Addis Ababa Science & Technology University
College of Electrical and Mechanical
Engineering
Department of Electromechanical Engineering
Electrical Machines
By: Birhanemeskel A. (MSc in Mechatronics)
1
Magnetics
Course
Outlines
Transformers
2
Chapter-Two
Transformers
➢ Transformer is considered to be a backbone of a power system.
➢ A transformer is an electromagnetic static device that transfers
AC electrical power from one circuit to the other at the same
frequency but the voltage level is usually changed.
3
➢ A transformer is a magnetically operated machine.
➢ The primary winding is connected to the incoming power supply. While,
the secondary winding is connected to the driven load.
➢ This is an isolation transformer. The secondary winding is physically and
electrically isolated from the primary winding.
➢ The two windings of an isolation transformer are linked together by the
magnetic field.
4
➢Based on their function, transformers are divided into:
1. Power transformers
2. Distribution transformers
3. Measuring transformers and
4. Auto-transformers
5
Power Transformer
➢It is a power transformer connected to the output of a generator
and used to step its voltage up to the transmission level.
➢ The term power transformer is used to refer to those transformers used
between the generator and the distribution circuits, and these are usually
rated at 500 kVA and above.
➢ Power transformers are available for step-up operation, primarily used at the
generator and referred to as generator step-up (GSU) transformers, and for
step-down operation, mainly used to feed distribution circuits.
6
Distribution Transformer
➢ Transformers smaller than 500 kVA are generally called distribution
transformers. Pole-top and small, pad-mounted transformers that serve
residences and small businesses are typically distribution transformers.
➢ A step-down transformer receives energy at a higher voltage and delivers it
at a lower voltage for distribution to various loads.
➢The usual consumer voltage requirement is 220v or 400v.
7
Measuring Transformer
B)Current Transformer
A)Voltage Transformer
➢Current transformer is used to
measure high current.
➢ As the name suggests, these
transformers are used in conjunction
with the relevant instruments such as
ammeters, voltmeters, watt meters and
energy meters
Voltage transformers are used where
the voltage of an AC circuit exceeds
750 V as it is not possible to provide
adequate insulation on measuring
instruments for voltage more than this.
8
Autotransformer
➢Transformers having only one winding are called autotransformers,
➢An autotransformer has the usual magnetic core but only one winding, which
is common to both the primary and secondary circuits.
9
Based on the construction of transformers,
a) Shell type transformer
- In this type, the laminated insulated sheet iron core surrounds the copper
windings.
b) Core type transformer.
- In this type, the copper windings surround the laminated sheet iron core.
10
The essential elements of a transformer:
a)Two coils having mutual inductance wound on a laminated steel core.
➢ Many transformers have separate coils and contain many turns of wire .
➢ The winding receiving electrical energy from the source is called the
primary winding.
➢ The winding which receives energy from the primary winding, via the
magnetic field, is called the “secondary” winding.
➢ Either the high/low voltage winding can be the primary or the secondary.
b)The two coils are insulated from each other and magnetic core.
➢ A magnetic circuit or core of a transformer is designed to provide a path for
the magnetic field, which is necessary for induction of voltages between
windings.
➢ Special paper and wood are used for insulation and internal structural
support
11
The essential elements of a transformer:
c) A suitable container for the assembled core and windings.
d) A suitable medium for insulating the core and its windings from
the container.
e) Suitable brushings for insulating and bringing out the terminals of
windings from the container
12
Accessories Of Transformer
Conservator
• This is an expansion tank. It function is to keep the transformer tank full of
oil irrespective whether expansion or contraction of oil take place.
• It mounted above the transformer and connected to the tank by a pipe.
Temperature gauge
• This indicates temperature of the latest oil in the tank. It is connected to an
alarm.
Oil gauge
• This indicates the level of the oil in the tank.
• Sometimes it is provided with the alarm contracts when the oil level falls
down below a minimum level, contacts close and give an alarm.
