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Home»Articles»Gradient Search Technique Applied to Dual-Optimal Design of a 3-Phase Core Type Transformer

Gradient Search Technique Applied to Dual-Optimal Design of a 3-Phase Core Type Transformer

Author : Raju Basak , Arabinda Das and Amarnath Sanyal
Volume 6 No.2 July-December 2017 pp 19-24

Abstract

Most of the power and distribution transformers in power system are 3-phase core type transformers. They are extensively used- as such their cost is a sizable proportion of the total system cost. Therefore they are to be designed cost-optimally. The optimality is with reference to an objective function, generally in presence of constraints. The design variables are to be varied within their given bounds and the optimal solution is to be reached in finite number of steps, satisfying the given constraints. The paper presents a method for optimizing the design, in presence of constraints specified by the customer and the regulatory authorities, through gradient search technique. The objective function is a weighted combination of the cost of the transformer and the running losses which is not a mathematically framed but obtained from the transformer design sub-routine through computer programme. The objective of this paper is to find out above objective function without mathematically framed function which leads to inaccuracy for approximation due to magnetic saturation and nonlinearity present in the system.
Most of the objective function is framed by taking few terms from a polynomial to avoid complicacy of the function, such as core loss expression obtained from curve with the variation of flux densities. The starting point has been chosen within the allowable parameter space- the steepest decent path has been followed for convergence. The step length has been judiciously chosen. The hyper surface has been found to be concave. As such no local minima problem is faced. The method is best as it its convergence is quickest.

Keywords

Dual Optimal design, three Phase transformer, objective function, Computer subroutine

Full Text:

References

Asian Journal of Electrical Sciences (AJES) is a quarterly international peer-reviewed journal of Electrical Sciences. One of the objectives of this journal is to disseminate knowledge on various research issues connected with the topics include, but are not limited to:

Telecommunications – transmission of information, coax cable, optical fiber or free space, amplitude modulation and frequency modulation, transmitters and receivers, transceiver.
Instrumentation – pressure, flow and temperature, electromagnetic theory, thermocouples, sensors of larger electrical systems, control engineering.
Computers – Computers and computer systems, hardware, software, software engineering.

Power engineering – generation, transmission and distribution of electricity, transformers, electric generators, electric motors, high voltage engineering and power electronics.
Control engineering – dynamic systems, design of controllers, electrical circuits, digital signal processors, microcontrollers and PLCs (Programmable Logic Controllers), industrial automation. Electronic Engineering -Electronic circuits, resistors, capacitors, inductors, diodes and transistors, radio engineering, radar, television, audio systems, computers and microprocessors.
Microelectronics – Electronic circuit, integrated circuit, semiconductor transistors, resistors, capacitors, inductors, Nanoelectronics.

Signal processing – signals, analog, digital, telecommunications, Digital Signal Processing, SDTV | HDTV sets, radios and mobile communication devices, Hi-Fi audio equipments, Dolby noise reduction algorithms, GSM mobile phones, mp3 multimedia players, camcorders and digital cameras, automobile control systems, noise cancelling headphones, digital spectrum analyzers, intelligent missile guidance, radar, GPS based cruise control systems, image processing, video processing, audio processing and speech processing systems.

Most of the power and distribution transformers in power system are 3-phase core type transformers. They are extensively used- as such their cost is a sizable proportion of the total system cost. Therefore they are to be designed cost-optimally. The optimality is with reference to an objective function, generally in presence of constraints. The design variables are to be varied within their given bounds and the optimal solution is to be reached in finite number of steps, satisfying the given constraints. The paper presents a method for optimizing the design, in presence of constraints specified by the customer and the regulatory authorities, through gradient search technique. The objective function is a weighted combination of the cost of the transformer and the running losses which is not a mathematically framed but obtained from the transformer design sub-routine through computer programme. The objective of this paper is to find out above objective function without mathematically framed function which leads to inaccuracy for approximation due to magnetic saturation and nonlinearity present in the system. Most of the objective function is framed by taking few terms from a polynomial to avoid complicacy of the function, such as core loss expression obtained from curve with the variation of flux densities. The starting point has been chosen within the allowable parameter space- the steepest decent path has been followed for convergence. The step length has been judiciously chosen. The hyper surface has been found to be concave. As such no local minima problem is faced. The method is best as it its convergence is quickest.

