chap 1: transformer 1 lecturers : ms sanna taking ms syarifah norfaezah mr amir razif emt 113/4...

Chap 1: Transformer 1

Lecturers :

Ms Sanna Taking

Ms Syarifah Norfaezah

Mr Amir Razif

Lecturers :

Ms Sanna Taking

Ms Syarifah Norfaezah

Mr Amir Razif

EMT 113/4EMT 113/4ELECTRICAL ELECTRICAL ENGINEERING ENGINEERING TECHNOLOGYTECHNOLOGY

EMT 113/4EMT 113/4ELECTRICAL ELECTRICAL ENGINEERING ENGINEERING TECHNOLOGYTECHNOLOGY


AssessmentsAssessmentsAssessmentsAssessments

(a) Coursework: 50 % (i) 30 % Practical:

- 70 % from Lab Reports.- 30% from Lab Test.

(ii) 20 % :- 15 % from Written Test 1 & Test 2- 5 % from Tutorials, Attendance &

Quizzes.(b) Final Exam: 50 %


Course OutlinesCourse OutlinesCourse OutlinesCourse Outlines

Electrical machines Transformer DC machines AC machines

Instrumentation DC Bridges AC Bridges Sensors and Transducers


List of Experiments

Lab 1 – Lab IntroductionLab 2 - Single Phase Transformer; voltage

and current ratioLab 3 – DC Series MotorLab 4 – Three Phase AC Induction MotorLab 5 – d'Arsonval Galvanometer Lab 6 – The Basic Voltmeter DesignLab 7 – The Wheatstone Bridge Lab 8 - Practical Test


Text BooksText BooksText BooksText Books

Chapman S.J., “Electric Machinery Fundamentals”, Fourth Edition, 2005, McGraw Hill, Singapore.

Z.A. Yamayee & J.L. Bala, “ Electromechanical Energy Devices & Power Systems”, 1994, Wiley & Sons, USA

Bhas S. Guru & Huseyin R. Hiziroglu, “Electric Machinery and Transformers”, 2001, Oxford University Press.

A.K. Sawhney & P.Sawhney, “A Course in Electronic and Electrical Measurement and Instrumentation” Dhanpat Rai & Co. (P) Ltd., 2001.

C.S Rangan, G.R. Sarma & V.S. Mani, “Instrumentation Devices & System” Tata, McGraw-Hill Publishing Company Limited, 2004.


Chapter 1 : TransformerChapter 1 : TransformerChapter 1 : TransformerChapter 1 : Transformer


ContentsContentsContentsContents

Introduction Ideal transformerPractical transformerTransformer equivalent circuit Transformer characteristicsOpen loop test, close loop testIntroduction to 3 phase

transformer


Elements of a Power Transmission and Distribution System.


Why need transformer ?

Power efficiency over a long distance

• Power at high voltage is necessary to decrease the lines losses.

• Power at low voltage is necessary to be used at safe level in home appliances and most equipments.


Introduction: Introduction: What is Transformer ?What is Transformer ?Introduction: Introduction: What is Transformer ?What is Transformer ?

Electrical device that closely related to electrical machines (device that can convert either mechanical energy to electrical energy or vice versa). It converts ac electrical energy at one voltage level to ac electrical energy at another voltage level.

Chapman S.J., “Electric Machinery Fundamentals”

Operates depending on the action of magnetic field.


Introduction Introduction Introduction Introduction

As a conclusion, transformer is a device that changes ac electric energy at one voltage level to ac electric energy at another voltage level through the action of magnetic field.

Similarly for motor and generator as illustrated below


Transformer classificationsTransformer classifications

Step-up transformers connected between the generator and transmission line. permit a practical design voltage for generators an efficient transmission line voltage

Step-down transformers connected between the transmission line and various electrical loads. permit the transmitted power to be used at a safe utilization voltage.


1. The primary winding -the input winding, connected to

an ac power source

2. The secondary winding is the output winding.

3. Consists of two or more coils of wire physically wrapped around the ferromagnetic core.

ConstructionConstruction ConstructionConstruction

1. Primary winding

2. Secondary winding

3. Core


ConstructionConstructionConstructionConstruction

The core is formed of a stack of steel laminations. The steel has a high magnetic permeability and provides a high-

performance path for the flux, which is mutual to the primary and secondary windings.

The core is built up of thin laminations, which are electrically insulated from each other.

Two types of core construction are used:- core type shell-type.