13
Accessories Of Transformer
Buchholz relay
• It is a gas operated relay. It is located in the pipe connected to the
conservator.
• When the a fault occurs in the transformer gas bubbles are released and
these operate the relay to give an alarm signal.
Breather
• To prevent entry of moisture in to the tank, a breather with silica gel is
provided in the transformer.
• Silica gel absorbs the moisture and allows only dry air to enter the tank
14
Working Principle of transformer
➢ When one coil is connected to a source of a.c voltage an alternating flux
setup in the laminated core, most of which is linked with the other coil in
which it produces mutually induced e.m.f. If the circuit of the second coil
is closed a current flows in it and so electrical energy is transferred entirely
magnetically from the first coil to the second coil.
➢ Hence magnetic flux linked with the secondary coil changes which induces
e.m.f. in the secondary.
15
EMF equation of the transformer
•
The induced e.m.f in a transformer is proportional to the product
of number of turns N and the rate of change of flux.
𝑑∅
𝑒=𝑁
𝑑𝑡
• When sinusoidal voltage is applied to the primary winding of a
transformer, a sinusoidal flux is set up in the iron core which links
with primary and secondary winding.
16
EMF equation of the transformer
• Let:
∅𝑚 = Maximum value of flux in Wb;
𝑓 = supply frequency in Hz (or c/s);
𝑁1 = No. of turns in primary;
𝑁2 = No. of turns in secondary;
• In a quarter cycle i.e,
•
1
4𝑓
𝑠𝑒𝑐, flux changes from 0 𝑡𝑜 + ∅𝑚 .
Average rate of change of flux =
∅𝑚 −0
1
4𝑓
= 4𝑓∅𝑚 𝑊𝑏/𝑠
17
• Now, the rate of change of flux per turn is the average induced emf per turn
in volt.
• Therefore, Average emf induced per turn = 4𝑓∅𝑚 volt
R.M.S. value
• For a sinusoidal wave,
= 𝐹𝑜𝑟𝑚 𝑓𝑎𝑐𝑡𝑜𝑟 = 1.11.
Average value
• The R.M.S value of emf induced/turn= 4.44𝑓∅𝑚 volt.
• rms value of emf induced in primary = emf induced/turn* 𝑁1 = 4.44𝑁1 𝑓∅𝑚
• rms value of emf induced in secondary = emf induced/turn* 𝑁2 =
4.44𝑁2 𝑓∅𝑚
• Voltage ratio =
𝐸2
𝐸1
=
4.44𝑁2 𝑓∅𝑚
4.44𝑁1 𝑓∅𝑚
=
𝑁2
𝑁1
= 𝐾(𝑡𝑟𝑎𝑛𝑠𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜)
• Since, ∅𝑚 = 𝐵𝑚 ∗ 𝐴; 𝐸1 = 4.44𝑁1 𝑓𝐵𝑚 ∗ 𝐴 , & 𝐸2 = 4.44𝑁2 𝑓𝐵𝑚 ∗ 𝐴
𝑣𝑜𝑙𝑡𝑠.
18
•
Example 1: The emf per turn of an 11 kV /415 V, 50 Hz singlephase core type transformer is 15 V. The maximum flux density in
the core is 2.5 T. Find number of primary and secondary turns and
net cross sectional area of core.
19
Ideal Transformer
➢An ideal transformer is a lossless device with an input winding and an output
winding.
➢It has the following properties:
✓ No iron and copper losses
✓ No leakage fluxes
✓ A core of infinite magnetic permeability and of infinite electrical
resistivity
✓ Flux is confined to the core and winding resistances are negligible.
➢ For ideal transformer E1=V1 and E2= V2
➢The input and output power in ideal transformer are the same, i.e. V1I1 =V2I2.
