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ISSN 2249-863X (Online)
ISSN 2321-4244 (Print)
JoPEPS
Journal of Power Electronics & Power Systems
September–December 2016
SJIF: 4.456
www.stmjournals.com
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Journal of Power Electronics & Power Systems
ISSN: 2249-863X(online), ISSN: 2321-4244(print)
Focus and Scope Covers
Power Transmission, Distribution and Generation
Power Electronics and Communication
Electric Machinery and Power Engineering Systems
Energy Management Systems
Energy Systems Modeling & Simulation
Energy Development
Supervisory Control
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It is my privilege to present the print version of the [Volume 6 Issue 3] of our Journal of Power
Electronics & Power Systems (JoPEPS), 2016. The intension of JoPEPS is to create an atmosphere
that stimulates vision, research and growth in the area of Power Electronics & Power Systems.
Timely publication, honest communication, comprehensive editing and trust with authors and
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I hope you will enjoy reading this issue and we welcome your feedback on any aspect of the Journal.
Dr. Archana Mehrotra
Managing Director
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Director's Desk
STM JOURNALS
1. Design of a Closed Loop Boost Converter with Parametric Variation Analysis of PI Controller for Constant Output Voltage Applications Shetu Roy, Mohammad Abdul Mannan 1
2. Performance Evaluation of Brushless DC Motor during Sinusoidal and Trapezoidal Back-EMF Waveform Rima M. Pujara, C.K. Vibhakar 14
3. Power Control of Doubly Fed Induction Generator (DFIG) Based on IP ControllerA.K.M Rejwanul Haque, Mohammad Abdul Mannan, Junji Tamura 23
4. A Disaggregated Optimization Approach for Competitive Procurement of Energy and Operating ReserveAnuj Banshwar, Yog Raj Sood, Rajnish Shrivastava 33
5. Application of Accelerated PSO and ANN for optimal Scheduling of Hydrothermal SystemS.K. Gupta, Manisha Malik, Diksha Gupta 42
6. Evaluation Algorithm for Discrimination between Fault and Power Swing Using Independent Component AnalysisV.J. Upadhyay, A. S. Pandya 53
7. Design and Simulation of Z-Source Inverter Fed Brushless DC Motor Drive Supplied With Fuel Cell for Automotive ApplicationsMohsen Teimoori, Sayyed Hossein Edjtahed, Abolfazl Halvaei Niasar 60
8. The Frequency Characteristics of Transformer Windings Considering the Separation-Dependence of the Inter-Turn Mutual ParametersMohamed M. Saied 72
ContentsJournal of Power Electronics & Power Systems
JoPEPS (2016) 1-13 © STM Journals 2016. All Rights Reserved Page 1
Journal of Power Electronics & Power Systems ISSN: 2249-863X(online), ISSN: 2321-4244(print)
Volume 6, Issue 3
www.stmjournals.com
Design of a Closed Loop Boost Converter with Parametric
Variation Analysis of PI Controller for Constant Output
Voltage Applications
Shetu Roy*, Mohammad Abdul Mannan Department of Electrical and Electronics Engineering, American International University, Bangladesh
Abstract The DC-DC converters have an unregulated input dc voltage and a constant or regulated
output dc voltage. Switching DC-DC voltage converters have two elements: A controller and
a power stage. The power stage regulates the switching elements and converts input voltage to
output voltage. The controller controls the switching operation to regulate the output voltage.
The two systems are linked by a feedback loop that compares the actual output voltage with
the desired output to derive the error voltage. This paper will focus on modeling, analysis,
design and simulation of DC-DC boost converter architecture and will present an optimized
controller for constant voltage applications. The constant output applications have been
established by using pulse width modulation (PWM) with a proportional-integral (PI)
controller. PI Controller is the most widely used controller in various industrial &
technological applications. Here, trial and error method is used to set the controller
parameters & to get constant outputs. The calculations of the boost converter have been
examined through simulation results using MATLAB Simulink.
