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Full-Text Articles in Physical Sciences and Mathematics

Uc Modules With Respect To A Torsion Theory, Seçi̇l Çeken, Mustafa Alkan Jan 2012

Uc Modules With Respect To A Torsion Theory, Seçi̇l Çeken, Mustafa Alkan

Turkish Journal of Mathematics

In this paper, we give some characterizations of modules M over a ring R such that every submodule has a unique closure relative to a hereditary torsion theory on Mod-R by using the concept of \tau-closed submodule which was studied in [2]. We compare UC and \tau-UC modules and examine the relationships between them. We also give some examples of \tau-UC and UC modules and submodules which have a unique \tau-closure and unique closure.


Contact Cr-Warped Product Submanifolds In Generalized Sasakian Space Forms, Si̇bel Sular, Ci̇han Özgür Jan 2012

Contact Cr-Warped Product Submanifolds In Generalized Sasakian Space Forms, Si̇bel Sular, Ci̇han Özgür

Turkish Journal of Mathematics

We consider a contact CR-warped product submanifold M=M_{\top} \times_fM_{\bot} of a trans-Sasakian generalized Sasakian space form \widetilde{M} (f_1,f_2,f_3). We show that M is a contact CR-product under certain conditions.


Results Of Generalized Local Cohomology Modules Of A-Minimax Modules, Hero Saremi Jan 2012

Results Of Generalized Local Cohomology Modules Of A-Minimax Modules, Hero Saremi

Turkish Journal of Mathematics

Let R be a commutative Noetherian ring, M a finitely generated R-module, and N a minimax R-module. It is shown that if a is an ideal of R, such that cd(a)=1, where cd is the cohomological dimension of a in R, then H_a^j(M, N) and Ext_R^i(M,H_a^j(N)) are a-cominimax for all i,j. Furthermore, if t is a non-negative integer such that H_a^j(M, N) is a-minimax for all j


Extensions And S-Comparability Of Exchange Rings, Chaoling Huang Jan 2012

Extensions And S-Comparability Of Exchange Rings, Chaoling Huang

Turkish Journal of Mathematics

Let S be a ring extension of R. In this note, for any positive integer s we study s-comparability related to ring extensions. We show that if S is an excellent extension of R, R and S are exchange rings, and R has the n-unperforation property. R satisfies s-comparability if and we only if so does S, and we prove that for a 2-sided ideal J of S, and an exchange subring R of the exchange ring S, which contains J as a direct summand, then R satisfies s-comparability if and only if so does R/J.


P-Rank And P-Groups In Algebraic Groups, Adrien Deloro Jan 2012

P-Rank And P-Groups In Algebraic Groups, Adrien Deloro

Turkish Journal of Mathematics

A few remarks on the measures of the p-rank of a group equipped with a dimension, including the refutation of a result of Burdges and Cherlin.


Flat Surfaces In The Minkowski Space E^3_1 With Pointwise 1-Type Gauss Map, Uğur Dursun, Emel Coşkun Jan 2012

Flat Surfaces In The Minkowski Space E^3_1 With Pointwise 1-Type Gauss Map, Uğur Dursun, Emel Coşkun

Turkish Journal of Mathematics

In this article, we obtain all nonplanar cylindrical surfaces in the Minkowski space E^3_1 with pointwise 1-type Gauss map of the second kind. We also prove that right circular cones and hyperbolic cones in E^3_1 are the only cones in E^3_1 with pointwise 1-type Gauss map of the second kind. We conclude that there is no tangent developable surface fully lying in E^3_1 with pointwise 1-type Gauss map of the second kind.


A New Formulation Method For Solving Kinematic Problems Of Multiarm Robot Systems Using Quaternion Algebra In The Screw Theory Framework, Emre Sariyildiz, Hakan Temeltaş Jan 2012

A New Formulation Method For Solving Kinematic Problems Of Multiarm Robot Systems Using Quaternion Algebra In The Screw Theory Framework, Emre Sariyildiz, Hakan Temeltaş

Turkish Journal of Electrical Engineering and Computer Sciences

We present a new formulation method to solve the kinematic problem of multiarm robot systems. Our major aims were to formulize the kinematic problem in a compact closed form and avoid singularity problems in the inverse kinematic solution. The new formulation method is based on screw theory and quaternion algebra. Screw theory is an effective way to establish a global description of a rigid body and avoids singularities due to the use of the local coordinates. The dual quaternion, the most compact and efficient dual operator to express screw displacement, was used as a screw motion operator to obtain the …


