OPTIMIZATION ASPECTS OF TRANSFORMER DESIGN

“OPTIMIZATION ASPECTS OF TRANSFORMER DESIGN” By Upadhyay Hiral Narendrakumar Enrollment No.130080737018 Supervised By, Mrs. D. K. Patel M.E (EPS), Assistant Professor, A thesis submitted to Gujarat Technological University in PartialFulfillment of the Requirements for the Degree of Engineering in Electrical Power System May 2015 Department of Electrical Engineering, BVM Engineering College, Vallabh Vidyanagar, Anand. i CERTIFICATE This is to certify that research work embodied in this thesis entitled “OPTIMIZATION ASPECTS OF TRANSFORMER DESIGN” was carried out by Miss HiralNarendrakumar Upadhyay (Enrollment No.130080737018) studying at Birla Vishvakarma Mahavidyalaya (008) for partial fulfillment of Master of Engineering degree to be awarded by Gujarat Technological University. This research work has been carried out under my guidance supervision it is up to my satisfaction. Date: Place: InstituteGuide: Institute Principal: MRS. D. K. Patel Dr. F.S.Umrigar Asst. Professor Principal M.E. (E.P.S) BVM ENGG. College Seal of Institute ii CERTIFICATE This is to certify that research work embodied in this thesis entitled “OPTIMIZATION ASPECTS OF TRANSFORMER DESIGN” was carried out by Miss Hiral Narendrakumar Upadhyay (Enrollment no.130080737018) studying at Birla Vishvakarma Mahavidyalaya(008) for partial fulfillment of Master of Engineering degree to be awarded by Gujarat Technological University. This research work has been carried out under my guidance supervision it is up to my satisfaction. Date: Place: Industrial Guide Industrial Guide MR. CHIRAG N. PAREKH, MS. AVNI S. PARIKH, Plant Coordinator, Senior Design Engineer, A.E.P.L., V. U. Nagar A.E.P.L., V. U. Nagar Seal of company iii CERTIFICATE This is to certify that research work embodied in this thesis entitled “OPTIMIZATION ASPECTS OF TRANSFORMER DESIGN” was carried out by Miss Hiral Narendrakumar Upadhyay (Enrollment no.130080737018) studying at Birla Vishvakarma Mahavidyalaya(008) for partial fulfillment of Master of Engineering degree to be awarded by Gujarat Technological University. This research work has been carried out under my guidance supervision it is up to my satisfaction. Date: Place: External Institute Guide: Mr. Rajesh C. Sanghvi Asst. Professor, APPLIED SCIENCE & HUMANITIES DEPT. GCET Engg. College (011) V.V Nagar, Anand. Seal of Institute iv COMPLIANCE CERTIFICATE Thisis to certify that research work embodied in this thesis entitled “OPTIMIZATION ASPECTS OF TRANSFORMER DESIGN” was carried out by Miss Hiral Narendrakumar Upadhyay (Enrollment no.130080737018) studying at Birla Vishvakarma Mahavidyalaya (008) for partial fulfillment of Master of Engineering degree to be awarded by Gujarat Technological University. He has complied to the comments given by the dissertation phase – I as well as Mid semester thesis reviewer to my satisfaction. Date: Place: Signature Signature Ms. Hiral Narendrakumar Upadhyay D. K. Patel Signature Dr. F.S. Umrigar Seal of institute v PAPER PUBLICATION CERTIFICATE This is to certify that research work embodied in this thesis entitled “OPTIMIZATION ASPECTS OF TRANSFORMER DESIGN” was carried out by Miss Hiral Narendrakumar Upadhyay (Enrollment no.130080737018) studying at Birla Vishvakarma Mahavidyalaya (008) for partial fulfillment of Master of Engineering degree to be awarded by Gujarat Technological University, has published article entitled Cost Minimization of power Transformer using Software based Approach for publication by “Upcoming Issues & Challenges in EE”(ISBN –9-789384-86934) at Parul Institute of Technology, at Vadodara, Gujarat during 3rd - 4th April 2015. Date: Place: Signature Signature Ms. Hiral Narendrakumar Upadhyay D. K. Patel Signature Dr. F. S. Umrigar Seal of the institute vi THESIS APPROVAL CERTIFICATE This is to certify that research work embodied in this thesis entitled “OPTIMIZATION ASPECTS OF TRANSFORMER DESIGN” was carried out by Miss Hiral Narendrakumar Upadhyay (Enrollment no.130080737018) studying at Birla Vishvakarma Mahavidyalaya (008) is approved for the degree of Master of Engineering with specialization of Electrical Power System by Gujarat Technological University. Date: Place: Examiners signature and name: ………………………. ( ) ………………………. ( ) vii UNDERTAKING ABOUT ORIGINALITY OF WORK We hereby certify that we are the sole authors of this thesis and that neither any part of this thesis nor the whole of the thesis has been submitted for a degree to any other University or Institution. We certify that, to the best of my knowledge, the current thesis does not infringe upon anyone’s copyright nor violate any proprietary rights and that any ideas, techniques, quotations, or any other material from the work of other people included in our thesis, published or otherwise, are fully acknowledged in accordance with the standard referencing practices. Furthermore, to the extent that we have included copyrighted material that surpasses the boundary of fair dealing within the meaning of the Indian Copyright (Amendment) Act 2012, we certify that we have obtained a written permission from the copyright owner(s) in the current thesis and have included copies of such copyright clearances to our appendix. We declare that this is a true copy of thesis, including any final revisions, as approved by thesis review committee. We have checked write up ofthe present thesis using anti-plagiarism database and it is in allowable limit. Even though later on in case of any complaint pertaining of plagiarism, we are sole responsible for the same and we understand that as per UGC norms, University can even revoke Master of Engineering degree conferred to the student submitting this thesis. Date: Place: Signature of student: Signature of Guide: Name of Student: Name of Guide: Enrollment No: Institute Code: viii DEDICATED TO MY PARENTS & BROTHER ix ANKNOWLEDGEMENT I wish to express my deepest gratitude to my internal guide PROF.D. K. PATEL Department of Electrical Engineering, Birla Vishvakarma Mahavidyalaya (Engineering College), Vallabh Vidyanagar, for his constant guidance, encouragement and support. I warmly acknowledge and express my special thanks for his inspiring discussions and infallible suggestions. I am also grateful to PROF. (DR.) N. G. MISHRA, Head Department of Electrical Engineering, Birla Vishvakarma Mahavidyalaya (Engineering College), Vallabh Vidyanagar, DR.F.S.UMRIGAR, PRINCIPAL Birla Vishvakarma Mahavidyalaya (Engineering College), VallabhVidyanagar for giving me an opportunity to perform the thesis work under the premises of the college. A Special thanks to Mr.CHIRAG PAREKH, Ms. AVNI S. PARIKH and Mrs. TEJAL PALat ATLANTA ELECTRICAL PVT. LTD.to provides me the knowledge about all the practical design procedure in detail. He continuously assisted me throughout the entire tenure of my dissertation work. He has been an unceasing source of inspiration for the completion of my dissertation work. I would like to express my sincere thanks to my external institute guide MR. RAJESH C. SANGHVI, Assistant Professor, Department of Mathematics, G H PATEL COLLGE OF ENGINEERING& TECHNOLOGY, V. V. NAGARfor his guidance and support towards my dissertation work. Last, but not the least I am very much obliged to my family members and friends who helped me directly or indirectly toward completion of my dissertation work. HIRAL UPADYAY (130080737018) x TABLE OF CONTENTS Title page i Certificate page ii Industrial certificate page iii External institute certificate page iv Compliance Certificate page v Paper publication certificate vi Thesis approval certificate vii Undertaking about originality of work viii Dedication page ix Acknowledgements x Table of Contents xi List of Figures xiv List of Tables xv Abstract xvi Organization of thesis Work xviii Chapter 1 introduction 01 1.1 Introduction 01 1.2 Objective 01 1.3 Motivation 02 1.4 Recent developments in transformer technology 03 1.4.1 Magnetic circuit 03 1.4.2 Windings 03 1.4.3 Insulation material 04 xi 1.5 Literature review 04 Chapter 2 Design of three phase power transformer 2.1 Conventional design of three phase core type transformer 18 18 2.1.1 Steps for design of each part of transformer 19 2.2 Flowchart of complete conventional design of transformer 32 Chapter 3 Optimization using ESM 33 3.1 Modifications in Conventional design program 33 3.2 Flowchart of optimal design using ESM 34 3.3 Results obtain using ESM 35 3.4 Design selection procedure 36 Chapter 4 Design Optimization using SQP Programming 38 4.1 Sequential quadratic programming 39 4.2 Optimization results for Active part of transformer 40 4.3 Results in graphical form obtained with optimization tool 41 4.4 optimization results for active part and tank 42 Chapter 5 optimized results using MATLAB TOOL for GA 43 5.1 Genetic Algorithm 44 5.2 Optimization results using GA 45 5.3 Results in graphical format for given transformer 46 Chapter 6 Analysis of proposed techniques 49 Chapter 7 Multiobjective optimization using NSGA-II 53 7.1 Method Description 53 7.2 Implementation of NSGA-II method 53 Conclusion 56 Future work 57 xii References 58 Appendix 59 I. Review Card 59 Plagiarism Report 64 III. Paper presentation certificate 70 IV. Abbreviations 72 V. Standard tables 74 VI. Result of ESM 84 II. xiii LIST OF FIGURES Figure 1.1Decision tree for selection of the appropriate interval for the magnetic Induction in power transformer 07 Figure 2.1 Flowchart of complete design of transformer 32 Figure 3.1Flowchart of proposed optimization technique by ESM 34 Figure 3.2 Design results for active part 35 Figure 3.3 Design results for transformer unit with seven constraints 36 Figure 4.1 Optimization toolbox in MATLAB 38 Figure 4.2 Optimization toolbox including results for active part 40 Figure 4.3 Optimization results in graphical form 41 Figure 4.4 Results obtain by “SQP” method for active part and tank 42 Figure 5.1 Optimization toolbox in MATLAB for “GA” 43 Figure 5.2 Optimization results with “GA” 45 Figure 5.3 Optimization results in graphical form 46 Figure 6.1 Comparison of “ESM” and “GA” (CASE-I) 49 Figure 6.2 Comparison of “ESM” and “GA” (CASE-II) 50 Figure 6.3 Comparison of “ESM” and “GA” (CASE-III) 51 Figure 7.1 Plot of NSGA-II for 50 population and 500 generation 54 xiv LIST OF TABLES Table 5.1 Result comparison of different mutation techniques and selection operator 47 Table 6.1 Comparison of “ESM” and “GA” (CASE-I) 49 Table 6.2 Comparison of “ESM” and “GA” (CASE-II) 50 Table 6.3 Comparison of “ESM” and “GA” (CASE-III) 51 Table 6.4 Analysis of proposed techniques 52 Table 7.1 Results obtained from “NSGA-II” after 500 generation for a population size of 50. 