electric power transformers

Electric Power Transformers

Some Images

Core-Type and Shell-Type• In practice, the primary

and secondary windings are wrapped one on top of the other.

• Transformer symbol (note the polarity markings)

Ideal Transformer

• No copper resistance• No core loss• No leakage flux• Infinite core permeability

(i.e., zero reluctance, and infinite inductance)

aNN

VV

s

p

s

p ==

aNN

II

p

s

s

p 1==

sp

windingssppsp

sp

sp

ZaZ

SIVIVSS

QQ

PP

2=

====

=

=

Practical Transformer• A practical transformer has

– Copper resistance– Leakage flux– Finite core permeability

(i.e., finite inductance)– Core loss

• Equivalent circuit model

Simplified Transformer Model

Model referred to primary side (r.t.p.)

Model referred to secondary side (r.t.s)

Approximate Transformer Model

Approximate model referred to primary side (r.t.p)

Approximate model referred to secondary side (r.t.s)

Simplest Transformer Model

Simplest model referred to primary side (r.t.p)

Simplest model referred to secondary side (r.t.s)

Determining the parameters of the transformer model

• Open circuit test (OCT): Apply rated voltage

PVR

QVXPSQVIS cm

2222 ==−==

Determining the parameters of the transformer model

• Short circuit test (SCT): Apply low voltage

2,2,22

IPR

IQXPSQVIS peqpeq ==−==

Per-Unit (pu) System

• Definition:• Common known bases: Vbase and Sbase

• Advantages of pu system:– Eliminates explicit voltage conversion at

every transformer,– pu impedance of a transformer r.t.p or

r.t.s is the same.– pu values fall within very narrow ranges

.,,,,,, ZIVSQPKKKK

base

actualpu ==

base

base

base

basebase

base

basebasebasebasebase S

VI

VZVSISQP

2,, =====⇒

Voltage Regulation

• Because of the transformer series impedance, the secondary voltage varies with the load (when the primary voltage is fixed).

• Phasor diagram:

%100*%100*,

,

,

,,

fls

flsp

fls

flsnls

V

VaV

VVV

VR−

=−

=

seqseqsp IjXIRVa

V++=

Transformer Efficiency

• Efficiency,

• Copper Loss,

• Core Loss,

%100*coscos%100*

)(%100*

ppp

sss

corecuout

out

in

out

IVIV

PPPP

PP

θθη =

++==

seqscu RIP ,2=

c

p

c

p

core RV

aRa

VP

2

2

2

/

)(==

Auto-Transformer• Used when changing the

voltage by small amounts.• No isolation between

primary and secondary sides.

cse

c

H

L

NNN

VV

+=

c

cse

H

L

NNN

II +

=

LLLHHHio IVSIVSS ====

seseccwinding IVIVS ==

se

cse

winding

io

NNN

SS +

=

3-Phase Transformers

• Three independent single-phase transformers

• Three-phase transformer wound on a single three-legged core.

• Possible connections:– Wye-Wye– Wye-Delta– Delta-Wye– Delta-Delta

Wye-Delta and Wye-Wye Connections

aVV

VV

S

P

LS

LP ==φ

φ

33

aVV

VV

S

P

LS

LP 33

==φ

φ

Per-Unit (pu) System in 3-Phase Circuits

• Definition:• Common known bases: VL,base and S3Ф,base

.,,,,,, ZIVSQPKKKK

base

actualpu ==

base

baseL

base

basebase

baseL

basebase

basebasebase

SV

IVZ

VSI

SQP

,3

2,,1

,

,3

,3,3,3

,3

,

φ

φ

φ

φφφ

==

=

==⇒

Transformer Ratings (V, f, S)• Voltage and frequency

ratings:– Prevents winding insulation

from breakdown,– Avoids operation in the deep

saturation region.– Reduction in supply

frequency also causes excessive magnetizing current.

• Apparent power rating sets the limits on the current flow (which controls transformer heating).

Homework

• Problems from Chapter 3: 5, 6, 7, 8, 12, 14, 18, 22.