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Transcript of Transformer 2W2

• 2

• E.m.f. equation of transformer2

m

m

mm

mmm

mmm

m

fNEfNE

NfNfEsmrNfNE

tEtNtdtdNe

tdtdNde

==

==

==

===

=

=

22

11

44.444.4

44.42

2...

2

coscos)sin(

sin

pi

pi

• Ideal Transformer

Conditions for the ideal transformer.a) no leakage fluxb) all core losses (both hysteresis and eddy) are zero

c) the windings have zero resistanced)the permeability of the core is infinite ( the exciting current is negligible)

1

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• 5Ideal Transformer Relation between current that flows in the primary

winding, ip(t) and current that flows in the secondary winding, is(t):

atiti

tiNtiN

S

P

SSPP

1)()(

)()(

=

=

aII

aVV

S

P

S

P

1=

=(2)

(3)

(4)

(5)

• 6Transformer Impedance Primary Impedance:

Primary Voltage:

Primary Current:

Primary impedance in terms of secondary impedance

P

PL I

VZ ='

SP aVV =

a

II SP =

LL

S

S

S

S

P

PL

ZaZIV

aaI

aVIVZ

2

2

'

/'

=

===

(15)

(16)

(17)

(18)

• 7Example 1

A transformer coil possesses 4000 turns and links an ac flux having a peak value of 2 mWb. If the frequency is 60 Hz, calculate the effective value of the induced voltage E.

Ans: 2131V

• 8Example 2

A coil having 90 turns is connected to a 120V, 60 Hz source. If the effective value of the magnetizing current is 4 A, calculate the following:

a. The peak value of fluxb. The peak value of the mmfc. The inductive reactance of the coild. The inductance of the coil.

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Equivalent Circuit a) referred to primary side b) referred to secondary side

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Approximate equivalent circuit

Approximate equivalent circuit c) Referred to primary side (no exicitation) d) Referred to secondary side (no excitation).

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Example 3A not-quite-ideal transformer having 90 turns on the primary

and 2250 turns on the secondary is connected to a 120 V, 60 hz source. The coupling between the primary and the secondary is perfect but the magnetizing current is 4 A. calculate:

a. The effective voltage across the secondary terminalsb. The peak voltage across the secondary terminals.c. The instantaneous voltage across the secondary when the

instantaneous voltage across the primary is 37 V.

Ans: 3000V, 4242 V, 925 V.

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Example 4An ideal transformer having 90 turns on the primary and 2250

turns on the secondary is connected to a 200 V, 50 Hz source. The load across the secondary draws a current of 2 A at a power factor of 80 per cent lagging. Calculate :

a. The effective value of the primary currentb. The instantaneous current in the primary when the

instantaneous current in the secondary is 100 mA.c. The peak flux linked by the secondary winding.

Ans: 50 A, 2.5 A, 10 mWb.

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Example 5Calculate voltage E and current I in the circuit

of Fig. shown below, knowing that the ideal transformer T has a primary to secondary turns ratio of 1;100.

Ans: 800 V, 2 A.

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Determination of transformer parameters: Short Circuit Test

Magnitude of series impedance:

Power factor:

SC

SCSE I

VZ =

SCSC

SC

IVPPF == cos

000

00

=

=

SC

SC

SC

SCSE I

VIVZ

)()( 22 SPSPSEeqeqSE

XaXjRaRZjXRZ

+++=

+=

• 27

Three Phase Transformer Three phase transformer consists of 3 transformers. It is connected independently or in combination of 3

transformers. Primary and secondary windings can be connected as wye

(Y) or delta () Thus, there are 4 types of connections:

Wye wye (Y-Y) Wye delta (Y-) Delta wye (-Y) Delta delta (-)

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3 phase Transformer

3 phase transformer connected independently

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Three Phase Transformer

Three phase transformer connected to a common core with three legs

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Connection Y-Y

Three Phase transformer Y-Y connection

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Transformer Connection Y-Y

aVV

VV

S

P

LS

LP==

33

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Transformer Y- Connection

aVV

VV

VV

LS

LP

S

P

LS

LP

3

3

=

=

• 33

Transformer -Y Connection

aVV

VV

VV

LS

LP

S

P

LS

LP

3

3

=

=

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Transformer - Connection

aVV

VV

S

P

LS

LP==

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