Core type shell type


Operation

AC voltage is applied to the primary winding, result an AC current. The AC primary current i1 sets up a time-varying magnetic flux φ in

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

= max sin t………(1.1)max


Electromagnetic forces (emf’s) are induced in N1 and N2

due to a time rate of change of φM (mutual flux), as

stated by the Faraday’s Law

dt

d

dt

de

Where,e = instantaneous voltage induced by magnetic field (emf) = number of flux linkages between the magnetic field and the electric circuit. = effective flux

The sign depends on Len’z law and the polarity of the circuit terminals.

…………………………(1.2)

Operation


The voltage induced in the primary is nearly equal to the applied voltage, and the voltage at the secondary winding also differs by only a few percent from the voltage induced into that winding.

Thus, the primary-to-secondary voltage ratio is essentially equal to the ratio of the number of turn in the two windings.

2

1

2

1

V

V

N

Na ………………………………(1.3)

According to Faraday’s law, the voltage induced is proportional to the number of the turn in the windings, thus

and ………………….……(1.4)

dt

dNe

11

dt

dNe

22

Operation


);(111dt

dNev )(222dt

dNev

2121 eeNN

…........…..(1.5)

By neglecting the power losses,

Power in primary winding = Power in secondary winding

2211 ieie ……………………………………………………...(1.6)

If the resistance is neglected, eqn (1.2) becomes.

Operation


)2sin( max ftdt

dN

dt

dNe

Substituting equation 1.1 into equation 1.4

Solve for this equation …then the rms value of the induced voltage is given as

maxmax

44.42

fN

NE

f = frequency in hertz ; also known as the emf equation

…………......……..1.7

……………….1.8

Operation


If, a > 1 Step down transformer

a < 1 Step up transformer

a = 1 Isolation Transformer

Where is the turn ratio.a

Combine equations 1.3; 1.4;1.5 and 1.6,

……………………………..............................(1.9)1

2

2

1

2

1

2

1

i

i

e

e

v

v

N

Na

In term of phasor quantities (or rms value), these quantities are

1

2

2

1

2

1

2

1

I

I

E

E

V

V

N

Na …...............

(1.8)

Operation


•If a load is connected to the secondary terminals, a current i2 will flow in the secondary winding and electric power will be transferred to the load.

•The direction of the current in the secondary winding is determined by Lenz’s law. The secondary current’s direction is such that the flux produced by this current opposes the changes in the original flux with respect to time and the flux varies sinusoidally.

Operation


Ideal Transformer

Characteristics of an ideal transformer Windings with zero impedance Lossless Infinite permeability core

Therefore, the efficiency = 100% Zero resistance result in zero voltage drops between the terminal

voltages and induced voltages

v1 = e1 v2 =e2

Sketch of ideal transformer Schematic symbol


Dot convention

• 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.


Transformer Characteristics

Transformer characteristics can be defined by:-

• Efficiency

• Voltage regulation.

Good transformers has high efficiency and low voltage regulation.

Through short circuit and open circuit test, parameter, power loss, efficiency and voltage regulation can be determined


Transformer Characteristics : Efficiency

In practice, the efficiency of a transformer is about 97% or better

Efficiency of a transformer is defined as

= (Output Power /Input Power ) X 100%

For a non-ideal transformer, the output power is less than the input power because of losses.

2 types of losses – Copper losses (winding or I2R losses)

- Core losses (Hysteresis & eddy-current losses )

%100XP

P

in

out

%100XPP

P

lossout

out


%

%

%

%

100

100

100

100

2

2

2

2

2

2

1

1

XPPP

P

XPP

P

XPP

P

XP

PP

CoreCopper

losses

losses

losses

12 PP Ideally,

For non-ideal transformer, losses are considered, therefore

lossesPPP 12

Then,

Transformer Characteristics : Efficiency


Voltage regulation - a measure of the change in the terminal voltage of the transformer with respect to loading.

Defined as

V.R

Transformer Characteristics : Voltage Regulation

1002

22X

V

VV

fullload

fullloadnoload

In calculation of voltage regulation, the equivalent circuit can be referred to primary and secondary side.

Good practice to have a small voltage regulation as possible.

