

IB

IC

IN = 0 Ia

IbIc

Va

Vb Vc

VAB

VBC

VCA

A

B

C

N

Za

IA

IN = 0Ia Va

Va=VAB/1.73

A

N

Per phase analysis using phase A

Zb

IB Vb

IN = 0

B

N

Vb=VBC/1.73

Ib

Per phase analysis using phase B

Zc

C

N

VC=VCA/1.73IC

Ic

Vc

Per phase analysis using phase C

n

A per phase analysis can be done on a balanced 3-phase system.

In a balance 3-phase 4-wire system, the magnitude of the current

on the neutral line is zero.

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Illustrative Problem 2

Repeat Illustrative problem # 1 using per phase analysis.

Za

Zc

Zb

3-phase Y-connected

Balanced Load, Za= Zb= Zc

A

B

C

VAB

VBC

VCA

IA

IB

IC

Ia

Ib Ic

Va

Vb Vc

3-phase transformer

impedance Z = 150 + j270

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Illustrative Problem No. 3

a

bc

A

B

C

230 V

N

IA

IB

IC

Ia

IbIc

Z

Z

Z

230 V 230 V

3-phase Alternator

Balance3-phase load,Z : R = 75, XL= 50

A balance 3-phase load is connected to a 3-phase alternator with

line-to-line voltage of 230 volts. Find:a) Load phase currents

b) Load line currents

c) Phasor diagram of phase and line currents.

+

-

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Balanced 3-Phase Loads

A

B

C

230 V

IA

IB

IC

Z

230 V

230 V

Balance3-phase

load,

Z : R = 75, XL= 50

Z

Z

IAB

IBC

ICA

Let:

VAB= 230 30o

VBC= 230 -90oVCA= 230 150

o

14.90)50()75( 22 Z

69.33

75

50tan 1

AIII CABCAB 55.214.90

230

for balance 3-phase load

Since Z is inductive, the load phase currents

will lag the line voltages by 33.69o. Hence,

69.355.2)69.3330(55.2AB

I

69.12355.2)69.3390(55.2BCI

116.3155.2)69.33150(55.2CA

I

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Balanced 3-Phase Loads

69.355.269.333055.2AB

I

69.12355.2)69.3390(55.2BCI

116.3155.2)69.33150(55.2CA

I

33.69o

33.69o

IAB

IBC

ICA

)(CAABCAABA

IIIII

)(ABBCABBCB

IIIII

)(BCCABCCAC

IIIII

IA

IB

IC

33.69o

86.31o

153.69o AI

III

AB

CBA

41.4)55.2(73.173.1

VABVCA120o

120o 120o

VBC

30o

(equal in RMS value but not

in phase)

IA

IB

IC

Z

Balance3-phase load, Z : R = 75, XL= 50

Z

Z

IAB

IBC

ICA

69.33

Vector calculator

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Assignment 1

a

bc

A

B

C

230 V

N

IA

IB

IC

Ia

IbIc

Z

Z

Z

230 V 230 V

3-phase Alternator

Balance3-phase load,

Z = 75+j 50 ZT= 0.3 + j0.4

A balance Y-connected 3-phase load is connected to a 3-phase alternator withline-to-line voltage of 230 volts. Using mesh and per phase methods, find:

a) Load phase currents

b) Load line currents

c) Phasor diagram of phase voltage and phase currents and line currents

Let:

VAB= 230 30o

VBC

= 230 -90o

VCA= 230 150o

+

-

ZT

ZT

ZT

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Power and Power Measurement in

Balanced Three-Phase Load