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1. students decided to try using the optimum core design as an initial starting point alternative 1 They are able to tweak the dimensions of the shell type transformer to obtain the right ration for the optimum design The following design alternatives are obtained and are displayed in Figs 8 11 The optimum design is obtained from the above three transformers The selected optimal design is quite successful in meeting all of the design specifications 8 99 2 99 15 2 6 99 1 99 05 24 Cc fo 2 99 O 98 95 a 2 98 9 98 85 0 Design 1 Design 2 Design 3 Design 1 Design 2 Design 3 Fig 8 Comparison of efficiency Fig 9 Comparison of copper core loss ratio In alternative 1 students changed the dimensions of the optimum core design as follows 1 core thickness from 0 15m to 0 239m 2 the width from 0 06m to 0 089m and 3 the window height from 0 2m to 0 354m They observed that for a significant increase in the efficiency of the transformer there are noticeable changes in the excitation current which tends toward the critical value of its design Similarly this upward trend of the excitation current is complemented by an increase in the overall transformer weight and ultimately the cost Thus alternative 1 is worthless Values for T 0 153m C 0 057m and H 0 267m are chosen for a second design alternative while T 0 191m C 0 0713m and H 0 283m are selected for a third desig2. 14 through 18 specify the coil constants Once the current density has been specified the wire size and the resistance can be obtained from wire tables 6 7 Inputs 19 20 and 21 are the basic core dimensions that are needed to interrelate with the various magnetic and electrical quantities a k T 2S S P 2C 2S P gt 2 c br 2c sr c et Fig 3 Geometry of a shell type transformer 4 0 Cost Function Since the transformer design is intended for educational purpose the following cost functional is specified as the total cost of the transformer Total transformer cost Total transformer mass kg Cost factor kg where Total transformer mass kg Total copper mass kg Mass of iron kg The optimum design is the one with the minimum value of the cost function 5 0 Students Preparatory Work All program variables are converted to the International Systems SI of units to ensure consistency in the design The transformer ratings and the primary and secondary voltages are used to calculate the primary and secondary currents respectively These determined values of the primary and secondary currents are used in conjunction with the current density to calculate the cross sectional area of primary and the secondary conductor correspondingly Since all Proceedings of the 2004 American Society for Engineering Education Annual Conference amp Exposition Copyright 2004 Americ
3. 60 degrees centigrade The cost of non metals is ignored 00000 0 3 0 Program Input The instructor provided students with an outline of the program that is available for use The program is designed so that the user will only have to operate in one screen When the program is accessed the user is immediately asked to input the first of twenty one data inputs and these inputs are manipulated to achieve the stated objectives The inputs are divided into three sections particularly Proceedings of the 2004 American Society for Engineering Education Annual Conference amp Exposition Copyright 2004 American Society for Engineering Education 7Ze 6 bed o Rated values such as the primary and secondary voltages transformer rating and frequency o A set of constants in this case the current density space factor stacking factor wire cross sectional areas resistance of the primary and secondary conductors and the copper and iron densities o A set of independent variables such as core thickness width of core leg window height and peak value of flux density The inputs from one to ten either specify the rating of the transformer or are constants Inputs 11 12 and 13 specify the magnetic condition of the core A reasonable value of flux density is chosen by the student just below the saturation region and the corresponding values of the field intensity and core loss factor are obtained from the magnetization curve Inputs
4. resistance per meter at reference temperature of 20 C is the temperature coefficient of copper 3 9 10 C and Ty is the reference temperature The weigh of the transformer is a function of the dimensions chosen for the core thickness core leg width and window height These dimensions determined the volume and ultimately the mass of iron needed for the core Also the dimensions coupled with the number of turns and wire size determined the copper mass needed for a particular design The cost of the transformer is derived from the actual weight as this is factored into the software as a constant at 4 4 kg That is weight and cost are directly related such that an inexpensive design is one that has a relatively low mass Proceedings of the 2004 American Society for Engineering Education Annual Conference amp Exposition Copyright 2004 American Society for Engineering Education G7Ze 6 abed Table I Wire table at 20 degree C AWG Maximum B amp S Resistance PERA aran Gauge ohms 1000ft 4 0 0 05045 0 000165 0 000107226 3 0 0 06361 0 000209 8 50321E 05 2 0 0 08021 0 000263 6 74192E 05 110 0 1011 0 000332 5 34773E 05 Secondary 2 0 1625 0 000533 3 36322E 05 4 0 2584 0 000848 2 11483E 05 6 0 4108 0 001347 1 33032E 05 8 0 6533 0 002143 8 36773E 06 10 1 039 0 003408 5 26128E 06 Primary 12 1 652 0 005419 3 30903E 06 6 0 Computer Student Interaction The