For an ideal transformer, V.R = 0 %


Power in an Ideal Transformer

•The power supplied to the transformer by the primary winding:

where

cos is the power factor

1 = the angle between the primary voltage and the primary current

•The power supplied by the transformer secondary winding:

Where

2 = the angle between the secondary voltage and the secondary current

For an ideal transformer, 1=2 ;same power factor, then

Pin = V1I1 cos 1

Pout = V2I2 cos 2

Pout = Pin


Power in an Ideal Transformer

The reactive power (Q)

The apparent (complex) power (S)

Qout = Qin = V1I1 sin = V2I2 sin (VAR)

Sout = Sin = V1I1 = V2I2 (VA)


Review

Unit transformer – Connected the output of a generator and used to step the voltage up to transmission levels (110kV)

Substation transformer – Connected at the other end of the transmission line which steps the voltage

down from transmission level to distribution levels

(2.3 to 34.5 kV). Distribution transformer – Takes the distribution voltage and steps it

down to the final voltage

(110V, 208V,220V,etc) Special-purpose transformers :

Potential transformer Current transformer


Exercises 1.1

Q1) A transformer has the following parameters; N1= 1000, N2 = 10, I1=200A, V1 = 100kV a) Determine I2 and V2 b) Which type of transformer is this?

Q2) A 250 kVA, 11 000V/400V, 50Hz single-phase transformer has 80 turns on the secondary. Calculate:a) The values of the primary and secondary currentsb) The number of primary turnsc) The maximum value of flux, Фm.

Q3) How many turns must the primary and the secondary windings of a 220 V-110 V, 60Hzideal transformer have if the core flux is not allowed to exceed 5 mWb?

Note: Assume the transformer is ideal for all casesAnswers will be given during class session


Transformer applications Transformer applications

1. Voltage level adjustment (step-up and step-down transformers).

2. Voltage and current measurement.

3. Isolation for safety (isolation transformers)

4. Impedance matching (for maximum power transfer from the source to the load)

The resistance of the load, as seen from the primary-side of the transformer by the source, equal to the internal source resistance. In other words, the objective is to realize: Rin = Rs.


Real, reactive and apparent power in transformer.

S = VI = P ± jQ

S = Apparent power, unit=VA.

P = Average power (also known as real power) , unit = Watt

Q = Reactive power, unit=VAR

Power factor also = ratio between real power and complex power

= P/S

cos

cos

VI

VI


Impedance transformation through the Transformer

L

L

L

I

VZ

S

S

S

S

p

p

L

I

Va

aI

aV

I

VZ 2

/'

2

2

I

V

I

VZ

s

s

L

Impedance - the ratio of the phasor voltage across it to the phasor current flowing through it.

Figure (b): Impedance scaling through a through transformer

Figure (a) Definition of Impedance

LL ZaZ 2'

From the eqn, It is possible to match the magnitude of a load impedance to a source impedance simply by picking proper turns ratio.


Practical transformer For the practical transformer,

The resistances and inductances on the primary and secondary windings

The leakage fluxes exist on both primary and secondary sides. The core experiences eddy current and hysteresis losses The permeability of the core material is finite resulting in a non-

zero reluctance. For a non-ideal/practical transformer, the output power is less than the input power because of losses.

2 types of losses – Copper losses (winding or I2R losses)

- Core losses (Hysteresis & eddy-current losses )

Two components of flux exist:leakage flux - flux links only the primary or secondary winding.mutual flux - links both primary and secondary windings


THE EQUIVALENT CIRCUIT OF A THE EQUIVALENT CIRCUIT OF A TRANSFORMERTRANSFORMER

EXACT EQUIVALENTEXACT EQUIVALENT APPROXIMATE EQUIVALENTAPPROXIMATE EQUIVALENT


Losses in transformer

Copper losses – The resistive heating losses in the primary and secondary windings

Eddy Current Losses - The resistive heating losses in the core of the transformer

Hysteresis losses - Associated with the re-arrangement of the magnetic domains in the core during each half cycle. They are complex, nonlinear function of the voltage applied to the transformer.

Leakage flux – the fluxes at primary and secondary which escape the core and pass through only one of the transformer windings.

These losses that occurred in real transformers are modeled in the transformer model

- Exact Equivalent model- Approximate model


EXACT EQUIVALENT MODEL Under load No-load


Exact Equivalent Model (Under Load)

Ideal Transformer

Copper Losses

Symbol Description

a Turns ratio

E1 E2 Primary and secondary induced voltages

V1 V2 Primary and secondary terminal voltages

I1 I2 Primary and secondary currents

I I0 No load current

r1 x1 Primary winding resistance and reactance

r2 x2 Secondary winding resistance and reactance

Im Xm Magnetizing current and reactance

Ic Rc Core loss current and resistance

Core excitation effect

Self inductance of the coil


No-Load

whereby

Power out = 0 (no load at secondary )

Power in = power out + power loss

Power loss = core loss + Cu loss

Cu = 0 (no load)

Power in = core loss

=Ic2Rc Watt

Exact Equivalent Model (No-Load)


The previous figures are accurate model of a transformer, but to analyze practical circuits

containing transformer, it is necessary to refer to its primary side or to its secondary side

because it is necessary to convert the entire circuit to an equivalent circuit at a single voltage level.