55 xv “OPTIMIZATION ASPECTS OF TRANSFORMER DESIGN” Submitted By Upadhyay Hiral Narendrakumar Supervised By D. K. Patel M.E (EPS), Assistant Professor, Birla Vishvakarma Mahavidyalaya, V.V.Nagar,Anand. Abstract Looking at the development in the construction, manufacturing process, variety of materials and application of transformer, it is necessary to focus on technology of transformer design. The transformer design proposed in the current work is capable to manage with the existing complex power system network. Also, the main aim of optimization of transformer is to fulfill all the design criteria and minimizing the manufacturing cost. The optimization of transformer using various tools and methods has been discussed in the report. In dissertation phase-I, two methods for optimization in active part design were approached. First is iterative programming method and second is using optimization toolbox in MATLAB. In the first method, some design variants are created and by varying them, based on application point of view the selection of optimum design was carried out. In second method, the optimization toolbox in MATLAB gives the final value of variable which satisfies the optimum design requirements. In dissertation Phase-II, the design of tank is included in design of active part. Here, also two methods are approached for optimization of transformer for minimization of cost. xvi Multiobjective optimization is also used by considering two objective functions as cost minimization and No-load losses minimization by Non-Dominating Sorting Genetic Algorithm-II(NSGA-II). xvii ORGANIZATION OF THESIS WORK Chapter 1: In this chapter, the basic detail of transformer and its needs are discussed. The objective of this thesis work and regarding the motivation is discussed. In Last, the literature survey papers are discussed with their aim and conclusion. Chapter 2: It includes the conventional design of power transformer is discussed in detail with equation and it taken from the industrial reference. Also the flow chart of the conventional design has been shown. Chapter 3: In this chapter, the ESM method is discussed to get the optimal design of power transformer. Firstly this method is used to solve the active portion of the given transformer and same were implementing for whole design includes tank design. Chapter 4: In this section, the SQP algorithm is discussed to optimize the design of power transformer. Chapter 5: It includes the optimization using GA of power transformer and use of different mutation techniques and different selection operator for accurate optimization. Chapter 6: Finally with the help of both the techniques, desired results in design optimization of transformer were gained. The comparison of both the techniques is given in this chapter. xviii Chapter 7: In this chapter, the NSGA-II algorithm is discussed with multi objective function. The two objective functionsis taken for optimization. Lastly, at the end of the thesisconclusion, future scope and references are discussed. xix CHAPTER 1 INTRODUCTION 1.1 INTRODUCTION As per IS-2026 and IEC-60076, the term transformer is defined by a static piece of apparatus with two or more windings which, by electromagnetic induction, transforms a system of alternating voltage and current into another system of voltage and current usually of different values and at the same frequency for the purpose of transmitting electrical power. The transformer is a most useful, static and efficient device among rest of devices used in electrical power system. Because of no rotating parts are exist in transformer technology the mechanical maintenance, noise and vibration are very less compare to any electrical machineries. The first transformer was invented by “stenly” in year of 1886. Whereas the primary elements like laminated core, copper winding and insulation system are remained more or less unchanged. As per [1] there was a huge improvement and technology innovation has been takes place. These innovations are relate to dimensions, losses, material being used and noise level reduced dramatically. But from last two decade the research is focused mainly on higher efficiency, higher service reliability and more economicalsolution. The recent development in technology and improved materials are being used in 21st century are discussed in upcoming literature work. 1.2 OBJECTIVE As per the above discussion the further research work will be mainly focused on economical solution of active part of transformer. It is to be observed in many manufacturing companies the whole design work can be executed with the help of excel program incorporating with large data base. 1 At the end of execution of program for given rating of transformer. All necessary dimensions are calculated. Further it will verify by the design engineer in the sense of as per predefined given design data. Later on these data can be forwarded to different manufacturing departments. But with the help of above procedure the designed data cannot be changed after single time execution of program. If any changes required to made in existing design than it is mandatory to select the necessary constant values and run it from begging and get the updated design. There are many drawbacks of excel program that are open loop program, less accurate and tedious methodology in order to get appropriate design as per customer need or application point of view. In order to fix the above indicated drawbacks in case of design of power transformer. It is necessary to develop the computer program that incorporate the required database and well defined objective like to minimization of active part cost, improve efficiency etc. There are many toolbox are available in the market for create design and analysis like MATLAB2011, FEM, ELECNET etc. The MATLAB2011 is used to create a design and analysis in form of instructions. The conventional design of power transformer includes the many formulae and data base for constant values. Firstly the research work is related to develop the conventional design program for given rating of power transformer in MATLAB2011 toolbox with necessary data base and proper selection of toolbox. After that it is used to get the optimized design as per predefined objective. With the help of proposed methodology it is possible to obtain well accurate design that will satisfy the customer need and also help in improve the product quality as well. 1.3 MOTIVATION This research work is concern regarding the whole design of power transformer and optimizes it for an objective given by AEPL. In the mid-year of 2014 the AEPL got the order from one customer to manufacturer the 15 MVA, 66 KV / 11 KV, Power 2 transformer with maximum no load losses should minimum. So base on that AEPL gives permission to make a design program such a way that will satisfy the one customer need. So it was great opportunity to take the challenge to make a design of power transformer such a way that will satisfy the customer needs (i.e. one customer). So basis of that the goal is to make a design program such a way that satisfying the customer need and it would be user friendly and more accurate to get the optimized design results. That is called as TRANSFORMER DSIGN OPTIMIZATION (TDO). 1.4 RECENT DEVELOPMENT IN TRANSFORMER TECHNOLOGY All the information regarding development in transformer technology is taken from IEEE survey, ATLANTA ELECTRICALS PVT LTD and other magazines 1.4.1 MAGNETIC CIRCUIT There has been a steady development of core steel material in the last century. The trend of reduction in transformer losses in the last few decades is related to a considerable increase in energy costs. One of the ways to reduce the core losses is to use better and thinner grades of core steels, but their price is higher. However, continuous efforts are directed at developing improved electrical steels with lower iron losses for energyefficient transformers. Generally the thickness of this lamination is 0.3 mm but there are so many types of laminations sizes are available in market. The M4, M5, M6, ZH90 are the type of CRGO steel having different lamination size with respect to maximum flux density. 1.4.2 WINDINGS The advent of high-temperature superconducting (HTS) materials has renewed interest in research and development of superconducting transformers. The principal advantages of HTS transformers are: much lower winding material content and losses, higher overload capacity and possibility of coreless design.The development of technology based on liquid nitrogen at temperatures up to 79 K has reduced the complexity and cost of superconducting transformer.The grade of the copper is EC having 99.9 %conductivity. Generally the round or strip copper conductors are used in manufacturing of windings. 3 1.4.3 INSULATING MATERIAL Transformers in electric power distribution and transmission systems are expected to function reliably and efficiently in the long term. The quality of the oil in a transformer plays an important role in performing this function, and the characteristics of transformer oil have been examined and reported on for decades.The majority of transformers use mineral oil in order to meet their cooling demands, due to the fact that mineral oil has not only a low price but also very good electrical insulating properties. However, nowadays, the mineral oil performance cannot meet the modern needs of transformers. Numerous activities have been initiated to improve the properties of mineral oil or to find other substitute liquids alternatively to conventional mineral oils, natural esters or vegetable oils have been used successfully as transformer dielectric coolants. Their application offers some advantages, such as safety against a fire incident, environmental friendliness and improved transformer performance. Also with the development in the SF6 gas for insulating medium in GIS the better cooling and reliable performance are obtained. 1.5 LITERATURE SURVEY 1) TRANSFORMER DESIGN & OPTIMIZATION: A LITERATURE SURVEY Author’s name:E. I. Amoiralis, M. A. Tsili, A. G. Kladas. Publication:IEEE Transaction on power delivery, volume.24. Year: October 2009 Purpose: The aim of this paper is give the information who is concerned with transformer design and its optimization, quality-enhancement activities in today’s competitive world. It is also useful to utility engineer, undergraduate and postgraduate students who wants to integrate traditional transformer design with modern computational methods. 4 General discussion: This paper is divided in six sections: The first section is gives information about the basics of transformer, various types of transformer and its rating, various parts of transformer like core(lamination), winding and cooling system. In second section, various method are used like Finite-element Method (2-D,3-D), analytical methods, AI techniques(stochastic methods, Gas), Experimental methods, Hybrid methods for analysis of characteristics of transformer. In this paper various characteristics are analyzed like No-load losses, load losses, leakage field and short circuit impedance, Inrush current, dynamic behavior of transformer under short circuit and seismic stress, Noise, Insulation, cooling using FEM (2-D, 3-D) method. In third section, transformer design can optimize using various objective functions and constrains. In transformer design optimization mostly two objective functions are considered: 1) Manufacturing Cost Optimization, 2) Operating Cost Optimization (losses should be minimum). It can optimize by varying some parameter like flux density, current density. For optimization, we can use various methods like trial and error, deterministic method, FEM and using various methods of Artificial intelligence (GA ANN). In the fourth section, the different variants are given on the basis of Post-design of transformer. Two different type of modeling are discussed:1) harmonic modeling, 2)Transient and Dynamic Modeling in detail, for more information regarding methodology and description please refer the paper. In the fifth section, According three different institution (ANSI/IEEE, CENELEC, IEC), the different standard are issued for all type of transformer. Some of the standards that applicable for distribution & power transformer are written in paper with it unique code. In sixth section, the list of books with author name, publication and publication year are given. This paper includes a list of 52 books on transformers. Necessary platform for further research are provided. 