EKT 451EKT 451CHAPTER 1CHAPTER 1

SHAIFUL NIZAM MOHYARUNIVERSITI MALAYSIA PERLIS

SCHOOL OF MICROELECTRONIC ENGINEERING

1.0 Transformer

Introduction to Transformer. Applications of Transformer. Types and Constructions of Transformers. General Theory of Transformer Operation. The Ideal Transformer. Real Single-Phase Transformer. The Exact Equivalent Circuit of a Real Transformer. The Approximate Equivalent Circuit of a Transformer. Transformer Voltage Regulation and Efficiency. Open Circuit and Short Circuit. Three Phase Transformer.

The Power Grid

Diagram courtesy howstuffworks.com

Power Grid

Generator0.5 – 5kV

Step-up Transformer

Step-down Transformer

Step-down Transformer

Step-down Transformer

Step-down Transformer

Generator0.5 – 5kV

Step-up Transformer

Power Plants

Intertie

Substation

120/240V residential

3-phase industrial

4-15 kV

35-70 kV100-750 kV

Transmission Tower

Substation

Utility Pole Carrying Three Phase

1.1 Introduction to Transformer. Transformer is a device

that changes ac electrical power at one voltage level to ac electric power at another voltage level through the action of magnetic field.

Figure 1.1 is the block diagrams of; (a) transformer,(b) electric motor(c) generator.

Figure 1.1: Block Diagrams of Transformer, an Electric Motor and a Generator.

Figure 1.2(a) A 500 MVA Power Transformer. (left)

(b) A Pole-Mount 15 kVA Distribution Transformer. (right) (Courtesy of ABB)

1.2 Applications of Transformer.Why do we need transformer ?(a)Step Up. Step up transformer, it will decrease the current to

keep the power into the device equal to the power out of it.

In modern power system, electrical power is generated at voltage of 12kV to 25kV. Transformer will step up the voltage to between 110kV to 1000kV for transmission over long distance at very low lost.

(b) Step Down. The transformer will stepped down the voltage to

the 12kV to 34.5kV range for local distribution in the homes, offices and factories as low as 120V (America) and 240V (Malaysia).

1.3 Types and Constructions of Transformer.

Power transformers are constructed on two types of cores;

(i) Core form.(ii) Shell form.

Figure 1.3: Core Form and Shell Form.

A) Core type B) Shell type

Core form. The core form construction consists of a simple rectangular laminated piece of steel with the transform winding wrapped around the two sides of the

rectangle.

Shell form. The shell form construction consists of a three-legged

laminated core with the winding wrapped around the center leg.

In both cases the core is constructed of thin laminations electrically isolated from each other in order to minimize eddy current. The coils are usually not directly connected. The common magnetic flux present within the coils connects the coils.

Construction. Transformer consists of two or more coils of wire

wrapped around a common ferromagnetic core. The coils are usually not directly connected.

The common magnetic flux present within the coils connects the coils.

There are two windings;(i) Primary winding (input winding); the winding that is

connected to the power source.(ii) Secondary winding (output winding); the winding

connected to the loads.

Figure 1.4: A Simple Transformer.

Operation.

When AC voltage is applied to the primary winding of the

transformer, an AC current will result iL or i2 (current at

load).

The AC primary current i2 set up time varying magnetic

flux in the core. The flux links the secondary winding of the transformer.

Operation. From the Faraday law, the emf will be induced in the

secondary winding. This is known as transformer action.

The current i2 will flow in the secondary winding and

electric power will be transfer to the load. The direction of the current in the secondary winding is

determined by Len’z law. The secondary current’s direction is such that the flux produced by this current opposes the change in the original flux with respect to time.

Cont’d…

FARADAY’S LAW

In 1831 two people, Michael Faraday in the UK and Joseph Henry in the US performed experiments that clearly

demonstrated that a changing magnetic field produces an induced EMF (voltage)

that would produce a current if the circuit was complete.

If current produces a magnetic field, why can't a magnetic field produce a

current ?

Michael Faraday

1.4 General Theory of Transformer Operation.

When the switch was closed, a momentary deflection was noticed in the galvanometer after which the current returned to zero.

When the switch was opened, the galvanometer deflected again momentarily, in the other direction. Current was not detected in the secondary circuit when the switch was left closed. 

Faraday found that the induced e.m.f. increases if (i) the speed of motion of the magnet or coil increases.(ii) the number of turns on the coil is made larger.(iii) the strength of the magnet is increased.

An e.m.f. is made to happen (or induced) in a conductor (like a piece of metal) whenever it 'cuts' magnetic field lines by moving across

them. This does not work when it is stationary. If the conductor is part of a complete circuit a

current is also produced.

Faraday’s Law

E = Electromagnetic force (emf)Φ = FluxN = Number of turnt = time

Any change in the magnetic environment of a coil of wire will cause a voltage (emf) to be "induced" in the coil. No matter how the change is produced, the voltage will be generated.

The change could be produced by changing the magnetic field strength, moving a magnet toward or away from the coil, moving the coil into or out of the magnetic field, rotating the coil relative to the magnet, etc.