New Change Impact Factor Estimation In Software Development, Murat Kahraman Güngör, Ersi̇n Elbaşi, James Walter Fawcett Jan 2012

New Change Impact Factor Estimation In Software Development, Murat Kahraman Güngör, Ersi̇n Elbaşi, James Walter Fawcett

Turkish Journal of Electrical Engineering and Computer Sciences

Change in software is always an essential part of software development and maintenance. Estimating a proposed change's effect on the later phases of the development helps project managers and developers with decision-making and predicting future progress. During development, on some occasions, speedy solutions are necessary to meet project schedules. Such quick changes may lead to major quality flaws in the long term, even though they solve local problems in the short term. Controlled management of change is achieved by being able to estimate the impact of changes. In this paper, we propose a new change impact factor estimation and present …


Action-Reaction Based Parameters Identification And States Estimation Of Flexible Systems, Islam Shoukry, Emrah Deni̇z Kunt, Asif Sabanovic Jan 2012

Action-Reaction Based Parameters Identification And States Estimation Of Flexible Systems, Islam Shoukry, Emrah Deni̇z Kunt, Asif Sabanovic

Turkish Journal of Electrical Engineering and Computer Sciences

This work attempts to identify and estimate flexible system's parameters and states by a simple utilization of the Action-Reaction law of dynamical systems. Attached actuator to a dynamical system or environmental interaction imposes an action that is instantaneously followed by a dynamical system reaction. The dynamical system's reaction carries full information about the dynamical system including system parameters, dynamics and externally applied forces that arise due to system interaction with the environment. This in turn implies that the dynamical system's reaction can be considered as a natural feedback as it carries full coupled information about the dynamical system. The idea …


Ttradeoff Tables For Compression Functions: How To Invert Hash Values Radeoff Tables For Compression Functions: How To Invert Hash Values, Orhun Kara, Adem Atalay Jan 2012

Ttradeoff Tables For Compression Functions: How To Invert Hash Values Radeoff Tables For Compression Functions: How To Invert Hash Values, Orhun Kara, Adem Atalay

Turkish Journal of Electrical Engineering and Computer Sciences

Hash functions are one of the ubiquitous cryptographic functions used widely for various applications such as digital signatures, data integrity, authentication protocols, MAC algorithms, RNGs, etc. Hash functions are supposed to be one-way, i.e., preimage resistant. One interesting property of hash functions is that they process arbitrary-length messages into fixed-length outputs. In general, this can be achieved mostly by applying compression functions onto the message blocks of fixed length, recursively. The length of the message is incorporated as padding in the last block prior to the hash, a procedure called the Merkle-Damgard strengthening. In this paper, we introduce a new …


Reducing Electromagnetic Interferences In Flyback Ac-Dc Converters Based On The Frequency Modulation Technique, Gökhan Çabuk, Selçuk Kilinç Jan 2012

Reducing Electromagnetic Interferences In Flyback Ac-Dc Converters Based On The Frequency Modulation Technique, Gökhan Çabuk, Selçuk Kilinç

Turkish Journal of Electrical Engineering and Computer Sciences

One of the most preferable types of switched-mode power supplies (SMPS) is the flyback converter, due to its wide range of application areas. Properties such as low cost, provision of multiple output voltage terminals, and higher efficiencies make it important, and hence its usage in technologies including cell phone chargers, personal computers, set-top boxes, and televisions is increasing. Special attention should be paid to the design of this type of converter due to its working principles and electromagnetic interference (EMI) performance. Rapid switching of high current and high voltage during the operation of SMPS causes an EMI problem. The level …


A Robust Adaptive Fuzzy Control Of A Unified Power Flow Controller, Sebaa Morsli, Allaoui Tayeb, Denai Mouloud, Chaker Abdelkader Jan 2012

A Robust Adaptive Fuzzy Control Of A Unified Power Flow Controller, Sebaa Morsli, Allaoui Tayeb, Denai Mouloud, Chaker Abdelkader

Turkish Journal of Electrical Engineering and Computer Sciences

This paper investigates the control of a unified power flow controller (UPFC) to improve the stability of a power system, hence providing security under increased power flow conditions. The proposed control methods include a direct proportional and integral (PI) controller and an adaptive fuzzy logic controller (AFLC). The performances of these controllers were evaluated under different operating conditions of the power system and the results demonstrated that PI and AFLC are very effective in improving the transient power system stability and very robust against variable transmission line parameters.