5 Conclusion: New technologies are developed in today’s competitive environment for design and optimization of transformer various methods, various consideration and standards are considered. So, this survey gives the information on main direction of the research and future trends for transformer design. 2) METHODOLOGY FOR THE OPTIMUM DESIGN OF POWER TRANSFORMERS USING MINIMUM NUMBER OF INPUTPARAMETERS Author’s name: Eleftherios Amoiralis, Pavlos S. Georgilakis, Erion Litsos. Publication: ICEM, PAPER NUMBER 470 Year: 2006 Purpose: The aim of this paper is to give the innovative methodology in conjunction with decision tree technique that can design and optimize the power transformer manufacturing cost (material cost plus labor cost) with the help of only ten primary input parameters. Proposed methodology: The design problem is considered as the minimization of the manufacturing cost of power transformer. For that the innovative approach is conjunction with decision tree technique is used to obtain the transformer design with cheapest cost. The DT methodology is applied for the following two functions, It is used to selection of the magnetic induction interval. It also applied for the selection of winding material (copper or aluminum) that leads to optimum transformer design. According to proposed technique the following ten parameters are taken as a primary input parameters, 1. Transformer rated power (RKVA), 2. Rated low voltage (LV), 3. Rated high voltage (HV), 4. Frequency (f), 6 5. Short-circuit impedance (Uk), 6. Maximum Load losses (CuLmax), 7. Maximum no load losses (Femax), 8. Connection of low voltage winding (LVCC), 9. Connection of high voltage winding (HVCC) and 10. Maximum ambient temperature (ta,max). With the help of above ten values the software automatically selects the four variables and the intervals of each one. The four design variables are given as follows, 1. The number of turns of the low voltage coil (nlv), 2. The width of the core leg (D), 3. The height of the core window (G) and 4. The magnetic induction (B). One case study is taken to prove the proposed methodology is most superior to the existing one for manufacturing of power transformer. 1.1 Decision tree for selection of the appropriate interval for the magnetic induction in power transformer 7 Results and discussions: For instance, a 630 kVA power transformer with CuLmax, FemaxandUk equal to 6500W, 1300W, and 4% respectively, costs4848€. This cost is 2.99 % more cheaply than the existing one. Also the proposed method achieves the approximately 4.23 % more optimum transformer design than the current methodology with only ten primary input parameters Conclusion: In this paper, the proposed methodology is conjunction with DT technique that design and optimize the power transformer manufacturing cost (material cost plus labor cost) by considering only ten primary input parameters. It takes only 90 seconds to reach the most appropriate and optimum design for the given power transformer. 3) NOVEL GAMMA DIFFERENTIAL EVOLUTION APPROACH MULTIOBJECTIVETRANSFORMER DESIGN OPTIMIZATION FOR Author’s name:Leandro dos Santos Coelho, Viviana Cocco Mariani, Mauricio V. Ferreira da Luz, and Jean Vianei Leite. Publication: IEEE Transactions on Magnetics, vol. 49 Year: MAY 2013 Key points: Purpose: The paper includes the novalgama differential evolution algorithm (NDE) proposed for solving multiobjective optimization problems for the design of single phase shell type transformer. Proposed methodology: The differential algorithm evolution method is very but powerful population based search technique for solving the global optimization problems. But with whole search process in a DE design and obtain the best values for the control parameters are a time consuming task. 8 To overcome this drawback the new approach has been discussed over here. This paper includes the novel DE (NDE) approach based on truncated gamma probability distribution function. By using this strategy the robustness and accuracy of DE is greatly improved. In order to enhance the performance of classical MODE, theadaptive MF and CR settings are addressed in the MONDEGusing a truncated gamma probability distribution function generatedin the range [0, 1].The common form of the probability distribution functions ofa univariate gamma distribution with two parameters (shape and scale). Results and discussions: The technical parameters for the transformer are presented in this paper are: shell core, drytype, single-phase, 400 VA, voltages V1= 110 V and V2 = 220 V, frequency 50 Hz, and minimum efficiency of 90%. The following control parametersfor the evaluatedMODE and MONDEG approaches: number ofindependent runs is 30 times, the population size (NP) is 30 individuals,the maximum size of external archive is 200,and stopping criterion of 300 generations, i.e., 9000 evaluationsof objective functions in each run. In MODE, MF andCR are adopted to be 0.6 and 0.8, respectively. The simulation result shows the effectiveness of the MODE and theproposed MONDEG algorithm. In terms of the solution quality,the amount of elements of the Pareto set found by MONDEGovertakes the MODE. Conclusion: With the help of DE the problem of premature convergence and the diversity of population are lost. This paper proposed a MONDEG algorithm to TDO. The result shows that the MONDEG generally overtakes anotherMODE algorithm in TDO in terms of solution quality. 9 4) MULTIOBJECTIVE OPTIMIZATION OF TRANSFORMER DESIGN USING ACHAOTIC EVOLUTIONARY APPROACH Author’s name: Leandro dos S. Coelho, Viviana C. Mariani Fabio A. Guerra, Mauricio V. F. da Luz, Jean V. Leite. Publication: IEEE Transactions on Magnetics, Vol. 50, No. 2. Year: February 2014 Purpose: The purpose of this paper is to design the transformer with multi objective optimization problem. The proposed technique for the MOP is unrestricted population size evolutionary multi objective optimization algorithm approach combined with chaotic sequence. Proposed methodology: The proposed technique for the MOP is unrestricted population size evolutionary multi objective optimization algorithm approach combined with chaotic sequence. Also with the help of example of 300 VA single phase transformer the results are compared with the analytical methodology. The MOP is applied for two objectives namely minimization of mass and minimization of losses. The required variables are core dimensions, turns of windings and current densities. Proposed CMOA approach the crossover is applied first to generatea trial vector, which is then used within the mutation operationto produce one offspring while, in DE (differential evolution), mutation is applied firstand then the crossover. Results and discussion: The result for the single phase transformer optimization has been discussed. Also shows the comparison with the analytical methodology. One can obtain the transformer with approximately half of the mass and the same efficiency. 10 Conclusion: The proposed chaotic multiobjective optimization approach is applicable to transformer design optimization. 5) DEVELOPMENT OF MATLAB – BASED SOFTWARE FOR THE DESIGN OF MAGNETIC CIRCUIT OF THREE – PHASE TRANSFORMER Author’s name: Obinwa Christian Amaefule, Afolayan Jimoh Jacob, Akaninyene Bernard Obot. Publication: Journal of Electrical and Electronic Engineering by science publishing group. Year: March 30, 2014 Purpose: The main aim of this paper is to develop the magnetic circuit of power transformer with the help of MATLAB – based software. Also it includes the sample design example with output results are demonstrated with the help of that tool. Proposed methodology: In order to calculate the necessary parameters to design the magnetic core certain steps are given below, Firstly, it is to be assumed that certain parameters are given (i.e. input parameters), Secondly, the algorithm was developed with mathematical expression to obtain the various parameters for magnetic circuit, Thirdly, MATLAB software will understand the input parameters and perform the mathematical operation based on given formulas. The output of magnetic parameters are in tabular form. Results and discussions: The given problem for the demonstration of this algorithm is of power transformer. The required technical details are given in paper. The power transformer is having KVA capacity is 8000, 3 phase, 220 KV / 11 KV, delta / delta type. 11 The GUI (graphical user interface) is created for insert the given data and to represent the output data in tabular format. Also It includes the graphical approach to represent the obtain results. Conclusion: An individual program was developed in MATLAB for the design of the magnetic circuit of three phase power transformer. Based on mathematical expression the algorithm works and giving the required output. The easiness of the mathematical models and the modular nature of the program make them appropriate for teaching and practical training on power transformer design. 6) A HEURISTIC SOLUTION TO THE MANUFACTURINGCOST OPTIMIZATION PROBLEM TRANSFORMER Author’s Name: Pavlos S. Georgilakis, Marina A. Tsili, Athanassios T. Souflaris. Publication: Journal of Materials Processing Technology Year: 2007 Purpose: The aim of proposed design optimization method is to design the transformer that meets the specification with minimum manufacturing cost. Proposed methodology: The procedure to finding the most optimum design for the transformer is possible with the help of suitable computer program. That program will allow producing the many numbers of possible solutions for which the all constraints values are to be satisfied. Finally among the acceptable solutions, the transformer with minimum manufacturing cost will be selected as most optimum design result. Results and discussions: An example is taken in this paper is having the KVA ratting of transformer is 160, 20 / 0.4 KV, 50 Hz. The current density is 3.2 A / mm2 and 3.7 A / mm2for Low voltage winding and high voltage winding respectively. 12 The height of core, width of core, LV turns and magnetic induction are taken as variables. The constraints are load losses (2350 W), no load loss (425 W) and % impedance (4 %). With the necessary computer program calculation the total 4480 solutions are generated that are satisfying the constraint values for given transformer ratting problem. Among that the top five results are taken and the first result is considered as most optimum result for transformer design. The manufacturer cost for that 2457.82$ with NLL (415 W), LL (2325 W) and impedance (3.90 %). Conclusion: The most optimum solution for minimum cost of transformer can be obtained by selecting the appropriate values for the input parameters so that the performance parameters are satisfying the constraints values. Among that best one is selected as a final optimum design with the help of suitable computer program. 