Non-Ideal Transformer with LOAD and Exact Equivalent Model

Referred to the primary

Referred to the secondary


The previous model more complex than necessary…………………..

APPROXIMATE EQUIVALENT

MODELThis model…… The excitation branch has a very small current compared to the load

current of the transformer Negligible voltage drop in R1 and X1

Excitation branch is moved to the front of the transformer Primary and secondary impedance left in series with each other

(impedances just added) creating the following…..


I2/a

Approximate Equivalent Circuits of a Transformer

Refe

rred

to

pri

mary

sid

e

Req_1 = R1 + a2R2

jXeq_1 = X1 +a2X2


Approximate Equivalent Circuits of a Transformer

Req_2 = R1/a2 + R2

jXeq_2 = X1/a2 + X2Refe

rred

to

secon

dary

sid

e

Excitation branch


Exercise 1.2

An ideal, single phase 2400 V-240 V transformer. The primary is connected to a 2200 V source and the secondary is connected to an impedance of 2Ω 36.9°.

a) Find the secondary output current and voltage.b) Find the primary input current.c) Find the load impedance as seen from the primary side.d) Find the input and output apparent powers.e) Find the output power factor.


Open circuit and short circuit test

Why need open circuit test and short circuit test ??? Experimentally determine the values of inductances and resistances in the transformer model.Open circuit test – transformer’s secondary winding is open-circuited - transformer’s primary

winding is connected to a full-rated line voltage.

Note: The open circuit test is conducted by applying rated voltage at rated frequency to one of the windings, with the other windings open circuited. The input power and current are measured. For reasons of safety and convenience, the measurements are made on the low-voltage (LV) side of the transformer.

HVLV


Open Circuit TestIn the open circuit test,• The terminals of the high voltage (HV) side of the transformers are

open circuited.• Full line voltage is applied at the low-voltage (LV) terminals• The input power, input voltage and input current are

measured • Get the power factor of the input current and both magnitude

and angle of the excitation impedance.• From these parameters, the values of RC and Xm is determined by

comparing the following equation.


Assignment #01

Based on the above equation, prove the following;


Short Circuit TestIn short circuit test

• The secondary terminals of the transformer are short-circuited • The primary terminals are connected to a fairly low-voltage

source. The input voltage is adjusted until the current in the short-circuited windings is equal to the rated voltage.

• The input power, voltage and current are again measured


The input voltage is so low – negligible current flows through the excitation branch.

If the excitation current is ignored, then all the voltage drop in the transformer can be attributed to the series elements in the circuit.

Short Circuit Test

Approximate model with no excitation branch;

Referred to primary side


Referred to secondary side


The magnitude and the angle of the series impedance referred to the primary side is

From the equation, the values of Reqp and X eqp is determined by comparing the above equation

Short Circuit Test

Note :

These same tests may also be performed on the secondary side of the transformer if it is convenient to do so.


Short Circuit TestIn short circuit test

• The secondary terminals of the transformer are short-circuited • The primary terminals are connected to a fairly low-voltage

source. The input voltage is adjusted until the current in the short-circuited windings is equal to the rated voltage.

• The input power, voltage and current are again measured


The input voltage is so low – negligible current flows through the excitation branch.

If the excitation current is ignored, then all the voltage drop in the transformer can be attributed to the series elements in the circuit.

Short Circuit Test


Referred to primary side


Referred to secondary side


The magnitude and the angle of the series impedance referred to the primary side is

From the equation, the values of Reqp and X eqp is determined by comparing the above equation

Short Circuit Test

Note :

These same tests may also be performed on the secondary side of the transformer if it is convenient to do so.


Phasor Diagram

What is phasor diagram? A sketch of phasor voltages and currents in the transformer.

Why need it? Easiest way to determine the effect of the impedances and

the current phase angles on the transformer voltage regulation.

It is easy to determine the effect of the impedances and the current phase angles on the transformer voltage regulation by drawing the phasor diagram.

