1Eeng 224

Chapter 12Three Phase Circuits

Huseyin BilgekulEeng224 Circuit Theory II

Department of Electrical and Electronic Engineering Eastern Mediterranean University

Chapter Objectives: Be familiar with different three-phase configurations and

how to analyze them. Know the difference between balanced and unbalanced

circuits Learn about power in a balanced three-phase system Know how to analyze unbalanced three-phase systems Be able to use PSpice to analyze three-phase circuits Apply what is learnt to three-phase measurement and

residential wiring

2Eeng 224

3Eeng 224

Three phase Circuits An AC generator designed to develop a single sinusoidal voltage for each rotation

of the shaft (rotor) is referred to as a single-phase AC generator.

If the number of coils on the rotor is increased in a specified manner, the result is a Polyphase AC generator, which develops more than one AC phase voltage per rotation of the rotor

In general, three-phase systems are preferred over single-phase systems for the transmission of power for many reasons.

1. Thinner conductors can be used to transmit the same kVA at the same voltage, which reduces the amount of copper required (typically about 25% less).

2. The lighter lines are easier to install, and the supporting structures can be less massive and farther apart.

3. Three-phase equipment and motors have preferred running and starting characteristics compared to single-phase systems because of a more even flow of power to the transducer than can be delivered with a single-phase supply.

4. In general, most larger motors are three phase because they are essentially self-starting and do not require a special design or additional starting circuitry.

4Eeng 224

a) Single phase systems two-wire typeb) Single phase systems three-wire type.Allows connection to both 120 V and 240 V.

Two-phase three-wire system. The AC sources operate at different phases.

Single Phase, Three phase Circuits

5Eeng 224

Three-phase Generator The three-phase generator has three induction coils placed 120° apart on the stator. The three coils have an equal number of turns, the voltage induced across each coil will have the same peak value, shape and frequency.

6Eeng 224

Balanced Three-phase Voltages

Three-phase four-wire system

Neutral Wire

A Three-phase GeneratorVoltages having 120 phase difference

7Eeng 224

Balanced Three phase Voltages

a) Wye Connected Source b) Delta Connected Source

a) abc or positive sequence b) acb or negative sequence

0

120

240

an p

bn p

cn p

V V

V V

V V

0

120

240

an p

bn p

cn p

V V

V V

V V

Neutral Wire

8Eeng 224

9Eeng 224

Balanced Three phase Loads

a) Wye-connected load b) Delta-connected load

1 2 3

Conversion of Delta circuit to Wye or Wye to Delta. Balanced Impedance Conversion:

Y

a b c

Z Z Z ZZ Z Z Z

1Z 3 Z3Y YZ Z

A Balanced load has equal impedances on all the phases

10Eeng 224

General Delta to Wye conversion

Delta to Wye Wye to Delta

works the same way for complex impedances

11Eeng 224

Three phase Connections Both the three phase source and the three phase load can be connected either Wye or DELTA.

We have 4 possible connection types.

• Y-Y connection

• Y-Δ connection

• Δ-Δ connection

• Δ-Y connection

Balanced Δ connected load is more common.

Y connected sources are more common.

12Eeng 224

Balanced Wye-wye Connection A balanced Y-Y system, showing the source, line and load impedances.

Source ImpedanceLine Impedance

Load Impedance

13Eeng 224

Balanced Wye-wye Connection

Phase voltages are: Van, Vbn and Vcn.

The three conductors connected from a to A, b to B and c to C are called LINES.

The voltage from one line to another is called a LINE voltage

Line voltages are: Vab, Vbc and Vca

Magnitude of line voltages is √3 times the magnitude of phase voltages. VL= √3 Vp

Line current In add up to zero. Neutral current is zero:

In= -(Ia+ Ib+ Ic)= 0

14Eeng 224

Balanced Wye-wye Connection

Magnitude of line voltages is √3 times the magnitude of phase voltages. VL= √3 Vp

3

0 , 120 ,

30

3 90

3 21

120

0

an p bn p cn p

ab an nb an bn

bc bn cn

ca cn an

p

p

an bn p

V

V V V V V V

V V V V V

V V V

V V V

V

V VV

Line current In add up to zero. Neutral current is zero:

In= -(Ia+ Ib+ Ic)= 0

15Eeng 224

Balanced Wye-wye Connection Phasor diagram of phase and line voltages

= 3 3 3 = 3L ab bc ca

an bn cn p

p an bn cn

V V V V

V V V V

V V V V

16Eeng 224

Single Phase Equivalent of Balanced Y-Y Connection

Balanced three phase circuits can be analyzed on “per phase “ basis..

We look at one phase, say phase a and analyze the single phase equivalent circuit.

