2. Introduction
• A transformer is a static machine.
• Though not an energy conversion device, it is indispensable in many energy
conversion systems.
• It is a simple device having two or more electric circuits coupled by a
common magnetic circuit.
• Analysis of transformers involves many principles that are basic to the
understanding of electric machines.
• Transformers are so widely used as electrical apparatus that they are
treated along with other electric machines in most books on electric
machines.
2
3. Cont’d
• Since a transformer plays a vital role in feeding an electrical network with
the required voltage, it becomes an important requirement of a power
system engineer to understand the fundamental details about a
transformer along with its analytical behavior in the circuit domain.
• On the onset of this discussion it is worth mentioning that a trans former,
irrespective of its type, contains the following characteristics:
i. it has no moving parts,
ii. no electrical connection between the primary and secondary windings,
iii. windings are magnetically coupled,
iv. rugged and durable in construction,
v. efficiency is very high i.e., more than 95 %, and
vi. frequency is unchanged.
3
4. Cont’d
• A transformer consists of two or more windings coupled by a mutual
magnetic field.
• Ferromagnetic cores are used to provide tight magnetic coupling and high
flux densities. Such are known as iron core transformers. They are invariably
used in high-power applications.
• Air core transformers have poor magnetic coupling and sometimes used in
low-power electronic circuits.
• Focus is on iron transformers in this chapter.
4
5. Cont’d
• Two types of core constructions:
• Core type: windings are wound around two legs of a magnetic core
of rectangular shape.
• Shell type: the windings are wound around the center leg of a three-
legged magnetic core.
• To reduce core losses, the magnetic core is formed of a stack of thin
laminations.
• Silicon-steel laminations of 0.014 inch thickness are commonly used
for transformers operating at frequencies below a few hundred
cycles.
5
7. Cont’d
• In core tye, The coils are not arranged with the primary winding on one leg and the secondary on the other but instead half
of the primary winding and half of the secondary winding are placed one over the other concentrically on each leg in order
to increase magnetic coupling allowing practically all of the magnetic lines of force go through both the primary and
secondary windings at the same time.
• However, with this type of transformer construction, a small percentage of the magnetic lines of force flow outside of the
core, and this is called “leakage flux”.
• Shell type transformer cores overcome this leakage flux as both the primary and secondary windings are wound on the
same centre leg or limb which has twice the cross-sectional area of the two outer limbs. The advantage here is that the
magnetic flux has two closed magnetic paths to flow around external to the coils on both left and right hand sides before
returning back to the central coils.
• This means that the magnetic flux circulating around the outer limbs of this type of transformer construction is equal to Φ/2.
As the magnetic flux has a closed path around the coils, this has the advantage of decreasing core losses and increasing
overall efficiency.
7
8. Cont’d
• L-shaped laminations are used for core-type construction and E-
shaped laminations are used for shell-type construction.
• To avoid a continuous air gap (which would require a large
exciting current), laminations are stacked alternately.
L-shaped Lamination
E-shaped Lamination
8
9. Cont’d
• For small transformers used in communication circuits at high frequencies (kilocycles to megacycles) and
low power levels, compressed powdered ferromagnetic alloys, known as permalloy, are used.
• Resentation of a two-winding transformer is shown.
• One winding is connected to an ac supply and is referred to as the primary winding.
• The other is connected to an electrical load and referred to as the secondary winding.
• HV (high-voltage) or HT(high-tension) winding: the winding with the higher number of turns.
• LV (low-voltage) or LT(low-tension) winding: the winding with the lower number of turns.
• The two vertical bars are used to signify tight magnetic coupling between the windings.
9
10. Cont’d
• To achieve tighter magnetic coupling between the
windings, they may be formed of coils placed one
on top of another (fig. a), “concentric coils”, or side
by side (fig. b) , “sandwiched coils”, in a “pancake”
coil formation where primary and secondary coils
are interleaved.
