Internship report report on harmonic analysis of transformer, internship report pdf, iit internship

IIT PATNA
SUMMER INTERNSHIP REPORT
ON
HARMONIC ANALYSIS OF TRANSFORMER
Duration: 4th June – 4th July 2019
Dr. Sanjoy Kumar Parida
Associate professor
IIT Patna
Aniket Raj
B.Tech 2nd
year
Electrical Engineering
Tezpur University
UNDER THE GUIDANCE OF SUBMITTED BY

ACKNOWLEDGEMENTS
I would like to express thanks and gratitude to my supervisor Dr. Sanjoy
Kumar Parida for giving me the opportunity of an internship under his
guidance.
During the project, I got a chance to improve my technical and practical
skills.
I would also like to thank the staff of Electrical engineering department
for constant support and providing place to work during project
period.
I would also like to thank Mr. Chiranjit Adhikary & Dr. Rumi Rajbongshi
Assistant Professor, Tezpur University who have been a constant moral
support.
Lastly, I would like to thank my family and friends for their kind
support. I feel grateful to Lord Almighty who has showered His graces
upon me during this period.

CONTENTS
1. INTRODUCTION
2. TRANSFORMER BASICS AND WORKING PRINCIPLE
3. THE OPEN-CIRCUIT TEST AND SHORT CIRCUIT TEST
4. HARMONIC
5. SIMULATIONS AND EXPERIMENTAL RESULTS
6. CONCLUSIONS AND FUTURE WORK
7. REFERENCES

CHAPTER 1
INTRODUCTION
Harmonics and distortion in power system current and voltage
waveforms have been present for decades. However, today a number
of harmonic producing devices is increasing rapidly.
The transformer designed to operate at rated frequency has had its
loads gradually replaced with non-linear loads that inject harmonic
currents. These harmonic currents will increase losses, additional
heating losses, shorter insulation lifetime, higher temperature and
insulation stress, reduced power factor, lower productivity, efficiency,
capacity and lack of system performance.
Therefore, the need for investigating the harmonic problems is
obvious.
Examples of linear loads are induction motor, heaters and
incandescent lamps. But the rapid increase in the electronics device
technology such as diode, etc cause industrial loads to become non-
linear.
A non-linear load is created when the load current is not proportional
to the instantaneous voltage. Non-linear currents are non sinusoidal,
even when the source voltage is a clean sine wave. The principle is that
the harmonic components are added to the fundamental current [1].
The primary effect of harmonic currents on transformers is the
additional heat generated by the losses caused by the harmonic
contents generated by the nonlinear loads.
There are three effects that result in increased transformer heating
when the load current includes harmonic components.
1. Rms current: If the transformer is sized only for the kVA
requirements of the load, harmonic currents may result in the
transformer rms current being higher than its capacity.
2. Eddy-current losses: These are induced currents in a transformer
caused by the magnetic fluxes.
3. Core losses: The increase in nonlinear core losses in the presence
of harmonics will be dependent under the effect of the
harmonics on the applied voltage and design of the transformer
core [2].

CHAPTER 2
Transformer Basics and Working Principle
Definition of Transformer
A transformer is a static device which transfers electrical energy from
one circuit to another through the process of electromagnetic
induction. It is most commonly used to increase (‘step up’) or decrease
(‘step down’) voltage levels between circuits.
Working Principle of Transformer
The working principle of a transformer is very simple. Mutual induction
between two or more windings (also known as coils) allows for
electrical energy to be transferred between circuits. This principle is
explained in further detail below.
Transformer Theory
Say you have one winding (also known as a coil) which is supplied by
an alternating electrical source. The alternating current through the
winding produces a continually changing and alternating flux that
surrounds the winding. If another winding is brought close to this
winding, some portion of this alternating flux will link with the second
winding. As this flux is continually changing in its amplitude and
direction, there must be a changing flux linkage in the second winding
or coil.
According to Faraday’s law of electromagnetic induction, there will be
an EMF induced in the second winding. If the circuit of this secondary
winding is closed, then a current will flow through it. This is the basic
working principle of a transformer. Let us use electrical symbols to help
visualize this. The winding which receives electrical power from the
source is known as the ‘primary winding’. In the diagram below this is
the ‘First Coil’.