𝐸2 𝑉2 𝑁2 𝐼1
=
=
= =𝐾
𝐸1 𝑉1 𝑁1 𝐼2
20
Power in Ideal Transformer
Real power P supplied to the transformer by the primary circuit is
𝑃𝑖𝑛 = 𝑉1 𝐼1 𝑐𝑜𝑠𝜃1
𝜃1 = 𝜃2 = 𝜃
Real power coming out of the secondary circuit is,
𝑃𝑜𝑢𝑡
𝐼1
= 𝑉2 𝐼2 𝑐𝑜𝑠𝜃2 = 𝐾𝑉1 ∗ 𝑐𝑜𝑠𝜃1 = 𝑉1 𝐼1 𝑐𝑜𝑠𝜃1 = 𝑃𝑖𝑛
𝐾
Thus for ideal transformer, the output power is equal to its input power.
21
Single-Phase Real Transformers
➢ A real transformer can be described by the following characteristics:
➢ There is a flux leakage which means that not all of the flux produced by one
winding will link the other winding.
➢ Primary and Secondary windings have resistances which means that the
applied voltage (source voltage) v1 is NOT the same as the induced primary
voltage e1; that is, v1 ≠ e1. Similarly, v2 ≠ e2.
➢ The magnetic core is NOT perfectly permeability which means that it
requires a finite mmf for its magnetization.
➢ Since the flux in the magnetic core is alternating, there exist hysteresis as
well as eddy current losses, collectively called core or iron losses.
22
Single-Phase Real Transformers
23
Transformer on No-load
➢ A transformer is said to be on no-load when its secondary winding is kept
open and no-load is connected across it.
➢ As such, no current flows through the secondary i.e., I2 = 0. Hence, the
secondary winding is not causing any effect on the magnetic flux set-up in
the core or on the current drawn by the primary.
➢ But the losses cannot be ignored. At no load, a transformer draws a small
current I0 (usually 2-10% of the rated value). This current has to supply the
iron losses (hysteresis and eddy current losses) in the core and a very small
amount of copper loss in the primary (the primary copper losses are so
small as compared to core losses that they are generally neglected moreover
secondary copper losses are zero as I2 is zero).
24
Transformer on No-load
When an ac power source is connected to a transformer, a current flows in its
primary circuit, even when the secondary circuit is open circuited. This current
is the current required to produce flux in the ferromagnetic core and is called
excitation current. It consists of two components:
a. The magnetization current Imag, which is the current required to produce the
flux in the transformer core.
b. The core-loss current Iw, which is the current required to make up for
hysteresis and eddy current losses
25
Transformer on No-load
Therefore, current Io lags behind the voltage vector V1 by an angle
𝜃0 (called hysteresis angle of advance) which is less than 90º. The
angle of lag depends upon the losses in the transformer.
𝑉1
➢ 𝐼𝑐 = 𝐼𝑤 = 𝐼𝑜 𝑐𝑜𝑠𝜃𝑜
➢ 𝐼𝑚𝑎𝑔 = 𝐼𝑜 𝑠𝑖𝑛𝜃𝑜
➢ No-load current or excitation
current
𝐼𝑜 =
𝐼𝑐 2 + 𝐼𝑚 2
26
Actual Transformer
An actual transformer has:
(i) Primary and secondary resistances R1 and R2,
(ii) Primary and secondary leakage reactance X1 and X2,
(iii) Iron and copper losses, and
(iv)exciting resistance R0 and exciting reactance X0.
27
Actual Transformer
➢ Primary impedance, 𝑍1 = 𝑅1 + 𝑗𝑋1
The resistance and leakage reactance of primary winding are responsible for
some voltage drop in primary winding.
𝑉ഥ1 = 𝐸1 + 𝐼ഥ1 𝑅1 + 𝑗𝑋1 = 𝐸1 + 𝐼ഥ1 𝑍1
Where, 𝐼ഥ1 = 𝐼′1 + 𝐼ഥ0
28
Actual Transformer
➢ Secondary impedance, 𝑍2 = 𝑅2 + 𝑗𝑋2
➢ Similarly, the resistance and leakage reactance of secondary winding are
responsible for some voltage drop in secondary winding.
