Lecture 1
Characteristics of a Transformer, Principles of Operation and Standard
Ratings
1.1 Introduction
One of the most important machines in electrical technology are transformers.
It is found almost
everywhere, where electricity is used such as in malls, schools, department stores, hotels and many other
establishments that needs electricity for daily activities. One may have thought what are these machines
for, what purpose does it serve and how important is this machine in the advancement of the technology
in this world. This lecture covers all about transformers components, its principles of operation and its
standard ratings.
Transformer is an electrical machine that changes the magnitude of an AC voltage form one voltage level
to another. Figure 1 shows a typical electric grid structure where transformers are being used. From the
generating station, electric power is being transmitted by through a step-up transformer, then through
transmission lines and then a step-down transformer. After the step-down transformer, power is being
distributed to customers.
Figure 1 Electricity Grid Structure (https://electrical-engineering-portal.com/electric-power-systems)
1.2 Characteristics of a Practical Transformer
Practical transformers are real transformers which differs from ideal transformers since ideal transformer
does not consider power losses like in copper losses, core losses and leakage flux. The discussion
throughout this lecture will focused on practical transformers.
Take a look at Figure 2. It shows a sketch of a real single-phase transformer. It consists of two windings.
One on the left side which is the primary winding and the other is on the other side which is called the
secondary winding. These windings are electrical wires wounded at each side of the core. N P and NS are
the number of turns at each winding. The subscript “P” and “S” indicates the number of turns in the
primary and secondary respectively. These windings are wrapped around a common ferromagnetic core.
The primary winding is connected to an ac voltage source. Now the windings in both sides are not
physically connected.
Figure 2 A Real Single-Phase Transformer
The following are the main characteristics of a practical transformer:
1. It uses electromagnetic induction in transforming voltage levels.
2. The input and output power of a transformer has the same frequency.
3. This electrical machine is static, therefore there are no losses due to air resistance and friction unlike
electric motors.
4. It has copper losses since the windings are electrical wire with resistance no matter how small.
5. It has core losses due to eddy currents and hysteresis losses.
1.3 Principles of Operation of a Transformer
A transformer obeys Faraday’s law. This law states that a voltage will be induced in a coil of conductor of
proper orientation which experiences a changing magnetic field. In equation form,
Equation 1
is the flux linkage in the coil where the voltage is induced which equal to:
Equation 2
∑
Equation 2 states that all the flux passing through each turn in the coil are added over all the turns of the
coil. But since the flux passing through each turn is different from the flux passing through the other
turns in a coil, it is necessary to get the average flux per turn in a coil which is equal to
̅
Equation 3
In Equation 3, ̅ is the average flux per turn in a coil which is equal to the total flux linkage or total flux
passing through the coil divided by the number of turns in a coil. Therefore, the Faraday’s law can be
written as
(
̅
)
Equation 4
Now, how does a transformer react when an AC voltage source is applied through its primary winding?
Take a look a Figure 3. When an AC voltage source is applied to the primary winding, current
( ) is
flowing through the coil and a magnetic field is produced with the direction of magnetic flux lines shown
in the figure. This is in accordance to Oersted’s Law which states that when a steady current pass through
a conductor, a magnetic field is produced around it.
determined through the right-hang rule.
The direction of the magnetic field can be
Figure 3 An AC voltage source is applied to the primary winding
Now here comes the core as shown in Figure 4. The purpose of the core is to allow majority of the
magnetic flux in the magnetic field to pass through it. In other words, majority of the flux will flow and
is concentrated through the core. The word majority is used since not all the magnetic flux that is
produced by the primary winding will flow through the core. This is because the core is a ferromagnetic
material which means that it has a specific permeability which restricts all the magnetic flux to pass
through it when it reaches saturation point. It can be seen that some of the magnetic flux leaks out thus
called as leakage flux, (
). The magnetic flux that flows
through the core and reaches the secondary coil is called the mutual flux which is also the flux linkage.
