ELECTRICAL MACHINES – I

ELECTRICAL & ELECTRONICS ENGINEERING

SINGLE-PHASE TRANSFORMERSSINGLE-PHASE TRANSFORMERSSINGLE-PHASE TRANSFORMERSSINGLE-PHASE TRANSFORMERS

REVIEW ONREVIEW ON

MGIT

DEFINATIONTRANSFORMER IS A STATIC DEVICE WHICH TRANSFERS POWER FROM ONE

CIRCUIT TO ANOTHER CIRCUIT WITHOUT CHANGE IN FREQUENCY USUALLY WITH THE CHANGED VALUES OF VOLTAGES & CURRENTS.

PARTS OF TRANSFORMER

BASED ON THE OPERATION….

ABOUT TRANSFORMER…… A TRANSFORMER DOES NOT CHANGE THE FREQUENCY OF THE SYSTEM, IT

CAN BE TREATED AS CONSTANT FREQUENCY DEVICE.

AS TRANSFORMER TRANSFERS SAME AMOUNT OF POWER FROM ONE CIRCUIT TO ANOTHER CIRCUIT , IT CAN BE TREATED AS CONSTANT POWER DEVICE.

T/F IS A ELECTROMAGNETIC ENERGY CONVERSION DEVICE(IF INTERNAL PROCESS IS CONSIDERED).

T/F CAN BE TREATED AS “PHASE SHIFTING DEVICE” SINCE IT OFFERS DISPLACEMENT OF 180 BETWEEN TWO CIRCUITS.

T/F IS A SINGLY EXCITED DEVICE, SINCE IT REQUIRES ONLY ONE EXTERNAL VOLTAGE SOURCE TO ENRGISE ANY NO. OF WINDINGS PLACED ON IT’S CORE.

AS THE AMOUNT OF FLUX IN THE ORE IS CONSTANT IRRESPECTIVE OF POWER TRANSFER , IT CAN BE TREATED AS “CONSTANT FLUX DEVICE”.

WORKING PRINCIPLE OF A TRANSFORMER

A T/F IS WORKS BASED ON “ FARDAY’S LAWS OF ELECTROMAGNETIC INDUCTION” PRINCIPLE.

“WHEN EVER THERE IS A RELATIVE SPACE (OR) RELAITVE TIME VARIATION BETWEEN MAGNETIC FIELD AND CONDUCTOR THE EMF WILL BE INDUCED IN THAT CONDUCTOR”

BASIC REQIUREMENTS TO GENERATE THE EMF:

MAGNETIC FILED

SET OF CONDUCTORS

RELATIVE SPACE VARIATION(OR) RELAIVE TIME VARIATION

METHODS TO GENERATE EMF

RELATIVE SPACE VARIATION(RSV) :

MAGNETIC FIELD ARE STEADY(OR) TIME

INVARIANT.

SET OF CONDUCTORS ARE BEING MOVED

DNAMICALLY (OR) MOTIONALLY INDUCED EMF EX: GENERATORS

THE DIRECTION OF DYNAMICALLY INDUCED EMF AN BE FOUND BY FRHR

RELAIVE TIME VARIATION(RTV):

MAGNETIC FIELD -- TIME VARYNG

SET OF CONDUCTORS-- STATIONARY

STATICALLY INDUCED EMF EX: TRANSFORMERS

THE DIRECTION OF DYNAMICALLY INDUCED EMF AN BE FOUND BY LENZ’S LAW

Laminated

soft iron core

Primary coil Secondary coil

Input voltage

(a.c.)

Output voltage (a.c.)

How Transformer works

EMF EQUATION OF A TRANSFORMERLet

N1 = Number of turns in primary windings.     N2 = Number of turns in second windings.

Øm  = Maximum flux in the core in Webbers.                                                           Øm = Bm.A,

f = Frequency of A.C input in Hz.

As shown in fig- The flux increases from its zero value to maximum value Øm

  in one quarter of the cycle i.e. in T/4 seconds.

Average rate of change of flux =

1

4 4

Tdt

f

md d

dt

CONT..Now Rate of change of flux per turn means ,the induced e.m.f per turn In volts.  Average e.m.f /per turn = 4f Øm volt.

If flux Øm varies sinusoidally, then r.m.s value of induced .e.m.f is obtained by multiplying the average value with form factor. Form factor =r.m.s value / Average value =1.11

  R.m.s value of e.m.f/turn = 1.11 4 f Øm = 4.44f Øm volt

Now R.m.s value of the induced e.m.f in the whole primary winding. =( induced e.m.f/turn) .* number of primary turns

E1 = 4.44fN1 Øm………………………………………(1)

E1 = 4.44fN1BmA.    (Øm= BmA)

Semelerly, r.m.s value of the e.m.f. induced in secondry is, E2 = 4.44fN2 Øm

E2 = 4.44fN2BmA.    (Øm= BmA)…………..(2) 

CONT…It’s seen from (1) and (2) that E1/N1=E2/N2= = 4.44f Øm.  It means that e.m.f/ turn is the same in both the primary and secondary windings.