The winding which gives the desired output voltage due to mutual
induction is commonly known as the ‘secondary winding’. This is the
‘Second Coil’ in the diagram above.
A transformer that increases voltage between the primary to
secondary windings is defined as a step-up transformer. Conversely, a
transformer that decreases voltage between the primary to secondary
windings is defined as a step-down transformer.
While the diagram of the transformer above is theoretically possible in
an ideal transformer – it is not very practical. This is because in open
air only a very tiny portion of the flux produced from the first coil will
link with the second coil, So the current that flows through the closed
circuit connected to the secondary winding will be extremely small
(and difficult to measure).
The rate of change of flux linkage depends upon the amount of linked
flux with the second winding. So ideally almost all of the flux of primary
winding should link to the secondary winding. This is effectively and
efficiently done by using a core type transformer. This provides a low
reluctance path common to both of the windings.

The purpose of the transformer core is to provide a low reluctance
path, through which the maximum amount of flux produced by the
primary winding is passed through and linked with the secondary
winding.
The current that initially passes through the transformer when it is
switched on is known as the transformer inrush current.
Transformer Parts and Construction
The three main parts of a transformer:
1. Primary Winding of Transformer
2. Magnetic Core of Transformer
3. Secondary Winding of Transformer
Primary Winding of Transformer
This part produces magnetic flux when it is connected to electrical
source.
Magnetic Core of Transformer
The magnetic flux produced by the primary winding, that will pass
through this low reluctance path linked with secondary winding and
create a closed magnetic circuit.
Secondary Winding of Transformer
The flux, produced by primary winding, passes through the core, will
link with the secondary winding. This winding also wounds on the same
core and gives the desired output of the transformer.[3]
Transformer classification:
Transformers are classified according to many aspects, the type of
insulation, the cooling method, the number of phases, the method of
mounting, purpose and service. We can distinguish the next
classifications:

1. According to method of cooling
a. Self air cooled (dry type)
b. Air-blast–cooled (dry type)
c. Liquid-immersed, self-cooled
d. Oil-immersed, combination self-cooled and air-blast
e. Oil-immersed, water-cooled
f. Oil-immersed, forced-oil–cooled
g. Oil-immersed, combination self-cooled and water-cooled
2. According to insulation between windings
a. Windings insulated from each other
b. Autotransformers
3. According to number of phases
a. Single-phase.
b. Poly-phase.
4. According to method of mounting
a. Pole and platform
b. Subway
c. Vault
d. Special
5. According to purpose
a. Constant-voltage
b. Variable-voltage
c. Current
d. Constant-current
6. According to service
a. Large power
b. Distribution
c. Small power
d. Sign lighting
e. Control and signaling
f. Gaseous-discharge lamp transformers

g. Bell ringing
h. Instrument
i. Constant-current
j. Series transformers for street lighting
Single phase transformer
There are two basic core designs for single-phase transformer: core
form and shell form.
Figure 2.3 Core and Shell forms with Windings
Due to insulation requirements, the low voltage (LV) winding normally
appears closest to the core, while the high voltage (HV) winding
appears outside. The windings are usually referred to as primary and
secondary winding(s) as denoted by the P and S.
In the shell form, the flux generated in the core by the windings splits
equally in both "legs" of the core. Winding configurations may vary
with core design and include concentric windings, pancake windings
and assemblies on separate legs. A commonly used equivalent circuit
for a single-phase model is shown below:
Figure 2.4 Simplified Single-Phase Transformer

