264 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 49, NO. 1, FEBRUARY 2002 Letters to the Editor________________________________________________________________ Fuzzy Logic Transformer Build Estimation Ravindra R. Mudholkar and Shashikant R. Sawant Abstract—Mechanical fitting of transformer windings tightly into the core ensures an efficient use of window space. Fuzzy logic transformer build estimation is intended to implement approximate solutions suggested in imprecise terms for better mechanical fit of windings into the core. For imperfect fit, it readjusts the buildup parameters in iterations to optimize mechanical fit. The results have demonstrated the potentiality of usage of fuzzy logic in the mechanical-fit process of a transformer. Index Terms—Build, buildup parameters, fuzzy logic, mechanical fit, transformer. I. INTRODUCTION:BUILD AND FUZZY DECISIONS Transformer designing is largely a cut-and-try procedure which be- gins with selection of core size and wire size made as a first approx- imation based on equations, experience, and/or rules of thumb. On achieving satisfactory electrical performance, the next step is to check for good mechanical fit of windings into the core window. Build forms an important dimension of windings. After working out total build using standard practices [1]–[3], the mechanical fit of windings into the available window space is checked. Whenever the total winding buildup is either too small or larger than the window space available, modulations of various buildup parameters are done until a reasonable fit of winding into the window results. Judgments and decisions taken by the expert for better fit are often vague propositions, e.g., “The core area could be increased by increasing the stack” or “ The wire size could be made a little smaller” or “ The flux density could be slightly decreased.” The mechanical-fit process thus involves indeterminate fuzzy con- cepts and fuzzy decisions. Fuzzy logic allows representing buildup pa- rameters and embedding an expert’s logical reasoning in the mechan- ical fit process. In the case of imperfect fit, buildup calculations are reviewed and several remedial solutions are employed [1]–[3]. How- ever, first, three of the following are chosen for illustration: 1) modification in the core area by changing stack; 2) reconsideration of wire size; 3) change in flux density; 4) combination of above measures; 5) or else, go for other lamination size. After applying these solutions, the new buildup figure arrived at is rechecked. If this results in a good mechanical fit, while changes caused in the other parameters remain within reasonable limits, the amended buildup data are approved and design proceeds further, otherwise, the design enters into a fresh iteration searching for another better try. II. DEVELOPMENT PHASES OF FUZZY LOGIC TRANSFORMER BUILD ESTIMATION (FLTBE) FLTBE is a novel fuzzy-based approach that deals with heteroge- neous data of both linguistic and numeric types, imprecise, vague in- Manuscript received March 18, 1999; revised July 16, 2001. Abstract pub- lished on the Internet December 5, 2001. The authors are with the Department of Electronics, Shivaji University, Kol- hapur 416004, India (e-mail: srs600112@yahoo.com). Publisher Item Identifier S 0278-0046(02)00915-2. formation, and concepts encountered in the mechanical-fit process and facilitates the expression of the reasoning process of an experienced designer with minimal rules. The Fuzzy Logic Transformer Design Algorithm (FLTDA) [4] rep- resents a fuzzy-logic-based complete transformer designing process comprising the following three phases: phase I: tentative selection of core size, approximate wire sizes, and computation of winding turns; phase II: mechanical-fit process; phase III: estimation and optimization of losses, temperature rise, and efficiency. A general schematic of FLTBE representing the second phase of FLTDA is shown in Fig. 1. It involves the following phases: 1) fuzzification; 2) knowledge representation; 3) inference scheme; 4) defuzzification. A. Fuzzification After investigating the process of mechanical-fit, build-status input variable “Build-up thickness (bld)” and build-adjust out variables “Stamping stack thickness (stk)”, “Flux density (fd)”, and “Wire-size ( )” ( for primary and for secondary) are selected for fuzzification. Their respective domains are worked out from standard relations between various variables [1]–[3] for standard data on output power demand, core, and wire sizes. The partition of domain (universe of discourse) for each variable is carried out based on trends in the empirical data and knowledge of the past transformer design problems. All the reference fuzzy sets are meaningfully labeled. Tuning of membership functions is carried out by trial and success optimization of results through a good number of sample designs. The triangular shape for membership functions has been chosen being common in engineering applications [5]–[7]. Membership functions for a sample design problem are shown in Fig. 2(a)–(d). B. Knowledge Representation Knowledge pertaining to the mechanical-fit process is formulated in terms of fuzzy inference rules, which refer to a good amount of data. Knowledge base thus comprises a data base and a rule base. Neat or- ganization of the data base contributes to the success of FLTBE. This includes: the membership functions representing linguistic values of variables involved in the mechanical-fit process, scaling factors, oper- ating ranges, and term sets for input/output parameters as given by 0278–0046/02$17.00 © 2002 IEEE