Editor-in-Chief
Dr. Koray Ulgen
Department of energy engineering, Ege University, Turkey
[email protected]
Editorial Advisory Board
Dr. Rasyidah Binti Mohamad Idris
Department of Electrical Power Engineering, Universiti Teknologi Malaysia
[email protected]
Dr. Norhaliza Abdul Wahab
Department of Control & Mechatronics Engineering, Universiti Teknologi Malaysia
[email protected]
Prof. Md Irfan Ahmed
Department of Electrical Engineering, Career Point University, Rajasthan, India
[email protected]
Dr. Sallehuddin Bin Ibrahim
Department of Control And Mechatronics Engineering, Universiti Teknologi Malaysia
[email protected]
Dr. Naziha bt. Ahmad Azli
Department of Electrical Power Engineering, Universiti Teknologi Malaysia
[email protected]
Dr. Sharul Kamal Bin Abdul Rahim
Department of Communication Engineering, Universiti Teknologi Malaysia
[email protected]
Dr. Jasrul Jamani Bin Jamian
Department of Electrical Power Engineering, Universiti Teknologi Malaysia
[email protected]
Dr. T. Rajesh
Department of EEE, INFO Institute of Engineering, Coimbatore, India
[email protected]
Dr. Mohamad Kamal B. A. Rahim
Department of Communication Engineering, Universiti Teknologi Malaysia
[email protected]
Dr. Sophan Wahyudi Bin Nawawi
Department of Control and Mechatronics Engineering, Universiti Teknologi Malaysia
[email protected]
Dr. Nor Hisham Haji Khamis
Department of Communication Engineering, Universiti Teknologi Malaysia
[email protected]
Dr. Cheng Siong Lim
Department of Control and Mechatronic Engineering,Universiti Teknologi Malaysia
[email protected]
Dr. Sharifah Kamilah Bt Syed Yusof
Department of Electrical Engineering Universiti Teknologi Malaysia
[email protected]
Dr. Shahdan Sudin
Department of Control and Mechatronic Engineering, Universiti Teknologi Malaysia
[email protected]
Dr. Razali Bin Ngah
Department of Electrical Engineering, Universiti Teknologi Malaysia
[email protected]

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    Editorial Note

    Editorial Dr. Koray Ulgen

    Editor-in-Chief
    Dr. Koray Ulgen
    Department of energy engineering, Ege University, Turkey
    [email protected]
    Editorial Advisory Board
    Dr. Rasyidah Binti Mohamad Idris
    Department of Electrical Power Engineering, Universiti Teknologi Malaysia
    [email protected]
    Dr. Norhaliza Abdul Wahab
    Department of Control & Mechatronics Engineering, Universiti Teknologi Malaysia
    [email protected]
    Prof. Md Irfan Ahmed
    Department of Electrical Engineering, Career Point University, Rajasthan, India
    [email protected]
    Dr. Sallehuddin Bin Ibrahim
    Department of Control And Mechatronics Engineering, Universiti Teknologi Malaysia
    [email protected]
    Dr. Naziha bt. Ahmad Azli
    Department of Electrical Power Engineering, Universiti Teknologi Malaysia
    [email protected]
    Dr. Sharul Kamal Bin Abdul Rahim
    Department of Communication Engineering, Universiti Teknologi Malaysia
    [email protected]
    Dr. Jasrul Jamani Bin Jamian
    Department of Electrical Power Engineering, Universiti Teknologi Malaysia
    [email protected]
    Dr. T. Rajesh
    Department of EEE, INFO Institute of Engineering, Coimbatore, India
    [email protected]
    Dr. Mohamad Kamal B. A. Rahim
    Department of Communication Engineering, Universiti Teknologi Malaysia
    [email protected]
    Dr. Sophan Wahyudi Bin Nawawi
    Department of Control and Mechatronics Engineering, Universiti Teknologi Malaysia
    [email protected]
    Dr. Nor Hisham Haji Khamis
    Department of Communication Engineering, Universiti Teknologi Malaysia
    [email protected]
    Dr. Cheng Siong Lim
    Department of Control and Mechatronic Engineering,Universiti Teknologi Malaysia
    [email protected]
    Dr. Sharifah Kamilah Bt Syed Yusof
    Department of Electrical Engineering Universiti Teknologi Malaysia
    [email protected]
    Dr. Shahdan Sudin
    Department of Control and Mechatronic Engineering, Universiti Teknologi Malaysia
    [email protected]
    Dr. Razali Bin Ngah
    Department of Electrical Engineering, Universiti Teknologi Malaysia
    [email protected]

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