Transformers

Transformers

Introduction

A transformer is a magnetically operated machine that can change values of voltage, current, and impedance without a change in frequency.

Transformers are the most efficient machines known. Their efficiencies commonly range from 90% to 99% at full load.

The function of a transformer, as the name implies,

is to transform alternating current energy from one

voltage into another voltage. The transformer has

no rotating parts, hence it is often called a static

transformer.

When energy is transformed into a higher voltage,

the transformer is often called a step-up

transformer but when the case is otherwise it is

called step-down transformer.

Most power transformer operate at constant

voltage i.e., if the power varies , the current varies

while the voltage remains fairly constant.

Applications

A transformers performs many important

functions in prominent areas of electrical

engineering.

In electrical power engineering, the transformer

makes it possible to convert electric power from a

generated voltage of 11kV(as determined by

generator design limitations) to higher values of

132kV, 220kV, 400kV, 500kV, and 765kV thus

permitting transmission of huge amounts of power

along long distances to appropriate distribution

points at tremendous savings in the cost of

transmission lines as well as in power losses.

At distribution points, transformers are used to reduce these high voltages to at a safe level of 400/230V for use in homes, offices etc.

In electric communication, circuits transformers are used for a variety of purposes,

In radio and television circuits .

Also used in telephone circuits, instrumentation circuits and control circuits.

A transformer operates on the principle of mutual inductance, between two (and sometimes more) inductively coupled coils.

A transformer is a device that :

a) Transfers electric power from one circuit to another

b) It does so without change of frequency

c) It accomplishes this by electromagnetic induction. (or mutual induction)

Types

of

Transformers

Type Uses

Power Transformer Transmission and

distribution of electric power.

Auto-transformer Converting voltages within

relatively limits to connect power

systems of different voltages, to

start A.C. motors, etc

Transformer for feeding

installations with static

converters.

Converting A.C .into

D.C.(rectifying) and converting

D.C. to A.C. (inverting)

Type Uses

Testing Transformers Conducting tests at high

and ultra-high voltages.

Power transformers

for special purposes

Furnace, welding etc

Radio Transformers Radio engineering etc

Construction Basic types of construction for transformer cores are:

A. Core type – the primary winding is on one leg of the transformer and the secondary winding is on the other leg.

- The copper virtually surrounds iron core.

-

B. Shell type - the iron surrounds the copper windings.

Cooling Methods

Two types of transformer according to

methods of cooling:

1. Dry type

2. Oil immersed type

Dry type transformers. Small transformers up to 25

kVA size are dry type and have the following

cooling arrangements:

a. Air natural

b. Air blast

Oil immersed transformers. Most transformers are

of this type. The oil provides better insulation than

air as it is a better conductor of heat than air.

Mineral oil is used for this purpose.

Transformer Test

1. Open-circuit or no-load test – conducted

the determine the no-load loss or core

loss.

2. Short –circuit or impedance test –

conducted to find full-load copper loss.

Transformer Losses

1. Iron losses or core losses

2. Copper Losses

Iron or core losses a. Hysteresis loss – since the flux in a transformer core is alternating,

power is required for the continuous reversals of the elementary magnets of which the iron is composed.

Hysteresis Loss = Kh f Bmax 1.6

f = frequency, Hz

Bmax = maximum flux density in core,

Kh = constant

b. Eddy current loss . This is due to the flow

of eddy currents in the core. Thin

laminations, insulated from each other,

reduce the eddy current loss to small

proportion.

Eddy current loss = Kef2Bmax

2

Copper Losses

These losses are due to the ohmic

resistance of the transformer windings.

Total Copper Loss = I12R1 + I2

2R2

Efficiency = OUTPUT

INPUT

= OUTPUT

OUTPUT+LOSSES

ALL-DAY EFFICIENCY

- the ratio of energy(kWh) delivered in a

24 hour period divided by the energy(kWh)

input in the same length of time.

ɲall-day = Output in kWh

Input in kWh (for 24 hours)

Transformer Formulas

The primary winding of a transformer is the

power input winding.

The secondary winding is the load winding, or

output winding. It is the side of the transformer that

is connected to the driven load.

Induced EMF Equation

E = 4.44NfΦm

E = rms voltage induced (volt)

N = number of winding turns

f = frequency in flux (Hertz)

Φm = peak value of the flux (weber)

Equivalent Circuit of Ideal Transformer

E1= 4.44N1f1Φm1

E2 = 4.44N2f2Φm2

E1 N1 I1 N2 1

E2 N2 I2 N1 a

Z1 N1

Z2 N2

a

a2

2

Examples

1. The maximum flux density in the core of a

3000/240-V, 50Hz single-phase

transformer is 1.25 Tesla. If the voltage

induced per turn is 8 volts, determine the

cross sectional of the core in cm2.

2. Calculate the total magnetic flux in a 60-

cycle transformer in which the induced emf

per turn of the winding is equal to 2V.

3. In a 400V, 50 c/s transformer, the total

iron loss is 2500W. When the supply is 220V

at 25 c/s, the corresponding loss is 850 W.

Calculate the eddy current loss at normal

frequency and power delivered.

4. 50 kVA, single-transformer has a full load

copper loss of 600 watts and an iron loss of

500 watts. Calculate the efficiency at 25% of

full load at a power factor of 0.85 lagging.

5. Determine the all day efficiency of a

50kVA distribution transformer having a full

load efficiency of 94% and the full load

copper loss is just equal to the constant iron

loss. The loading is as per the following

schedule at unity power factor; no load for

10 hrs, 25% of full load for 6 hrs, half load

for 5 hrs, and full load for 3 hrs.