topic 7 transformers

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Power Systems Analysis ECNG 3012 7-Jan-May 2010

Transformers

! Power Transformers! Regulating transformers

! Measurement transformers

!

Very Efficient ( ~ 100%)

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Transformers

Coils linked by thesame magnetic

flux.

How many coils?

How linked?

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Ideal Transformer

N1 N2

+ +

_ _

e1 e2

i1(t) i2(t)

+

_

+

_

v1

v2 Z2Z’2

V1

V2

E1

E2

N1

N2

= =I1

I2

=N2

N1

Z2 = V2

I2

=N1 N2 V1

I1N1 N2

Z’ 2 =N2

N1

2

Z2

More realistic- Inductances are finite- Not all flux links all windings- Windings have a resistance- Core has some losses

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Real Transformers

N1 N2

+ +

_ _

e1e2

im

Lm

i1(t) i’2(t) i2(t)

Ideal transformer

Real

Transformer

R 1 Ll1 R 2 Ll2

+ +

_ _

v1v2

*Add leakages

*Core loss - hysteresis

- eddy currents

*Winding resistances

*Laminations to

reduce eddy currentloss

R he

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Determining Transformer ModelParameters

! Open Circuit Test" Core loss, Rhe"Magnetizing inductance, Lm

! Short Circuit Test"Winding resistance, R1,R2" Leakage inductance, Ll1, Ll2

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Transformer Equivalent Circuit

Bm

I1 I2

Ideal: N1 /N2 = a

r1 x1

+ +

_ _

V1 V2

a2r2a2

x2

GcI2 /a

aV2

R 1 X1+

_

V1

+

_

V2

Neglect exciting current Add r1 + a2r2

x1+ a2x2

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Three-Phase Transformers

The three-phase transformer can be built by: – the interconnection of three single-phase transformers.

– using an iron core with three limbs.

! The usual connections for three-phase transformers are:

– wye / wye rarely used.

– wye / delta frequently used step down.(345 kV/69 kV).

– delta / delta used medium voltage (15 kV) (open delta).

– delta / wye step up transformer in a generation station.

! For most cases the neutral point is grounded.

! Turn ratio measured line-line voltage primary vs line-line voltagesecondary.

! Power rating is three-phase rating.

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Three-phase Transformer

A B C

a b c

N

VAN

Vab

VB N

Vbc

Vca

VC N

! Each leg has aprimary and asecondary winding.

! The voltages andcurrents are in phase

in the windingslocated on the sameleg.

! The primary phase-to-line voltage generatesthe secondary line-to-

line voltage. Thesevoltages are in phase.

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Three-phase Transformers

A

B

C

?

?

?

Vector group

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Autotransformer

Two types power in the autotransformer

1 . Electromagnetic conversion ( the same asthe conventional transformer )

2 . Electrical conduction.

Advantages :

1 . An autotransformer provides a higher power rating for the same cost

2 . It operates more efficiently since the loses remain the same.

Disadvantages :

Loss of electrical isolation between the high and low voltage sides . Ground

fault can flow easily from one side to the other .

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Tap-Changer

Designed for smalladjustment of voltages(±10%)

1. For control of voltagemagnitude/reactive powerflow : LTC.

2. For control of phaseangle/real power flow: phase

shifter

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Regulating Transformers – Tap Changer

1:t

+

Vi

_

+

V j

_

+

tVi

_

Y

I jIi

Tap changing side

tY t(t-1)Y (1-t)Y

+

Vi

_

+

V j

_

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Three Winding Transformer

Zp Zs

Zt

Z ps

ZstZ pt

t

s p

Zp = ! ( Zps + Zpt – Zst)

Zs = ! ( Zps + Zst – Zpt)

Zt = ! ( Zst + Zpt – Zps)

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Transformer Plate

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topic 7 transformers

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