Keywords: Boost converter, duty cycle, PI controller, PWM Generator (DC-DC), trial &
error method
INTRODUCTION DC-DC converters are one of the most
important parts for alternative and renewable
energy conversion, modern devices and many
industrial applications. These converters are
essentially used to produce a regulated DC
voltage from an unregulated DC source which
includes the output of a rectifier, a solar cell or
a battery etc. A DC-DC switching converter is
always known to be a high efficient regulator
over a linear regulator because of its higher
efficiency. Various kinds of DC-DC
converters are used in Power Electronics and
control of power systems. Among them, the
boost converters have the highest applicable
sides. This converter is much used in Power
Electronics sectors [1]. Unlike other
converters, boost converter is always efficient
for higher output voltage, so it is very
important for increasing output DC voltage in
many kinds of applications [2]. It is a very
useful power stage system and most of the
times used as a step-up power stage converter.
The main purpose of this research paper is to
design a AC to DC boost converter with
constant voltage applications. Necessity of
constant voltage has been discussed with PI
controller because the non-linearity can arise
from parasitic parameter in boost converter.
The non-linearity can cause a serious
instability problem for boost converter control.
It makes the controller design difficult due to
sensitivity disturbances. The boost converters
also have two modes of operation similar to
other converters: Continuous Conduction
Mode and Discontinuous-Conduction Mode.
In this paper, constant output voltage has been
modified by analyzing the on-off conditions of
continuous conduction mode, so this converter
can be introduced as an AC to DC converter
[4]. At first AC is converted into DC using the
uncontrolled bridge rectifier, then this DC
input is converted into higher or constant DC
output voltage. The converter has been
designed in Matlab Simulink to analyze the
performance under the parametric variation of
conventional PI Controller.
This paper concerns with design and
simulation of a boost converter operated in
JoPEPS (2016) 14-22 © STM Journals 2016. All Rights Reserved Page 14
Journal of Power Electronics & Power Systems ISSN: 2249-863X(online), ISSN: 2321-4244(print)
Volume 6, Issue 3
www.stmjournals.com
Performance Evaluation of Brushless DC Motor during
Sinusoidal and Trapezoidal Back-EMF Waveform
Rima M. Pujara1,*, C.K. Vibhakar
2
Department of Electrical Engineering, V.V.P Engineering College, Rajkot, Gujarat, India
Abstract Due to increasing popularity and wide application in the drive system BLDC motor is widely
used. An undesirable signal in the brushless dc motor is a ripple in torque, which is in
challenging motor control and some machine tools. This article represents the performance
evolution of BLDC motor by using the sinusoidal and trapezoidal back EMF waveform for
getting the efficient operation of BLDC motor drives. In sinusoidal back EMF waveform
requires sinusoidal flux density; it also requires the high-resolution rotor position sensors. In
trapezoidal back EMF waveform, it requires lower resolution sensor. Non-ideal properties of
any source causes either phase current or back EMF waveform to depart from their entirely
sinusoidal waves, which will typically give rise to an undesired pulsating torque components.
In current waveform actually, inverter contribute to the torque ripple owing to the time
harmonics. BLDC motor is an actually electronic commutated motor. Torque control is
accomplished by challenging the back EMF waveform. BLDC motor is powered by the
semiconductor devices such that MOSFET. The corresponding results have been comparing
using MATLAB/ SIMULINK.
Keywords: BLDC motor, stator current, rotor angle, rotor position, ripple torque, stator back
EMF and hall effect signals
INTRODUCTION The brushless dc motor is supplied by the
integrated inverter produced ac signal to drive
the electric motor. Rotor housed the permanent
magnet and because of that, it is called as the
PMSM. In BLDC motor, three coils are wound
on to the stator and one by one coil will be
excited. Ripple torque is a combination of non-
zero phase inductances and finite inverters dc
voltages which prevent the phase current
excitation waveform from its changing the
levels instantaneously. Low power driving
arrangements are provided by the
semiconductor devices like MOSFET. The
stator of the BLDC motor is laminated by steel
stacked (Figure 1). The stator winding of the
motor is connected in either star or delta. For
reducing ripple torque, star connection is
preferred because half voltage is applied
between the stator winding.