• Where the coils are placed one on top of another,
the low-voltage winding is placed nearer the core
and the high-voltage winding on top.
• The primary and secondary windings in a physical
transformer are wrapped one on top of the other
with the low-voltage winding innermost. Such an
arrangement serves two purposes:
1. It simplifies the problem of insulating the high-voltage
winding from the core.
2. It results in much less leakage flux than would be the
case if the two windings were separated by a distance
on the core.
10
11. Cont’d
• Transformers have widespread use. Their primary function is to change voltage
level.
• Electrical power is generated in a power house at voltage in the range between
11,000 and 20,000 Volts.
• However, in domestic houses electric power is used at 110 or 220 volts.
• Electric power is transmitted from a power plant to a load center at 200,000 to
500,000 volts.
• Transformers are used to step up and step down voltage at various stages of
power transmission.
11
13. Cont’d
• Transformers are widely used in low-power electronic or control circuits to
isolate one circuit from another circuit or to match the impedance of a
source with its load for maximum power transfer.
• Transformers are also used to measure voltages and currents; theses are
known as instrument transformers.
13
16. Ideal Transformer
• The main points of an ideal transformer are:
i. no winding resistance,
ii. no leakage flux (all the flux are confined to the core and link both windings
iii. Self inductance and mutual inductance are zero,
iv. no losses due to resistance, no losses due to hysteresis or eddy current (no core
losses) and
v. Permeability of the core is infinite (therefore, the exciting current required to
establish flux in the core is negligible; that is the net mmf required to establish a
flux in the core is zero)
16
23. Cont’d
• Again, the magnetomotive force produced by the primary current will be
equal to the magnetomotive force produced by the secondary current
and it can be expressed as,
• it is concluded that the ratio of primary to secondary current is inversely
proportional to the turns ratio of the transformer.
23
25. Cont’d
• How does the power going into the primary circuit of the ideal
transformer compare to the power coming out of the other side?
• The power out of a transformer is
• Applying the turns- ratio equations gives:
• Thus, the output power of an ideal transformer is equal to its input power.
25
26. Cont’d
• The same relationship applies to reactive power Q and apparent
power S:
26
28. Cont’d To summarize, in an ideal
transformer, voltages are
transformed in the direct ratio of
turns, currents in the inverse ratio,
and impedances in the direct ratio
squared; power and volt-amperes
are unchanged.
28
29. Polarity
• Windings on transformers or other electrical machines are marked to indicate terminals of like polarity.
Consider two windings below. Terminals 1 and 3 are identical, because currents entering these terminals
produce fluxes in the same direction in the core that forms the common magnetic path. For the same reason,
terminals 2 and 4 are identical.
• If these two windings are linked by a common time-varying flux, voltages will be induced in these windings
such that, if at a particular instant the potential of terminal 1 is positive with respect to terminal2, then at
the same instant the potential of terminal 3 will be positive wrt terminal 4.
29
32. Cont’d
• Polarities of windings must be known if transformers are connected in parallel to share
a common load. Figure below shows the parallel connection of two single-phase
transformers.
32
40. Practical Transformer
• Certain assumptions were made for ideal transformer which are not valid in
practical transformer for example, in a practical transformer:
• The windings have resistances
• Not all windings link the same flux,
• Permeability of the core in not infinite
• Core losses occur when the core material is subjected to time-varying flux
• In the analysis of a practical transformer, all these imperfections must be
considered.
40
44. Cont’d
A practical transformer is therefore equivalent to an ideal transformer plus external
impedances that represent imperfections of an actual transformer.
44
45. Referred Equivalent Circuits
• The ideal transformer in fig c can be moved to the right or left by referring
all quantities to the primary or secondary side, respectively. The equivalent
circuit with the ideal transformer moved to the right is shown below.
45
46. Cont’d
• For convenience, the ideal transformer is usually not shown and the equivalent circuit
is shown below, with all quantities (voltages, currents, and impedances) referred to
one side. The referred quantities are indicated with primes.
