EMT 113/4
ELECTRICAL
ENGINEERING
TECHNOLOGY
Lecturers :
Ms Sanna Taking
Ms Syarifah Norfaezah
Mr Amir Razif
Chap 1: Transformer
1
Assessments
(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 %
Chap 1: Transformer
2
Course Outlines

Electrical machines
Transformer
DC machines
AC machines
Instrumentation
DC Bridges
AC Bridges
Sensors and Transducers







Chap 1: Transformer
3
List of Experiments
Lab
Lab
Lab
Lab
Lab
Lab
Lab
Lab
1
2
3
4
5
6
7
8
–
–
–
–
–
–
-
Lab Introduction
Single Phase Transformer; voltage and current ratio
DC Series Motor
Three Phase AC Induction Motor
d'Arsonval Galvanometer
The Basic Voltmeter Design
The Wheatstone Bridge
Practical Test
Chap 1: Transformer
4
Text 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.
Chap 1: Transformer
5
Chapter 1 : Transformer
Chap 1: Transformer
6
Contents
 Introduction
 Ideal transformer
 Practical transformer
 Transformer equivalent circuit
 Transformer characteristics
 Open loop test, close loop test
 Introduction to 3 phase transformer
Chap 1: Transformer
7
Elements of a Power Transmission and Distribution System.
Chap 1: Transformer
8
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.
Chap 1: Transformer
9
Introduction:
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.
Chap 1: Transformer
10
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
Chap 1: Transformer
11
Transformer 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.
Chap 1: Transformer
12
Construction
1. Primary winding
2. Secondary
winding
3. Core
1.
2.
3.
The primary winding -the input winding, connected to
an ac power source
The secondary winding is the output winding.
Consists of two or more coils of wire physically wrapped around the
ferromagnetic core.
Chap 1: Transformer
13
Construction




The core is formed of a stack of steel laminations.
The steel has a high magnetic permeability and provides a highperformance 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
Chap 1: Transformer
shell type
14
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
 = max sin t………(1.1)
Chap 1: Transformer
15
Operation

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
e
d
d

dt
dt
…………………………(1.2)
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.
Chap 1: Transformer
16
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.
a
N1 V 1

N2 V2
………………………………(1.3)
According to Faraday’s law, the voltage induced is proportional to the
number of the turn in the windings, thus
e1 
d
N1
dt
and
e2 
d
N2
dt
Chap 1: Transformer
………………….……(1.4)
17
Operation
If the resistance is neglected, eqn (1.2) becomes.
N 1 e1

N 2 e2
v1  e1  N
d
1(
);
dt
d
v 2  e 2  N 2( )
dt
…........…..(1.5)
By neglecting the power losses,
Power in primary winding = Power in secondary winding
ei ei
1
1
2
2
……………………………………………………...(1.6)
Chap 1: Transformer
18
Operation
Substituting equation 1.1 into equation 1.4
d
d
eN
 N ( max sin 2ft )…………......……..1.7
dt
dt
Solve for this equation …then the rms value of the induced voltage is given as
E
N max
2
 4.44 fN max
……………….1.8
f = frequency in hertz ; also known as the emf equation
Chap 1: Transformer
19
Operation
Combine equations 1.3; 1.4;1.5 and 1.6,
N 1 v1 e1 i 2
a
  
N 2 v 2 e 2 i1
……………………………..............................(1.9)
In term of phasor quantities (or rms value), these quantities are
N 1 V 1 E1 I 2
a


 …...............(1.8)
N 2 V 2 E2 I1
Where
a
is the turn ratio.
If,
a > 1  Step down transformer
a < 1  Step up transformer
a = 1  Isolation Transformer
Chap 1: Transformer
20
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.
Chap 1: Transformer
21
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
Chap 1: Transformer
Schematic symbol
22
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.
Chap 1: Transformer
23
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
Chap 1: Transformer
24
Transformer Characteristics : Efficiency
Efficiency of a transformer is defined as

= (Output Power /Input Power ) X 100%
P

X 100%
P
out
in
In practice, the efficiency of a transformer is about 97% or better
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 )
P

X 100%
P P
out
out
loss
Chap 1: Transformer
25
Transformer Characteristics : Efficiency
P P
Ideally,
2
1
For non-ideal transformer, losses are considered, therefore
P P P
2
1
losses
PP

P
X 100%
P

P P
X 100%
P

P P
X 100%
losses
1
Then,
1
2
losses
2
2
2

losses
P
P P
2
2
Copper
P
Chap 1: Transformer
X 100%
Core
26
Transformer Characteristics : Voltage Regulation
Voltage regulation - a measure of the change in the terminal voltage of
the transformer with respect to loading.
 Defined as

V.R

V2 noload  V2 fullload
V2 fullload
X 100
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 %
Chap 1: Transformer
27
Power in an Ideal Transformer
•The power supplied to the transformer by the primary winding:
where
Pin = V1I1 cos 1
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
Pout = V2I2 cos 2
2 = the angle between the secondary voltage and the secondary current
For an ideal transformer,
1=2 ;same power factor, then
Pout = Pin
Chap 1: Transformer
28
Power in an Ideal Transformer
The reactive power (Q)
Qout = Qin = V1I1 sin  = V2I2 sin  (VAR)
The apparent (complex) power (S)
Sout = Sin = V1I1 = V2I2 (VA)
Chap 1: Transformer
29
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



Chap 1: Transformer
30
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 currents
b) The number of primary turns
c) The maximum value of flux, Фm.
Q3) How many turns must the primary and the secondary windings of a 220 V-110 V,
60Hz ideal transformer have if the core flux is not allowed to exceed 5 mWb?
Note: Assume the transformer is ideal for all cases
Answers will be given during class session
Chap 1: Transformer
31
Transformer applications
1.
2.
3.
4.
Voltage level adjustment (step-up and step-down transformers).
Voltage and current measurement.
Isolation for safety (isolation transformers)
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.
Chap 1: Transformer
32
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