JoPEPS (2016) 23-32 © STM Journals 2016. All Rights Reserved Page 23
Journal of Power Electronics & Power Systems ISSN: 2249-863X(online), ISSN: 2321-4244(print)
Volume 6, Issue 3
www.stmjournals.com
Power Control of Doubly Fed Induction Generator
(DFIG) Based on IP Controller
A.K.M Rejwanul Haque1, Mohammad Abdul Mannan
1,*, Junji Tamura2
1Department of Electrical and Electronics Engineering, Faculty of Engineering, American
International University Bangladesh (AIUB), Dhaka, Bangladesh 2Department of Electrical and Electronics Engineering, Kitami Institute of Technology, 165 Koen-
cho, Kitami, Hokkaido, 090-8507 Japan
Abstract Conventionally, the indirect power control of Doubly Fed Induction Generator (DFIG) has
been developed based on conventional Proportional-Plus-Integral (PI) controller due to its
simple construction and implementation. The steady-state error minimization, overshoot
elimination and disturbance rejection are not possible where the gains of PI controller are
chosen by trial and error method. The steady-state error and disturbance rejection can be
possible if the gains of PI controller are chosen by proper choosing of poles. But the
overshoot elimination is not possible where PI based control is designed. In this paper,
Integral-Plus-Proportional (IP) controller is proposed to design for power control of the
DFIG. The IP controller is well suited to minimized the overshoot problem which is arisen in
PI controller. The performance of proposed IP controller for power control of the DFIG
system is analyzed and investigated through the simulation work. The results of simulation
works are presented to demonstrate the effectiveness of propose IP controller compared with
conventional PI controller. The proposed IP controller shows the superior performance over
PI controller in terms of minimization of overshoot.
Keywords: Stator flux orientation control, Active and reactive power control, PI controller, IP
controller, Doubly fed induction generator
INTRODUCTION The demand of energy is emergent in a rapid
manner due to various reasons such as
environmental and economic complications.
The utilization of renewable source is
increased to meet the ever increasing energy
demand [1] due to the depletion of available
fossil fuel based conventional energy and
concern regarding environmental degradation.
Wind energy which is one of the potential
sources of clean renewable energy [2] and a
relatively low cost of electricity production [3]
system is became an important renewable
energy source and currently have the largest
utilization. The wind generation system is
connected to the electrical grid with other
generation systems using fossil fuel or nuclear
energy supplies electric power to enhance the
base power [4, 5]. The wind energy capacity in
worldwide has reached close to 320 GW by
the end of 2013 [6].The permanent-magnet
synchronous generator (PMSG) [6, 8] or DFIG
[9, 10] has recently been used as the generator
of electric power from wind energy.