• By analyzing this equivalent circuit the referred quantities can be evaluated, and the
actual quantities can be determined from them if the turns ration is known.
46
49. Determination of Equivalent Circuit Parameters (Determining the
Values of Components in the Transformer Model)
49
50. Cont’d
• These parameters can be directly and more easily determined by
performing tests that involve little power consumption.
• Two tests, no-load test (or open-circuit test) and short-circuit test, will
provide information for determining the parameters of the equivalent
circuit of a transformer.
50
52. No-load Test (or Open-Circuit Test)
• In the open-circuit test, a transformer's
secondary winding is open-circuited, and its
primary winding is connected to a full-rated line
voltage.
• It is performed by applying a voltage to either the
HV side or LV side, whichever is convenient. Thus if
a 1100/110 volt transformer were to be tested, the
voltage would be applied to the LV winding,
because a power supply of 110 volts is more readily
available than a supply of 1100 volts.
• Rc and Xm are determined from this test.
• The open-circuit test connections are shown in
Figure below.
• The primary current is the exciting current and the
losses measured by the wattmeter are essentially
the core losses. 52
57. Cont’d
• In the short-circuit test, the secondary terminals of the transformer are short-
circuited, and the primary terminals are connected to a fairly low-voltage source,
as shown in Figure.
• The input voltage is adjusted until the current in the short-circuited windings is
equal to its rated value . (Be sure to keep the primary voltage at a safe level.
It would not be a good idea to burn out the transformer's windings while
trying to test it.).The input voltage, current, and power are again measured.
• For convenience, the high-voltage side is usually taken as the primary in this
test.
• Because the equivalent series impedance in a typical transformer is relatively
small, typically an applied primary voltage on the order of 10 to 15 percent
or less of the rated value will result in rated current.
57
58. Cont’d
• In the equivalent circuit for the transformer, the impedance of the excitation
branch (shunt branch composed of Rc and Xm) is much larger than that of
the series branch (composed of Req and Xeq).
• Since the input voltage is so low during the short-circuit test, 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.
58
59. Cont’d
• Figure shows the equivalent circuit with
transformer secondary impedance referred
to the primary side and a short circuit
applied to the secondary.
• The short- circuit impedance Zsc looking
into the primary under these conditions is
•
59
61. Cont’d
• Typically the instrumentation used for this test will measure the rms magnitude of
the applied voltage Vsc, the short-circuit current Isc, and the power Psc. Based upon
these three measurements, the equivalent resistance and reactance (referred to
the primary) can be found from
61
66. TRANSFORMER VOLTAGE REGULATION AND EFFICIENCY
• Most loads connected to the secondary of a transformer are designed to operate at
essentially constant voltage.
• Because a real transformer has series impedances within it, the output voltage of a
transformer varies with the load even if the input voltage remains constant. To
conveniently compare transformers in this respect, it is customary to define a
quantity called voltage regulation (VR).
• The voltage regulation of a transformer is defined as the change in secondary
terminal voltage as the load current changes from no load to full load condition and is
usually expressed as a percentage of the full-load value.
66
70. The Transformer Phasor Diagram
• To determine the voltage regulation of a transformer, it is
necessary to understand the voltage drops within it. Consider
the simplified transformer equivalent circuit below
• The effects of the excitation branch on transformer voltage
regulation can be ignored, so only the series impedances
need be considered .
• The voltage regulation of a transformer depends both on the
magnitude of these series impedances and on the phase angle
of the current flowing through the transformer.
• The easiest way to determine the effect of the impedances and
the current phase angles on the transformer voltage
regulation is to examine a phasor diagram, a sketch of the
phasor voltages and currents in the transformer.
70
71. Cont’d
• In all the following phasor diagrams, the
phasor voltage Vs is assumed to be at an
angle of 0°, and all other voltages and
currents are compared to that reference.