5. the initial estimates In this manner the judgment of the student does not affect the success and the quality of the design but only the computer time and expense A testing experiment is described in a fourth paper 4 in which students design build and test a simple single phase transformer that used in many textbooks to specifications provided by the instructor However it does not appear to be a design experience in the classical design principles In addition students cannot actually simulate and analyze the performance of the design Proceedings of the 2004 American Society for Engineering Education Annual Conference amp Exposition Copyright 2004 American Society for Engineering Education l pZe 6 abed This paper demonstrates the use of a novel PC based interactive computer program that has been written specifically for the design and analysis of single phase transformers The program and user manual is developed in house and in close cooperation with industrial users The paper takes the student step by step through the understanding of transformer designs The approach followed in this paper is to use the computer for the tasks it does best storage and retrieval of data also making routine calculations but leaving the judgment to the students It is our intention to keep the real skill and the decision making resident with the students themselves The computerized interactive approach is used basically for the following ra
6. to obtain the corresponding value at 60 degrees Consequently the primary coils of the optimal transformer which have an area of 5 0 10 m are designed using American Wire Gauge AWG 1 0 This gauge number actually corresponds to a primary wire of cross sectional area 5 26 10 Since the exact wire gauge corresponding to the primary wire with the above cross sectional area could not be found wire gauge 10 was used for the primary coils The wire gauge number for the secondary coils is chosen in a similar manner The secondary coils are designed using AWG 1 0 This gauge number actually corresponds to a secondary wire with cross sectional area of 5 35 10 m Since the cross sectional area of 5 35 10 m is extremely close to the area of the secondary wire AWG 10 is used to design the secondary coils In addition the magnetic field intensity and the core loss factor are determined for each increment of desired flux density before design alternatives are initiated For a selected flux density the corresponding magnetic field intensity and core loss factor are obtained from the magnetizing curve and the core loss curve respectively The flux density and magnetic field intensity are both found from the magnetization curve and the core loss factor corresponding to the chosen flux density is obtained from the core loss curve The following equation is used to obtain the extrapolation results at 60 degrees 7 R R 1 0 T T where Rois the
7. Session 3433 Design and Analysis of Single Phase Power Transformers for Undergraduate Engineering Students Ahmed Rubaai Mohamed Chouikha Donatus Cobbinah and Abdul Ofoli Electrical and Computer Engineering Department Howard University 2300 6 Street Northwest Washington DC 20059 Abstract This paper describes a method for design optimization of single phase power transformers using an interactive PC based computer program The computer program is developed in house and in close cooperation with industrial users A procedure is developed to illustrate the effect of parameter variation on the design of transformers in order to achieve minimum cost of production The procedure illustrates that there are many possible designs within a very small increment of cost The objective is to assist undergraduate students to understand the design process determining the efficiency size weight and cost of actual transformers while meeting multiple transformer specifications 1 Introduction Most technical papers on computer aided design of power transformers utilize optimization routines which guide the choice of the independent variables to optimize a design 1 3 Thus the computer program regulates the design skill and isolates the student from the design process In these approaches the initial estimates are introduced in the computer and the computer automatically achieves a design which meets all specifications regardless of any error in
8. action on Power Systems Vol 5 No 2 pp 499 505 May 1990 Ahmed Rubaai EECE 318 Energy Conversion User Manual Howard University Washington DC 2001 D Macllister Electric Cables Handbook Granada Publishing Co 1982 C C Barres Power Cables Their Design and Installation Chapman and Hall Ltd 1966 Proceedings of the 2004 American Society for Engineering Education Annual Conference amp Exposition Copyright 2004 American Society for Engineering Education Ol rZe 6 ebed Ahmed Rubaai received the M S E E degree from Case Western Reserve University Cleveland Ohio in 1983 and the Dr Eng degree from Cleveland State University Cleveland Ohio in 1988 In the same year he joined Howard University Washington D C as a faculty member where he is presently a Professor of Electrical Engineering His research interests include high performance motor drives research and development of intelligent applications for manufacturing systems and computer aided design for undergraduate engineering education Dr Rubaai is a recipient of the 1997 and 1998 Howard University Faculty Teaching Excellence Award He was also the recipient of the ASEE Middle Atlantic Section Distinguished Educator Award in April 2001 In addition he served as General Chair and Technical Committee Program Chair for the 1998 ASEE Fall Regional Conference of the Middle Atlantic Section He was also the recipient of the IEEE Industry Applications Society Pri