Advantages have been variously attributed to
high power density for PMSG [11] and
reduced rating of power converters for DFIG
[12]. However, the PMSM suffers from high
cost of materials and manufacturing. The
DFIG is widely used due to a partial back-to-
back converter [13–15], which only handles
with the slip power. Compared to the WECS
that has a full rated power back-to-back
converter, such as permanent magnetic
synchronous generator (PMSG), squirrel-cage
induction generator (SCIG), the DFIG
technology with converters rated at about 25–
30% of the generator rating are used. Thus, the
DFIG-based wind turbines offer variable speed
operation, reduce flicker, four-quadrant active
and reactive power capabilities, lower
converter cost, and reduced power loss
compared to WECS using PMSG and SCIG
with full-sized converters. By controlling of
JoPEPS (2016) 33-41 © STM Journals 2016. All Rights Reserved Page 33
Journal of Power Electronics & Power Systems ISSN: 2249-863X(online), ISSN: 2321-4244(print)
Volume 6, Issue 3
www.stmjournals.com
A Disaggregated Optimization Approach for Competitive
Procurement of Energy and Operating Reserve
Anuj Banshwar1,*, Yog Raj Sood
1, Rajnish Shrivastava
2
1Department of Electrical Engineering, National Institute of Technology, Hamirpur,
Himachal Pradesh, India 2Department of Civil Engineering, Maulana Azad National Institute of Technology, Bhopal,
Madhya Pradesh, India
Abstract In restructured environment, Ancillary Services (AS) plays a vital role, as they are required
for reliable and secure operation of the power system. Operating Reserve (OR), as one of the
main AS, is a capability of a power system to prevent any unexpected imbalances caused by
generation, transmission or equipment outage has been considered in this work. The
approach is based on disaggregated clearing of energy and OR, which can support the
development of an effective reserve allocation and pricing methodology. This approach is
based on sequential clearing of Energy Market (EM) and Reserve Market (RM) with the
objective of procurement cost minimization. The optimization problem is formulated and
solved using Optimal Power Flow (OPF) technique which considers all transmission
constraints and power flow limits. In this model, the energy is procured first in EM followed
by OR in RM. The procurement of both energy and OR using sequential approach has been
demonstrated by considering modified IEEE 5-unit test system.
Keywords: Electric power deregulation, auction design, operating reserve, sequential
dispatch, energy market, reserve market
INTRODUCTION An electric power system has been dominated
by large systems over the years that had an
overall right over all the activities related to
generation, transmission and distribution of
power within their own territory. These
systems have been called as Vertically
Integrated Systems (VISs). These VISs were
responsible for providing power to everyone in
their obliged region. Since the 1990s, power
utilities worldwide have undergone a process
of restructuring in order to introduce
competition in the system. These reforms
include a clear separation between generation
and sale of electricity, and network
operations [1].
Earlier, VISs responsible for three major
actions viz. generation, transmission and
distribution have been now separated into
independent activities as Generating
Companies (GENCOs), Transmission
Companies (TRANCOs) and Distribution
Companies (DISCOs). In this paradigm,
GENCOs sell electricity either through
contracts with customers or by bidding short-
term energy into the spot market managed by
System Operator (SO). GENCOs interact with
SO by offering bids for providing the system
demand and AS. The SO is responsible for
trading energy to supply the demand in the
Forward Markets (FM) and for trading the AS
in both forward and Real Time Markets
(RTM).
FM operates on a day-ahead or hour-ahead
timeline, where customers (or retailers) on the
basis of their load demand bids into the market
definite time before the real time delivery
[2,3]. Almost all EM in the world institutes
such markets for energy transactions. RTMs
are used for matching generation equals to
demand on a real-time basis. The objective of
these markets is to efficiently obtain the
resources essential to meet the reliability of the
system. Such markets are instituted in
Australian (NEM), and the Ontario Electricity
Market (OEM) [4].
JoPEPS (2016) 42-52 © STM Journals 2016. All Rights Reserved Page 42
Journal of Power Electronics & Power Systems ISSN: 2249-863X (online), ISSN: 2321-4244(print)
Volume 6, Issue 3
www.stmjournals.com
Application of Accelerated PSO and ANN for Optimal
Scheduling of Hydrothermal System
S.K. Gupta1,*, Manisha Malik
1, Diksha Gupta
2
1Department of Electrical Engineering, Deenbandhu Chhotu Ram University of Science and
Technology, Murthal, Sonepat, Haryana, India 2Department of Electrical Engineering, University Institute of Engineering and Technology,
Kurukshetra University, Kurukshetra Haryana, India
Abstract A short range problem of hydrothermal scheduling of hydrothermal system with cascaded is
analyzed in this paper. The net head, water discharge rate and water transport delay between
connected reservoirs is considered in the problem. The developed algorithm is demonstrated
on a test system consisting one thermal plant and four cascaded hydro plants. The results
obtained by the APSO technique are compared to PSO and conventional technique. It is found
that result obtained by APSO approach is superior in term of fuel cost and lesser
computational time. The results of PSO, APSO and conventional technique are taking as
inputs for the training to ANN system. ANN provides better result as comparison of PSO,
APSO and conventional technique.