For the purpose of discussion, let us assume that a current
( ) is flowing through the secondary coil
which can only happen if a load is connected to the secondary coil. This secondary current also produces
a magnetic field in the secondary winding which flow through the core and also has leakage flux.
Figure 4 A Single-Phase Transformer with magnetic flux flowing through the core
The total average flux in the primary is the sum of the mutual flux or the flux component linking both
coils and the leakage flux in the primary which is given by:
̅
Equation 5
Similarly, in the secondary winding, the total average flux in the secondary is the sum of the mutual flux
or the flux component linking both coils and the leakage flux in the secondary which is given by:
̅
Equation 6
Voltage Ratio on a Transformer
Looking back at Equation 4, it can be written as
( )
( )
(
(
)
̅
(
)
)
Equation 7
( )
Equation 8
Equation 7 can also be written as,
( )
where
( )
( ) is the primary voltage due to the mutual flux and
( ) is the primary voltage due to the
leakage flux and similarly in the secondary coil we get,
( )
(
)
(
( )
where
Equation 9
)
( )
Equation 10
( )
( ) is the secondary voltage due to the mutual flux and
the leakage flux. Working on
( )
(
) and
( )
(
( ) is the secondary voltage due to
) we get
( )
( )
Equation 11
The variable “a” in Equation 11 is called the turns ratio of the transformer which is equal to the ratio of
the primary voltage caused by the mutual flux to the secondary voltage caused by the mutual flux. A
transformer should be well-designed so that the leakage flux is very small which is
and
. Consequently, the relationship of the primary input voltage to the secondary output voltage
can be approximated to
( )
( )
Equation 12
It can be seen in Equation 12 that the voltages across a transformer can be related to each other with the
use of the turns ratio “a” which is just the ratio of the number of turns in the primary winding to the
number if turns in the secondary winding.
Current Ratio on a Transformer
Take a look at Figure 5. This time a load is connected to the secondary side of the transformer which
causes current
to flow. Using the dot convention which determines the polarity of the voltages and
currents, the current
produces a positive magnetomotive force since it is flowing into the dot of the
primary winding and current
produces a negative magnetomotive force since it is flowing away from
the dot of the secondary winding. Therefore, the net magnetomotive force in the core is equal to
Equation 13
Equation 13 means that the net magnetomotive force is equal to the total flux in the core times the
reluctance of the core. Since one of the goals of designing a transformer is to minimized the reluctance of
the core which means the for a well-designed transformer, the reluctance will be approximately zero.
Equation 13 will then be reduced to
Equation 14
Equation 14 is the current ratio across the transformer which means that the ratio of the primary current to
the secondary current is inversely proportional to the turns ratio of the transformer.
How does a transformer transfer energy from primary side to the secondary side?
The items below summarizes the principles of operation of a transformer:
1. A voltage is applied in the primary side of the transformer which results to a current
primary winding since it is a close circuit.
flowing in the
Figure 5 A Single-Phase Transformer with a load connected at secondary side
2. The current
produces a magnetic field in the primary coil.
3. The magnetic flux produced in the primary coil minus the leakage flux (which is called the mutual
flux) will flow through the core and then links through the secondary coil which wrapped on the same
core and in close proximity with the primary coil.
4. The flux linkage (mutual flux) changes with time with respect to the AC voltage is the one inducing
voltage in the secondary coil. This time the secondary side already has a voltage across its terminals.
5. And lastly, the magnitude of the voltages and currents in the secondary depends on the turns ratio of
the transformer or the ratio of the number of turns in the primary winding to the number of turns in the
secondary winding.
In a practical transformer, there will be energy lost in the transformer which means that the energy in the
primary side is not equal but really close to the energy transferred in the secondary side.
Examples
1. When operated at 120 V in the primary of an iron core transformer, the current in the primary is 4
amps. Find the current in the secondary if the voltage is stepped up to 500 V.