7) TRANSFORMER DEIGN AND APPLICATION CONSIDERATION FOR NONSINUSOIDAL LOAD CURRENTS Author name: Linden W. Pierce Publication: IEEE Transactions on industry applications. Year: May / June 1996 Purpose: In this paper the use of adjustable speed drive need the transformer that will cope up with high levels of harmonic currents. The design of transformer for the non-sinusoidal load currents covers analysis of eddy loss calculation and hot spot temperature rise calculations are involved. Also include the recommended practices given by ANSI/IEEE C57.110 and the K factor. That will help to procurements a transformer from the manufacturer that will operate in harmonic environment without failure. 13 Proposed methodology: Actually there is no exact method to calculate the precise value of eddy loss distribution in the windings and hot spot temperature rise. But some of the ways are given in paper are discussed below. At present situation the manufacturers are add the percentage value of eddy loss based upon experience with particular type of transformer under consideration. By equalizing the height of windings (Primary and Secondary) reduces the eddy loss at the winding end. With development of computer programs and methods it is possible to calculate the precise electrical fields and eddy loss in transformer. Also many commercial computer programs are available in order to extract the eddy loss from the total loss are given in the 1989 IEEE spectrum article by cendes. Result and discussion: The developments of IEEE standard considering the non-sinusoidal load currents are discussed. It covers electromagnetic and thermal analysis for the accurate design of transformer. With the develop software and methods the accurate measurement for the eddy loss and hot spot temperature are obtain. With the help of examples for dry type and oil filled type transformer the calculations for eddy loss and hot spot temperature rise are discussed. Conclusion: For industrial area with the primary load as drive system requires the transformer above 300 KVA. The levels of harmonic content are to be specified. The design consideration of transformer for the non-sinusoidal load currents should include the analysis of eddy loss distribution and the hottest spot temperature rise in structural parts. As discussed earlier there is no test method is available for the calculation of the eddy loss from the stray loss. In fact many manufacturers are simple add the 15˚ C to average winding rise for oil filled transformer and 30˚ C for dry type transformer. 14 So simple, practical methods are needed in order to determine the required transformer KVA ratting for new installation with non-sinusoidal current limits. The combination of analysis and testing according to IEEE standard C57.110 is the economical practical approach in this direction. 8) DESIGN OPTIMIZATION OF HIGH-TEMPERATURE SUPERCONDUCTING POWER TRANSFORMERS Author’s name: Thomas L. Baldwin, John I. Ykema, Cliff L. Allen and James L. Langston. Publication: IEEE Transactions on applied superconductivity. Year: June 2003 Purpose: The aim of this paper is to utilize the high temperature superconducting material as a winding material and the necessary modifications are to be required in design and optimization of power transformer. The design results for the three phase 3.5 MVA power transformer are discussed. Proposed Methodology: The design of high temperature superconducting power transformer is always concern about the coil quenching phenomena. Coil quenching phenomena will help to improve the performance of power transformer in short circuit and inrush current condition without any interruption. Results and discussion: In the proposed design methodology the warm-bore cryostat contains the HTS windings Bi-2223 tape windings are used. The windings are cooled with the help of two cyrocoolers. Also the nonlinear constraints like coil design, conductor stress, leakage reactance and cooling system has been discussed. The concentric cylindrical coils are selected as a winding. Also the necessary graphs are also given in order to obtain the required current density in Bi-2223 material. As a comparison between the aluminum and copper conductor for current density ranges from 15 1 to 1.45 A / mm2(rms) the AC losses in HTS tapes operating temperature at 77 K is approximately 100 times smaller. In the case of stress produced by the short circuit and inrush phenomena, the Bi-2223 tape material experiences the 5% reduction in the critical current at the critical stress point. Therefore most of the transformer designs normally between 1.6 to 1.8 T about 10 % to 20 % lesser to the saturation flux density. In order to get the necessary leakage reactance in the case of Bi-2223, the finite element methods that are directly solve the Maxwell equation are used. In HTS transformer design the current densities should be increases for optimum usage of conductor due to high cost of superconducting material. In the proposed methodology the winding temperature to replace the current density variable is being used to get optimization. Conclusion: The LH and LHL design concepts are discussed in this paper. Compare to LH, the LHL design provides a lower electrical length, reduced leakage channel flux and reduction in AC conductor losses. Where a LH design exceeds the mechanical limit therefore it is not feasible for optimum design. By HTS power transformer technology is the superior for the lowest possible cost for the special application. Also with the help of more design changes and computer aided design program, we can expand the new characteristics of HTS power transformer. 9) A PARALLEL MIXED INTEGER PROGRAMMING-FINITE ELEMENT METHOD TECHNIQUE FOR GLOBAL DESIGN OPTIMIZATION OF POWER TRANSFORMER Author’s name: Eleftherios I. Amoiralis; Marina A. Tsili; Pavlos S. Georgilakis; Antonios G. Kladasand Athanassios T. Souflaris. Publication: IEEE transaction on magnetics, volume 44, no 6. Year: June 2008 16 Purpose: The main purpose of this paper is to reach to the global optimization of wound core type power transformer with the help of mathematic technique based on mixed integer nonlinear programming methodology. Algorithm: A parallel mixed integer programming implements the branch and bound algorithm conjunction with the finite element model. Results and discussion: The main aim of this proposed technique is to minimize active part cost of the transformer. The necessities are obtained by seeking the sets of five variables. The variables are the core constructional parameters, type of magnetic core materials, the magnetic induction, and number of turns. The results for active part cost are compared with the existing manufacturing procedure. With the help of proposed technique, the cost for the active part cost is reaches to average 3.94% lower than the existing methodology used by manufacturers. Conclusion: From this research paper is to be concluded that the, a parallel MIP technique is superior methodology in order to reach the global optimum point. The parallel MIP methodology is very effective in nature as well as having high execution speed to reach the solution space for global optimization of power transformer. As mention in previous paragraph, with the help of proposed technique the 3.94 % average cost saving is obtain compare to existing manufacturing technique. Also this approach will helpful for other machines. 17 CHAPTER 2 DESIGN OF THREE PHASE POWER TRANSFORMER Atlanta Transformers manufactures transformers over a large range of KVA ratting and kV class. The demand of transformers is also very large. Dispatch of a transformer to the consumer is also a long procedure. Procedure: 1) Design the transformer; prepare necessary charts and drawing based on input data KVA, kV, vector group for connection of winding, frequency, etc. 2) Manufacturing process 3) Various tests to be performed on transformer 4) Dispatch The present work is to design a three phase core type power transformer. It is a first part of the manufacturer procedure. Next task is to obtain optimal design for given transformer. 2.1 CONVENTIONAL DESIGN OF THREE PHASE CORE TYPE TRANSFORMER The whole design of transformer is split into three main parts in an appropriate way. The design of active part is as per the [6] and tank design is as per [7].Design calculation is done based on given rating of transformer and which is followed by computer program written in MATLAB. On execution of this program we get the total design of transformer and get results in the excel sheet which is exported by the MATLAB code. This design may be optimal or may not be optimal. So, the next is to modify the design with the variation of some factor and some constraints are added into the program. When this program is run, it will give the feasible and possible solutions based on customer requirement and optimization criteria. In this chapter it gives the conventional design procedure and next chapters give the information regarding transformer design optimization. 18 2.1.1 SEQUENCIAL STEPS FOR CONVENTIONAL DESIGN OF EACH PART OF THE TRANSFORMER Consider a Core type power transformer, of 15000 KVA, 66000/11000 volts, 3-ph, 50 Hz, vector group=Dyn11 The conventional design steps are as given below: 1) Core Design 2) Winding Design 3) Parameters calculation 4) Insulation Design 5) Frame Design 6) Connection Design 7) Tank Design 8) Performance Calculations 9) Oil Calculations 10) Cost Calculations. Now we will see one by one in sequence. 1) Core design Based on KVA rating calculate Et, Et =V(ph) / T= K√ Q Where, K is a constant (ratio of core to copper) which is taken between0.35 to 0.55. Assume Flux Density Bm = 1.45 to 1.75 Wb/ m2 Now calculate the Ai (iron area) Et = 4.44 × Øm × f But Øm = Bm× Ai Hence Et = 4.44× Bm× Ai× f So, Et×104 Ai = 4.44×Bm×f 19 Core diameter d = √(Ai / 0.69) × 10 Find Modified area: Find no. of steps No’s of Steps: = (core dia×0.04) > 17 =17 Otherwise no. of steps=core dia×0.04 Find maximum and minimum step width Constant (G) = (core dia) 2-((core dia2- (core dia× 0.2)2)0.5 - (core dia× 0.027)) 2 Take the rounded value (*by 5 & / by 5) If G is less than 50 then, take Minimum step width =5otherwise minimum step width=G Maximum width (1st step) = (core dia× 0.98) Take the rounded value (*by 5 & / by 5) Step No 2 Width = Maximum width-10 (then increase 10-15-25 gradually up to 17th step) Find thickness of steps: Step No 1 thickness = ((Coredia) 2 - (step 1 width) 2)0.5 Step No 2 thickness = ((Coredia) 2 - (step 2 width) 2)0.5-(thickness of 1st step) Step No 3 thickness = ((Coredia) 2-(step 3 width) 2)0.5-(thickness of 1st step+ thickness of 2ndstep) Find area of steps: Area of (N step) = N step width × N step thickness ×0.0095 Area of (2ndstep) = 2nd step width × step thickness ×0.0095 Multiplying factor for first stepwidth = if core dia< 300 then 5 otherwise 10 Find modified area: Total area = Sum of all step area – {(0.1*core dia) if core dia>390 otherwise 0} 20 2) Winding design There are two windingsin a transformer:1) HV winding, 2) LV winding A. High voltage design High voltage winding is delta connected. First of all calculate the Turns, current, Area for high voltage winding. HV turns = High voltage (v1) ÷ E.M.F per turn (Et)………………………....Normal tap turns HV per phase current= KVA ÷ (3 × V1) No’s of HV Windingdisc= HV Minimum Tap turns [(Max. Tap turns − Min. Tap turns) ÷ (% Positive variation + % Negative variation) ÷ (% variation betweer steps) Tapping Discs= (% positive variation+% Negative variation)÷( % of variation between Steps) HV Winding Copper Area= HV wdg. Phase Amp.