Lyapunov's Direct Method For Stabilization Of The Furuta Pendulum, Türker Türker, Haluk Görgün, Gali̇p Cansever Jan 2012

Lyapunov's Direct Method For Stabilization Of The Furuta Pendulum, Türker Türker, Haluk Görgün, Gali̇p Cansever

Turkish Journal of Electrical Engineering and Computer Sciences

This paper presents a novel stabilization result for the Furuta pendulum for a large region of attraction including almost all of the upper half plane. The solution is obtained via constructing a Lyapunov function after set of coordinate changes. Then, a set of differential equations are solved to achieve asymptotic stability which is proved in accordance with La Salle's invariance principle. The effectiveness of the proposed stabilization method is illustrated with simulation studies.


Energy Savings In Simultaneous Multi-Threaded Processors Through Dynamic Resizing Of Datapath Resources, Gürhan Küçük, Mi̇ne Mesta Jan 2012

Energy Savings In Simultaneous Multi-Threaded Processors Through Dynamic Resizing Of Datapath Resources, Gürhan Küçük, Mi̇ne Mesta

Turkish Journal of Electrical Engineering and Computer Sciences

Nowadays, all the designers of systems from high-performance servers to battery-operated handheld devices aim for reliability, high-performance and longevity. Central within these aims the issue of processor power consumption is becoming increasingly important. In this study, we aim to adapt our already-proven method for single-threaded superscalar processors to simultaneous multi-threaded (SMT) processors for energy savings. The original method focused on resizing datapath resources according to the demands of running applications. To achieve this, the targeted resources are physically divided into multiple partitions, and turned on and off according to the needs of the applications. Since, the energy consumption of the …


An Improved Distributed Power-Control Scheme For Cellular Mobile Systems, Hamid Farrokhi, Mostafa Rezayi Jan 2012

An Improved Distributed Power-Control Scheme For Cellular Mobile Systems, Hamid Farrokhi, Mostafa Rezayi

Turkish Journal of Electrical Engineering and Computer Sciences

In this paper, a new distributed power-control (DPC) scheme is suggested to improve convergence speed and system robustness against carrier-to-interference-ratio (CIR) estimation errors. To expedite the CIR balancing in our DPC scheme, an instability detection rule was used. As compared with Foschini's DPC (FDPC) method, numerical results indicated that the proposed algorithm achieves performance improvements in terms of outage probability as well as in the algorithm's convergence speed. More specifically, by appropriate selection of some parameters, the algorithm speed reduces from about 90 iterations in FDPC to 9 iterations in the proposed algorithm. The system robustness against CIR estimation errors …


Tunable Srr-Based Substrate For A Microstrip Patch Antenna, Adnan Sondaş, Mustafa Hi̇kmet Bi̇lgehan Uçar, Yunus Emre Erdemli̇ Jan 2012

Tunable Srr-Based Substrate For A Microstrip Patch Antenna, Adnan Sondaş, Mustafa Hi̇kmet Bi̇lgehan Uçar, Yunus Emre Erdemli̇

Turkish Journal of Electrical Engineering and Computer Sciences

In this paper, a microstrip patch antenna over an artificial substrate composed of split-ring resonator (SRR) elements is introduced. As the SRR-based substrate provides miniaturization for the patch, metallic loadings placed between the rings of the SRR elements offer frequency-tuning capability. Practical switch models are employed in lieu of those loadings to demonstrate dynamic control of the operational frequency. The full-wave analysis and design of the proposed tunable patch were carried out using CST Microwave Studio, and the cross-comparisons were provided via Ansoft HFSS. Preliminary measurements are also presented, demonstrating the prospective performance of the proposed design.