This model is sufficient to model the short circuit behavior of a single-
phase transformer. It includes the winding resistance and leakage as
well as the core losses so it is widely used for all core and winding
configurations of the single-phase two-winding variety [4]
CHAPTER 3
The Open-Circuit Test
As the name implies, one winding of the transformer is left open while
the other is excited by applying the rated voltage. The frequency of the
applied voltage must be the rated frequency of the transformer.
Although it does not matter which side of the transformer is excited, it
is safer to conduct the test on the low-voltage side. If we assume that
the power loss under no load in the low-voltage winding is negligible,
then the corresponding approximate equivalent circuit as viewed from
the low-voltage side is given in Figure 3.1 From the approximate
equivalent of the transformer as referred to the low-voltage side
(Figure 3.1), it is evident that the source supplies the excitation current
under no load. One component of the excitation current is responsible
for the core loss, whereas the other is responsible to establish the
required flux in the magnetic core. In order to measure these values
exactly, the source voltage must be adjusted carefully to its rated
value. Since the only power loss in Figure 3.1 is the core loss, the
wattmeter measures the core loss in the transformer.
The core-loss component of the excitation current is in phase with the
applied voltage while the magnetizing current lags the applied voltage
by 90 degree. If 𝑉 𝑂𝐶 is the rated voltage applied on the low-voltage
side, I 𝑂𝐶is the excitation current as measured by the ammeter, and
𝑃 𝑂𝐶is the power recorded by the wattmeter, then the apparent power
at no-load is at a lagging power-factor angle of
𝑆 𝑜𝑐 = 𝑉𝑜𝑐 𝐼 𝑜𝑐
∅ 𝑜𝑐 = cos−1
𝑃𝑜𝑐
𝑆 𝑜𝑐

Figure 3.1 The approximate equivalent circuit of a two-winding transformer under open-circuit
test. [10]
The core-loss and magnetizing currents are
𝐼𝑐 = 𝐼𝑜𝑐 cos(∅ 𝑜𝑐)
𝐼 𝑚 = 𝐼𝑜𝑐 sin(∅ 𝑜𝑐)
The core-loss and magnetizing currents are
𝑅 𝑐 =
𝑉𝑜𝑐
𝐼𝑐
=
𝑉𝑜𝑐
2
𝑃𝑜𝑐
𝑋 𝑀 =
𝑉𝑜𝑐
𝐼 𝑀
=
𝑉𝑜𝑐
2
𝑄 𝑜𝑐
Where
𝑄 𝑜𝑐 = √ 𝑆 𝑜𝑐
2
− 𝑃𝑜𝑐
2

The Short-circuit Test
This test is designed to determine the winding resistances and leakage
reactance. The short-circuit test is conducted by placing a short circuit
across one winding and exciting the other from an alternating-voltage
source of the frequency at which the transformer is rated. The applied
voltage is carefully adjusted so that each winding carries a rated
current. The rated current in each winding ensures a proper simulation
of the leakage flux pattern associated with that winding. Since the
short circuit constrains the power output to be zero, the power input
to the transformer is low.
The measurement of the rated current suggests that, for safety
purposes, the test be performed on the high-voltage side.
Since the applied voltage is a small fraction of the rated voltage, both
the core loss and the magnetizing currents are so small that they can
be neglected. The approximate equivalent circuit of the transformer as
viewed from the high-voltage side is given in Figure 2.15. In this case,
the wattmeter records the copper loss at full load.
If 𝑉 𝑆𝐶, 𝐼 𝑆𝐶 and 𝑝 𝑠𝑐 are the readings on the voltmeter, ammeter, and
wattmeter,
Then
𝑅 𝑒𝑝 =
𝑃𝑠𝑐
𝐼𝑠𝑐
2
Is the total resistance of the two windings as referred to the high-
voltage side. The magnitude of the impedance as referred to the high-
voltage side is
𝑍 𝑒𝑝 =
𝑉𝑠𝑐
𝐼𝑠𝑐
Therefore, the total leakage reactance of the two windings as referred
to the high voltage side is
𝑋 𝑒𝑝 = √ 𝑍 𝑒𝐻
2
− 𝑅 𝑒𝐻
2

If we define the a-ratio as
𝑎 =
𝑁𝑠
𝑁𝑝
Figure 3.2 Approximated equivalent circuit of the transformer in short circuit case [12]
Where 𝑅 𝑝 is the resistance of the high-voltage winding, 𝑅 𝑠 is the
resistance of the low-voltage winding, 𝑋 𝑝 is the leakage reactance of
the high-voltage winding and 𝑋 𝑠 is the leakage reactance of the low-
voltage winding.
However, there is no simple way to separate the two leakage reactancs
(𝑅 𝑝 and, 𝑅 𝑠). The same is also true for the winding resistances if the
transformer is unavailable. If we have to segregate the resistances, we
will assume that the transformer has been designed in such a way that
the power loss on the high-voltage side is equal to the power loss on
the low-voltage side. This is called the optimum design criterion and
under this criterion [12].
𝐼 𝑝
2
𝑅 𝑝 = 𝐼𝑠
2
𝑅 𝑠
Which yields?
𝑅 𝑝 = 𝑎2
𝑅 𝑠 = 0.5𝑅 𝑒𝑝
and
𝑋 𝑝 = 𝑎2
𝑋𝑠 = 0.5𝑋 𝑒𝑝