÷Assumed Current Density Current density can be from 1.5 to 3.5 A/ mm2 accordingly we can select the size of copper strip for winding. HV Turns/ Disc = No of Normal Turns ÷ Normal Disc Tap Turns/ Disc = No of Tapping Turns ÷ Tapping Disc Total No of Discs = Normal Discs + Tapping Disc Axial Height of HV winding(Unshrunked) To find axial height of HV winding, select the value of tap break insulation dovetail blocks(from standard data 10 mm to 50 mm), insulation between disc dovetail blocks (from standard data 2 mm to 10 mm) and also select the appropriate height and thickness of conductor which is selected from excel sheet in program, axially parallel conductor and Radially parallel conductor. The standard tables are given in APPENDIX-2. 21 Axial Height (Unshrunked) = (Total discs × Conductor height (with Covering)) ×axially parallel conductors+ ((Total discs-1)× Insulationbetween discs) + (Tap brake Insulation) Axial Shrunked Height = App. 2 to 3 % less than Unshrunked Height HV wining Radial Depth = (Conductor Thickness × No Parallel Cond. (radially) × (Turns/disc)) × 2.03 × 0.5 Where 2.04 & 0.5 are constants. B. Low voltage design Low voltage winding is star connected. First of all calculate the Turns, current, Area for low voltage winding. LV turns= (Low voltage (V2) ÷√3) ÷ E.M.F per turn (Et) LV per phase current = KVA ÷ (V2 ×√3) LV Winding Copper Area=LV wdg. Phase Amp. ÷ Assumed Current Density Current density Can be from 1.5 to 3.5 A/ mm2. Accordingly we can select the height and width ofcopper strip for winding from tables. LV Turns/ Disc = No of Turns ÷ No of Discs LV Winding Axial Height Insulation between disc Dovetail blocks……….. (From standard data 2 mm to 10 mm) Tap Break insulation Dovetail blocks...……..... (From standard data 10 mm to 50 mm) Axial Height (Unshrunked) = (Total discs × Conductor height (with Covering)) + ((Total discs-1) × Insulation between discs) + (Tap brake Insulation) 22 Axial Shrunked Height = App. 2 to 3 % less than Unshrunked Height LV wining Radial Depth = (Conductor Thickness ×No Parallel Cond. (Radially) × (Turns/Disc)) × 2.03× 0.5 Where 2.04 & 0.5 are constants. 3) Parameters calculation A. Winding parameters LVid = Core Diameter + (2× Core to LV Clearance) LV Mean id = LVid + Radial depth LVOd = LV Mean + Radial depth HiLo gap between HV & LV Winding = From specified Data say 10 mm to 60 mm(FROM TABLE) HiLo Mean = LVOd + HiLo gap HVid = Hilo Mean + HiLo gap HV Mean = HVid + Radial Depth HVOd = HV mean + Radial depth B. Core parameters Core Axial Height= HV Final Axial Height (Shrunked) + Top HV Winding Insulation + Bottom HV Winding Insulation + Pressing Ring Thickness + Thickness of SER Core Leg Center= HVOd + Phase to Phase Clearance Window Height =Axial height + 180 Core Length= (3 × Window Height ÷ 10 + (4 × leg center) ÷ 10 + 2.1 × core diameter ÷ 10) 4) Insulation design Width of yoke liner=HVOd+12 Height of yoke liner =HVOd + core axial height + leg center 23 Weight of yoke liner = (3×Width of yoke liner × Height of yoke liner×1.17)÷1000000 Width of core to LV first wedges (wclwl) =12 Height of core to LV first wedges (Hclwl) =core axial height-10 Weight of core to LV first wedges = (7×wclw1×Hclw1×1.17)/1000000 Width of core to LV first cylinder (wclcl) = (core dia+ (7×2) +5) ×𝜋+100 Height of core to LV first cylinder (Hclcl) =core axial height -10 Weight of core to LV first cylinder = (5×wclc1×Hclc1×1.17)÷1000000 Width of bottom block=top block (wlbb) =40 Height of bottom block=top block (Hlbb) =radial depth of LV+9 Weight of bottom block= (21×wlbb×Hlbb×1.17)÷1000000 Weight of top block= (10×wlbb×Hlbb×1.17)÷1000000 Width of LV top washer= bottom washer (wlbw) =LVid+5 Height of LV top washer=bottom washer (Hlbw) =LVOd Weight of top & bottom washer=2×(2×wlbw×Hlbw×1.17)÷1000000 Here weight of insulation between core to LV wedges, cylinder, top and bottom block is calculated. For LV to HV insulation weight calculationsare similarto that of core to LV winding. Width of phase barrier (wphb) = HVOd+10 Height of phase barrier (Hphb) = core axial height -5 Weight of phase barrier = (3×wphb×Hphb×1.17)÷1000000 Width of LV winding (wlwb) =40 Height of LV block (Hlwb) =radial depth of LV+9 Weight of LV winding block = (4×wlwb×Hlwb×1.17)÷1000000 Height of HV winding block (Hhwb) = radial depth of LV+12 Weight of HV winding block = (4×wlwb×Hhwb×1.17)÷1000000 Height of HV tap winding block (Hhwb) =(31×wlwb×Hhwb×1.17)÷1000000 Winsu=Wyl+Wclw1+Wclc1+Wclw2+Wclh+Wltb+Wlbb+Wlbw+Wlhw1+Wlhc1+W lhw2+Wlhc2+Wlhw3+Whbb+Whtb+Wphb+Wlwb+Whwb+Whtwb 24 5) Frame design Ht. of channel =((2÷3)×core dia) The weight of channel is depends on the Size of channel and it is selected based on standard (ISMC) which is given in APPENDIX. Total length of channel (lg) =(2×Core leg center)+ HVOd Weight of channel=((lg÷1000)×channel weight)×4 Weight of frame = weight of channel×2.1 6) Connection design Length of HV connection (LHV) =(4×core leg center)+(4×Height of window)+1500)×1.73 Length of LV connection (LLV) =(2×Core leg center)+(1.5×Height of window) Weight of HV connection (Whv) = (LHV×Ahv×8.9÷1000000)×1.05 Weight of LV connection (Wlv) = (LLV×Alv×8.9÷1000000)×1.05 Weight of connection =Whv+Wlv 7) Tank design Length(L)=(2×Core leg center)+ HVOd + C + D Width (B) = HVOd + A + Bh Height (H)=HVOd+(2×core dia)+t + b A, Bh, C, D, t, b are selected from the standard table which is given in APPENDIX. Mainly there are three types of tank are used: 1) rectangular type 2) semi oval type 3) oval type tank Based on tank type its volume is calculated which is as follows: 1) Rectangular type tank Volume of tank= 𝐿 × 𝐵 × 𝐻 2) Semi oval type tank 𝐵 Volume of tank= (𝐿 − 2 ) × 𝐵 × 𝐻 + 0.785 × 𝐻 × 𝐵2 2 3) Oval type tank Volume of tank=(𝐿 − 𝐵) × 𝐵 × 𝐻 + 0.785 × 𝐻 × 𝐵^2 25 Design pressure inside tank: 1) Pressure due to weight of core and coil assembly at bottom plate of the tank Pcc = (weight of core + weight of winding)/( L×B) 2) Pressure due to oil Poil=oil density×height of oil up to conservator head 3) Additional pressure (Ptest) is provided by customer. If customer is not mention then take 0.35 kg/cm2 as per general practice. 4) Total pressure on tank side and tank cover Pts=Poil + Ptest 5) Total pressure on bottom plate of tank Pbp = Pcc + Poil + Ptest If Pbp less than 1.0 kg/cm2 then manufacturer have to design bottom plate for 1.0 kg/cm2. 6) Permissible stress for mild steel (M.S) plates. Side and top cover (𝜎) = 2100 kg/ cm2 Bottom plate (𝜎) = 1500 kg/ cm2. Design of tank plates with stiffener: 1) Bottom plates: Thickness of bottom plates (Tbp) = [ 𝐿2 𝐵2 )×( ) 𝑛+1 𝑛+1 2 2 𝐿 𝐵 𝑃𝑠×( 4×𝜎×(( 𝑛+1 )×( 𝑛+1 ] )) 10.92×k×𝑃𝑏×𝐵4 Deflection of bottom plates = 𝐸×𝑇𝑏𝑝3 Where k = −1.2 × Pb × b4 × 12 × (1 − mu2 ) E × Tbp3 2) Side plates: Thickness of side plates (Tsp) = [ Deflection of tank wall(dsp)= 0.5 0.5 0.312×𝑃𝑠×𝐿2 ×𝐻 2 ] 2 2 𝜎×(𝐿 ×𝐻 ) ((0.135×Ps×H4 𝐻 𝐿 𝐸×𝑇𝑠𝑝3 ×(1+2.21( )3 26 3) Top plates: 𝐿2 𝐵2 )×( ) 𝑛+1 𝑛+1 2 2 𝐿 𝐵 𝑃𝑠×( Thickness of top plates (Ttp) =[ 2×𝜎×(( 𝑛+1 )×( 𝑛+1 0.5 ] )) Length of bottom plate (Lbp) = L+(2×Tsp)+20 Width of bottom plate (Bbp) = B+(2×Tsp)+20 Weight of bottom plate (Wbp) = (Lbp×Bbp×Tbp×0.062)÷1000000 Length of side plate longer side (Lwl) = L+(2×Tsp)+10 Weight of side plate longer side (Wwl) = (2×Lwl×H ×Tw×0.062)÷1000000 Width of side plate shorter side (Bwl) =B+(2×Tsp)+10 Weight of side plate shorter side (Wws) = (2 ×Bwl×H×Tsp×0.062)÷1000000 Weight of side plates (Ww) =Wwl+Wws Curb width (Cw) is selected from the standard table which is given in APPENDIX. Length of top plate (Ltp) = Lbp+(Cw×2) Width of top plate (Btp) = Bbp+(Cw×2) Weight of top plate (Wtp) = (Ltp×Btp×Ttp×0.062)÷100000 Weight of tank (Wt) = Wbp+Ww+Wtp Tank stiffener design The design of stiffener as follows: To get the dimension of stiffener first section modulus is evaluate, Zws=0.0000595×Ps×L÷ (n+1)×H2 Based on section modulus and tank wall thickness stiffener thickness (Tst), height (Hbst) and width (wst) are selected from the standard table given in APPENDIX. Length of stiffener (Lst) = (2×Hbst) + wst Height of stiffener (Hst) = H-60 Weight of stiffener per unit (Wstpu) = (n×Hst×Lst×Tst×0.062)÷1000000 Weight of total stiffener (Wst) = 2×n×Wstpu To calculate the deflection of wall plates first inertia is calculated: W1=Hbst-Tst W2=wst-(2 ×Tst) 27 A1=(30×Tw)+(2×Tst)+W2)×Tw A2 = A3=(W1+Tst)×Tst A4=W2×Tst Y1=Tw ÷ 2 Y2 = Y3 =Tw+ ((W1+Tst) ÷ 2) Y4=Tw+W1+(Tst ÷ 2) 𝑌= (𝐴1 × 𝑌1) + (2 × (𝐴2 × 𝑌2)) + (𝐴4 × 𝑌4) 𝐴1 + 𝐴2 + 𝐴3 + 𝐴4 2 ((30 × 𝑇𝑤) + (2 × 𝑇𝑠𝑡) + 𝑊2) × 𝑇𝑤 3 𝑇𝑤 𝐼1 = + (𝐴1 × (𝑌 − ( )) ) 12 2 𝑇𝑠𝑡 × (𝑊1 + 𝑇𝑠𝑡)3 + (𝐴2 × (𝑌 − 𝑌2)2 ) 12 (𝑊1 × 𝑇𝑠𝑡)3 𝐼4 = + (𝐴4 × (𝑌4 − 𝑌)2 ) 12 𝐼2 = 𝐼3 = Inertia Is=I1+I2+I3+I4 So, the deflection is 𝐷𝑤𝑠𝑠 = 5 × 𝑃𝑠 × 𝐻 × 𝐻𝑠𝑡 4 384 × 𝐸 × 𝐼𝑠 Deflection is calculated in mm. 8) Performance calculation Core Weight [7.65 × (Window height ÷ 10 ) + (4 × leg center ÷ 10) + (2.1 × core diameter ÷ 10)] × Ai = 1000 Where 7.65 is density of sheet steel & 3,4& 2.1 are standard constant LV Winding Copper ( LV mean id × π×conductor cosssectional area ×nos of Turns ×8.89 ×3) = 1000000 Where 8.89 copper density and 3 for 3- phase. HV Winding Copper 28 = ( HV mean id × π × conductor cosssectional area × nos of Turns × 8.89 × 3) 1000000 % Reactance (% X) = 0.0059 × 𝐿𝑉 𝑡𝑢𝑟𝑛𝑠 × 𝐿𝑉 𝑝ℎ𝑎𝑠𝑒 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 × 𝜋 × 2.22 × 𝐾1 𝐸𝑡 ×𝐾2 Where 0.0059 and 2.22 are constants. K1 =(LV mean id ÷ 1000) × LV Radial depth + 3 × (Hilo mean ÷ 1000) × HV Hilo gap + (HV mean ÷ 1000) × HV Radial depth Where 3is constant. K2 = LV Radial + HV Radial + HVLV Hilo Gap ÷ 3 + HV Axial height (Shrunk) + LV Axial height (Shrunk) ÷ 2 % Resistance (%R) L.L @ 75 ℃ % R = 10 ×KVA % Impedance (% Z) %Z = √ (%R² + %X²) % Efficiency Output power %η=(Output power+ Total losses) Core Losses = (1.1×Core Weight × Watts/ Kg) Where, Frame factor = ((4÷3×core leg center)+window height)÷d Frame Factors, Material Factors & Watts/Kg also derive from standard tables which are given in APENDIX. Total losses LV Cu losses = LV bare weight × current density² × 2.4 HV Cu losses = HV bare weight × current density² × 2.4 To determine eddy current loss, stray loss and gradient of the HV and LV winding first length of mean turns (MLT) are evaluates. 