Fuzzy Logic Control For A Wind/Battery Renewable Energy Production System, Onur Özdal Mengi̇, İsmai̇l Hakki Altaş Jan 2012

Fuzzy Logic Control For A Wind/Battery Renewable Energy Production System, Onur Özdal Mengi̇, İsmai̇l Hakki Altaş

Turkish Journal of Electrical Engineering and Computer Sciences

In this study, a designed proportional-integral (PI) controller and a fuzzy logic controller (FLC) that fix the voltage amplitude to a constant value of 380 V and 50 Hz for loads supplied from a wind/battery hybrid energy system are explained and compared. The quality of the power produced by the wind turbine is affected by the continuous and unpredictable variations of the wind speed. Therefore, voltage-stabilizing controllers must be integrated into the system in order to keep the voltage magnitude and frequency constant at the load terminals, which requires constant voltage and frequency. A fuzzy logic-based controller to be used …


Discrete Particle Swarm Optimization For The Team Orienteering Problem, Ai̇şe Zülal Şevkli̇, Fati̇h Erdoğan Sevi̇lgen Jan 2012

Discrete Particle Swarm Optimization For The Team Orienteering Problem, Ai̇şe Zülal Şevkli̇, Fati̇h Erdoğan Sevi̇lgen

Turkish Journal of Electrical Engineering and Computer Sciences

In this paper, a novel discrete particle swarm optimization (PSO) algorithm is proposed to solve the team orienteering problem (TOP). Discrete evaluation is achieved by redefining all operators and operands used in PSO. To obtain better results, a strengthened PSO, which improves both exploration and exploitation during the search process, is employed. Our algorithm achieves the best known solutions in a short time compared to previous heuristics for the TOP.


A Modified Particle Swarm Optimization Algorithm And Its Application To The Multiobjective Fet Modeling Problem, Ufuk Özkaya, Fi̇li̇z Güneş Jan 2012

A Modified Particle Swarm Optimization Algorithm And Its Application To The Multiobjective Fet Modeling Problem, Ufuk Özkaya, Fi̇li̇z Güneş

Turkish Journal of Electrical Engineering and Computer Sciences

This paper introduces a modified particle swarm algorithm to handle multiobjective optimization problems. In multiobjective PSO algorithms, the determination of Pareto optimal solutions depends directly on the strategy of assigning a best local guide to each particle. In this work, the PSO algorithm is modified to assign a best local guide to each particle by using minimum angular distance information. This algorithm is implemented to determine field-effect transistor (FET) model elements subject to the Pareto domination between the scattering parameters and operation bandwidth. Furthermore, the results are compared with those obtained by the nondominated sorting genetic algorithm-II. FET models are …


Performance Comparison Of New Nonparametric Independent Component Analysis Algorithm For Different Entropic Indexes, Yusuf Sevi̇m, Ayten Atasoy Jan 2012

Performance Comparison Of New Nonparametric Independent Component Analysis Algorithm For Different Entropic Indexes, Yusuf Sevi̇m, Ayten Atasoy

Turkish Journal of Electrical Engineering and Computer Sciences

Most independent component analysis (ICA) algorithms use mutual information (MI) measures based on Shannon entropy as a cost function, but Shannon entropy is not the only measure in the literature. In this paper, instead of Shannon entropy, Tsallis entropy is used and a novel ICA algorithm, which uses kernel density estimation (KDE) for estimation of source distributions, is proposed. KDE is directly evaluated from the original data samples, so it solves the important problem in ICA: how to choose nonlinear functions as the probability density function (pdf) estimation of the sources.


Performance Analysis Of Wind Turbine-Driven Permanent Magnet Generator With Matrix Converter, Ramasamy Bharanikumar, A Nirmal Kumar Jan 2012

Performance Analysis Of Wind Turbine-Driven Permanent Magnet Generator With Matrix Converter, Ramasamy Bharanikumar, A Nirmal Kumar

Turkish Journal of Electrical Engineering and Computer Sciences

Wind energy, among all of the renewable energy sources, has made rapid developments and significant inroads in electrical power systems. With the increased use of wind energy conversion systems (WECSs), several technologies have been developed. Since WECSs are more cost competitive, the comparison of different wind generator systems is the need of the hour. Permanent magnet generators employing these technologies have some significant advantages over conventional generators, such as no need of excitation, low volume and weight, high precision, and deletion of the gearbox. A variable-speed WECS with a permanent magnet generator and a matrix converter is proposed in this …


Economic Analysis Of A Wind-Battery Hybrid System: An Application For A House In Gebze, Turkey, With Moderate Wind Energy Potential, Bahti̇yar Dursun, Ci̇han Gökçöl Jan 2012