By applying Kirchhoff 's voltage law to
the equivalent, the primary voltage can
be found as
• A transformer phasor diagram is just a
visual representation of this equation.
71
73. Cont’d
• The copper loss can be determined if the winding currents and their resistances are known:
• The copper loss is a function of the load current.
• The core loss depends on the peak flux density in the core, which in turn depends on the voltage
applied to the transformer. Since a transformer remains connected to an essentially constant voltage,
the core loss is almost constant and can be obtained from the no-load test of a transformer.
• To calculate the efficiency of a tr ansformer at a given load, just add the losses from each
resistor and apply Equation (2-67). Since the output power is given by
73
74. Example:
• A 15-kVA, 2300/230-V transformer is to be tested to determine its
excitation branch components, its series impedances, and its voltage
regulation. The following test data have been taken from the primary
side of the transformer:
74
82. All-Day (Energy) Efficiency, nAD
• The transformer in a power plant usually operates near its full capacity and is taken out of
circuit when it is not required. Such transformers are called power transformers, and they
are usually designed for maximum efficiency occurring near the rated output.
• A transformer connected to the utility that supplies power to your house and the locality is
called a distribution transformer. Such transformers are connected to the power system
for 24 hours a day and operate well below the rated power output for most of the time. It
is therefore desirable to design a distribution transformer for maximum efficiency
occurring at the average output power.
• A figure of merit that will be more appropriate to represent the efficiency performance of
a distribution transformer is the “all-day” or “energy” efficiency of the transformer. This is
defined as follows:
• If the load cycle of the transformer is known, the all-day efficiency can be determined.
82
84. TRANSFORMER TAPS AND VOLTAGE REGULATION
• On some occasions it is desirable to change voltage levels by only a small
amount to obtain a variable ac voltage at the secondary.
• For example, it may be necessary to increase a voltage from 110 to 120 V
or from 13.2 to 13.8 kV These small rises may be made necessary by
voltage drops that occur in power systems a long way from the generators.
• In such circumstances, it is wasteful and excessively expensive to wind a
transformer with two full windings, each rated at about the same voltage.
A special-purpose transformer, called an autotransformer is used instead.
• Distribution transformers have a series of taps in the windings to permit
small changes in the turns ratio of the transformer after it has left the
factory. A typical installation might have four taps in addition to the nominal
setting with spacings of 2 .5 percent of full-load voltage between them. Such
an arrangement provides for adjustments up to 5 percent above or below
the nominal voltage rating of the transformer.
84
85. Cont’d
• A diagram of a step- up autotransfonner is shown in Figure.
• In Fig. a, a two-winding transformer is shown with N1
and N2 turns on the primary and secondary windings
respectively.
• Substantially the same transformation effect on voltages,
currents, and impedances can be obtained when these
windings are connected as shown in Fig. b.
• Note that, however, in Fig. b, winding bc is common to
both the primary and secondary circuits. This type of
transformer is called an autotransformer. It is little more
than a normal transformer connected in a special way.
85
86. • In fig b the first winding is shown connected in an additive manner to the
second winding.
• Now, the relationship between the voltage on the first winding and the
voltage on the second winding is given by the turns ratio of the trans-
former. However, the voltage at the output of the whole transformer is the
sum of the voltage on the first winding and the voltage on the second
winding.
86
87. Cont’d
• One important difference between the two-winding transformer and
the autotransformer is that the windings of the two-winding
transformer are electrically isolated whereas those of the
autotransformer are connected directly together.
• Also, in the autotransformer connection, winding ab must be provided
with extra insulation since it must be insulated against the full
maximum voltage of the autotransformer.
• Autotransformers have lower leakage reactances, lower losses, and
smaller exciting current and cost less than two-winding transformers
when the voltage ratio does not differ too greatly from 1:1.
87
89. Cont’d
• For ampere-turn balance:
• The advantage of an autotransformer connection are lower leakage reactances, lower
losses, lower exciting current, increased kVA rating , and variable output voltage when
a sliding contact is used for the secondary.