29 MLTL = 𝜋 × 𝐿𝑉𝑚𝑒𝑎𝑛𝑖𝑑 MLTH = 𝜋 × 𝐻𝑉𝑚𝑒𝑎𝑛𝑖𝑑 Evaluate winding surface (WS) area for LV and HV winding as: WSLV = 0.67×2×𝑀𝐿𝑇𝐿×(𝐷𝐿𝑣𝑟+(𝐴𝑝𝑐𝑙×𝐻𝑙𝑐𝑖))×𝑁𝑙𝑣𝑑𝑖𝑠𝑐 1000000 0.67×2×𝑀𝐿𝑇𝐻×𝐷ℎ𝑣𝑟×(𝑁𝑙𝑣𝑑𝑖𝑠𝑐+( WSHV = 𝑁𝑡𝑎𝑝𝑑𝑖𝑠𝑐 )) 2 1000000 Eddy current losses (ELVloss) are determined for LV and HV winding as: 𝑐𝑡𝑙𝑣 4 (𝑁𝑙𝑣𝑑𝑖𝑠𝑐+(𝑟𝑝𝑐𝑙×𝑐𝑡𝑙𝑣𝑖)) ELVloss=10 × ((𝑇𝑙𝑣𝑝𝑑 + 𝑐𝑡𝑙𝑣𝑖)2 − 0.2) × ( 10 ) × ( 𝑓 2 𝑐𝑡ℎ𝑣 4 ) 10 10 × ((𝑇ℎ𝑣𝑝𝑑 + 𝑟𝑝𝑐)2 − 0.2) × ( EHVloss= ((𝑁ℎ𝑣𝑑𝑖𝑠𝑐×𝑎𝑝𝑐×𝐻𝑐)+(𝑁ℎ𝑣𝑡𝑎𝑝𝑑𝑖𝑠𝑐×𝑎𝑝𝑐×𝐻𝑐)) ( 𝐻𝑙𝑎𝑥𝑠ℎ 2 ) × (50) + 1 2 × 𝑓 2 ) × (50) + 1 𝐻𝑎𝑥𝑠ℎ To evaluate gradient (G) watt per meter (W/m2) square are determined for HV and LV windings: W/m2LV=𝐶𝑢𝑙𝑣𝑙𝑜𝑠𝑠 + 𝐸𝐿𝑉𝑙𝑜𝑠𝑠 + 10 ÷ 3 ÷ WSLV W/m2HV=𝐶𝑢ℎ𝑣𝑙𝑜𝑠𝑠 + 𝐸𝐻𝑉𝑙𝑜𝑠𝑠 + 10 ÷ 3 ÷ WSHV GLV= W/m2LV 100 + W/m2LV 200 × 𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑐𝑢𝑛𝑑𝑢𝑐𝑡𝑜𝑟 𝑓𝑜𝑟 𝐿𝑉 2 W/m2HV W/m2HV 𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑐𝑢𝑛𝑑𝑢𝑐𝑡𝑜𝑟 𝑓𝑜𝑟 𝐻𝑉 GHV= 100 + 200 × 2 Stray losses (Sloss) are evaluated as: %𝑋×𝐸𝑡 1.7 ) 222 𝑆𝐿𝑉𝑙𝑜𝑠𝑠 = 1200 × ( 2000 0.5 × (𝐻𝑙𝑎𝑥𝑠ℎ) × (𝑄 ÷ 1000 ÷ 100)0.25 SHVloss= 10 + 𝐶𝑢𝑙𝑣𝑙𝑜𝑠𝑠 + 𝐸𝐿𝑉𝑙𝑜𝑠𝑠 + 𝑆𝐿𝑉𝑙𝑜𝑠𝑠 + 𝐶𝑢ℎ𝑣𝑙𝑜𝑠𝑠 + 𝐸𝐻𝑉𝑙𝑜𝑠𝑠 Total Losses= Core losses + (LV Copper Loss + HV Copper Losses) + 0.2 × (LV Copper Loss + HV Copper Losses) Where 0.2 is indicate stray losses. To calculate actual losses calculated stray losses are considered. Total Losses= Core losses + LV Copper Loss + HV Copper Losses + LV stray loss + HV stray loss 30 9) Oil calculation Basically volume is calculated as weight per density so here volume of copper, core, connection, insulation, and frame is calculated. Volume of copper (Vcu) = weight of copper ÷ density of copper Volume of core (Vcore) = Weight of core ÷ density of core Volume of connection (Vcnct) = Weight of connection ÷ density of connection Volume of insulation (Vinsu) = Weight of insulation ÷ density of insulation Volume of frame (Vframe) = Weight of frame ÷ density of frame Volume of activepart = Vcu+Vcore+Vcnct+Vinsu+Vframe Volume of oil = Volume of tank - Volume of activepart 10) Cost calculation Cost is calculated for each part of the transformer as Cost of copper (Ccu) =550 × Wcu Cost of lamination (Ccore)=150 × Wcore Cost of oil (Coil)=68 × (Voil÷1000000) Cost of insulation (Cinsu) = 160 × Winsu Cost of connection =550 ×Wcnct Cost of frame= 72 × Wframe Cost of tank=(Wt × 75)+(Wst × 75) Here, 550, 150, 68, 160, 72, 75 are manufacturing cost per kg of copper, lamination, oil, insulation, frame, tank (MS) plates respectively as per the market cost. So the total cost of main parts of transformer is determined as, Tocost=(Ccu+Ccore+Coil+Cinsu+Cframe+Ccnctn+Ctank) × 1.3 Where 1.3 is a factor used to evaluate the total cost of main parts of transformer. 31 2.2 FLOWCHART OF COMPLETE CONVENTIONAL DESIGN OF TRANSFORMER START INPUT DATA KVA, V1, V2, F, Bm, KFACTOR, NO. OF STIFFENERS DESIGN OF MAGNETIC FRAME DESIGN OF HIGH VOLTAGE WINDING DESIGN OF LV WINDING TANK DESIGN PERFORMANCE PARAMETER CALCULATIONS TOTAL COST OF TRANSFORMER UNIT END 2.1 Flowchart of complete design of transformer 32 CHAPTER 3 OPTIMIZATION TECHNIQUE USINGEXHAUSTIVE SEARCH METHOD 3.1 MODIFICATIONSIN CONVENTIONAL DESIGN PROGRAM TO GET OPTIMUM DESIGN The conventional design program may or may not be the optimal design. Now, to obtain optimum design, optimization objective and design constraints are inserted into the conventional design program which is in MATLAB tool. 1) Insert “FOR” Loops for the subsequent parameters to iterate the entire program between minimumand maximum acceptable limit for selecting the possible design variants. a. “K-factor” which is varies between 0.35 - 0.55. b. “Bm” (Core flux density) which is varies from 1.45 - 1.75Wb. c. “Delta(Current density of HV winding & LV winding) which varies from 1.9 to 3.5 A/mm2. d. “Stiffener which is varies from 2 to 8 nos. 2) Insert also min. or max. range of essential objective function values as constraint value i.e. % Z, No load loss. 3) To get the possible design variant some standard parameters are required which are given in the APPENDIX then after run the program to acquire various feasible design variants. 4) Print all feasible results in excel sheet. 5) From program results selectappropriate design based on requirement of customer i.e. high efficiency,% Z, low weight, low cost etc. 33 3.2 FLOWCHART OF OPTIMAL DESIGN OF 3-PHASE CORE TYPE TRANSFORMER BY ITERATIVE COMPUTER PROGRAM START READ INPUT DATA ( KVA, V1,V2, FREQUENCY) SET BOUND VALUES OF K-FACTOR, Bm, DELTA OF HV & LV WINDING & STIFFENER SELECT THE SUITABLE VALUES FOR CALCULATION OF DESIGN PARMETERS FROM STANDARD TABLES ON EXCELSHEET RUN PROGRAM WITH MAX. & MIN. VALUE OF K, Bm, DELTA OF HV & LV WINDING, No. of STIFFENER DESIGN OF LAMINATION (CORE) DESIGN OF HV WINDING DESIGN OF LV WINDING TANK DESIGN CALCULATION OF PERFORMANCE PARAMETERS COST OF TRANFORMER UNIT ARE SPECIFIED CONSTRAITS SATISFIED? GO FOR NEXT ITERATION OBJECTIVE FUNCTION ACHIEVED? PRINT OUTPUT FOR ALL POSSIBLE DESIGN VARIANTS IN EXCEL SHEET SELECT THE SUITABLE OPTIMAL DESIGN BASED ON OPTIMIZATION CRITERIA END Fig.3.1 Flowchart of proposed optimization technique by iterative programming 34 3.3 RESULTS FROM ABOVE PROGRAM METHODOLOGY The input data are considered for Core type power transformer, Q= 15000 KVA, V1=11000 volts, V2=66000 volts, 3-ph, f=50 Hz, vector group=Dyn11 1. After execution of the program using “ESM” 470 results are obtained satisfying constrains (i.e. no load loss (<=11000 watt), load loss(<=70000 watt), %z (7-10), efficiency (>=99%) (without considering the tank design)) which are in detail at APPENDIX-3 (Dissertation Phase-I work). Figure 3.2: Design results for active part 35 2. After execution of the program using “ESM” 18 results are obtained satisfying constrains (i.e. no load loss, load loss, %z, efficiency gradient of LV windingand HV winding (9-23)and deflection (5-9 mm) on tank wall (with considering the tank design))(Dissertation Phase-II MSR work). Figure 3.2: design results for transformer unit for 7 constraints 3.4DESIGN SELECTION PROCEDURE After getting the possible solution, we can select the alternative i.e. k-factor, Bm, 𝛿 of HV& LV and numbers of stiffeners based on optimization criterion, 1) If the maximum efficiencyis required then select preference no. = 17 (99.25). 2) If minimum is core losses required then selectpreference no. = 1 (9092.52 kW). 36 3) If minimum Cost is required then select preference no. = 19 (61.36 lac). 4) If good quality strength is required (% impedance) then select preference no. = 19(8.50). 37 CHAPTER 4 DESIGN OPTIMIZATION USING SEQUENCIAL QUADRATIC PROGRAMMING In this method optimization toolbox of MATLAB 2011 is used &program for optimization is created. In this tool, pair of required files is fetched in the optimization toolbox. First, theobjective functionis created. After creating objective function file it is fetched into the optimization toolbox. Secondly, the constraints files are created and fetched into the optimization toolbox. There are many algorithms given in the optimization toolbox. Then after select the algorithm according to requirement. The figure of optimization toolboxMATLAB2011 is given below. Fig.:4.1Optimization Toolbox in MATLAB 38 4.1 SEQUENTIAL QUADRATIC PROGRAMMING (SQP) The sequential quadratic programming(SQP) is a most popular method to get the solution of optimization problem through nonlinear constraint minimization. It also delivers algorithmic tools to get the solution of large-scale technological relevant problems. Basically this algorithm is theoretically related to get solution for a set of nonlinear equations by Newton’s method and Kuhn-Tucker conditions for the Lagrangian of the constrained optimization problem. Here, the total cost of transformer is chosen as objective function. The main aim of the current work is tominimize the total cost of transformer active parts which includes cost of copper material, cost of CRGO (core laminations),insulating material(Parma wood) and mild steel (for tank plates and stiffeners). To minimize the cost first, an objective function file is created in which all calculations about the variables i.e. K-factor (0.35 to 0.55), flux density (Bm=1.45 to 1.75Wb/m²), current density of LV and HV (𝛿=1.9 to 3.5 A/mm2)and no. of stiffeners (n= 2 to 8)which are carried out. Secondly the constraint file is created by inserting constraints as No-load losses (≤ 11000 watt), Load losses (≤ 70000 watt), short circuit impedance (7 ≤ %Z ≤ 10), efficiency (%η ≥ 99), gradient of HV and LV winding (9 ≤ G ≤23) and deflection (5 ≤ dwss ≤ 9 mm). Third one constant data file is created for the calculation of parameters which are not depending on objective variables. After creating objective function file and constant data file, the constraint file is created. Then all the above 3 files are fetched in the optimization toolbox. After selecting of appropriate algorithm, giving bound values of variables press START button in the dialog box of optimization toolbox. The number of iterations will run and finally we will get the optimized result in the optimization tool box. Also we will get the value of variables i.e. K-factor, maximum flux density (Bm), current density(𝛿) of HV and LV and no. of stiffeners. Figure4.2 shows, the design variables satisfying the constraints and providing the feasible design. The results obtained by the optimization toolbox is representing in the graphical form. 39 4.2 OPTIMIZATION RESULT FOR ACTIVE PART OF POWER TRANSFORMER (DISERTATION PHASE-I WORK) The input data are consider for Core type power transformer, Q= 15000 KVA, V1=11000 volts, V2=66000 volts, 3-ph, f=50 Hz, vector group=Dyn11 Fig.: 4.2Optimization toolbox including results for active part 40 4.3 RESULTS IN GRAPHICAL FORM OBTAINED WITH OPTIMIZATION TOOLBOX Fig.:4.3Optimization results in graphical form When constraints, objective function, constant data files are inserted into the optimization toolbox, the optimization algorithm(SQP) will give the better solution from these variants. For these obtained value of K-factor, maximum flux density, current density(𝛿) of HV and LV satisfied the constraints (No- load losses, Load losses, % Z, % effi.) and optimization toolbox gives final values for K-factor, maximum flux density(Bm), current density(𝛿) of HV and LV are 0.375, 1.743wb/m², 2.023A/mm2 and2.035A/mm2 respectively. Hence, the optimization toolbox is capable for giving extremely accurate values of variables & that within the satisfied constraints. 41 4.4 OPTIMIZATION RESULT OF A POWER TRANSFORMER INCLUDING ACTIVE PART AND TANK (DISSERTATION PHASEII MSR WORK) Fig.: 4.4Results obtained by SQP method for active part and tank Here in the transformer design is proceeded including the tank design. The added variable as no. of stiffeners and constraints are considered as gradient of LV and HV, deflection at transformer side walls. On performing the simulation using optimization toolbox by considering SQP methodology the results so obtained are not found to be feasible as is clear from the above figure.Hence, Genetic Algorithm method is applied. 42 CHAPTER 5 OPTIMIZED DESIGN USING MATLAB TOOL FOR GENETIC ALGORITHM (GA) In this method optimization toolbox of MATLAB is used &program for optimization is created. The procedure of the creation of objective function file and constraint file is same as the SQP. The figure of optimization toolboxMATLAB2011 is given below for GA. Fig.:5.1Optimization Toolbox in MATLAB for GA 43 5.1 GENETIC ALGORITHM (GA) John Holland introduced GA for the first time in 1970. Genetic algorithm is used for solution of both unconstrained and constrained optimization problems which is inspired by natural selection and biological evolution. The GArepetitively modifies a population for individual solutions. At each generation, the GA selects randomly individuals from the current generation and uses them to reproduce for next generation. The genetic algorithm uses mainly three operators at each generation to produce the next generation from the current population. Selection is done based by selecting a two parent string which contributes to the population at the next generation.Crossover is done by swappingor combining from two parent string for a children string for next generation. Mutation is used for maintaining the diversity and it modify a chromosome for next generation. In genetic algorithm there are three types of operator. The first is selection, second is crossover and third one is mutation. There are many types of selection i.e. roulette selection, tournament selection, rank selection, stochastic selection. There are many types of crossover i.e. single point, double point, multipoint, intermediate crossover. There are different techniques for mutation i.e. adaptive feasible, constraint dependent, Gaussian mutation. Here, as an objective function the total cost of transformer is chosen. The procedure of the creation of objective function file and constraint file and also the range of variable and constraintsare same as the SQP. After selecting of GA, giving bound values of variables press START button in the dialog box of optimization toolbox. The number of generations will run and finally we will get the optimized result of objective function value and variables in the optimization tool box. Figure5.2 shows, the design variables satisfying the constraints and provide the feasible design results. The result obtained by the optimization toolbox is representing in the graphical form in figure 5.3. 