Journal of Power Electronics & Power Systems vol 6 issue 3

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JoPEPS

ISSN 2249-863X (Online) ISSN 2321-4244 (Print)

Journal of Power Electronics & Power Systems SJIF: 4.456

September–December 2016

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Journal of Power Electronics & Power Systems ISSN: 2249-863X(online), ISSN: 2321-4244(print)

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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 readers have been the hallmark of our journals. STM Journals provide a platform for scholarly research articles to be published in journals of international standards. STM journals strive to publish quality paper in record time, making it a leader in service and business offerings. The aim and scope of STM Journals is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high level learning, teaching and research in all the Science, Technology and Medical domains. Finally, I express my sincere gratitude to our Editorial/ Reviewer board, Authors and publication team for their continued support and invaluable contributions and suggestions in the form of authoring write-ups/reviewing and providing constructive comments for the advancement of the journals. With regards to their due continuous support and co-operation, we have been able to publish quality Research/Reviews findings for our customers base. I hope you will enjoy reading this issue and we welcome your feedback on any aspect of the Journal.

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Journal of Power Electronics & Power Systems

Contents

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 Controller A.K.M Rejwanul Haque, Mohammad Abdul Mannan, Junji Tamura

23

4. A Disaggregated Optimization Approach for Competitive Procurement of Energy and Operating Reserve Anuj Banshwar, Yog Raj Sood, Rajnish Shrivastava

33

5. Application of Accelerated PSO and ANN for optimal Scheduling of Hydrothermal System S.K. Gupta, Manisha Malik, Diksha Gupta

42

6. Evaluation Algorithm for Discrimination between Fault and Power Swing Using Independent Component Analysis V.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 Applications Mohsen Teimoori, Sayyed Hossein Edjtahed, Abolfazl Halvaei Niasar

60

8. The Frequency Characteristics of Transformer Windings Considering the Separation-Dependence of the Inter-Turn Mutual Parameters Mohamed M. Saied

72


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) 1-13 Š STM Journals 2016. All Rights Reserved

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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. Vibhakar2 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 nonzero 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) 14-22 Š STM Journals 2016. All Rights Reserved

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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 Mannan1,*, Junji Tamura2 1

Department of Electrical and Electronics Engineering, Faculty of Engineering, American International University Bangladesh (AIUB), Dhaka, Bangladesh 2 Department of Electrical and Electronics Engineering, Kitami Institute of Technology, 165 Koencho, 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-toback 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) 23-32 © STM Journals 2016. All Rights Reserved

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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 Sood1, Rajnish Shrivastava2 1

Department of Electrical Engineering, National Institute of Technology, Hamirpur, Himachal Pradesh, India 2 Department 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 shortterm 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].

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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 Malik1, Diksha Gupta2 1

Department of Electrical Engineering, Deenbandhu Chhotu Ram University of Science and Technology, Murthal, Sonepat, Haryana, India 2 Department 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) 42-52 © STM Journals 2016. All Rights Reserved

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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. Pandya2 1

Department of Electrical Engineering, Lalbhai Dalpatbhai College of Engineering, Ahmedabad, Gujarat, India 2 Department 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].

JoPEPS (2016) 53-59 © STM Journals 2016. All Rights Reserved

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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 Edjtahed2, Abolfazl Halvaei Niasar2,* 1

Department of Electrical and Computer Engineering, University of Kashan, Kashan, Iran Department of Electrical Engineering, University of Allameh Feiz Kashani, Kashan, Iran

2

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, Shootthrough 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].

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.

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].

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].

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, HallEffect sensors are generally used [3, 4].

It has many usages for increasing the output voltage and inherent protection against shootthrough in DC bus, high efficiency, drive strength, and reduce cost and size of the passive elements and the elimination of dead time.

JoPEPS (2016) 60-71 Š STM Journals 2016. All Rights Reserved

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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 integrodifferential 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, nonuniform, 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 closedform 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 locationdependent coefficients in the time domain. An

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JoPEPS

ISSN 2249-863X (Online) ISSN 2321-4244 (Print)

Journal of Power Electronics & Power Systems SJIF: 4.456

September–December 2016

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