𝑉2 = 𝐸2 − 𝐼ഥ2 𝑅2 + 𝑗𝑋2 = 𝐸2 − 𝐼ഥ2 𝑍2
29
The Equivalent Circuit of a Transformer
The losses that occur in transformers have to be accounted for in any
accurate model of a transformer.
1. Copper (I2R) losses. Copper losses are the resistive heating losses
in the primary and secondary windings of the transformer. They
are proportional to the square of the current in the windings.
2. Eddy current losses. Since flux in the core of a transformer is
alternating, it links with the magnetic material of the core itself
also. This induces an emf in the core and circulates eddy currents.
Power is required to maintain these eddy currents. This power is
dissipated in the form of heat and is known as eddy current loss.
This loss can be minimized by making the core of thin
laminations. 𝑝𝑒 = 𝐾𝑒 𝑉𝑓 2 𝑡 2 𝐵2 𝑚
30
3. Hysteresis losses: When the magnetic material is subjected to
reversal of magnetic flux, it causes a continuous reversal of
molecular magnets. This effect consumes some electric power
which is further dissipated in the form of heat as loss. This loss is
known as hysteresis loss. This loss can be minimized by using
silicon steel material for the construction of core.
4. Leakage flux. The fluxes which escape the core and pass through
only one of the transformer windings are leakage fluxes. These
escaped fluxes produce a self-inductance in the primary and
secondary coils, and the effects of this inductance must be
accounted for.
31
The Equivalent Circuit of a Transformer
i.
Equivalent circuit when all the quantities are referred to primary circuit,
➢ The secondary resistance when referred to primary side, its value is
𝑅2′
=
𝑅2
.
𝐾2
➢ Similarly, the secondary reactance when referred to primary side, its value
is
𝑋2′
=
𝑋2
.
2
𝐾
32
The Equivalent Circuit of a Transformer
i.
Equivalent circuit when all the quantities are referred to primary circuit,
➢ All the quantities when referred to the primary side are shown in figure
below.
33
The Equivalent Circuit of a Transformer
ii. Equivalent circuit when all the quantities are referred to secondary circuit,
➢ The primary resistance when referred to secondary side, 𝑅1′ = 𝐾 2 𝑅1 .
➢ The primary reactance when referred to secondary side, 𝑋1′ = 𝐾 2 𝑋1 .
➢ The excitation resistance when referred to secondary side, 𝑅0′ = 𝐾 2 𝑅0 .
➢ The excitation reactance when referred to secondary side, 𝑋0′ = 𝐾 2 𝑋0 .
34
The Equivalent Circuit of a Transformer
ii. Equivalent circuit when all the quantities are referred to primary circuit,
➢ All the quantities when referred to the secondary side are shown in figure
below.
➢ For many practical applications,
approximate
models
of
the
transformers are used.
➢ The values of the components of the
transformer
model
can
be
determined experimentally by opencircuit and short-circuit tests.
35
Example 2:
A 50-kVA 2400:240-V 60-Hz distribution transformer has a leakage impedance
of 0.72 + j0.92 ohm in the high-voltage winding and 0.0070 + j0.0090 ohm in
the low-voltage winding. At rated voltage and frequency, the impedance Zφ of
the shunt branch (equal to the impedance of Re and jXm in parallel)
accounting for the exciting current is 6.32 + j43.7 ohm when viewed from the
low-voltage side.
Draw the equivalent circuit referred to:
a. the high-voltage side
b. the low-voltage side and label the impedances numerically
36
Transformer Tests
➢ It is possible to experimentally determine the parameters of the
approximate equivalent circuit model of the transformer. An adequate
approximation of these values can be obtained with only two tests. These
are;
1. Open-circuit test
2. Short-circuit test
1. Open-Circuit Test or No-load test
➢ This test is carried out at rated voltage to determine the no-load loss or
core loss or iron loss. It is also used to determine no-load current I0
which is helpful in finding the no-load parameters i.e., exciting resistance
R0 and exciting reactance X0 of the transformer.