CHAPTER 4
HARMONIC
Effect of power system harmonics on transformers
Transformer losses are classified into load and no-load losses. No-load
losses are those losses in a transformer whenever the transformer is
energized. No-load losses include, eddy current losses, magnetic
hysteresis, winding resistance to exciting current, and the losses of
dielectric materials. Load losses are those losses that exist with the
loading of transformers. Load losses vary with the square of the load
current and the dc resistance in the windings (𝐼2 𝑅 losses), core clamps,
the loss due to leakage fluxes in the windings, parallel winding strands
and other parts. For distribution transformers, the major source of
load losses is the 𝐼2 𝑅 losses in the windings.[5]
Total Harmonic Distortion (THD)
The total harmonic distortion of a signal is a measurement of the
harmonic distortion present. It is defined as the ratio of the sum of the
powers of all harmonic components to the power of the fundamental
frequency. Harmonic distortion is caused by the introduction of
waveforms at frequencies in multiplies of the fundamental. THD is a
measurement of the sum value of the waveform that is distorted.
%𝑇𝐻𝐷 =
√∑ (𝑥𝑖)2∞
𝑖=2
| 𝑋1|
The total harmonic content THD (Total Harmonic Distortion), of the
current or voltage can be calculated as can be seen from these two
equations.
%𝑇𝐻𝐷𝐼 =
√∑ (𝐼 𝑛)2∞
𝑖=2
| 𝐼1|
%𝑇𝐻𝐷 𝑉 =
√∑ (𝑉𝑛)2∞
𝑖=2
| 𝑉1|
Where, 𝑉 𝑛 represents the voltage harmonics and 𝐼 𝑛the current
harmonic contents of the system.

Effects of Harmonics on Transformers
Transformers are designed to deliver the required power to the
connected loads with minimum losses at fundamental frequency.
Harmonic distortion of the current, in particular, as well as the voltage
will contribute significantly to additional heating. There are three
effects that result in increased transformer heating when the load
current includes harmonic components:
1. RMS current. If the transformer is sized only for the KVA
requirements of the load, harmonic currents may result in the
transformer RMS current being higher than its capacity. The increased
total RMS current results increase conductor losses.
The %THD is a ratio of the root-mean-square (RMS) value of the
harmonic current to the RMS value of the fundamental.
%𝑇𝐻𝐷 =
√∑ (𝐼ℎ)2∞
ℎ=1
| 𝐼1|
2. Eddy-current losses. These are induced currents in the transformer
caused by the magnetic fluxes. These induced currents flow in the
windings, in the core, and in the other connecting bodies subjected to
the magnetic field of the transformer and cause additional heating.
This component of the transformer losses increases with the square of
the frequency of the current causing the eddy current. Therefore, this
becomes a very important component of transformer losses for
harmonic heating.
3. Core losses. The increase in core losses in the presence of the
harmonics will be dependent on the effect of the harmonics on the
applied voltage and the design of the transformer core. Increasing the
voltage distortion may increase the eddy currents in the core
laminations. The net impact that this will have depends on the
thickness of the core laminations and the quality of the core steel. The

CHAPTER 5
SIMULATIONS AND EXPERIMENTAL RESULTS
Experimental Results
The transformer used in the experiment is a single phase 1 KVA, 230
V/115 V Transformer, a Meco-g Portable Multifunction Meter is used
to measure voltage, current and power consumed and YOKOGAWA
power analyzer is used to Fast Fourier Transform (FFT) analysis.