• The disadvantage is the direct connection between the primary and secondary sides.
89
90. THREE-PHASE TRANSFORMERS
• Almost all the major power generation and distribution systems in the
world today are three- phase ac systems.
• Since three-phase systems play such an important role in modern life,
it is necessary to understand how transformers are used in them.
• Transformers for three-phase circuits can be constructed in one of two
ways.
• One approach is simply to take three single-phase transformers and
connect them in a three-phase bank.
• An alternative approach is to make a three-phase transformer
consisting of three sets of windings wrapped on a common core. These
two possible types of transformer construction are shown in Figures
below.
90
92. • The construction of a single three-phase transformer is the
preferred practice today, since it is lighter, smaller, cheaper, and
slightly more efficient.
• The older construction approach was to use three separate
transformers.
• That approach had the advantage that each unit in the bank
could be replaced individually in the event of trouble, but that
does not outweigh the advantages of a combined three- phase
unit for most applications .
• However, there are still a great many installa-tions consisting of
three single -phase units in service.
Three-Phase Transformer Connections:
• A three-phase transformer consists of three transformers,
either separate or combined on one core.
92
94. Wye-wye (Y-Y) Connections:
• In a Y-Y connection, the primary voltage
on each phase of the transformer is given
by
• The primary-phase voltage is related to
the secondary-phase voltage by the turns
ratio of the transformer.
• The phase voltage on the secondary is
then related to the line voltage on the
secondary by
• Therefore, the overall voltage ratio on the
transformer is:
94
3
P LP
V V
3
LS S
V V
3
3
P
LP
LS S
V
V
a Y Y
V V
95. The Y-Y connection has two very serious problems :
1. If loads on the transformer circuit are unbalanced, then the voltages on
the phases of the transformer can become severely unbalanced.
2. Third-harmonic voltages can be large.
• If a three-phase set of voltages is applied to a Y-Y transformer, the voltages
in any phase will be apart from the voltages in any other phase.
However, the thirdharmonic components of each of the three phases will be
in phase with each other, since there are three cycles in the third harmonic
for each cycle of the fundamental frequency. There are always some third-
harmonic components in a transformer because of the nonlinearity of the
core, and these components add up.
95
0
120
96. • The result is a very large third-harmonic voltage on top of the 50 or 6O-Hz
fundamental voltage. This third-harmonic voltage can be larger than the
fundamental voltage it self.
Both the unbalance problem and the thirdharmonic problem can be solved
using one of two techniques:
1. Solidly ground the neutrals of the transformers, especially the primary
wind-ing's neutral. This connection permits the additive thirdharmonic
components to cause a current flow in the neutral instead of building up
large voltages. The neutral also provides a return path for any current
imbalances in the load.
2. Add a third (tertiary) winding connected in to the transformer bank. If a
third -connected winding is added to the transformer, then the third-
harmonic components of voltage in the will add up, causing a circulating
current flow within the winding. This suppresses the third-harmonic
components of voltage in the same manner as grounding the transformer
neutral.
96
97. • The - connected tertiary windings need not even be brought out of the
transformer case, but they often are used to supply lights and auxiliary
power within the substation where it is located.
• The tertiary windings must be large enough to handle the circulating
currents, so they are usually made about onethird the power rating of
the two main windings.
• One or the other of these correction techniques must be used any time
a YY transformer is installed.
• In practice, very few Y-Y transformers are used, since the same jobs can
be done by one of the other types of three-phase transformers.
97
98. Wye-delta (Y- ) Connections:
• In this connection, the primary line voltage is related
to the primary phase voltage by , while
the secondary line voltage is equal to the secondary
phase voltage . The voltage ratio of each
phase is
so the overall rxnship b/n the line voltages on the
primary side of the bank & the secondary side of the
bank is
98
P
S
V
a
V
3
LP P
V V
LS S
V V
