EET 103EET 103

TransformerTransformer

Chapter 5Chapter 5

1

A transformer is a device that changes ac electric A transformer is a device that changes ac electric energy at one voltage level to ac electric energy energy at one voltage level to ac electric energy at another voltage level through the action of a at another voltage level through the action of a magnetic field.magnetic field.

Introduction to TransformerIntroduction to Transformer

2

• Transformers are constructed of two coils or more placed around the common freeomagnetic core so that the charging flux developed by one will link to the other.

• The coil to which the source is applied is called the primary coil.

• The coil to which the load is applied is called the secondary coil.

Introduction to TransformerIntroduction to Transformer

3

The most important tasks performed by The most important tasks performed by transformers are:transformers are:

•Changing voltage and current levels in electric power systems.

•Matching source and load impedances for maximum power transfer in electronic and control circuitry.

•Electrical isolation (isolating one circuit from another or isolating DC while maintaining AC continuity between two circuits).

4

5

Mutual Inductance• Mutual inductance exits between coils of the

same or different dimensions.

• Mutual inductance is a phenomenon basic to the operation of the transformer.

6

Mutual Inductance• A transformer is constructed of 2 coils placed so that

the changing flux developed by one will link the other.

• The coil to which the source is applied is called primary• The coil which the load is applied is called secondary.

7

Mutual Inductance (Cont…)

8

9

An ideal transformer is a lossless device with an An ideal transformer is a lossless device with an input winding and output winding. input winding and output winding.

Ideal TransformerIdeal Transformer

aN

N

v

v

s

p

s

p

a = turns ratio of the transformera = turns ratio of the transformer

sspp iNiN

ai

i

s

p 1

10

Power in ideal transformerPower in ideal transformer

coscos ssppoutin IVIVPP

sinsin ssppoutin IVIVQQ

ssppoutin IVIVSS

Where Where is the angle between voltage and current is the angle between voltage and current

11

Impedance transformation through the Impedance transformation through the transformertransformer

The impedance of a device – the The impedance of a device – the ratioratio of the of the phasor voltage across it in the phasor current phasor voltage across it in the phasor current flowing through itflowing through it

L

LL I

VZ

LL ZaZ 2'

12

Non-ideal or actual transformerNon-ideal or actual transformer

Mutual flux

13

Losses in the transformerLosses in the transformer

• Copper (I2R) losses: Copper losses are the resistive heating in the primary and secondary windings of the transformer. They are proportional to the square of the current in the windings.

• Eddy current losses: Eddy current losses are resistive heating losses in the core of the transformer. They are proportional to the square of the voltage applied to the transformer.

14

• Hysteresis losses: Hysteresis losses are associated with the arrangement of the magnetic domain in the core during each half cycle. They are complex, nonlinear function of the voltage applied to the transformer.

• Leakage flux: The fluxes ΦLP and ΦLS which escape the core and pass through only one of the transformer windings are leakage fluxes. These escaped fluxes produce a self inductance in the primary and secondary coils, and the effects of this inductance must be accounted for.

Losses in the transformerLosses in the transformer

15

Transformer equivalent circuitTransformer equivalent circuit

EEpp = primary induced voltage = primary induced voltage EEss = secondary induced voltage = secondary induced voltage

VVpp = primary terminal voltage = primary terminal voltage VVss = secondary terminal voltage = secondary terminal voltage

IIpp = primary current = primary current IIss = secondary current = secondary current

IIee = excitation current = excitation current IIMM = magnetizing current = magnetizing current

XXMM = magnetizing reactance = magnetizing reactance IICC = core current = core current

RRCC = core resistance = core resistance RRpp = resistance of primary winding = resistance of primary winding

RRss = resistance of the secondary winding = resistance of the secondary winding XXpp = primary leakage reactance = primary leakage reactance

XXss = secondary leakage reactance = secondary leakage reactance

Ie

ImIc

16

Dot conventionDot convention

1.1. If the primary voltage is positive at the dotted end of If the primary voltage is positive at the dotted end of the winding with respect to the undotted end, then the the winding with respect to the undotted end, then the secondary voltage will be positive at the dotted end secondary voltage will be positive at the dotted end also. Voltage polarities are the same with respect to also. Voltage polarities are the same with respect to the dots on each side of the core.the dots on each side of the core.

2.2. If the primary current of the transformer flows into the If the primary current of the transformer flows into the dotted end of the primary winding, the secondary dotted end of the primary winding, the secondary current will flow out of the dotted end of the secondary current will flow out of the dotted end of the secondary winding.winding.