9. addition to holding the flux density fixed one of the other independent variables is also held constant routinely while varying the other two This is done to approximate the best range for the core thickness core leg width and window height Instantaneously students had acquired a profound knowledge or the trade off relationships among the design parameters so they pooled all the observed trends together in an effort to increase the efficiency of the transformer In order to illustrate the impact of the flux density on the design process student chosen new values for C 0 05m T 0 135m and H 0 07m as the new benchmark or reference point by holding them constant and then vary the flux density As the flux density is increased from the range of 1 2 to 1 4 the cost of the transformer decreased Interestingly the efficiency at the Proceedings of the 2004 American Society for Engineering Education Annual Conference amp Exposition Copyright 2004 American Society for Engineering Education LVle 6 ebed rated load remained almost constant as for every 0 025 increment of the flux density the efficiency decreased by less than 0 001 percent Even though it is favorable for the transformer weight and cost to decrease as flux density is increased the excitation current increased with flux density while the copper to core loss ratio decreased This further increased the complexity of the design That is in order to meet the design specifica
10. an Society for Engineering Education v vZe 6 ebed conductors are manufactured to meet international standards with respect to cross sectional area wire gauge the calculated areas are used to select standard wire size for the primary and secondary windings from a wire table Table I 6 provided the resistance based on the cross sectional area at 20 degrees C For the selected wire gauge which best satisfied the design specifications for the primary conductor the corresponding resistance per unit length at the given temperature is also noted Since this value is not at the required temperature for the design students extrapolated it to 60 C A similar procedure is used to determine the resistance per unit length of the secondary conductor at 60 C One of the most important factors in transformer design is the resistance per meter of the primary and secondary wires at the specified design temperature The resistance per meter at the design temperature allows the designer to choose the wire gauges that are capable of carrying the primary and secondary currents If the resistance per meter is known the corresponding wire gauge can be found from a wire table Unfortunately in many cases the resistance per meter in the wire table may have been calculated at a different temperature to the temperature that is required in the design This problem is encountered in this transformer design Therefore the resistance per meter had to be extrapolated
11. ation Annual Conference amp Exposition Copyright 2004 American Society for Engineering Education LEYE 6 ebed
12. class is divided into teams to endorse team work Each team is given the same material costs for known materials but each team uses distinct transformer type modeled by the program Primarily the students examine the input requirements of the computer program and determine how they will obtain an initial set of input variables Students also study the trade off relationships that exist between the various inputs and outputs The program serves as an aid to the students allowing them to dispose of the numerous and tedious calculations in a short period of time The program variables representing the basic geometry of the core in addition to the rating data and the electrical specifications are initialized with feasible input values by the students With this information a complete set of performance calculations is made These calculations include the cross sectional area of the core and both the high and low voltage coils the mean length of the flux path peak flux and RMS value of the magneto motive force the core losses the mean length of a turn the total length the resistance the copper losses the number of turns for both high and low voltage coils the volume and mass of both the steel core and the copper windings of the transformers the overall core dimensions the copper to core loss ratio the KVA to kg ratio efficiency the excitation current and the estimated cost of the design The students then use these values to determine if the perfor
13. d a new set of independent variables for a second design alternative students chosen T 0 135m C 0 05m and H 0 15m for alternative 2 A closer inspection of this alternative reveals that the Proceedings of the 2004 American Society for Engineering Education Annual Conference amp Exposition Copyright 2004 American Society for Engineering Education 8 7Ze 6 bed copper to core loss ratio is not even close to the desired range and burdensome weight for the transformer A third alternative with T 0 135m C 0 05m and H 0 2m produced a transformer with a full rated load efficiency of 95 1509 This design satisfies the excitation current but copper to core loss ratio is too large and there is increase in the transformer weight However alternative 3 shows a better efficiency over alternative 2and a cost of about 25 0 less than alternative 2 Design alternative 4 is a good quality design that meets all the specified criteria with T 0 15 m C 0 06m and H 0 2m Thus this transformer provides an optimum design with a full rated efficiency of 96 0314 a copper to core loss ratio of 1 89596 which fell within the specified range of 1 2 to 2 69 The transformer s excitation current of 0 176077A also remained below the 0 2A maximum limit set in the design specification Improved performance is provided in a compact 44 242 kg transformer at a manufacturer cost of 433 7 9 0 Design of a shell Type Transformer For the shell design