ΔtNE

Inserting a magnet into a coil also produces an induced voltage or current.

The faster speed of insertion/ retraction, the higher the induced voltage.

According to the Faraday’s law of electromagnetic induction, electromagnetic force (emf’s) are induced in N1

and N2 due to a time rate of change of M,

(1.1)

where

e = instantaneous voltage induced by magnetic field (emf),

= number of flux linkages between the magnetic field and the electric circuit.

= effective flux

dt

dN

dt

de

dt

dNe

22 ;11

dt

dNe

Figure 1.5: Basic Transformer Components.

Lenz’s Law states that the direction of e1 is such to produce a current that opposes the flux changes.

If the winding resistance is neglected, then equation (1.1) become;

(1.2)

Taking the voltage ratio in equation (1.2) results in,

(1.3)

);(111 dt

dNev

)(222 dt

dNev

2

11

2 e

e

N

N

Cont’d…

Neglecting losses means that the instantaneous power is the same on both sides of the transformer;

(1.4)

Combining all the above equation we get the equation (1.5) where a is the turn ratio of the transformer.

(1.5)

a > 1 Step down transformer a < 1 Step up transformer a = 1 Isolation Transformer

Cont’d…

2211ieie

1

2

2

1

2

1

i

i

v

v

N

Na

The flux varies sinusoidally such that;

The rms value of the induce voltage is;

)2sin( max ftdt

dN

dt

dNe

maxmax

44.42

fN

NE

max

= max sin t

Losses are composed of two parts;(a) The Eddy-Current lost. (b) The Hysteresis loss.

Eddy current lost is basically loss due to the induced current in the magnetic material. To reduce this lost, the magnetic circuit is usually made of a stack of thin laminations.

Hysteresis lost is caused by the energy used in orienting the magnetic domains of the material along the field. The lost depends on the material used.

Figure 1.5: A Magnetic Hysteresis or B-H Curve of Core Steel.

Example 1: Transformer.

How many turns must the primary and the

secondary windings of a 220 V-110 V, 60 Hz

ideal transformer have if the core flux is not

allowed to exceed 5mWb?

1.5 The Ideal Transformer.

An Ideal transformer is a lossless device with an input winding and an output winding.

Zero resistance result in zero voltage drops between the terminal voltages and induced voltages

Figure 1.6 shows the relationship of input voltage and output voltage of the ideal transformer.

Figure 1.6: An Ideal Transformer and the Schematic Symbols.

The relationship between voltage and the number of turns.

Np , number of turns of wire on its primary side. Ns , number of turns of wire on its secondary side. Vp(t), voltage applied to the primary side.

Vs(t), voltage applied to the secondary side.

where a is defined to be the turns ratio of the transformer.

aN

N

tv

tv

s

p

s

p )(

)(

The relationship between current into the primary side, Ip(t), of transformer versus the secondary side, Is(t), of the transformer;

In term of phasor quantities; - Note that Vp and Vs are in the same phase angle. Ip

and Is are in the same phase angle too. - the turn ratio, a, of the ideal transformer affects the magnitude only but not the their angle.

)()( tINtIN sspp atI

tI

s

p 1

)(

)(

aV

V

s

p aI

I

s

p 1

The dot convention appearing at one end of each winding tell the polarity of the voltage and current on the secondary side of the transformer.

If the primary voltage is positive at the dotted end of the winding with respect to the undotted end, then the secondary voltage will be positive at the dotted end also. Voltage polarities are the same with respect to the doted on each side of the core.

If the primary current of the transformer flow into the dotted end of the primary winding, the secondary current will flow out of the dotted end of the secondary winding.

1.5.1 Power in an Ideal Transformer.

Power supplied to the transformer by the primary circuit is given by ;

where, qp is the angle between the primary voltage and the primary current.

The power supplied by the transformer secondary circuit to its loads is given by the equation;

where, qs is the angle between the secondary voltage and the secondary current.

Voltage and current angles are unaffected by an ideal transformer , qs – qs = q. The primary and secondary windings of an ideal transformer have the same power factor.

sssout IVP cos

pppin IVP cos

The power out of a transformer;

Apply Vs= Vp/a and Is= aIp into the above equation gives,

The output power of an ideal transformer is equal to the input power.

The reactive power, Q, and the apparent power, S;

In term of phasor quantities; Note that Vp and Vs are in the same phase angle. Ip and

Is are in the same phase angle too. The turn ratio, a, of the ideal transformer affects the

magnitude only but not the their angle.

cosssout IVP

inppout

pp

out

PIVP

aIa

VP

cos

cos)(

outssppin

outssppin

SIVIVS

QIVIVQ

sinsin

Example 2: Ideal Transformer.

Consider an ideal, single-phase 2400V-240V transformer.

The primary is connected to a 2200V source and the secondary

is connected to an impedance of 2 W < 36.9o,find,(a) The secondary output current and voltage.(b) The primary input current.(c) The load impedance as seen from the primary side.(d) The input and output apparent power.(e) The output power factor.