SO in ideal Transformer on no-load, V1=E1 and E2=V2

VOLTAGE TRANSFERMATION RATIO:

2 2 2

1 11

4.44

4.

(2)

(1) 44

fN Øm N

fN Ø

Eequ

eq E mu N

SO in ideal Transformer on no-load, V1=E1 and E2=V2

2 2 2

1 1 1

E V NK

E V N

WHERE “ K ” IS CALLED VOLTAGE TRANSFERMATION RATIO CONSTANT

TRANSFORMER ON –NO LOAD

PRACTICLE T/F ON –NO LOAD

TYPES OF TRANSFORMERS

THERE ARE TWO GENERAL TYPES OF TRANSFORMERS. CORE TYPE TRANSFORMERSHELL TYPE TRANSFORMER THESE TWO DIFFER BY THE MANNERTHE WINDINGS WOUND AROUND THE MAGNETIC CORE. INORDER TO REDUCE THE EDDY CURRENT LOSSES THE CORE IS LAMINATED

INORDER TO REDUCE THE CORE LOSSES THE CORE S MANUFACTURED FROM THE COLD ROLLED GRAIN ORIENTED SHEET STEEL (C.R.G.O)

THERE ARE TWO TYPES OF WINDINGS EMPLOYED FOR TRANSFORMERSCONCENTRICINTERLEAVED

CONCENTRIC COILS ARE USED FOR CORE TYPE TRANSFORMERS

INTERLEAVED WINDINGS ARE USED FOR SHELL TYPE TRANSFORMERS.

T/F TYPES

Shell type T/F is used for LV

Core type T/F is used for HV

Toroid T/F are used for LV preferably in energy conversion systems & for LED.

CONSTRUCTION OF A TRANSFORMER CORE

CORE STAGGERING

SHELL TYPE T/F CORE STAGGERING

CORE TYPE TRANSFORMER

STEPPED CORE

SHELL TYPE TRANSFORMER

ECE 441 22

ΦP = net flux in window of primary ΦS = net flux in window of secondary

Φlp = leakage flux of primary Φls = leakage flux of secondary

ΦM = mutual flux

ΦP = ΦM + Φlp

ΦS = ΦM – Φls

EFFECT OF LEAKAGE FLUXES IN THE TRANSFORMER

PHASOR DIAGRAM OF A T/F WITH LAGGING PF

PHASOR DIAGRAM OF A T/F WITH LEADING PF

PHASOR DIAGRAM OF A T/F WITH UNITY PF

AB AC AD

AB AC AD

GRAINS DIRECTION AT DIFFERENT POINTS

EQUIVALENT RESISTANCE IN A T/F:

2 2 12 2 1 2

21 22 22

1

1 22 2

I R I R

IR R

I

RR

K

IN ORDER TO TRANSFER RESISTNCE FROM ONE SIDE TO ANOTHER SIDE THE POWER LOSS SHOULD BE SAME.

SECONDARY TO PRIMARY:

101 1 2

201 1 2

R R R

RR R

K

PRIMARY TO SECONDARY :

2 2 11 1 2 1

21 11 12

2

1 21 1

I R I R

IR R

I

R K R

102 2 1

202 2 1

R R R

R R K R

LEAKAGE FLUX IN A T/F

EQUIVALENT CIRCUIT OF A TRANSFORMER

EQUIVALENT REACTANCE IN A T/F:

IN ORDER TO TRANSFER REACTANCE FROM ONE SIDE TO ANOTHER SIDE THE PER UNIT DROP SHOULD BE SAME.

12 2 1 2

2

1 2 12 2

1 2

1 22 2

1

I X I X

E E

I EX X

I E

XX

K

101 1 2

201 1 2

X X X

XX X

K

SECONDARY TO PRIMARY:

NOW TOTAL IMPEDANCE REFERRED TO PRIMARY SIDE IS :

2 201 01 01Z R X

PRIMARY TO SECONDARY :

11 1 2 1

1 2

1 1 21 1

2 1

1 21 1

I X I X

E E

I EX X

I E

X K X

102 2 1

202 2 1

X X X

X X K X

NOW TOTAL IMPEDANCE REFERRED TO SECONDARY SIDE IS :

2 202 02 02Z R X

EXACT EQUIVALENT CIRCUIT OF A T/F WITH SECONDARY PARAMETERS REFERRED TO PRYMARY

APPROXIMATE EQUI CKT

EQUIVALENT CIRCUIT OF A T/F WITH PRYMARY PARAMETERS REFERRED TO SECONDARY

EFFECIENCY OF A T/F:The ratio of power output to power input of a T/F is called its efficiency (η).

Due to the losses in a transformer, its output power is less than the input power.