37
1. Open-Circuit Test or No-load test
➢ Usually, this test is performed on low voltage side of the transformer, i.e.,
all the measuring instruments such as voltage (V), wattmeter (W) and
ammeter (A) are connected in low-voltage side (say primary). The primary
winding is then connected to the normal rated voltage V1 and frequency as
given on the name plate of the transformer.
38
1. Open-Circuit Test or No-load test
➢ Since the secondary (high voltage winding) is open circuited, the current
drawn by the primary is called no-load current I0 measured by the ammeter
A. The value of no-load current I0 is very small usually 2 to 10% of the
rated full-load current. Thus, the copper loss in the primary is negligibly
small and no copper loss occurs in the secondary as it is open. Therefore,
wattmeter reading W0 only represents the core or iron losses for all
practical purposes. These core losses are constant at all loads. The voltmeter
V’ if connected on the secondary side measures the secondary induced
voltage V2.
➢ Let the wattmeter reading= 𝑊0
➢ Voltmeter reading = 𝑉1
➢ Ammeter reading = 𝐼0
➢ Then, iron losses of the transformer, 𝑃𝑖 = 𝑤0 = 𝑉1 𝐼0 cos(∅0 )
39
1. Open-Circuit Test or No-load test
➢
➢
𝑤0
No-load power factor,cos ∅0 =
𝑉1 𝐼0
𝑤0
Working current, 𝐼𝑤 = 𝐼0 cos ∅0 =
𝑉1
➢ Magnetization current, 𝐼𝑚 =
𝐼0 2 − 𝐼𝑤 2
➢ Therefore, the no-load parameters are
i. Equivalent exciting resistance, 𝑅0 =
ii. Equivalent exciting reactance, 𝑋0 =
𝑉1
𝐼𝑤
𝑉1
𝐼𝑚
➢ The Iron losses measured by this test are used to determine transformer
efficiency and parameters of exciting circuit of a transformer.
40
2. Short-Circuit Test
➢This test is carried out to determine the following:
i.
Copper losses at full load (or at any desired load). These losses are
required for the calculations of efficiency of the transformer.
ii. Equivalent impedance (Zes or Zep), resistance (Res or Rep) and leakage
reactance (Xes or Xep) of the transformer referred to the winding in which
the measuring instruments are connected. Knowing equivalent resistance
and reactance, the voltage drop in the transformer can be calculated and
hence regulation of transformer is determined.
41
2. Short-Circuit Test
➢This test is usually carried out on the high-voltage side of the transformer
i.e., a wattmeter W, voltmeter V and an ammeter A are connected in highvoltage winding (say secondary).
➢The other winding (primary) is then short circuited by a thick strip or by
connecting an ammeter A’ across the terminals. A low voltage at normal
frequency is applied to the high voltage winding with the help of on
autotransformer so that full-load current flows in both the windings,
measured by ammeters A and A’.
➢Since a low voltage (usually 5 to 10% of normal rated voltage) is applied to
the transformer winding, therefore, the flux set up in the core is very small
about 1/30th to 1/8th of normal flux. The iron losses are negligibly small due
to low value of flux as these losses are approximately proportional to the
square of the flux.
42
2. Short-Circuit Test
➢Hence, wattmeter reading Wc only represents the copper losses in the
transformer windings for all practical purposes. The applied voltage V2sc is
measured by the voltmeter V which circulates the current I2sc (usually full
load current) in the impedance Zes of the transformer to the side in which
instruments are connected.