Keywords: Hydrothermal scheduling, Particle Swarm Optimization, Artificial Neural
Network, Accelerated Particle Swarm Optimization
INTRODUCTION Present power system consists of hydro and
thermal power stations both. There is need of
economic loading of integrated system. Many
heuristic methods such as: differential
evolution (DE) evolutionary programming
(EP) simulated annealing (SA) genetic
algorithm (GA) and PSO have been applied
for solving the hydrothermal scheduling
problem [1–12]. But these algorithms endure
from some drawbacks when applied to HTS
problem. Zhang J, Lin S, and Qiu W proposed
a modified chaotic differential evolution
approach by for handling constraints of the
hydrothermal scheduling problem [13].
Basu M. presented an improved differential
evolution technique for optimal scheduling of
hydrothermal system [14]. Wang Y and Zhou
J proposed an improved self-adaptive particle
swarm optimization technique to solve the
hydrothermal scheduling problem by adjusting
the parameter of particle swarm optimization
[15]. Reservoir volume constraints and the
inequality constraints in langrage multiplier
techniques have more difficulties to calculate
the schedules and require some special
process. The method of dynamic programming
and problem of dimensionality explosion used
the simulated annealing for the hydro thermal
scheduling purpose to overcome the above
difficulty. For the simulated annealing, tuning
related control parameters in the annealing
schedule is difficult and it may be too slow
when applied in hydrothermal scheduling
(HTS) problem. PSO and DE have exhibited
good properties of fast convergence in
optimization of HTS problem, but the main
drawback is that it reduces their global search
ability and premature degrades their
performance. The solution is optimal in EP
than the simulated annealing due to implicit
parallelism employed in evolutionary
programming. GA and EP provide a
reasonable solution occasionally, the main
disadvantage of GA and EP for solving HTS
problem is slow convergence.
To overcome the drawbacks of the above
mentioned methods, an improved accelerated
particle swarm optimization algorithm (APSO)
is proposed in this paper. In proposed
algorithm new factor is introduced which
increase the searching speed significantly. In
JoPEPS (2016) 53-59 © STM Journals 2016. All Rights Reserved Page 53
Journal of Power Electronics & Power Systems ISSN: 2249-863X(online), ISSN: 2321-4244(print)
Volume 6, Issue 3
www.stmjournals.com
Evaluation Algorithm for Discrimination between Fault
and Power Swing Using Independent Component Analysis
V.J. Upadhyay1,*, A. S. Pandya
2
1Department of Electrical Engineering, Lalbhai Dalpatbhai College of Engineering, Ahmedabad,
Gujarat, India 2Department of Electrical Engineering, Government Polytechnic, Rajkot, Gujarat, India
Abstract The analysis of faults and disturbances in power systems is a basic requirement for a secure
and reliable electrical power supply. Independent component analysis (ICA) is an efficient
computational method used to find out hidden components in a set of sampled data. The basic
target of ICA is to find a linear representation and relation between nongaussian data
captured during disturbance, so that the components are statistically independent, or as
independent as possible. This paper explains the application of ICA as an abrupt change
detection technology to detect the abrupt changes in segmented current and voltage signals,
which are recorded during fault or disturbance. Also show how the detected abrupt change in
signal segment is discriminated in fault and power swing.