∴ Power output = Power input – Total losses ∴ Power input = Power output + Total losses = Power output + Pi + PCu

GENERALLY EFFICIENCY CAN BE EXPRESSED IN %

EFFICIENCY OF A T/F AT ANY LOAD X IS GIVEN BY

WHERE IS CALLED VA RATING OF THE TRANSFORMER 2 2FLV I

CONT…..

CONDITION FOR MAXIMUM EFFICIENCY IN A T/F:

During working of a transformer at constant voltage and frequency, its efficiency varies with the load. Its efficiency increases as the load increases. At a certain load, its efficiency becomes maximum. If the transformer is further loaded, its efficiency starts decreasing.

To determine the condition of maximum efficiency, let us assume that the power factor of the load remains constant and the secondary terminal voltage (V2) is constant. Therefore, efficiency becomes only a function of load current (I2).For maximum efficiency

CONT..

22 02iP I R i cuP P

TO ACHIEVE THE MAXIMUM EFFICIENCY IN A T/F THE COPPER LOSSES(VARIABLE LOSSES) SHOULD BE EQUAL TO IRON LOSSES(CONSTANT LOSSES)

AT THAT CONDITION LOAD CURRENT IS GIVEN BY

202

iPIR

ALL DAY EFFICIENCY The ratio of output in watts to input in watts is called commercial efficiency of a

transformer.

. Distribution transformers are used for supplying lighting and general networks.

In Distribution transformers Core loss occurs through out the day. Copper loss occurs only when they are loaded and hence is less important.

To judge their performance, all-day efficiency (or) operational efficiency is calculated.

The all-day efficiency is defined by

The all-day efficiency is less than the commercial efficiency of a transformer.

CONSTRUCTIONAL & DESIGN DEFFERENCES B/W POWER T/F & D.T/F

POWER TRANSFORMER DISTRIBUTION TRANSFORMER > 33 KV <33KV

Consumers are not directly connected Consumers are directly connected

Load fluctuations are Less Load Fluctuations are More

Fully loaded through out 24 hours Loaded based on load cycle of consumers

Cu losses & core losses takes place Cu losses load cycle of consumer & core losses takes place for 24 hrs

Cu loss are kept min while designing Core losses are kept min while designing

CRGO steel Amorphous steel

Specific weight less Specific weight more

Avg load on PT/F is nearer to full load Avg load on D.T/F is 70-75 % of full load

Max. effi will occur at nearer to full load Max. Effi will occur at 70-75 % of full load

Full load cu loss = core losses Full load cu loss= 2* core loss

Power efficiency All day efficiency

LOSSES IN A T/F

CORE LOSSESCOPPER LOSSES

EFFECT OF VOLTAGE & FREQUENCY ON CORE LOSSES

It is known that for a transformer,

                 V = 4.44 f Φm  N = 4.44 f Bm  A N Where        A = area...                Bm   α   (V/f)                         .......... For constant A and N

CONDITIONS

HYSTERISIS LOSS EDDDY CURRENT LOSS

CORE LOSS

‘f’ is Decreased Hysteresis losses increases

Eddy current Losses Constant

As hysteresis losses increases core losses

Increases

‘v’ is DecreasedHysteresis losses

DecreasesEddy current

Losses Decreases Core losses Decreases

maxx

hW B fv 2 2 2maxeW KB f t i h eW W W

tanv

cons tf

h

h

w f

w Af

2

2

e

e

W f

W Bf

2iW Af Bf

tanv

cons tf

1.6

0.6h

vw A

f 2

eW Bv1.6

20.6i

vw A Bv

f

CONT……

VOLTAGE REGULATION OF A T/F

THE CHANGE IN VOLTAGE FROM NO-LOAD TO FULL LOAD IS CALLED VOLTAGE REGULATION

FOR LAGGING PF

VOLTAGE REGULATION CURVE

KAPP VOLTAGE REGULATION DIAGRAM

DRAWING ALGORITHMIn order to create the diagram it is necessary to know the equivalent

reactance X02 and resistance R02 of the transformer as referred to the secondary side.

The following algorithm should be used:

Draw phasor OL representing secondary terminal voltage V2 on load. Draw OX representing the phase of the secondary current at an angle Φ2 to

OL such that cosΦ2 is the power factor of the load. Draw phasor LM (I2 R02 - voltage drop on resistance referred to the secondary

side) parallel to OX, and then MN (I2 X02 - voltage drop on reactance referred to the secondary side).

The resulting NL is the total voltage drop. Transfer the impedance triangle NLM to OO'P which gives O'L = ON = 0V2.

Therefore, for given secondary current the locus of N is a circle with centre O and radius 0V2, while the locus of L has the same radius but with the centre O'

To find the voltage drop on full load at any power factor the radius OQS should be drawn at at angle Φ to OX. If the impedance triangle is drawn in position UQT then OU = OS. The length of QS represents the voltage drop