17

Exact equivalent circuit the actual transformerExact equivalent circuit the actual transformer

a.a. The transformer model referred to primary sideThe transformer model referred to primary side

b.b. The transformer model referred to secondary The transformer model referred to secondary sideside

18

Approximate equivalent circuit the actual Approximate equivalent circuit the actual transformertransformer

a. The transformer model referred to primary side

b. The transformer model referred to secondary side

19

Exact equivalent circuit of a transformer Exact equivalent circuit of a transformer refer to primary siderefer to primary side

Ep = primary induced voltage Es = secondary induced voltageVp = primary terminal voltage Vs = secondary terminal voltageIp = primary current Is = secondary currentIe = excitation current IM = magnetizing currentXM = magnetizing reactance IC = core currentRC = core resistance Rp = resistance of primary winding

Rs = resistance of the secondary winding Xp = primary leakage reactance

Xs = secondary leakage reactance

20

a/III sep

MCe III

ppppp E)jXR(IV

CCp RIE

)jX(IE MMp

)jX//R(IE MCep

Primary sidePrimary side Secondary sideSecondary side

ssssS V)jXR(IE

Lss ZIV

s

p

p

s

s

p

s

p

N

N

I

I

E

E

V

Va

The Equation:The Equation:

21

R pI p X p

V p E p aV s

a 2 R sI s /aa 2 X s

I e

Exact equivalent circuit of a transformer referred to Exact equivalent circuit of a transformer referred to primary sideprimary side

V p /a

aI pR p /a 2 X p /a 2 I s

E p /a = E sV s

R s X s

aI c

R c/a 2X M /a 2

aI m

aI e

Exact equivalent circuit of a transformer referred to Exact equivalent circuit of a transformer referred to secondary sidesecondary side

22

Approximate equivalent circuit of a transformer referred Approximate equivalent circuit of a transformer referred to primary sideto primary side

Approximate equivalent circuit of a transformer referred to Approximate equivalent circuit of a transformer referred to secondary sidesecondary side

Vp/a

aIp

+

-

ReqsIsjXeqs

Rc/a2 jXM/a2 Vs

+

-

Reqs=Rp / a2+Rs

Xeqs=Xp / a2+Xs

Vp

Ip

+

-

ReqpIs/ajXeqp

RcjXM

aVs

+

-

Reqp=Rp+a2Rs

Xeqp=Xp+a2Xs

23

Open circuit testOpen circuit test

Provides magnetizing reactance and core loss Provides magnetizing reactance and core loss resistanceresistance

Obtain components are connected in parallelObtain components are connected in parallel

Parameter determination of the transformerParameter determination of the transformer

24

Experiment SetupExperiment Setup

In the open circuit test, In the open circuit test, transformer rated voltagetransformer rated voltage is applied to the is applied to the primary voltage sideprimary voltage side of the of the transformer with the secondary side left open. transformer with the secondary side left open. Measurements of power, current, and voltageMeasurements of power, current, and voltage are are made on the made on the primaryprimary side. side.

Since the secondary side is open, the input Since the secondary side is open, the input current Icurrent IOCOC is equal to the excitation current is equal to the excitation current

through the shunt excitation branch. Because this through the shunt excitation branch. Because this current is very small, about 5% of rated value, current is very small, about 5% of rated value, the voltage drop across the secondary winding the voltage drop across the secondary winding and the winding copper losses are neglected.and the winding copper losses are neglected.

25

oc

ococ V

IY

ococ

oc

IV

PcosPF

ococ

oc

IV

Pcos 1

MCMC

oc

ococ X

jR

jBGV

IY

11

AdmittanceAdmittance

Open circuit Power FactorOpen circuit Power Factor

Open circuit Power Factor AngleOpen circuit Power Factor Angle

Angle of current always lags angle of voltage by Angle of current always lags angle of voltage by

26

Short circuit testShort circuit test

– Provides combined leakage reactance and Provides combined leakage reactance and winding resistancewinding resistance

– Obtain components are connected in seriesObtain components are connected in series

27

Experiment SetupExperiment Setup

In the short circuit test, In the short circuit test, the secondary side is the secondary side is short circuitedshort circuited and the and the primaryprimary sideside is is connected toconnected to a variable, a variable, low voltage sourcelow voltage source. .

Measurements of power, current, and voltage Measurements of power, current, and voltage are made on the primary side. The are made on the primary side. The applied applied voltagevoltage is adjusted until rated short circuit is adjusted until rated short circuit currents flows in the windings.currents flows in the windings.

This voltage is generally much smaller than the This voltage is generally much smaller than the rated voltage.rated voltage.