43
2. Short-Circuit Test
➢ Let the wattmeter reading= 𝑊𝑐
➢ Voltmeter reading = 𝑉2𝑠𝑐
➢ Ammeter reading = 𝐼2𝑠𝑐
➢ Then, full load copper losses of the transformer, 𝑃𝑐 =
2
➢ 𝑊𝑐 = 𝐼2𝑠𝑐 𝑅𝑒𝑠 , so 𝑅𝑒𝑠 =
➢ 𝑍𝑒𝑠 =
➢ 𝑋𝑒𝑠 =
𝐼2𝑓𝑙 2
( ) 𝑊𝑐
𝐼2𝑠𝑐
and
𝑊𝑐
𝐼2𝑠𝑐 2
𝑉2𝑠𝑐
𝐼2𝑠𝑐
2
𝑍𝑒𝑠 − 𝑅𝑒𝑠
2
44
Efficiency of transformer
➢The efficiency of transformer depends on losses.
➢The loss occurring in a transformer can be divided into two parts.
i. Copper loss in primary and secondary winding as (I21R1 +I22 R2 ). It
depends upon the square of the load current.
ii. Iron losses in the core due to hysteresis and eddy currents.
For a given frequency, the power losses in the core (iron losses) increase with
the voltage e1 (or e2).
𝑂𝑢𝑡𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑟
𝑂𝑢𝑡𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑟
Efficiency ()=
=
𝐼𝑛𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑟
𝑂𝑢𝑡𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑟 + 𝐿𝑜𝑠𝑠𝑒𝑠
𝑃𝑜𝑢𝑡
Efficiency ()=
𝑃𝑜𝑢𝑡 + 𝑃𝐿𝑜𝑠𝑠𝑒𝑠
45
Rating of the transformer
➢ As seen cooper loss of a transformer depends on the current and iron loss
on voltage. Hence total loss of transformer depends on volt-ampere(VA)
and not on phase angle between current and voltage i.e. it is independent
on load power factor. That is why rating of transformer is in KVA and not in
KW.
➢ A transformer is described by its rated apparent power.
46
Transformer Voltage Regulation
➢ Because a real transformer has series impedance within it,
the output voltage of a transformer varies with the load
even if the input voltage remains constant.
➢ The voltage regulation of a transformer is the change in
the magnitude of the secondary terminal voltage from noload to full-load.
𝑉𝑠 (𝑛𝑜−𝑙𝑜𝑎𝑑)−𝑉𝑠 (𝑓𝑢𝑙𝑙−𝑙𝑜𝑎𝑑)
%voltage regulation =
∗ 100%
𝑉𝑠 (𝑟𝑎𝑡𝑒𝑑)
➢ The purpose of voltage regulation is to determine the
percentage of voltage drop between no load and full load.
47
Parallel operation of transformers
➢ When the primaries and secondaries of the two or more transformers are
connected separately to the same incoming and outgoing lines to share the
load, the transformers are said to be connected in parallel.
➢ The two single-phase transformers A and B are placed in parallel as shown
in Figure below. Here the primary windings of the two transformers are
joined to the supply bus-bars and the secondary windings are joined to the
load through load bus-bars.
48
Parallel operation of transformers
Two single-phase transformers in parallel
49
Necessity of Parallel operation of transformers
i.
When the load on the transmission lines increases beyond the capacity of
the installed transformer. To overcome this problem one way is to replace
the existing transformer with the new one having larger capacity (this is
called augmentation of transformer) and the other way is to place one more
transformer is parallel with the existing one to share the load. The cost of
replacing the transformer is much more than placing another one in
parallel with the existing one.
ii. Sometimes, the amount of power to be transformed is so high that it is not
possible to build a single unit of that capacity, then we have to place two
or more transformers in parallel.
iii. At the grid sub stations, spare transformers are always necessary to insure
the continuity of supply in case of breakdown.
50
Condition for Parallel operation of single-phase transformers
i.
