Electrical engineering

Transformer

presented by,

A.Johny Renoald AP/EEE

Electrical department.

Transformer

An A.C. device used to change high voltage low current A.C. into low voltage high current A.C. and vice-versa without changing the frequency

In brief,

1. Transfers electric power from one circuit to another

2. It does so without a change of frequency

3. It accomplishes this by electromagnetic induction

4. Where the two electric circuits are in mutual inductive influence of each other.

Principle of operation

It is based on principle of MUTUAL INDUCTION. According to which an e.m.f. is induced in a coil when current in the neighbouring coil changes.

Constructional detail : Shell type

• Windings are wrapped around the center leg of a laminated core.

Core type

• Windings are wrapped around two sides of a laminated square core.

Sectional view of transformers

Note: High voltage conductors are smaller cross section conductors than the low voltage coils

Construction of transformer from stampings

Core type

Fig1: Coil and laminations of core type transformer

Fig2: Various types of cores

Shell type

• The HV and LV windings are split into no. of sections

• Where HV winding lies between two LV windings

• In sandwich coils leakage can be controlled

Fig: Sandwich windings

Cut view of transformer

Transformer with conservator and breather

Working of a transformer

1. When current in the primary coil changes being alternating in nature, a changing magnetic field is produced

2. This changing magnetic field gets associated with the secondary through the soft iron core

3. Hence magnetic flux linked with the secondary coil changes.

4. Which induces e.m.f. in the secondary.

Ideal Transformers• Zero leakage flux:

-Fluxes produced by the primary and secondary currents are confined within the core

• The windings have no resistance:

- Induced voltages equal applied voltages

• The core has infinite permeability

- Reluctance of the core is zero

- Negligible current is required to establish magnetic flux

• Loss-less magnetic core

- No hysteresis or eddy currents

Ideal transformer

V1 – supply voltage ; I1- noload input current ; V2- output voltgae; I2- output currentIm- magnetising current; E1-self induced emf ; E2- mutually induced emf

Φ C

vp

ip

P

Np

Φ= Npip/S …….(1)where S is the reluctance

A transformer consists of a core made of laminated iron separated by insulators and a coil of Np turns wound around the core. This coil is supplied with an a.c voltage supply vp which then produces a current ip. Due to this current , a flux Φ is produced which is given by an equation

dt

dN pp

ϕ=v

)(dt

dNp

2p

p iv ×ℜ

=

Since current varied with time , Φ also varied with time. A back electromagnetic force (e.m.f) will be produced which is given by the equation.

Substitute Φ = Npip/S into the above equation , then

……(2)

……(3)

( )dt

2sindNpp

ftv m πΦ=

Φ = Φm sin 2πft

If ip is sinusoidal, the flux produced also sinusoidal, i.e

therefore

vp = NP2πfΦmcos 2πft = NP2πfΦmsin (2πft + π/2)

The peak value = Vpm = NP2πfΦm

and vp is leading the flux by π/2.

mmpm

p f44.4πf2707.02

VV Φ=Φ×== PP NNThe rms value

……(4)

……(5)

……(6)

……(7)

Phasor diagram: Transformer on No-load

Transformer on load assuming no voltage drop in the winding

Fig shows the Phasor diagram of a transformer on load by assuming1.No voltage drop in the winding2.Equal no. of primary and secondary turns

Transformer on load

Fig. a: Ideal transformer on loadFig. b: Main flux and leakage flux in a transformer

Phasor diagram of transformer with UPF load

Phasor diagram of transformer with lagging p.f load

Phasor diagram of transformer with leading p.f load

Equivalent circuit of a transformer

No load equivalent circuit:

Equivalent circuit parameters referred to primary and secondary sides respectively

Contd.,• The effect of circuit parameters shouldn’t be changed while

transferring the parameters from one side to another side

• It can be proved that a resistance of R2 in sec. is equivalent to R2/k2

will be denoted as R2’(ie. Equivalent sec. resistance w.r.t primary) which would have caused the same loss as R2 in secondary,

22

2

2

1

2'2

222

'2

21

k

R

R

=

=

=

RI

I

RIRI

Transferring secondary parameters to primary side

Equivalent circuit referred to secondary side

•Transferring primary side parameters to secondary side

Similarly exciting circuit parameters are also transferred to secondary as Ro’ and Xo’

equivalent circuit w.r.t primary

where

Approximate equivalent circuit

• Since the noload current is 1% of the full load current, the nolad circuit can be neglected

Transformer Tests

Electrical Machines

•The performance of a transformer can be calculated on the basis of equivalent circuit•The four main parameters of equivalent circuit are:

- R01 as referred to primary (or secondary R02)- the equivalent leakage reactance X01 as referred to primary

(or secondary X02)- Magnetising susceptance B0 ( or reactance X0)- core loss conductance G0 (or resistance R0)

•The above constants can be easily determined by two tests- Oper circuit test (O.C test / No load test)- Short circuit test (S.C test/Impedance test)

•These tests are economical and convenient- these tests furnish the result without actually loading the transformer

In Open Circuit Test the transformer’s secondary winding is open-circuited, and its primary winding is connected to a full-rated line voltage.

