chap 1: transformer 1 lecturers : ms sanna taking ms syarifah norfaezah mr amir razif emt 113/4...
TRANSCRIPT
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
Chap 1: Transformer 2
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 %
Chap 1: Transformer 3
Course OutlinesCourse OutlinesCourse OutlinesCourse Outlines
Electrical machines Transformer DC machines AC machines
Instrumentation DC Bridges AC Bridges Sensors and Transducers
Chap 1: Transformer 4
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
Chap 1: Transformer 5
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.
Chap 1: Transformer 6
Chapter 1 : TransformerChapter 1 : TransformerChapter 1 : TransformerChapter 1 : Transformer
Chap 1: Transformer 7
ContentsContentsContentsContents
Introduction Ideal transformerPractical transformerTransformer equivalent circuit Transformer characteristicsOpen loop test, close loop testIntroduction to 3 phase
transformer
Chap 1: Transformer 8
Elements of a Power Transmission and Distribution System.
Chap 1: Transformer 9
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 10
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.
Chap 1: Transformer 11
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
Chap 1: Transformer 12
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.
Chap 1: Transformer 13
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
Chap 1: Transformer 14
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
Chap 1: Transformer 15
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
Chap 1: Transformer 16
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
Chap 1: Transformer 17
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
Chap 1: Transformer 18
);(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
Chap 1: Transformer 19
)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
Chap 1: Transformer 20
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
Chap 1: Transformer 21
•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
Chap 1: Transformer 22
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
Chap 1: Transformer 23
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 24
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 25
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
Chap 1: Transformer 26
%
%
%
%
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
Chap 1: Transformer 27
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 %
Chap 1: Transformer 28
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
Chap 1: Transformer 29
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)
Chap 1: Transformer 30
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 31
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
Chap 1: Transformer 32
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.
Chap 1: Transformer 33
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
Chap 1: Transformer 34
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.
Chap 1: Transformer 35
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
Chap 1: Transformer 36
THE EQUIVALENT CIRCUIT OF A THE EQUIVALENT CIRCUIT OF A TRANSFORMERTRANSFORMER
EXACT EQUIVALENTEXACT EQUIVALENT APPROXIMATE EQUIVALENTAPPROXIMATE EQUIVALENT
Chap 1: Transformer 37
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 38
EXACT EQUIVALENT MODEL Under load No-load
Chap 1: Transformer 39
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
Chap 1: Transformer 40
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)
Chap 1: Transformer 41
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 42
Non-Ideal Transformer with LOAD and Exact Equivalent Model
Referred to the primary
Referred to the secondary
Chap 1: Transformer 43
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…..
Chap 1: Transformer 44
I2/a
Approximate Equivalent Circuits of a Transformer
Refe
rred
to
pri
mary
sid
e
Req_1 = R1 + a2R2
jXeq_1 = X1 +a2X2
Chap 1: Transformer 45
Approximate Equivalent Circuits of a Transformer
Req_2 = R1/a2 + R2
jXeq_2 = X1/a2 + X2Refe
rred
to
secon
dary
sid
e
Excitation branch
Chap 1: Transformer 46
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 47
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
Chap 1: Transformer 48
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.
Chap 1: Transformer 49
Assignment #01
Based on the above equation, prove the following;
Chap 1: Transformer 50
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
Chap 1: Transformer 51
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
Approximate model with no excitation branch;
Referred to secondary side
Chap 1: Transformer 52
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.
Chap 1: Transformer 53
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
Chap 1: Transformer 54
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
Approximate model with no excitation branch;
Referred to secondary side
Chap 1: Transformer 55
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.
Chap 1: Transformer 56
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 57
Lagging Power Factor
Phasor Diagram
Unity Power Factor
Leading Power Factor
Chap 1: Transformer 58
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 59
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.
Chap 1: Transformer 60
Solution
The transformer model referred to its primary voltage level
The transformer model referred to its secondary voltage level
Q1.2a
Chap 1: Transformer 61
Solution
Open circuit test
Short circuit test
Chap 1: Transformer 62
Solution
= 192Ω
= 38.4Ω = 159.0 kΩ
= 38.4kΩ
Chap 1: Transformer 63
Introduction to Three Phase Transformer
Chap 1: Transformer 64
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.
Introduction to Three Phase Transformer
Chap 1: Transformer 65
(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.
Introduction to Three Phase Transformer
Chap 1: Transformer 66
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.
Introduction to Three Phase Transformer
Chap 1: Transformer 67
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 () 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
Chap 1: Transformer 68
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
Chap 1: Transformer 69
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