Open circuit test results:
The open circuit test was per formed on the transformer to find the
core losses of the transformer. The secondary of the transformer was
left open circuited. The primary side is connected to Meco-g Portable
Multifunction Meter to measure the no load power loss, open circuit
voltages and open circuit current .
𝑽 𝒐𝒄(v) 𝑰 𝒐𝒄(𝑨) 𝑷 𝒐𝒄(𝑾)
115 0.563 38
Table1. Open circuit test results
Short circuit test results:
The short circuit test was done on the primary side of the transformer.
The secondary was short circuited and reduced voltage was applied to
the primary side to flow rated current in the primary winding. The
following results were obtained:
𝑽 𝒔𝒄(v) 𝑰 𝒔𝒄(𝑨) 𝑷 𝒔𝒄(𝑾)
12.2 4.326 52
Table2. Short circuit test results
230 V, 50 Hz
115/230 V
230/115 V
230 V, 50 Hz

From the above open circuit and short circuit tests the parameters of
the given transformer was calculated, The following values are
obtained:
Parameter Value
𝑽𝒑 230 V
𝑽𝒔 115 V
𝑹 𝒄 348.02 Ω
𝑿 𝒎 252.30 Ω
𝑳 𝒎 0.80309 H
𝑹 𝒔𝒄 2.77 Ω
𝑿 𝒔𝒄 0.52867 Ω
𝑳 𝒔𝒄 1.6828 mH
𝑹 𝒑 1.385 Ω
𝑳 𝒑 0.84138 mH
𝑹 𝒔 0.34625 Ω
𝑳 𝒔 0.21035 mH
Table 3: Transformer Technical Parameters
hh
k
Figure 5.3 equivalent circuit of transformer
𝑅 𝑝 = 1.385 Ω 𝐿 𝑝 = 0.844138 𝑚𝐻 𝑅 𝑠 = 0.34625 Ω
Ω
𝐿 𝑠 = 0.21035 𝑚𝐻
𝑅 𝑐 = 348.02 Ω 𝐿 𝑚

Harmonic Analysis under Cases of Linear and Nonlinear Load
Conditions (single phase transformer)
Case-1 (Linear Load)
No 𝐕𝐋 (𝐕) 𝐈 𝑳 (𝐀) 𝐏𝐨𝐮𝐭 (𝐖) 𝐑 𝐋 (Ω) Ø (°) PF 𝐔𝒕𝒉𝒅 % 𝐈𝒕𝒉𝒅 % 𝑷 𝒕𝒉𝒅 %
1 115.0 0.719 83 160 359.14 0.999 5.334 5.327 0.283
2 115.0 1.195 137 96 359.38 0.999 5.230 5.224 0.273
3 114.0 2.120 242 53.8 0.48 1 5.435 5.421 0.294
Tables 4: Linear Load Condition (single phase transformer)
(1)
(2)

Case-2: Capacitive Nonlinear Load Condition (single phase
transformer)
No 𝐕𝐋 (𝐕) 𝐈 𝑳 (𝐀) 𝐏𝐨𝐮𝐭 (𝐖) 𝐑 𝐋 (Ω) 𝐂 𝐋 (µ𝐅) Ø (°) PF 𝐔𝒕𝒉𝒅 % 𝐈𝒕𝒉𝒅 % 𝑷 𝒕𝒉𝒅 %
1 115.5 0.693 77 160.3 69.95 344.13 0.9619 5.173 5.401 0.290
2 115.2 1.176 95 68.7 45.58 314.55 0.7015 5.085 7.149 0.514
3 115.3 2.045 136 32.52 69.11 305.22 0.5767 5.360 9.090 0.829
Tables 5: Capacitive Non-Linear Load Condition (single phase transformer)
(1)
(2)

(3)
Case-3: Inductive Nonlinear Load Condition (single phase transformer)
No 𝐕𝐋 (𝐕) 𝐈 𝑳 (𝐀) 𝐏𝐨𝐮𝐭 (𝐖) 𝐑 𝐋 (Ω) 𝑳 𝐋 (𝐇) Ø (°) PF 𝐔𝒕𝒉𝒅 % 𝐈𝒕𝒉𝒅 % 𝑷 𝒕𝒉𝒅 %
1 87.2 0.715 51 99.76 0.2232 34.65 0.8226 5.455 1.469 0.028
2 86.9 1.190 81 57.199 0.1445 321.30 0.780 5.706 1.423 0.022
3 113.4 2.117 193 43.064 0.1014 36.66 0.8022 5.052 1.382 0.022
Tables 6: inductive Non-Linear Load Condition (single phase transformer)
(1)