Economic Analysis Of A Wind-Battery Hybrid System: An Application For A House In Gebze, Turkey, With Moderate Wind Energy Potential, Bahti̇yar Dursun, Ci̇han Gökçöl

Turkish Journal of Electrical Engineering and Computer Sciences

In this study, the energy demand of a house in Gebze, Turkey, is met by using wind energy as a primary energy source combined with rechargeable batteries. The wind-battery system is simulated by MATLAB while considering that energy continuity is maintained by using a sufficient number of batteries. A life-cycle cost analysis is carried out over a 20-year system lifetime because the operating time of the hybrid system is subject to the turbine life, usually assumed to be 20 years. The wind turbine generators considered are of various nominal powers, ranging from 0.6 to 450 kW. For each wind turbine, …


Short-Term Wind Speed Estimation Based On Weather Data, Okan Özgönenel, David W.P. Thomas Jan 2012

Short-Term Wind Speed Estimation Based On Weather Data, Okan Özgönenel, David W.P. Thomas

Turkish Journal of Electrical Engineering and Computer Sciences

For accurate and efficient use of wind power, it is important to know the statistical characteristics, availability, diurnal variation, and prediction of wind speed. Prediction of wind power permits the scheduling of the connection or the disconnection of wind turbines to achieve optimal operating costs. In this paper, a simple and accurate method for predicting wind speed based on weather-sensitive data is presented. The proposed wind speed prediction system is cost-effective and only needs wind speed data at 40 m and weather data to forecast wind speeds at 50 m and 60 m for the current and next months. Hellman …


Compact Dual-Band Split-Ring Antenna For 2.4/5.2 Ghz Wlan Applications, Siddik Cumhur Başaran Jan 2012

Compact Dual-Band Split-Ring Antenna For 2.4/5.2 Ghz Wlan Applications, Siddik Cumhur Başaran

Turkish Journal of Electrical Engineering and Computer Sciences

This paper presents a compact dual-band printed antenna for 2.4/5.2 GHz WLAN applications. The radiating elements of the proposed antenna are composed of rectangular split-ring elements and metallic loadings placed appropriately between the rings. The antenna size is very compact (22 \times 26 \times 1.6 mm), and it can be integrated easily with other RF front-end circuits. It is demonstrated that the proposed antenna can completely cover the required bandwidths of IEEE 802.11b (2.4-2.484 GHz) and IEEE 802.11a (5.15-5.35 GHz) with satisfactory radiation characteristics. Analysis and design of the proposed antenna was carried out with the Ansoft highfrequency structure simulator. …


Multiobjective Fet Modeling Using Particle Swarm Optimization Based On Scattering Parameters With Pareto Optimal Analysis, Fi̇li̇z Güneş, Ufuk Özkaya Jan 2012

Multiobjective Fet Modeling Using Particle Swarm Optimization Based On Scattering Parameters With Pareto Optimal Analysis, Fi̇li̇z Güneş, Ufuk Özkaya

Turkish Journal of Electrical Engineering and Computer Sciences

In this paper, design-oriented field effect transistor (FET) models are produced. For this purpose, FET modeling is put forward as a constrained, multiobjective optimization problem. Two novel methods for multiobjective optimization are employed: particle swarm optimization (PSO) uses the single-objective function, which gathers all of the objectives as aggregating functions; and the nondominated sorting genetic algorithm-II (NSGA-II) sorts all of the trade-off solutions on the Pareto frontiers. The PSO solution is compared with the Pareto optimum solutions in the biobjective plane and the success of the first method is verified. Furthermore, the resulting FET models are compared with similar FET …


A Procedure To Specify The Weighting Matrices For An Optimal Load-Frequency Controller, Silvio José Pinto Simões Mariano, Jose Álvaro Nunes Pombo, Maria Do Rosário Alves Calado, Luis António Fialho Marcelino Ferreira Jan 2012

A Procedure To Specify The Weighting Matrices For An Optimal Load-Frequency Controller, Silvio José Pinto Simões Mariano, Jose Álvaro Nunes Pombo, Maria Do Rosário Alves Calado, Luis António Fialho Marcelino Ferreira