Both the transformers should have same transformation ratio i.e., the
voltage ratings of both primaries and secondaries must be identical. If the
turn-ratios or voltage ratings are not the same, a circulating current will
flow even at no-load.
ii. Both the transformers should have the same percentage impedance. If the
percent impedance or the ratios of resistance to reactance are not the same,
the sharing of load between the transformers when applied will no longer
be proportional to their KVA ratings. Hence, the capacities of the
transformers can not be utilized to a full extent.
iii. Both the transformers must have the same polarity i.e., both the
transformers must be properly connected with regard to their polarities.
51
Three-Phase Transformers
➢ Three phase system is invariably adopted for generation, transmission and
distribution of electrical power due to economical reasons.
➢ Usually, power is generated at the generating stations at 11 kV (or 33 kV),
whereas, it is transmitted at 750 kV, 400 kV, 220 kV, 132 kV or 66 kV
due to economical reasons.
➢ At the receiving stations, the voltage level is decreased and power is
transmitted through shorter distances. While delivering power to the
consumers, the voltage level is decreased to as low as 400V (line value) for
safety reasons.
➢ Thus to increase the voltage level at the generating stations, step-up
transformers and to decrease the voltage level at the receiving stations, step
down transformers are employed.
52
Merits of Three-Phase Transformers over Bank of Three SinglePhase Transformers
➢ The voltage level in three-phase system at the generating stations and at
the receiving stations can be changed either by employing a bank of three
single-phase transformers or by employing one three phase transformer.
➢ One three phase transformer is preferred over a bank of three single phase
transformers because of the following reasons.
i. It requires smaller quantity of iron and copper. Hence, its cost is nearly
15% lesser than a bank of three single phase transformers of equal rating.
ii. It has smaller size and can be accommodated in smaller tank and hence
needs smaller quantity of oil for cooling.
iii. Because of smaller size, it occupies less space; moreover it has less weight.
iv. It needs less number of bushings.
v. It operates at slightly better efficiency and regulation.
53
Three-Phase Transformers
➢ These transformers suffer from the following disadvantage.
i. It is more difficult and costly to repair three-phase transformers.
ii. It is difficult to transport single large unit of three-phase transformer than
to transport three single phase transformers individually.
➢ The advantages of three-phase transformer (such as lower cost, lower
weight, lower space requirement etc.) over weighs its disadvantages and