Vs is assumed to be at an angle of 0 degree, and all other voltages and currents are compared to that references.

A transformer phasor diagram is presented by applying Kirchhoff's Voltage law to the transformer equivalent circuit and an equation will be as follows.


Lagging Power Factor

Phasor Diagram

Unity Power Factor

Leading Power Factor


Exercise 1.2

An ideal, single phase 2400 V-240 V transformer. The primary is connected to a 2200 V source and the secondary is connected to an impedance of 2Ω 36.9°.

a) Find the secondary output current and voltage.b) Find the primary input current.c) Find the load impedance as seen from the primary side.d) Find the input and output apparent powers.e) Find the output power factor.


Exercise 1.3

A transformer has the following impedances of a 20-kVA, 8000/240-V, 60Hz transformer is determined. The open circuit test and the short circuit tests are performed on the secondary side of the transformer, and the following data were taken:

a) Sketch the approximate circuit model of the transformer referred to: i) primary voltage level ii) secondary voltage level

b) Find the impedances of the approximate equivalent circuit referred to the primary side and secondary side. c) Sketch the circuit for both cases.


Solution

The transformer model referred to its primary voltage level

The transformer model referred to its secondary voltage level

Q1.2a


Solution

Open circuit test

Short circuit test


Solution

= 192Ω

= 38.4Ω = 159.0 kΩ

= 38.4kΩ


Introduction to Three Phase Transformer


Almost all the major power generation and distribution systems in the world today are three-phase ac system.

Two ways of constructing transformer of three-phase circuit;(i) Three single phase transformers are connected in three-phase bank.



(ii) Make a three-phased transformer consisting of three sets of windings wrapped on a common core.

The three-phased transformer on a common core is preferred because it is lighter, smaller, cheaper and slightly more efficient.



Advantages three phase transformer Less material for the same three phase power and voltage ratings.Smaller/lighter because all connection are made internallyLess cost to manufacture.Less external wiringIt has slightly better efficiency

Disadvantages three phase transformerFailure of one phase puts the entire transformer out of service.




The primary and secondary windings of the three phase transformer may be

independently connected in either a WYE (Y) or DELTA () connectionAs a result, four types of three phase transformers are commonly use. wye-wye (Y-Y) seldom used, imbalance and 3rd harmonics

problems wye-wye-delta (Y-Y-Δ)

frequently used to interconnect high voltage networks (240 kV/345 kV). The delta winding filters the 3rd harmonics, equalizes the unbalanced current, and provides a path for ground current

wye-delta (Y-Δ) frequently used as step down (345 kV/69 kV) delta-delta (Δ-Δ) used for medium voltage (15 kV), one of the

transformers can be removed (open delta) delta-wye (Δ-Y) step-up transformer in a generation station


Faraday’s Law : “the e.m.f (electromotive force) induced between the ends of a loop or coil is proportional to the rate of change of magnetic flux enclosed by the coil; or the e.m.f induced between the ends of a bar conductor is proportional to the time rate at which magnetic flux is cut by the conductor."

Lenz’s Law: "A change in the magnetic flux passing through or linking with, a loop or coil causes e.m.f to be induced in a direction to oppose any change in circuit conditions, this opposition being produced magnetically when current flows in response to the induced e.m.f’’

A transformer is a device that changes ac electric energy at one voltage level to ac electric energy at another voltage level through the action of magnetic field.

Transformer construction; primary winding, secondary winding and core. The powered inductor in a transformer is called the primary winding. The un-powered inductor in a transformer is called the secondary

winding. For an ideal transformer; efficiency = 100% and V.R=0% Power in an Ideal Transformer ;

(S = Apparent power, unit=VA) (P = Average power (also known as real power) , unit = Watt) (Q = Reactive power, unit=VAR)

Review


ReviewTransformer characteristics can be defined by:-

Efficiency Voltage regulation.

Good transformers has high efficiency and low voltage regulation.

Through short circuit and open circuit test, parameter, power loss, efficiency and voltage regulation can be determined

Phasor diagram : sketch of phasor voltages and currents in the transformer.

Power transmission and distribution System ; Unit transformer, substation transformer and distribution transformer.

Special purpose transformers :Potential transformer - Used to measure a high ac voltage. Current transformer (C.T) - used to measure a high ac current

chap 1: transformer 1 lecturers : ms sanna taking ms syarifah norfaezah mr amir razif emt 113/4...

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