Turkish Journal of Electrical Engineering and Computer Sciences

The linear quadratic optimal regulator is one of the most powerful techniques for designing multivariable control systems. The performance of the system is specified in terms of a cost, which is the integral of a weighted quadratic function of the system state and control inputs, that is to be minimized by the optimal controller. The components of the state cost weighting matrix, Q, and the control cost weighting matrix, R, are ours to choose in mathematically specifying the way we wish the system to perform. Changing these matrices, we can modify the transient behavior of the closed-loop system. This paper …


A Simulator Based On An Energy-Efficient Gpr Algorithm Modified For The Scanning Of All Types Of Regions, Levent Seyfi̇, Ercan Yaldiz Jan 2012

A Simulator Based On An Energy-Efficient Gpr Algorithm Modified For The Scanning Of All Types Of Regions, Levent Seyfi̇, Ercan Yaldiz

Turkish Journal of Electrical Engineering and Computer Sciences

An improved simulator is presented for the simulation of an energy-efficient ground-penetrating radar (GPR) using the 2D finite-difference time-domain method in the MATLAB environment. This simulator is novel in that it improves on previous work that did not involve scanning a buried object or the intermittent sublayer beneath the ground using an energy-efficient algorithm. The present simulator examines the scanned region and automatically chooses either a common algorithm or an energy-efficient algorithm, depending on the region. The simulator provides the possibility of using an energy-efficient GPR without the need for the operator to determine the suitability of the scanned region. …


Joint Source-Channel Coding For Error Resilient Transmission Of Static 3d Models, Mehmet Oğuz Bi̇ci̇, Andrey Norkin, Gözde Akar Jan 2012

Joint Source-Channel Coding For Error Resilient Transmission Of Static 3d Models, Mehmet Oğuz Bi̇ci̇, Andrey Norkin, Gözde Akar

Turkish Journal of Electrical Engineering and Computer Sciences

In this paper, performance analysis of joint source-channel coding techniques for error-resilient transmission of three dimensional (3D) models are presented. In particular, packet based transmission scenarios are analyzed. The packet loss resilient methods are classified into two groups according to progressive compression schemes employed: Compressed Progressive Meshes (CPM) based methods and wavelet based methods. In the first group, layers of CPM algorithm are protected unequally by Forward Error Correction (FEC) using Reed Solomon (RS) codes. In the second group, embedded bitstream obtained from wavelet based coding is protected unequally with FEC as well. Both groups of methods are scalable with …


Investigating The Relation Between Optimum Guard Interval And Channel Delay Spread For A Mc-Cdma System, Çeti̇n Kurnaz, Hülya Gökalp Jan 2012

Investigating The Relation Between Optimum Guard Interval And Channel Delay Spread For A Mc-Cdma System, Çeti̇n Kurnaz, Hülya Gökalp

Turkish Journal of Electrical Engineering and Computer Sciences

This paper demonstrates a novel approach to determining the optimum guard interval for a multicarrier code division multiple access (MC-CDMA) system. Analytical expressions for useful and interference power are derived as a basis for comparison. From these, an expression for the signal-to-noise ratio of a detected bit is derived and used to determine the optimum guard interval for a given channel profile and system parameters. In contrast to other works, we use channel models based on actual measurements and we highlight important differences from theoretical models to support our approach. From our results, we propose an empirical rule for optimum …


A Novel Three-Phase Transformer Hysteresis Model In Matlab^{Tm} Simulink, Okan Özgönenel, Kami̇l Ri̇fat İrfan Güney, Ömer Usta, Hasan Di̇ri̇k Jan 2012

A Novel Three-Phase Transformer Hysteresis Model In Matlab^{Tm} Simulink, Okan Özgönenel, Kami̇l Ri̇fat İrfan Güney, Ömer Usta, Hasan Di̇ri̇k

Turkish Journal of Electrical Engineering and Computer Sciences

This paper presents a new transformer model displaying hysteresis using the MATLAB{\texttrademark} Simulink environment. The proposed model displays a complete scheme for the simulation of 3-phase transformers. The new model is mainly based on the transmission line model and the Jiles-Atherton model of a power system using lumped parameters. Jiles-Atherton model parameters were determined by curve fitting and numerical optimization iteration. The developed model is particularly suitable for fault analysis and protective relaying studies under harmonic conditions where the transformer is driven into the nonlinear regime. The performance of the method was evaluated by both theorical and experimental data.