Simulation Results and Figures:
Case-1 (For Linear Load)
No 𝐕𝐋 (𝐕) 𝐈 𝑳 (𝐀) 𝐏𝐨𝐮𝐭 (𝐖) 𝐑 𝐋 (Ω) PF 𝐔𝒕𝒉𝒅 % 𝐈𝒕𝒉𝒅 %
1 113.9 0.712 81.08 160 1 0.47 0.47
2 113.6 1.183 134.4 96 1 0.69 0.69
3 112.9 2.099 236.7 53.8 1 0.71 0.71
Tables 7: Linear Load Condition (single phase transformer without core saturation)
Figure S1: Simulink model for linear load condition without core saturation

Figure 1a: FFT analysis of current waveform
Figure 1b: FFT analysis of Voltage waveform

Case-2: Capacitive Nonlinear Load Condition
No 𝐕𝐋 (𝐕) 𝐈 𝑳 (𝐀) 𝐏𝐨𝐮𝐭 (𝐖) 𝐑 𝐋 (Ω) 𝐂 𝐋 (µ𝐅) PF 𝐔𝒕𝒉𝒅 % 𝐈𝒕𝒉𝒅 %
1 114.1 0.683 75.07 160.3 69.95 0.9621 0.15 0.15
2 113.9 1.163 92.76 68.7 45.58 0.7004 1.62 1.15
3 113.9 2.016 131.9 32.52 69.11 0.5749 2.31 1.83
Tables 8: Capacitive Non-Linear Load Condition (single phase transformer)
Figure S2: Simulink model for Capacitive Non-Linear Load Condition without core saturation
Figure 2a: FFT analysis of current waveform Figure 2b: FFT analysis of Voltage waveform

Case-3: Inductive Nonlinear Load Condition (single phase
transformer)
No 𝐕𝐋 (𝐕) 𝐈 𝑳 (𝐀) 𝐏𝐨𝐮𝐭 (𝐖) 𝐑 𝐋 (Ω) 𝑳 𝐋 (𝐇) PF 𝐔𝒕𝒉𝒅 % 𝐈𝒕𝒉𝒅 %
1 113.8 0.933 86.89 99.76 0.2232 0.8181 0.68 0.48
2 113.5 1.555 138.5 57.199 0.1445 0.7842 0.67 0.48
3 113.1 2.114 193.1 43.064 0.1014 0.8057 0.12 0.14
Tables 8: Inductive Non-Linear Load Condition (single phase transformer)
Figure S3: Simulink model for inductive Non-Linear Load Condition without core saturation
Figure 3a: FFT analysis of voltage waveform Figure 3b: FFT analysis of current waveform

CHAPTER 6
Conclusions and Future work
Conclusions
This study suggests that harmonics distortion results due to non-linear
loads causes. Three such cases of linear & non-linear loads with
resistive, inductive and capacitive scenarios were studied.
In case of linear load, we observed that the total harmonic distortion
in current and voltage is nearly same for both using experimentation
and using simulation in MATLAB but in case of non-linear load, the
total harmonic distortion in current and voltage are different for
MATLAB simulation in compare with experimentation. This is because
simulation in MATLAB involved linear approximation.
Future work
This work can be considered as preliminary study of harmonic
distortion for transformers. In this work, we have used only linear
transformer in simulation. Future work includes the simulation using
saturated non-linear transformers which can be compared with
experimental results.

REFERENCES
[1] Odendal, E.J, Prof., “Power Electronics Course notes”, Durban,
University of Natal, pg. 8.36.
[2] S.B.Sadati, A. Tahani, Darvishi, B., Dargahi, M., Yousefi, H.,“
Comparison of distribution transformer losses and capacity under
linear and harmonic loads,” Power and Energy Conference, 2008.
PECon 2008. IEEE 2nd International, 1-3 Dec. 2008 Page(s):1265 –
1269.
[3]https://www.electrical4u.com/what-is-transformer-definition-
working-principle-of-transformer/
[4] Michael A. Bjorge, “Investigation of Short-Circuit Models for A Four-
Winding Transformer”, MS Thesis, Michigan Tech University, 1996.
[5] Energy efficient transformers, Barry W. Kennedy Kennedy, Barry W.
1998

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