hence are invariably employed in the power system to step-up or stepdown the voltage level.
54
Three-Phase Transformer Connection
Three-phase transformers have four standard connections. These are:
A. Star-Delta ( Y-)
B. Delta-Star (-Y)
C. Delta-Delta (-)
D. Star-Star (Y-Y)
Note:
1. For star connections,
i. 𝑉𝐿 = 3𝑉𝑃
ii. 𝐼𝐿 = 𝐼𝑃
2. For delta-connections,
i. 𝑉𝐿 = 𝑉𝑃
ii. 𝐼𝐿 = 3𝐼𝑃
55
Three-Phase Transformer Connections
A. Star-Delta ( Y-)
𝑉𝑝2 𝑁2 𝐼𝑝1
=
=
=𝐾
𝑉𝑝1 𝑁1 𝐼𝑝2
➢
➢
➢
𝑉
𝑉𝑝1 = 𝐿1
3
𝐾𝑉
𝑉𝐿2 = 𝐿1
3
𝐼𝑝1
𝐼𝑝2 =
𝐾
➢ 𝐼𝐿2 =
𝐼𝐿1
𝐼𝐿2
I
𝑉V𝐿1
3aI
V
𝑉𝑝1
3
V
3a
𝑉𝐿2
𝐼I𝑝1
𝐼𝑝2
aI
3𝐼𝑝1
𝐾
56
Three-Phase Transformer Connections
B. Delta-Star ( -Y)
𝑉𝑝2 𝑁2 𝐼𝑝1
=
=
=𝐾
𝑉𝑝1 𝑁1 𝐼𝑝2
➢ 𝑉𝑝1 = 𝑉𝐿1
➢ 𝑉𝐿2 = 3𝑉𝑝2 = 3𝐾𝑉𝑝1
➢ 𝐼𝐿1 = 3𝐼𝑝1
➢ 𝐼𝐿2 = 𝐼𝑝2 =
𝐼𝑝1
𝐾
=
𝑉𝐿2
𝐼𝑝1
𝐼𝐿1 𝐼
𝑝2
𝐼𝐿1
𝐾 3
𝑉𝐿1 𝐼𝑝1
𝐼𝑝2
𝐼𝐿2
𝑉𝑝2
𝑉𝐿2
57
Three-Phase Transformer Connections
C. Delta-Delta ( - )
𝑉𝑝2 𝑁2 𝐼𝑝1
=
=
=𝐾
𝑉𝑝1 𝑁1 𝐼𝑝2
➢ 𝑉𝑝1 = 𝑉𝐿1
➢ 𝑉𝐿2 = 𝑉𝑝2 = 𝐾𝑉𝑝1
➢ 𝐼𝐿1 = 3𝐼𝑝1
➢ 𝐼𝐿2 = 3𝐼𝑝2 =
3𝐼𝑝1
𝐾
=
𝐼𝐿1
𝐾
𝐼𝐿2
𝐼𝐿1
𝑉𝐿1 𝐼𝑝1
𝑉𝐿1 𝐼𝑝1
𝐼𝑝2
𝐼𝑝2
𝑉𝑝2
𝐿2
𝑉𝑉𝐿2
58
Three-Phase Transformer Connections
D. Delta-Delta ( - )
𝑉𝑝2 𝑁2 𝐼𝑝1
=
=
=𝐾
𝑉𝑝1 𝑁1 𝐼𝑝2
➢ 𝑉𝐿1 = 3𝑉𝑝1
➢ 𝑉𝐿2 = 3𝑉𝑝2 = 3𝐾𝑉𝑝1 = 𝐾𝑉𝐿1
𝐼𝐿2
➢ 𝐼𝐿1 = 𝐼𝑝1
➢ 𝐼𝐿2 = 𝐼𝑝2 =
kI
𝐼𝑝1
𝐾
=
𝐼𝐿1
𝐾
V
𝑉V𝐿1
𝑉𝑝1
3
𝐼I𝑝1
kI
𝐼𝑝2
V
𝑉𝑝2
3k
V
𝑉𝐿2
k
59
Conditions for satisfactory operation of transformers in parallel
Transformation or turn-ratios and voltage ratings are same.
i. Polarities of the transformers are same.
ii. Percentage impedances of the transformers are same.
iii. Ratios of resistance to reactance are same.
iv. Phase displacement between primary and secondary windings of the
transformers is the same.
v. Phase sequences of the transformers are same
60
Conditions for satisfactory operation of transformers in parallel
61
Example 3:
A 50 Hz, three-phase core type transformer is to be built for an 11
kV /440 V ratio, connected in delta-star. The cores are to have a
square section and the coils are of circular. Taking an induced emf of
15 V per turn and maximum core flux density of about 1.1 T. Find
the primary and secondary number of turns and cores cross-sectional
area neglecting insulation thickness.
62
Transformer Design Aspects
➢The major considerations to develop a good design are
a.
b.
c.
Cost
Durability
Compliance with performance criteria as per the specification.
➢ These requirements are conflicting and usually it is difficult to meet all of
them.
➢ It is impossible to design a machine which is cheep and is also durable at
the same time. A machine which is expected to have long life span must use
high quality materials which are expensive.
63
Transformer Design Aspects
➢The basic structural parts of a transformer which engineers should design
carefully are;
- Magnetic parts (iron core)
- Conductor parts (windings)
- Insulating parts (dielectrics)
- Ventilation and cooling parts(thermal)
- Mechanical parts
64
65