Because the circuıit is balanced, we can easily obtain other phase values using their phase relationships.

ana

Y

VI

Z

17Eeng 224

18Eeng 224

Balanced Wye-delta Connection

ABAB

BCBC

CACA

VIZV

IZ

VI

Z

Line currents are obtained from the phase currents IAB, IBC and ICA

3 30

3 30

3 30

a AB CA

b BC AB

c CA BC

AB

BC

CA

I I I

I I I

I

I

I II

I

3

L a b c

p AB BC CA

L p

I I I I

I I I I

I I

Three phase sources are usually Wye connected and three phase loads are Delta connected. There is no neutral connection for the Y-∆ system.

19Eeng 224

Balanced Wye-delta Connection

3Z

Single phase equivalent circuit of the balanced Wye-delta connection

Phasor diagram of phase and line currents

3

L a b c

p AB BC CA

L p

I I I I

I I I I

I I

20Eeng 224

Balanced Delta-delta Connection Both the source and load are Delta connected and balanced.

, ,a AB CA b BC AB c CA BCI I I I I I I I I

, ,BC CAABAB BC CA

V VVI I IZ Z Z

21Eeng 224

Balanced Delta-wye Connection

30

3pV

Transforming a Delta connected source to an equivalent Wye connection Single phase equivalent of Delta Wye connection

22Eeng 224

Chapter 12Three Phase Circuits

Huseyin BilgekulEeng224 Circuit Theory II

Department of Electrical and Electronic Engineering Eastern Mediterranean University

Chapter Objectives: Be familiar with different three-phase configurations and

how to analyze them. Know the difference between balanced and unbalanced

circuits Learn about power in a balanced three-phase system Know how to analyze unbalanced three-phase systems Be able to use PSpice to analyze three-phase circuits Apply what is learnt to three-phase measurement and

residential wiring

23Eeng 224

Power in a Balanced System The total instantaneous power in a balanced three phase system is constant.

2 cos( ) 2 cos( 120 ) 2 cos( 120 )

2 cos( ) 2 cos( 120 ) 2 cos( 120 )

2 cos( )cos( ) cos( 120 )cos( 120 ) cos( 120 )co

AN p BN p CN p

a p b p b p

a b c AN a BN b CN c

p p

v V t v V t v V t

i I t i I t i I t

p p p p v i v i v i

p V I t t t t t

s( 120 )

1cos cos [cos( ) cos( )] Using the identity and simplif

The instantenous power is not function of time.The total power behav

n2

e

yi g

3 cos p p

t

A B A B A B

p V I

s similar to DC power.This result is true whether the load is Y or connected.

The average power per phase .3

cos 3

p p p

pp

pP I

P

V

24Eeng 224

Power in a Balanced System The complex power per phase is Sp. The total complex power for all phases is S.

p p

p p p p p

2p p p p

Complex power for each phas

3 cos

1 1= cos = sin 3 3

S V I

3 3 cos 3 cos

3 3 sin 3 sin

S=3S 3V

e

I 3

p p

p p p p p p p

a b c p p p L L

p p p L L

p

p V I

P p V I Q p V I S V I

P jQ

P P P P P V I V I

Q Q V I V I

I Z

p L

2p

p , , and are

Total

all rm

complex powe

s values, is the load impedance angl

3

3

r

eL

p

L L

VZ

P jQI

VV I

IV

S

25Eeng 224

Power in a Balanced System

Notice the values of Vp, VL, Ip, IL for different load connections.

2p2

p p p

p

p

p L, , and are all rms values, is the load impe

To

da

3S=3S 3V I 3

nce

al c

an3

omplex ower

gle

p

L

pp

L L

V

VI Z

Z

PV

V II

jQI

S

VLVL

VL

Vp Vp

VpIp

Ip Ip

VL

Vp

Ip

VL

VL Vp

Vp

Ip

Ip

Y connected load. Δ connected load.

3L p L pV V I I 3L p L pV V I I

26Eeng 224

Power in a Balanced System

27Eeng 224

Single versus Three phase systems Three phase systems uses lesser amount of wire than single phase systems for the same line voltage VL and same power delivered.

a) Single phase system b) Three phase system

2 2

'2 '2

Wire Material for Single phase 2( ) 2 2 (2) 1.33Wire Material for Three phase 3( ) 3 3

r l rr l r

If same power loss is tolerated in both system, three-phase system use only 75% of materials of a single-phase system

28Eeng 224

29Eeng 224

VL=840 V (Rms)

Capacitors for pf Correction

IL

30Eeng 224

73650 50.68A3 3 840

Without Pf Correction

LL

SIV

31Eeng 224

Unbalanced Three Phase Systems An unbalanced system is due to unbalanced voltage sources or unbalanced load. In a unbalanced system the neutral current is NOT zero.

Unbalanced three phase Y connected load.

Line currents DO NOT add up to zero.

In= -(Ia+ Ib+ Ic) ≠ 0

32Eeng 224

33Eeng 224

Three Phase Power Measurement Two-meter method for measuring three-phase power

34Eeng 224

Residential Wiring

Single phase three-wire residential wiring