• Usually conducted on H.V side

• To find

(i) No load loss or core loss

(ii) No load current Io which is helpful in finding Go(or Ro ) and Bo (or Xo )

20

200

20

oc00

20oc

0

0o000

22000m

00wc

000

000

B esusceptanc Exciting &

V

WG econductanc Exciting ;GV W

Y ;YVI

sinI I

cosI I

cos

cosloss Core

GY

V

I

-IIIor

Ior

IV

W

IVW

w

oc

oc

−=

=∴=

=∴=

==

=

=

==

φ

φ

φ

φ

µ

Open-circuit Test

00

00

00

00

V

IB

V

IG

I

VX

I

VR

w

w

µ

µ

=

=

=

=

Short-circuit TestIn Short Circuit Test the secondary terminals are short circuited, and the primary terminals are connected to a fairly low-voltage source

The input voltage is adjusted until the current in the short circuited windings is equal to its rated value. The input voltage, current and power is measured.

• Usually conducted on L.V side• To find

(i) Full load copper loss – to pre determine the efficiency

(ii) Z01 or Z02; X01 or X02; R01 or R02 - to predetermine the voltage regulation

Contd…

201

20101

01

2sc

01

012

sc

X

WR

W losscu load Full

RZ

I

VZ

I

RI

sc

sc

sc

sc

−=∴

=

=

==

Transformer Voltage Regulation and Efficiency

Electrical Machines

The output voltage of a transformer varies with the load even if the input voltage remains constant. This is because a real transformer has series impedance within it. Full load Voltage Regulation is a quantity that compares the output voltage at no load with the output voltage at full load, defined by this equation:

%100down Regulation

%100up Regulation

,

,,

,

,,

×−

=

×−

=

nlS

flSnlS

flS

flSnlS

V

VV

V

VV ( )

( )%100

/down Regulation

%100/

up Regulation

V

Vk noloadAt

,

,

,

,

p

s

xV

VkV

xV

VkV

nlS

flSP

flS

flSP

−=

−=

=

Ideal transformer, VR = 0%.

voltageload-no

voltageload-fullvoltageload-noregulationVoltage

−=

=

1

212 N

NVV

p

s

p

s

N

N

V

V =recall

Secondary voltage on no-load

V2 is a secondary terminal voltage on full load

−

=

1

21

21

21

regulationVoltage

NN

V

VNN

VSubstitute we have

Transformer Phasor Diagram

01/27/15 38Electrical Machines Aamir Hasan Khan

To determine the voltage regulation of a transformer, it is necessary understand the voltage drops within it.



Ignoring the excitation of the branch (since the current flow through the branch is considered to be small), more consideration is given to the series impedances (Req +jXeq).

Voltage Regulation depends on magnitude of the series impedance and the phase angle of the current flowing through the transformer.

Phasor diagrams will determine the effects of these factors on the voltage regulation. A phasor diagram consist of current and voltage vectors.

Assume that the reference phasor is the secondary voltage, VS. Therefore the reference phasor will have 0 degrees in terms of angle.

Based upon the equivalent circuit, apply Kirchoff Voltage Law,

SeqSeqSP IjXIRVk

V++=



For lagging loads, VP / a > VS so the voltage regulation with lagging loads is > 0.

When the power factor is unity, VS is lower than VP so VR > 0.