28

sc

scsc I

VZ

scsc

sc

IV

PcosPF

scsc

sc

IV

Pcos 1

spspeqeqsc XaXjRaRjXRZ 22

Impedances referred to the primary side Impedances referred to the primary side

Power Factor of the currentPower Factor of the current

Angle Power FactorAngle Power Factor

00

00

sc

sc

sc

scsc I

V

I

VZ

ThereforeTherefore

29

The equivalent circuit impedances of a 20-kVA, The equivalent circuit impedances of a 20-kVA, 8000/240-V, 60-Hz transformer are to be 8000/240-V, 60-Hz transformer are to be determined. The open circuit test and the short determined. The open circuit test and the short circuit test were performed on the primary side of circuit test were performed on the primary side of the transformer and the following data were taken:the transformer and the following data were taken:

Find the impedances of the approximate equivalent circuit referred to the primary side and sketch that circuit

Open- circuit test (on Open- circuit test (on primary)primary)

Short- circuit test (on Short- circuit test (on primary)primary)

Voc = 8000 VVoc = 8000 V Vsc = 489 VVsc = 489 V

Ioc = 0.214 AIoc = 0.214 A Isc = 2.5 AIsc = 2.5 A

Poc = 400 WPoc = 400 W Psc = 240 WPsc = 240 W

30

Voltage Regulation (VR)Voltage Regulation (VR)

The voltage regulation of a transformer is defined The voltage regulation of a transformer is defined as the change in the magnitude of the secondary as the change in the magnitude of the secondary voltage as the current changes from full load to voltage as the current changes from full load to no load with the primary held fixed. no load with the primary held fixed.

%100,

,, XV

VVVR

flS

flSnlS

%100,

,

XV

Va

V

VRflS

flSp

aVV P

S

At no load,At no load,

I s

V p /a

R eq X eq

V s

+

-

+

-

31

V s

I sR eq

jI sX eq

V p /a

I s

Phasor DiagramPhasor Diagram

Lagging power factorLagging power factor

V s I sR eq

jI sX eq

V p /a

I s

Unity power factorUnity power factor 32

I s

V s

I sR eq

jI sX eq

V p /a

Leading power factorLeading power factor

33

EfficiencyEfficiencyThe efficiency of a transformer is defined as the ratio of the The efficiency of a transformer is defined as the ratio of the power output (Ppower output (Poutout) to the power input (P) to the power input (Pinin).).

%100XP

P

in

out

%100XPP

P

lossesout

out

%100cos

cosX

PPIV

IV

corecuss

ss

Pcore = Peddy current + Physteresis

Pcu= Pcopper losses

34

35

PPcu cu = Copper losses are resistive losses in the primary and = Copper losses are resistive losses in the primary and

secondary winding of the transformer core. They are modeled by secondary winding of the transformer core. They are modeled by placing a resistor placing a resistor RRpp in the primary circuit of the transformer and in the primary circuit of the transformer and

resistor resistor RRss in the secondary circuit. in the secondary circuit.

PPCORECORE = Core loss is resistive loss in the primary winding of the = Core loss is resistive loss in the primary winding of the

transformer core. It can be modeled by placing a resistor transformer core. It can be modeled by placing a resistor RRcc in the in the

primary circuit of the transformer.primary circuit of the transformer.

Example Example

A 15 kVA, 2400/240-V transformer is to be tested A 15 kVA, 2400/240-V transformer is to be tested to determine its excitation branch components, to determine its excitation branch components, its series impedances and its voltage regulation. its series impedances and its voltage regulation. The following test data have been taken from the The following test data have been taken from the primary side of the transformerprimary side of the transformer

Open- circuit testOpen- circuit test Short- circuit testShort- circuit test

Voc = 2400 VVoc = 2400 V Vsc = 48 VVsc = 48 V

Ioc = 0.25 AIoc = 0.25 A Isc = 6.0 AIsc = 6.0 A

Poc = 50 WPoc = 50 W Psc = 200 WPsc = 200 W

36

The data have been taken by using the The data have been taken by using the connections of open circuit test and short circuit connections of open circuit test and short circuit testtest

a.a.Find the equivalent circuit of this transformer Find the equivalent circuit of this transformer referred to the high voltage side.referred to the high voltage side.

b.b.Find the equivalent circuit of this transformer Find the equivalent circuit of this transformer referred to the low voltage side.referred to the low voltage side.

c.c.Calculate the full load voltage regulation at 0.8 Calculate the full load voltage regulation at 0.8 lagging power factor and 0.8 leading power lagging power factor and 0.8 leading power factor.factor.

d.d.What is the efficiency of the transformer at full What is the efficiency of the transformer at full load with a power factor of 0.8 lagging? load with a power factor of 0.8 lagging?

37