Modeling of Power

Transformers

A Static Device

Transformers

The transformer enables us to utilize different voltage

levels across the system for the most economical

value.

Stepping up the generator voltage to high voltage, is

done through power transformers to minimize losses

and increase the transmission capacity of the lines.

This transmission voltage level is then stepped down in

many stages for distribution and utilization purposes.

General Theory

A transformer contains two or more windings linked by a mutual field.

The primary winding is connected to an alternating voltage source.

The input current results in an alternating flux whose magnitude depends on the voltage and number of turns of the primary winding.

The alternating flux links the secondary winding and induces a voltage in it with a value that depends on the number of turns of the secondary winding.

Transformers

Basic components of single phase transformer

Laminated iron core

Primary winding

NP

Secondary winding

NS LoadSupply

Transformers

5.2 Single phase transformer arrangement

PrimaryWinding

SecondaryWinding

Multi-layerLaminatedIron Core

X1X

2H1 H2

WindingTerminals

Transformers

Polarity for transformer

0 5 10 15 20100

0

100

Vp t( )

Vs t( )

t

milli s

0 5 10 15 20100

0

100

Vp t( )

Vs t( )

t

milli s

H1

H2

X2

X1

VpVs

H1

H2 X2

X1

Vp Vs

(a) (b)

Transformers

Small transformer construction

a) Lamination b) Iron core with winding

Iron core

Terminals

Secondarywinding

Insulation

Transformers

Dry-type three-phase transformer

Transformers

Oil Insulated and cooled transformer

Winding

Iron corebehind the steel

bar

Radiator

Steeltank

Insulation

Bushing

Power Transformers

Transformation ratio

Primary (supply) Secondary (Load)

Transformers at no load

The no load current I is needed to supply the no load

losses and to magnetize the transformer core.

Im

Ic E1

I

c

E1

I

I

Ic Im

Loaded Transformer

Z2’ is the load impedancereferred to the primary

Transformer losses

The transformer losses are divided into electrical losses

(copper losses) and Magnetic losses (Iron losses).

Copper losses in both the primary and secondary windings.

Magnetic losses, these losses are divided into eddy current

losses and hysteresis losses.

2221

21 RIRI

mhysteriseseddymag IVPPP 1

Equivalent circuit

V1: Primary voltage (supply)I1 : Primary current.V2: Secondary voltage (load)I2: : Secondary current

Exact Circuit

Approximate Circuit

The no load current ranges from 1% to 3% of the full load current.Therefore, the circuit can be simplified to circuit (b).

(a) (b)

Phasor Diagram

)('2

'21 eqeq jXRIVV

Performance Measures

The percent regulation

The transformer efficiency

Voltage Regulation

sincos '2

'2

'21 eqeq XIRIVVVR

Example

A 100-kVA, 400/2000 V, single-phase transformer has the following parameters

R1 = 0.01 R2 = 0.25 ohms

X1 = 0.03 ohms X2 = 0.75 ohms

The transformer supplies a load of 90 kVA at 2000 V and 0.8 PF lagging.

Calculate the primary voltage and current using the simplest equivalent circuit.

Find also the V.R. and efficiency for the transformer