Keywords: Distance protection, Abrupt change detection, Power Swing, Disturbance analysis,
Relay performance
INTRODUCTION Power system instability problem has been a
growing problem since the last couple of
decades and is emerging as a dominant threat
for secure and reliable operation of power
systems. The system stability is at risk as large
amounts of power are commonly transferred
across a transmission system which was not
designed for such transactions. Also the power
system is designed to withstand larger types of
faults, line switching, and certain system
disturbances may cause loss of synchronism
between a generator and rest of the utility
system, or between interconnected power
systems of neighboring utilities. Large, stable
or unstable, power swings can cause unwanted
relay operations at different position of
system, which can again increases the severity
of the power-system disturbance and possibly
lead to cascading outages [1]. It is very
difficult for a protective system to avoid
unwanted tripping during stable power swing
condition. So this limitation of system makes
the detection of abrupt change a very
important process. The first meaning of abrupt
change is a time instant at which properties of
a signal data suddenly change [2]. So many
methods are used to detect this abrupt changes
occurred during different kinds of faults and
disturbances occurred in power system [3]. In
this paper independent component analysis is
used as an abrupt changes detection algorithm
to find instants of abrupt changes in signal
during fault in power system. Independent
component analysis (ICA) is a computational
method for separating a multivariate signal
into additive subcomponents by assuming that
the subcomponents are nongaussian signals
and that they are all statistically independent
from each other. ICA is a special case of blind
source separation [4].
ABRUPT CHANGES DETECTION
PROCESS The basic meaning of abrupt change is, a time
instant at which properties of the parameters
under considerations of system suddenly
change, but before and after which properties
remain constant in some sense, e.g., stationary
[4]. Abrupt change detection algorithm is a
combination of following processes:
Segmentation of fault signal.
Construction of feature vector.
Application of pattern matching
algorithm [5].
60Page © STM Journals 2016. All Rights Reserved 71-60JoPEPS (2016)
Journal of Power Electronics & Power Systems ISSN: 2249-863X (online), ISSN: 2321-4244(print)
Volume 6, Issue 3 www.stmjournals.com
Design and Simulation of Z-Source Inverter Fed Brushless
DC Motor Drive Supplied With Fuel Cell for Automotive
Applications
Mohsen Teimoori1, Sayyed Hossein Edjtahed
2, Abolfazl Halvaei Niasar
2,*
1Department of Electrical and Computer Engineering, University of Kashan, Kashan, Iran
2Department of Electrical Engineering, University of Allameh Feiz Kashani, Kashan, Iran
Abstract This paper presents design and simulation of Z-source inverter fed brushless DC motor drive
supplied with fuel cell for automotive applications. The brushless DC (BLDC) motor are used
due to many advantages such as high efficiency, high torque, high reliability, high-power
density, lower maintenance compared to other motors in electric transport applications. The
BLDC motor drive is with voltage source inverter (VSI) or current source inverter (CSI)
because of low efficiency, high thermal loss, and inductor and capacitor large values
inherently unreliable. Also shoot-through in DC bus in VSI and open circuit in DC link in CSI
causes damage to the power source connected to the inverter, such as fuel cells, solar cells or
the battery. In VSI and CSI are for increasing and decreasing the output voltage needs to
separate DC-DC Buck and Boost converter. But their disadvantages have been overcome in
the Z-source inverter using two inductors and capacitors. Also the Z-source inverter has
inherent protection against shoot-through in the DC bus and boost voltage ability. In this
paper the BLDC motor drive supplied to the fuel cell via a Z-source inverter are designed and
evaluated. The simulation results show that the output voltage of fuel cell less can be settled in
desired zone with changing capacitors and inductors and operating duty cycle.
Keywords: Brushless DC motor (BLDC), impedance source inverter (ZSI), fuel cell, Shoot-
through duty cycle, conventional inverter
INTRODUCTION Electric motors have been known as one of the
major consumers of electrical power today.
The brushless DC (BLDC) motor is used
because very high efficiency, high-power
density and torque, simple structure, low
maintenance costs and easy control method in
automotive appliances, aerospace and
industrial widely [1].
A brushless motor is a synchronous rotating
machine, which has permanent magnet rotor
and certain situations of rotating shaft rotor
use for electronic commutation [2].