44 5.2 OPTIMIZATION RESULT OF A POWER TRANSFORMER USING GA The input data are consider for Core type power transformer, Q= 15000 KVA, V1=11000 volts, V2=66000 volts, 3-ph, f=50 Hz, vector group=Dyn11 Fig.: 5.2 Optimization toolbox using GA including results for whole transformer 45 5.3 RESULTS IN GRAPHICAL FORM OBTAINED WITH OPTIMIZATION TOOLBOX Fig.:5.3Optimization results in graphical form When constraints, objective function, constant data files are inserted into the optimization toolbox, the optimization algorithm (GA) will give the better solution from these variants. By running this algorithm it satisfiesallthe constraints (No- load losses, Load losses, % Z, % effi., gradient of LV and HV windings, deflection on tank plate wall) and optimization toolbox gives final values of variable as K-factor, maximum flux density(Bm), current density(𝛿) of HV and LV and no. of stiffeners are 0.478, 1.574wb/m², 2.181A/mm2, 2.904A/mm2 and 2.014 respectively and objective function as cost minimization is 61.92 lac. Hence, the optimization toolbox is capable for giving extremely accurate values of variables & that within the satisfied constraints. 46 There are many types of selection operator and mutation techniques as discussed earlier. Someof the design results using different mutation techniques and selection operator are as shown below: Sr. Selection Roulette wheel No techniques selection . > Stochastic selection Tournament selection Mutation Constraint Adaptive Constraint Adaptiv Constraint Adaptive techniques dependent feasible dependent feasible dependent > e feasible 1. k-factor 0.449 0.417 0.417 0.459 0.43 0.412 2. Bm (wb/m²) DelLV(A/ mm2) DelHV(A/ mm2) Stiffener 1.624 1.664 1.644 1.568 1.622 1.622 2.13 2.496 2.499 2.524 2.422 2.469 2.894 2.577 2.577 2.568 2.574 2.593 2.4 2.25 2 2.368 2.002 2.242 10.56 10.62 10.30 10.51 10.42 10.49 67.23 67.87 68.16 65.01 66.89 68.70 8. No-load losses (kW) Load losses (kW) %Z 9.68 9.10 9.40 8.16 9.58 9.41 9. %η 99.19 99.22 99.21 99.25 99.23 99.21 10. GLV 9.97 9.29 9.28 9 10.75 9.32 11. GHV 20.36 22.55 22.54 22.45 21.71 22.90 12. Deflection (mm) Wcore (kg) 8.39 7.72 6.80 7.75 6.07 7.60 9059.9 88396.23 8550.97 9960.9 8944.08 8298.06 3762.95 3773.26 3. 4. 5. 6. 7. 13. 4 14. Wcu (kg) 3711.45 3726.14 3743.29 3570.5 6 15. 16. Wconction (kg) Winsu (kg) 36.32 35.21 35.31 35.67 35.48 35.19 280.46 266.72 267.32 264.31 270.33 267.96 47 17. 18. 19. 20. Wframe (kg) Wtankplate (kg) Wstiffener (kg) Ccore (Rs.) 762.03 727.80 730.25 738.81 734.30 727.34 1197.90 1088.56 1208.81 1149.4 1230.41 1085.32 2 417.76 404.54 275.23 392.50 272.63 400.43 1358995 1258435 1277397 149414 1341613 1244709 2069621 2075298 376976 362890 349731 42291. 42291.11 43253.19 112729.2 111432.1 6003753 5843655 2 21. Ccu (Rs.) 2041301 2049818 2058810 196380 9 22. Coil (Rs.) 396755 23. Cinsu (Rs.) 44874.1 351160 354722 42676.53 42772.58 11 24. Ctank (Rs.) 121172.2 115984.1 111303.5 115645 .2 25. Total cost 6005692.2 5830266 5875511 (Rs.) 609852 0 Table 5.1 Result comparison of different mutation techniques and selection operator As show in table 5.1 using GA in optimization toolbox, there are various mutation techniques and selection operator are used for result comparison. Here, as the objective function is cost minimization so if we select a design as per cost then we can select a roulette wheel-selection and adaptive feasible mutation technique. 48 CHAPTER 6 ANALYSIS OF PROPOSED TECHNIQUES Analysis of both the proposed techniques for a given power transformer is below. CASE-I 70 60 50 40 30 20 10 0 ESM GA Fig 6.1 Comparison of ESM and GA (CASE-I) ESM GA Closs (kW) 9.152 10.06 Deflection (mm) 8.9 6.9 Cost (lac) 64.74 61.9 Table 6.1 Comparison of ESM and GA (CASE-I) From the above figure, it is clear that the no load losses obtained by using ESM method are less than that of GA but correspondingly the deflection is greater in ESM . Due to less deflection maintenance, cost of tank reduced. On welded joint oil leakage can be avoided. 49 CASE-II 70 60 50 40 30 20 10 0 ESM GA Gradient of HV Loadloss (kW) Cost(lakh) Figure 6.2 Comparison of ESM and GA (CASE-II) ESM GA Gradient 22.79 22.70 Load losses 67.60 67.17 Cost 64.17 61.9 Table 6.2 Comparison of ESM and GA (CASE-II) From the above figure, it is clear that the load losses obtained by using ESM method are less than that of GA but correspondingly the cost obtained by using ESM method are high than that of GA so manufacturing cost is high as well as operating cost is high in ESM. 50 CASE-III 80 60 40 20 0 ESM GA Closs (kW) Deflection Cost (lakh) (mm) Fig 6.3 Comparison of ESM and GA (CASE-III) ESM GA No-Load losses (kW) 9.991 10.06 Deflection (mm) 7.9 6.9 Cost (lac) 61.36 61.9 Table 6.3 Comparison of ESM and GA (CASE-III) From the above figure, it is clear that the manufacturing cost obtained by using ESM method are less than that of GA but correspondingly the deflection obtained by using ESM method are high than that of GA. Ultimately it will affect to the transformer tank. 51 ESM GA This method provides all the possible Optimization toolbox gives the final value of variables which are quite a large in number. variables which satisfy the constraint values. Manual selection of optimum design based It gives the value of variables where the fitness on application point of view. function is minimum. Numbers of iterations are more. Numbers of generations are less. It is time consuming and tedious method. Less time is required to get optimum value. It is less accurate. It is more accurate. Table 6.4 analysis of both proposed techniques 52 CHAPTER 7 MULTIOBJECTIVE OPTIMIZATION USING NON-DOMINATED SORTING GENETIC ALGORITHM (NSGA-II) 7.1 METHOD DESCRIPTION In this method, the use of multi objective function is done to obtain a pareto-optimal solution, instead of one objective function. In multiobjective function the objective functions are conflicting functions. Now-a-days a number of methodologies are available to solve the multiobjective functions. There are many classical methods also well-known including decision-making methods for multiobjective optimization. In these methods, by multiplying a weight it converts into a single objective and it is applied many times to obtain different solutions. So, by applying this method we can obtain a multiple paretooptimal solution in first trial. There are some analysis points over other methods of NSGA-II as high computational complexity, lack of elitism and need to specify sharing parameters [9]. In this algorithm it has a high computational complexity to get a better optimization. Due to elitism it gives the speedily performance of GA and if good solutions are found then it prevents that solution. In traditional methods, we have to provide some sharing parameter specification, to make sure diversity in population. In NSGA-II replace the sharing function by a crowded-comparison operator. Diversity should be maintained for population. 7.2 IMPLEMENTATION OF “NSGA-II” By using this approach, two objective functions are considered, cost minimization and no-load losses minimization. To minimize these objective functions first, an objective function file is created in which all calculations about the variables i.e. K-factor (0.35 to 0.55), flux density (Bm =1.45 to 1.75Wb/m²), current density of LV and HV (𝛿=1.9 to 3.5 A/mm2)and no. of stiffeners (n= 2 to 8), objective function, constraints as No-load losses (≤ 11000 watt), Load losses (≤ 70000 watt), short circuit impedance (7 ≤ %Z ≤ 10), efficiency (%η ≥ 99), gradient of HV and LV winding (9 ≤ G ≤ 23) and deflection (5 ≤ dwss ≤ 9 mm)which are carried out. One another file is created where, no. of 53 population, no. of generation, lower and upper bound of variables, number of variables, number of objectives and number of constraints are defined. By running this file it run for defined number of population (here 50) and number of generation (here 500). In this approach, namely, Intermediate crossover, Gaussian mutation technique and tournament selection operator are used. The detailed discussion of this algorithm and standard code is available at [8-10]. The graph of two objective functions for 500 generation is shown in figure 7.1 Fig. 7.1 Plot of NSGA-II for 50 population and 500 generation The following table shows the results output from the NSGA-II methodology. It indicates the total eight numbers of successive possibilities for the two objective functions. From this table the following results are derived 1) For the total cost (5656071.37) result the No-load loss is going to increase about (10.99 KW) with accomplish of all constraints values within range. 2) For the total cost (6369877.50) result the no load loss is going to reduce about (8.3 KW) with accomplish of all constraints values within range. 3) But also with the cost (5963666.22) result the no load loss (9.458 KW) is top result among all the successive possibilities. 54 K Bmwb DelHV A/mm2 stiffnr /m² DelVA/ mm2 Ldloss (kW) 68.308 Z effi GL GH 2.25 Closs (kW) 10.52 9.88 99.2 9.22 20.05 Dwss (mm) 8.32 0.403 1.68 2.56 2.6 0.403 1.71 2.56 2.6 2.15 10.99 67.828 8.82 99.2 9.23 22.06 8.03 0.419 1.45 2.56 2.6 2.21 8.379 68.592 9.34 99.1 10.2 17.13 7.21 0.409 1.56 2.56 2.603 2 9.069 69.649 7.81 99.2 9.17 21.65 7.42 0.406 1.59 2.566 2.6 2 9.458 69.449 9.92 99.2 9.18 18.82 7.06 0.412 1.5 2.563 2.604 2.16 8.517 68.243 8.78 99.2 11.1 22.44 8.09 0.403 1.66 2.564 2.602 2.17 10.229 68.560 8.92 99.2 9.21 22.02 6.61 0.419 1.48 2.565 2.602 2.34 8.471 69.838 7.26 99.2 21.11 8.22 0.406 1.6 2.564 2.603 2 9.4557 69.180 8.88 99.2 10.0 9 9.18 22.82 6.94 Table 7.1 Results obtained from “NSGA-II” after 500 generation for a population size of 50 55 Tocost (Rs.) 57270 34.47 56560 71.37 63698 77.50 60466 73.91 59636 66.22 62086 66.18 57907 15.48 62529 83.08 59265 79.62 CHAPTER 8 CONCLUSION In the present work, the two methods of optimization (ESM and GA) for transformer design were approached. First method is iterative computer programming and second method is optimization toolbox. Also for the optimization multiobjective optimization is done by considering two objective functions. In ESM method a large variety of results were obtained, of which a few were able to satisfy the limitations of cost, no load losses, load losses and deflection. On analysis of the results so obtained it was found that a number of results could comply with the limitations but would fail practically due to unfeasible combination of parameters (eg. current density of HV < LV). Optimum design of power transformer satisfying major constraintsis obtained using optimization toolbox in MATLAB.Comparison of two different optimization processes could be carried out to conclude GA method to be more effective. The NSGA-II method is used to obtain the multiobjective optimization for the given power transformer. In this method, two objective functions are taken i.e. total cost and no load loss minimization. The results were shown with successive possibilities. Over all it gives better design optimization solution of given power transformer. 