Solution:
2. A transformer with 480 turns on the primary and 60 turns on the secondary draws 0.6 amps from a 120
V line. Find .
Solution:
How does a transformer affect the overall efficiency of electricity distribution?
Looking at example 1, you will notice that the transformer being used is a step-up transformer which
steps up the voltage from 120 V to 500 V. The result of this transformation is that the current is reduced
from 4 amperes to 0.96 amperes. The power lost in the transmission lines is
or
for three-phase. The main goal is to make the current flowing in the transmission lines as low as possible
so that the power losses is minimum and you can do that using a transformer. This is how significant
transformers are in the electricity distribution.
1.4 Standard Rating of Transformers
There are four major ratings of a transformer. These are the voltage, frequency, current and apparent
power. Theses standard rating will be discussed in the section.
1.4.1 Voltage Rating
The voltage rating of a transformer has two function.
1. To protect the winding insulation from failing because of an excessive voltage applied.
2. To have an idea about the magnetizing current and its magnetization curve of a transformer
Winding insulation may fail if excessive voltage is applied across the winding. If the applied voltage will
exceed the dielectric strength of the insulating material, it will become conductive which will result to
possible electric fault like short circuit.
If an AC voltage
( )
Is applied to the primary winding of a transformer, the magnetic flux of a transformer is given by
( )
( )
∫ ( )
∫
( )
Equation 15
Looking at Equation 15, if the input voltage ( ) is increased by 20 percent, the flux will also increase by
20 percent referring at Figure 6. However, the 20 percent increase of flux will require a magnetization
current greater that the 20 percent which is harmful to the insulation of the primary winding. The
maximum applied voltage (therefore the RATED VOLTAGE) is set by the maximum acceptable
magnetization current in the core.
Figure 6 Required Magnetization current with respect to the change in flux
1.4.2 Frequency Rating
In Equation 15, if maximum flux is held constant where
, the equation will reduce to
( )
Equation 16
If a 60 Hz transformer is to be operated on 50 Hz, its applied voltage must also be reduced by one-sixth or
the peak flux in the core will be too high. The most commonly used frequency ratings are 60 Hz and 50
Hz. In the Philippines, the standard frequency is 60 Hz for electricity grid.
1.4.3 Apparent Power Rating of a Transformer
Together with the voltage rating, the primary purpose of the apparent power of the transformer is to set
the current flows through the transformer windings. The heating of the transformer coils depends on the
current flow through it. The apparent power rating of the transformer has to account for the nature of the
load since loads are not purely resistive. For example, 100 MVA transformer can serve a maximum of
100 MW purely resistive load. But in reality, loads are inductive in nature therefore, if a load with 0.8
power factor that means that 100MVA x 0.8pf = 80 MW real power and a 20 MVAR reactive power.
Review Questions
1. Is the turns ratio of a transformer the same as the ratio of voltages across the transformer? Why or why
not?
2. Why does the magnetization current impose an upper limit on the voltage applied to a transformer
core?
3. The ampere current in primary side of a transformer is directly proportional to ampere current in
secondary. True or False?
4. Why transformers are not used in DC Power Supply system?
5. Which part of a transformer undergoes most damage from overheating?
Problem Solving
1. A Transformer has 1000 turns on the primary winding and has 100 turns in the secondary windings. If
the voltage of 250V is applied to the primary windings. What will be the secondary voltage of the
transformer?
2. If the transformer ratio is in the order of 1:16, what will the ratio of the primary and secondary
currents?
3. A 1-Phase Transformer having voltage rating of 1 kV primary / 100V secondary. Current flowing
through the secondary windings is 10 A with 0.8 lagging power factor. Calculate the Power or rating of
the secondary winding of the transformer.
4. If the copper loss of a transformer is 400 watts at full load. If the load on the transformer is reduced to
half. Then what will the copper loss in the transformer?