VI cos 
VI
 cos 
Chap 1: Transformer
33
Impedance transformation through the
Transformer
Impedance - the ratio of the phasor
voltage across it to the phasor
current flowing through it.
V
Z 
I
L
L
L
Figure (a) Definition of Impedance
V V
Z  
I I
s
2
s
2
L
V
aV
V
Z'  
a
Figure (b): Impedance scaling through a through transformer
I I /a
I
p
S
2
S
L
From the eqn, It is possible to match the
magnitude of a load impedance to a source
impedance simply by picking proper turns
ratio.
Chap 1: Transformer
p
S
Z'  a Z
S
2
L
L
34
Practical transformer
For the practical transformer,
Two components of flux exist:
leakage flux - flux links only the primary or
secondary winding.
mutual flux - links both primary and
secondary windings
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 )
Chap 1: Transformer
35
THE EQUIVALENT CIRCUIT OF A
TRANSFORMER


EXACT EQUIVALENT
APPROXIMATE EQUIVALENT
Chap 1: Transformer
36
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
Chap 1: Transformer
37
EXACT EQUIVALENT MODEL


Under load
No-load
Chap 1: Transformer
38
Exact Equivalent Model (Under Load)
Ideal Transformer
Self inductance of
the coil
Symbol
Description
a
Turns ratio
E1
E2
Primary and secondary induced voltages
V1
V2
Primary and secondary terminal voltages
Copper Losses
I1
I2
Primary and secondary currents
I
I0
No load current
Core excitation effect
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
Chap 1: Transformer
39
Exact Equivalent Model (No-Load)
No-Load
Power out = 0 (no load at secondary )
Power in = power out + power loss
w
Power loss = core loss + Cu loss h
e
Cu = 0 (no load)
r
e
Power in = core loss
b
=Ic2Rc Watt
y
Chap 1: Transformer
40
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.
Chap 1: Transformer
41
Non-Ideal Transformer with LOAD and Exact Equivalent Model
Referred to the primary
Referred to the secondary
Chap 1: Transformer
42
The previous model more complex than necessary…………………..
APPROXIMATE
EQUIVALENT
MODEL
This 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…..
Chap 1: Transformer
43
Referred to
primary side
Approximate Equivalent Circuits of a Transformer
I2/a
Req_1 = R1 + a2R2
jXeq_1 = X1 +a2X2
Chap 1: Transformer
44
Referred to secondary side
Approximate Equivalent Circuits of a Transformer
Req_2 = R1/a2 + R2
jXeq_2 = X1/a2 + X2
Excitation branch
Chap 1: Transformer
45
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.
Chap 1: Transformer
46
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.
LV
HV
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.
Chap 1: Transformer
47
Open Circuit Test
In 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.
Chap 1: Transformer
48
Assignment #01
Based on the above equation, prove the following;
Chap 1: Transformer
49
Short Circuit Test
In 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
Chap 1: Transformer
50
Short Circuit Test
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.

Approximate model with no excitation branch;
Approximate model with no excitation branch;
Referred to primary side
Referred to secondary side
Chap 1: Transformer
51
Short Circuit Test
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
Note :
These same tests may also be performed on the secondary side of the
transformer if it is convenient to do so.
Chap 1: Transformer
52
Short Circuit Test
In 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
Chap 1: Transformer
53
Short Circuit Test
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.

Approximate model with no excitation branch;
Approximate model with no excitation branch;
Referred to primary side
Referred to secondary side
Chap 1: Transformer
54
Short Circuit Test
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
Note :
These same tests may also be performed on the secondary side of the
transformer if it is convenient to do so.
Chap 1: Transformer
55
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.
Chap 1: Transformer
56
Phasor Diagram
Lagging Power Factor
Unity Power Factor
Leading Power Factor
Chap 1: Transformer
57
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.
Chap 1: Transformer
58
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
the primary side and secondary side.
to
c) Sketch the circuit for both cases.
Chap 1: Transformer
59
Solution
Q1.2a
The transformer model referred to its primary voltage level
The transformer model referred to its secondary voltage level
Chap 1: Transformer
60
Solution
Open circuit test
Short circuit test
Chap 1: Transformer
61
Solution
= 38.4Ω
= 159.0 kΩ
= 192Ω
= 38.4kΩ
Chap 1: Transformer
62
Introduction to Three Phase
Transformer
Chap 1: Transformer
63
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.
Chap 1: Transformer
64
Introduction to Three Phase Transformer
(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.
Chap 1: Transformer
65
Introduction to Three Phase Transformer
Advantages three phase transformer
Less material for the same three phase power and voltage ratings.
Smaller/lighter because all connection are made internally
Less cost to manufacture.
Less external wiring
It has slightly better efficiency
Disadvantages three phase transformer
Failure of one phase puts the entire transformer out of service.
Chap 1: Transformer
66
Introduction to Three Phase Transformer
The primary and secondary windings of the three phase transformer may be
independently connected in either a WYE (Y) or DELTA () connection
As a result, four types of three phase transformers are commonly use.
wye-wye (Y-Y)
wye-wye-delta
(Y-Y-Δ)
wye-delta (Y-Δ)
delta-delta (Δ-Δ)
delta-wye (Δ-Y)
seldom used, imbalance and 3rd harmonics
problems
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
frequently used as step down (345 kV/69 kV)
used for medium voltage (15 kV), one of the
transformers can be removed (open delta)
step-up transformer in a generation station
Chap 1: Transformer
67
Review
 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)
Chap 1: Transformer
68
Review
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
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
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