56 FUTURE SCOPE Different types of tank design can be done and other techniques for power transformer design optimization can be applied with different combination of objective function and variables using different algorithm techniques. 57 REFERENCES 1) R. Baehr in “Transformer technology state of the art and trends of future development”, electra, No. 198, October 2001. 2) Pavloss. georgilakis in “spot light in modern power transformer design”, springer Dordrecht Heidelberg, London, New York, 2009, ISSN 1612-1287. 3) S.V.Kulkarni and S.A.Khaparde in “transformer engineering design and practice”; marcel Dekker, Inc., 2005. 4) Eleftherios I. Amoiralis, Member, IEEE, Marina A. Tsili, Member, IEEE, and Antonios G. Kladas, Member, IEEE, “Transformer Design and Optimization:A Literature Survey”, ieee transactions on power delivery, vol. 24, no. 4, october 2009. 5) MATLAB 2011 “Optimization Toolbox”. 6) Practical Lab manual of Atlanta Electricals Private Limited. 7) A. V. Chiplonkar by “Design, Operation and Maintenance of Core Type Oil Filled Power Transformer”, Pramod bajaj Ghosalkar, Parth Offset, 2008. 8) K. Deb by “Multi-objective Optimization using evolutionary Algorithms”, John Wiley and sons, New York, NY, USA, 2009. 9) K. Deb, A. Pratap, S. Agrawal & T. Meyarivan by “A Fast and Elitist Multiobjective Genetic Algorithm : NSGA-II”, IEEE Transactions on Evolutionary Computations, Vol. 6, No. 2, April-2002. 10) http://www.mathworks.in/matlabcentral/fileexchange/31166-ngpm-a-nsga-iiprogram-in-matlab-vl-4. 58 APPENDIX 1) Review card 59 60 61 62 63 2) Plagiarism report 64 3) Paper present certificate 65 66 4) Abbreviations Q: KVA rating of Power Transformer, V1: Voltage of High voltage side V2: Voltage of Low voltage side K: Constant factor Bm: Maximum flux density in Wb/m² Et:Emf/Turn Ai: Area of Iron d: Diameter of core Thv: Turns of High voltage winding Ihv: Current in High voltage winding Ahvcu: Area of High voltage winding Nhvdisc: Normal disc for High voltage winding Thvpd: Turns/disc for High voltage winding Nhvtapdisc : Tap disc for High voltage winding Ttappd: Turns/disc for Tap voltage winding Todisc: Total High voltage winding discs Hc:Conductor bare height of High voltage winding cthv:Conductor bare thickness of High voltage winding apc:Axially parallel conductors rpc: Radially parallel conductors Inhvdisc: Insulation between disc Intap: Tap break insulation Hci: Height of HV conductor with paper covering cthvi: Thickness of HV conductor with paper covering Delmodi: Modified current density Haxunsh: axial unshrunkheight of HV winding Haxsh: axial shrunk height of HV winding dhvr: Radial depth of HV winding HVti: Top insulation of HV winding HVbi: Bottom insulation of HV winding Tlv: Turns for Low voltage winding 67 Ilv: current in Low winding Alvcu: area for Low voltage winding Nlvdisc: Total disc in Low voltage winding Tlvpd: turns/disc in Low voltage winding Hlc: Bare height of LV voltage winding ctlv: Bare thickness of LV voltage winding apcl: Axially parallel conductor in LV winding rpcl:Radially parallel conductor in LV winding Inlvdisc: Insulation between discs in LV winding Hcli: Height of LV conductor with covering cthvi: Thickness of LV conductor with covering Dellvmodi: Modified current density in LV winding Hlaxunsh: Axial unshrunkheight of LV winding Hlaxsh: Shrunk height of LV winding dlvr: Radial depth of LV winding LVid: Inner diameter of LV winding LVmeanid: Mean inner diameter of LV winding LVod: outer diameter of LV winding Hgap: Hilo gap between LV and HV winding Hmean: Hilo mean gap HVid: inner diameter of HV winding HVmeanid: Mean inner diameter of HV winding HVod: outer diameter of HV winding HVtser: Thickness of static end ring HVprt: pressing ring thickness Clc: Core leg center %X: Reactance in percentage value %Z: Impedance value in percentage %R: Resistance value in percentage Hw: Height of window Hcax: Core length wcore: Weight of core material 68 wlvcu: Weight of LV winding copper whvcu: Weight of HV winding copper wcu: Total Weight of copper closs: Core losses %effi.: Efficiency in percentage Lvculoss: LV copper loss HVculoss: HV copper loss Toloss: Total copper loss Costlami: Cost of core stampings Costcu: Cost of winding material Tocost: Total cost of transformer unit. Glv: Gradient of LV Glv: Gradient of LV Dwss: deflection on tank plates 5) STANDARD TABLES The impulse and power frequency level selection is taken from the following table. The selection of other parameters is based on this level. High voltage (KV) Impulse voltage (KVP) Power frequency voltage (KVrms) 0.4 - 3 1.2 40 10 3.7 60 20 7.3 75 28 12.1 95 38 17.6 125 50 24.1 170 70 36.1 250 95 52.1 325 140 72.6 450 185 100.1 550 230 69 123.1 650 275 Table A1: impulse and power frequency levels The required clearance between CORE to LV diametrically is selected according to power frequency level. PF voltage Rating (KVA) (KVrms) >2000 >1600<2000 <1600 0.4 14 12 10 3.1 25 25 25 20.1 28 28 28 50.1 32 32 32 70.1 38 38 38 140.1 75 75 75 Table A2: CORE to LV clearance in mm The selection of clearance between HV & LV and HV MAIN & HV TAP radially is selected from the following table. HV PF voltage (KVrms) HV & LV HV MAIN & HV TAP HV impulse HV impulse HV impulse HV impulse < 550 kvp > 550 kvp < 550 kvp > 650 kvp 1 13 NA NA 13 28.1 15 NA NA 15 50.1 18 NA NA 18 HV PF voltage (KVrms) HV & LV HV MAIN & HV TAP HV impulse HV impulse HV impulse HV impulse < 550 kvp > 550 kvp < 550 kvp > 650 kvp 70.1 30 30 28 28 140.1 48 55 46 52 70.1 30 30 30 30 140.1 48 55 48 55 Table A3: clearance between HV & LV and HV MAIN & HV TAP radially in mm 70 Now further top and bottom clearances are selected as per standard values given in following table Rated KV Top clearance Bottom clearance 11 20 20 22 30 30 33 40 40 66 60 60 132 delta 120 100 132 1 coil (star) 100 60 132 2 coil 60 60 220-950 215 115 1050 235 125 Table A.4: Minimum top and bottom clearance in mm The selection of paper covering is based on KV class of the transformer. The following table shows some standard values from that the paper covering is selected for different size of copper conductor. Rated Paper covering thickness in mm KV Rating up to 1600 KVA Rating above 1600 KVA 0.433 0.3 0.4 3.3 0.3 0.4 Rated Paper covering thickness in mm KV Rating up to 1600 KVA Rating above 1600 KVA 6.6 0.3 0.4 11 0.5 0.5 22 0.5 0.5 33 0.5 0.5 66 - 1.2 132 (550 BIL) - - 220 (950 BIL) - 1.8 71 220 (1050 BIL) - 2 Table A5: selection of paper covering in mm The NO LOAD losses depend on multiplying factor, material factor and frame factor. The standard values required for calculating the NO LOAD losses are taken from the tables given below. KVA rating Multiplying factor 1-500 1.3 501-1000 1.25 1001-2000 1.2 2001-5000 1.15 Above 5001 KVA 1.1 Table A.6: selection of multiplying factor Material Factor M4 1 M5 1.09 M6 1.17 Moh 0.87 Hib 0.7 Table A.7: selection of material factor Stacking ratio Frame factor 2.00 1.42 2.25 1.39 2.50 1.37 2.75 1.34 3.00 1.32 3.25 1.30 3.50 1.28 72 3.75 1.27 4.00 1.26 4.25 1.25 4.50 1.24 4.75 1.23 5.00 1.22 5.25 1.21 5.50 1.20 5.75 1.195 6.00 1.190 6.50 1.180 7.00 1.170 7.50 1.160 8.00 1.15 Table A.8: selection of stacking factor The selection of pressing ring thickness done based on the table given below. Rating Pressure ring thickness (KVA) Material Mild steel Pherma wood Pherma wood Max. Negative tap ≤ 20 to ≥ 40 ≤ 10 to ≥ 20 ≥ 10 1 15 20 0 1001 20 20 20 3001 35 40 40 5001 45 50 50 25001 50 70 70 (%) Table A9: Pressure ring thickness in mm 73 The selection of the copper conductor for high voltage and low voltage winding is based on available sizes of the conductor from suppliers. Table 2.10gives the available sizes of the copper conductor for windings. Serial no. Size Paper covering in mm (Height × Thickness) in mm 22 6.80 × 1.70 0.5 23 6.80 × 1.50 0.5 31 10.00 × 2.20 1.2 37 9.0 × 2.6 0.4 60 11.00 × 3.00 0.5 84 13.20 × 2.50 1.2 89 10.50 × 1.40 0.4 110 12.00 × 2.60 0.5 180 11.50 × 3.70 0.7 196 12.50 × 2.00 0.4 198 12.50 × 2.00 0.4 330 12.00 × 1.70 0.3 201 9.20 × 1.62 0.4 202 9.20 × 1.62 0.4 203 9.20 × 1.62 0.4 210 10.00 × 4.50 0.5 RT362 10.50 × 1.50 0.5 RT365 10.50 × 1.50 0.5 RT364 10.40 × 3.20 0.4 RT-397 10.40 × 3.20 0.3 RT401 10.0 × 1.80 0.35 RT402 6.80 × 1.70 0.5 RT395 12.80 × 2.20 0.4 RT396A 12.80 × 2.20 0.4 RTJ404 8.50 × 1.90 0.4 74 Serial no. Size Paper covering in mm (Height × Thickness) in mm RTJ406 14.00 × 2.50 0.8 RTF405 12.00 × 2.60 0.4 RTF406 12.00 × 2.60 0.4 RTF407 12.00 × 2.60 0.4 RTF407 11.50 × 2.50 0.4 RTF408/9/10 8.50 × 1.90 0.4 RTF411 8.80 × 1.50 0.3 22 6.80 × 1.70 0.5 23 6.80 × 1.50 0.5 31 10.00 × 2.20 1.2 37 9.0 × 2.6 0.4 60 11.00 × 3.00 0.5 84 13.20 × 2.50 1.2 89 10.50 × 1.40 0.4 110 12.00 × 2.60 0.5 180 11.50 × 3.70 0.7 196 12.50 × 2.00 0.4 198 12.50 × 2.00 0.4 202 9.20 × 1.62 0.4 203 9.20 × 1.62 0.4 210 10.00 × 4.50 0.5 211 10.00 × 4.00 0.5 212 13.00 × 2.80 0.5 213 13.30 × 2.70 0.5 214 15.00 × 2.80 0.5 215 15.00 × 3.00 0.5 216 14.00 × 3.00 0.4 217 14.00 × 3.00 0.4 75 Serial no. Size Paper covering in mm (Height × Thickness) in mm 225 6.80 × 1.70 0.5 226 6.80 × 1.70 0.5 207 500 SQ 500 SQ 208 500 SQ 500 SQ 209 500 SQ 500 SQ RT345 8.50 × 1.80 0.8 RT323 8.00 × 1.60 0.8 RT167 16.30 × 1.93 0.6 RT314 16.3 × 1.93 0.5 RT315 16.1 × 2.0 0.5 RT319 9.2 × 2.2 0.5 RT320 11.6 × 1.5 0.5 RT322 12.0 × 2.6 0.5 RT323 12.0 × 2.6 0.5 RT324 12.0 × 2.6 0.5 RT325 12.2 × 2.4 0.5 RT337 10.4 × 3.2 0.4 RT175 11.5 × 2.0 0.5 RT-322 10.4 × 3.2 0.5 95 10.5 × 1.50 1 RT 9.15 × 2.40 0.4 RT376 12.00 × 2.30 0.5 RT377 12.00 × 2.20 0.5 RT381 8.50 × 1.50 0.6 RT382 13.20 × 2.30 0.4 RT384 8.50 × 1.50 0.8 RT-386 12.20 × 2.60 0.4 RT-387 8.50 × 2.00 0.3 76 Serial no. Size Paper covering in mm (Height × Thickness) in mm RT-390 9.60 × 2.05 0.3 RT-391 9.60 × 2.05 0.3 RT-392 9.60 × 2.05 0.3 RT-393 11.00 × 3.20 0.5 RT-394 11.00 × 3.20 0.5 PAK 11.00 × 3.6 0.5 PAK 11.00 × 3.6 0.5 RT-396 8.70 × 2.00 0.7 RT-398 11.50 × 1.60 0.7 RT-399 14.40 × 1.50 0.7 RT-400 15.50 × 2.50 0.5 RT362 10.50 × 1.50 0.5 RT365 10.50 × 1.50 0.5 RT364 10.40 × 3.20 0.4 RT-397 10.40 × 3.20 0.3 RT401 10.0 × 1.80 0.35 Table A10: Available copper conductor sizes in market The selection of curb width and height is based on kVA rating kVA 160 500 1000 10000 15000 20000 25000 50000 100000 W 40 50 65 75 75 100 100 125 150 T 10 10 12 20 20 20 20 20 25 Table A11: Available curb sizes in market 77 The selection of channel weight based on frame area area of frame 75 100 125 150 175 200 225 250 300 350 channel weight 6.8 9.2 12.8 16.4 19.2 22.2 26 30.4 35.9 42.2 Table A12: Available channel weight in market The designs of tank plates based on below clearances Top KV A B C Clearance. 1 120 160 70 150 33 120 160 70 150 66 160 160 80 150 132 260 160 100 150 220 400 200 120 150 Table A13: Available clearances in market The design of tank plated of top and bottom plates based on clearances which are given below: Rated KV 11 22 33 66 132 Delta 132 1Coil(Y) 132 2 coil 220-950 1050 Top Clearance 20 mm 30 40 60 120 100 60 215 235 Bottom Clearance 20mm 30 40 60 100 60 60 115 125 Table A13: Available clearances in market 78 6) RESULT OF ESM 79 80 81 82 83 84 85 86 87