To rotate a BLDC motor stator windings
should be energized according to the position
of rotor, therefore knowing the information of
the rotor angular position is essential to control
BLDC motor drive. For this purpose, Hall-
Effect sensors are generally used [3, 4].
Inverters are equipment that is used to convert
direct current (DC) to alternating current (AC).
The voltage source inverter (VSI) has less
output voltage than DC supply voltage [5], and
to increase the output voltage the boost
converter is needed.
Incurrent source inverter (CSI), output voltage
is greater than DC supply voltage, and to
reduce the output voltage, the buck converter
is used. To overcome these problems
impedance source inverter (ZSI) can be
used [17].
It has many usages for increasing the output
voltage and inherent protection against shoot-
through in DC bus, high efficiency, drive
strength, and reduce cost and size of the
passive elements and the elimination of dead
time.
JoPEPS (2016) 72-81 © STM Journals 2016. All Rights Reserved Page 72
Journal of Power Electronics & Power Systems ISSN: 2249-863X (online), ISSN: 2321-4244(print)
Volume 6, Issue 3
www.stmjournals.com
The Frequency Characteristics of Transformer Windings
Considering the Separation-Dependence of the Inter-Turn
Mutual Parameters
Mohamed M. Saied* Professor (Emeritus), IEEE Senior Member, Independent Researcher, 6-Hassan-Mohamed str.,
El-Haram, Giza, Cairo, Egypt
Abstract The paper presents a direct method for the determination of the frequency characteristics of
transformer windings. The dependence of both the inter-turn mutual inductances and
capacitances on the separation between these winding turns is taken into consideration. From
measured data available in the literature, a formula for this dependence is derived. The
voltage and current distributions along the winding will be governed by two integro-
differential equations in terms of the location along the winding and the frequency. A direct
solution of these equations will be presented. It does not require any numerical iterative
techniques or finite difference analyses. The frequency response, including the series and
parallel resonance frequencies as well as the winding’s frequency-dependent input impedance
for sample case studies are presented and discussed. Different transformer’s neutral
treatments are addressed. These results are compared with the corresponding ones ignoring
the non-uniformity of the mutual elements. In order to validate the proposed method, the
paper is concluded by addressing special cases with known exact solutions.
Keywords: Power transformers, winding, modeling, distributed parameter circuits, non-
uniform, frequency response, resonance, impedance characteristics, mutual parameters,
integro-differential equations
INTRODUCTION The time- and frequency-domain analyses of
transformer windings were the topic of
numerous studies such as those documented in
many findings [1–14, 17]. In particular, the
frequency, and the complex s-domain
approach, has been successfully used in
several situations in order to derive closed-
form analytical expressions for the voltages
and current distributions along the
transformers’ windings and for identifying
their series and parallel resonance frequencies
[4–6].
In the work [7], which is based on a
concentrated parameter approach, the winding
is represented by the cascade connection of an
adequate number of non-identical ladder
circuits. This is followed by solving the
corresponding set of simultaneous differential
and algebraic equations. The model could be
refined by applying an alternative
concentrated-parameter recursive s-domain
analytical solution technique [8]. Investigators
[10, 11] suggest a more accurate and efficient
approach based on the distributed parameter
analysis applying the concept of the
frequency- and location-dependent A, B, C, D
circuit constants, adopted from the
transmission line theory.
The majority of the currently available
procedures for analyzing transformer windings
with non-uniformly distributed parameters
apply numerical techniques. The study [12]
presents a direct analytical procedure for
analyzing windings with non-uniform
location-dependent series inductance. It is
based on the assumption of a quadratic
distribution for the winding’s series
inductance. The analysis of windings
exhibiting non-uniform inter-turn insulation
capacitance is given in [13]. The approach is
based on the numerical solution of a system of
partial differential equations with location-
dependent coefficients in the time domain. An
ISSN 2249-863X (Online)
ISSN 2321-4244 (Print)
JoPEPS
Journal of Power Electronics & Power Systems
September–December 2016
SJIF: 4.456
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