With a leading power factor, VS is higher than the referred VP so VR < 0


Electrical Machines

For lagging loads, the vertical components of Req and Xeq will partially cancel each other. Due to that, the angle of VP/a will be very small, hence we can assume that VP/k is horizontal. Therefore the approximation will be as follows:

Formula: voltage regulation

leadingfor '-' and laggingfor ''

V

sincos

V

Vregulation %

luesprimary va of In terms

leadingfor '-' and laggingfor ''

V

sincos

V

Vregulation %

valuessecondary of In terms

1

10111011

1

'21

20

20222022

20

220

+

±=

−=

+

±=

−=

where

XIRIV

where

XIRIV

φφ

φφ

Transformer Efficiency

Electrical Machines

Transformer efficiency is defined as (applies to motors, generators and transformers):

%100×=in

out

P

Pη

%100×+

=lossout

out

PP

Pη

Types of losses incurred in a transformer:Copper I2R lossesHysteresis lossesEddy current losses

Therefore, for a transformer, efficiency may be calculated using the following:

%100cos

cosx

IVPP

IV

SScoreCu

SS

θθη

++=

Losses in a transformer

Core or Iron loss:

Copper loss:

Condition for maximum efficiency

Contd.,

The load at which the two losses are equal =

All day efficiency

hours) 24 (kWhin Input

kWhin output

in wattsinput

in wattsput out efficiency commercialordinary

day forall =

=

η

•All day efficiency is always less than the commercial efficiency

Three-Phase Transformers

Three-phase transformer construction.

Construction• A three-phase transformer is constructed by

winding three single-phase transformers on a single core.

• Three-phase transformers are connected in either wye (star) or delta configurations.

• Two or three single-phase transformers can be connected together to deliver three-phase power. This is referred to as a transformer bank.

• This allows greater maintenance and replacement options.

THREE PHASE SYSTEM

BASICS

Line voltage VL= voltage between lines

Phase voltage Vph= voltage between a line and

neutral

THREE PHASE SYSTEM

BALANCED STAR

Line Voltage VL= √3 Vph

Line current IL = Iph

THREE PHASE SYSTEM

BALANCED DELTA

Line Voltage VL= Vph

Line current IL = √3 Iph

THREE PHASE TRANSFORMERS

Almost all major generation & Distribution Systems in the world are three phase ac systems Three phase transformers play an important role in these systems

3 phase transformers can be constructed from

3 single phase transformers

2 single phase transformers

using a common core for three phase windings

3 phase Transformer connections

By connecting three single phase transformers

1. Star- Star connection

2. Delta- Delta connection

3. Star – Delta connection

4. Delta – Star connection

Star- Star connection

This connection satisfactory only in balanced load otherwise neutral point will be shifted.


Advantages

1.Requires less turns per winding ie cheaper Phase voltage is 1/√3 times of line voltage

2.Cross section of winding is large ie stronger to bear stress during short circuit Line current is equal to phase current

3. Less dielectric strength in insulating materials phase voltage is less


Disadvantages1.If the load on the secondary side unbalanced then the shifting of neutral point is possible

2.The third harmonic present in the alternator voltage may appear on the secondary side. This causes distortion in the secondary phase voltages 3. Magnetizing current of transformer has 3rd harmonic component

Delta - Delta connection

This connection is used for moderate voltages


Advantages

1.System voltages are more stable in relation to unbalanced load

2. If one t/f is failed it may be used for low power level i.e.-V connection

3. No distortion of flux ie 3rd harmonic current not flowing to the line wire


Disadvantages

1. Compare to Y-Y require more insulation

2. Absence of star point i.e. fault may severe

Star- Delta connection

Used to step down voltage ie end of transmission line


Advantages1.The primary side is star connected. Hence fewer number of turns are required. This makes the connection economical

2.The neutral available on the primary can be earthed to avoid distortion.

3.Large unbalanced loads can be handled satisfactory.


Disadvantages

1.The secondary voltage is not in phase with the primary. (30 ⁰ phase difference )

2.Hence it is not possible to operate this connection in parallel with star-star or delta-delta connected transformer.

Delta - Star connection

This connection is used to step up voltage ie. Beginning of high tension line

Delta - Star connection

Features

secondary Phase voltage is 1/√3 times of line voltage

neutral in secondary can be grounded for 3 phase 4 wire system

Neutral shifting and 3rd harmonics are there

Phase shift of 30⁰ between secondary and primary currents and voltages

Scott -connection

Parallel operation of two phase transformers

1. The voltage ratio must be the same.

2. The per unit impedance of each machine on its own base must be the same.

3. The polarity must be the same, so that there is no circulating current between the transformers.

4. The phase sequence must be the same and no phase difference must exist between the voltages of the two transformers.

Tap changing transformer

Tap changing transformer• Regulating the voltage of a transformer is a

requirement that often arises in a power application or power system. In an application it may be needed

1. To supply a desired voltage to the load.

2. To counter the voltage drops due to loads.

3. To counter the input supply voltage changes on load.

Electrical engineering

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