14. gn is the product of a brute force method Values for the independent variables were arbitrarily chosen and the practicality of these random designs are analyzed for trends The independent variables are then incremented in a controlled and systematic manner to improve the performance characteristics of the transformer Students realized from the B H curve that the possible choices of the flux density are within the range of 12 kilogauss just above the knee of the curve to 14 kilogauss so increments of the flux density are read off from the curve In the preliminary stages of the design a flux density B 1 12 Tesla and the corresponding values for the magnetic field intensity and core loss factor are determined from the B H curve Next values for T 0 5 m C 0 25 m and H 0 075 are arbitrarily chosen to complete their initial design These values are used in conjunction with the other predetermined constants and rated values after which the design is simulated The output is observed and recorded for future reference At this time students are unable to meet any of the design specifications The efficiency is just over 90 and the copper to core loss ratio is 3 34 In addition the cost of this design is almost 5000 00 From these results students recognized that the core leg width and the thickness of the transformer are too high By keeping the flux density fixed this brute force approach is applied in choosing other values for T C and H In
15. mance requirements for the transformer design have been met In most cases the calculated performance will not agree with the specifications and it will be necessary to modify the initial estimates This modification of estimates is not a part of the computer program and is left to the judgment of the students Thus the judgment of the students does affect the success and the quality of the design When any of the performance specifications supplied by the students are not met students adjust the appropriate input data and re executing the program This process continued until any one of the following occurs 1 all input specifications are met 2 the performance specifications are deemed impossible to achieve with the physical characteristics of the design or 3 the number of iterations reaches twenty Even though the program aided the students in the design process it did not optimize their design alternatives as the output files only show the practical feasibility of the inputted parameters As a result the students had to analyze and interpret the output of the program for each design alternative and then developed a systematic procedure to optimize their design Initially Students spent hours using a rugged and brute force method to choose the independent Proceedings of the 2004 American Society for Engineering Education Annual Conference amp Exposition Copyright 2004 American Society for Engineering Education 9 7Ze 6 aed va
16. mum cost Students optimized their design by determining how close they have come to meeting the transformer specifications Upon completion of the design the students have been through the entire design process from initial design through redesign and analysis They have dealt with multiple specifications that can conflict such as balancing efficiency copper to core loss ratio and exciting current They have seen a number of trade offs that can be made in the design process The procedure was completed by using the decision making process to rationally select the design which best satisfied the criteria 11 0 Program Availability The program utilized in this paper is available to Electrical Engineering Educators at no cost Interested individuals may contact the lead author at arubaai howard edu 12 0 References M Polujadoff and R D Findlay A procedure for illustrating the effect of Variation of parameters on Optimal Transformer Design IEEE Trans Power Systems Vol 1 No 4 pp 202 206 November 1986 W M Grady et al A PC base Computer Program for Teaching the Design and Analysis of Dry Type Transformers IEEE transactions on Power Systems Vol 7 No 2 pp 709 717 May 1992 O W Anderson Optimized Design of Electric Power Equipment IEEE Transactions on Power Systems Vol 4 No 1 pp 11 15 January 1991 W T Jewel Transformer Design in the Undergraduate Power Engineering Laboratory IEEE Trans
17. n alternative Alternative 2 shows a slightly better weight over alternative 3 and also a cost of about 15 3 less than alternative 3 but the copper to core loss ratio is enormous and surpasses the transformer specifications As a result this transformer is omitted in favor of alternative 3 Clearly alternative 3 provides an optimum design with a full rated efficiency of 99 15 a copper to core loss ratio of 2 603 and a cost of 430 5 Proceedings of the 2004 American Society for Engineering Education Annual Conference amp Exposition Copyright 2004 American Society for Engineering Education 6 7Ze 6 aed 150 5 600 PA _ 500 2 100 amp 400 7 a 8 300 50 200 100 0 o Design 1 Design 2 Design 3 Design 1 Design 2 Design 3 Fig 10 Weight Comparison Fig 11 Cost comparison 10 0 Conclusions This paper described a method to design a single phase transformer A set of design steps has been built up to influence a set of independent variables in order to attain the most economical design by minimizing losses and weight while meeting performance specifications The critical relationship between flux density and cost was analyzed It is depicted that for a chosen value of the flux density there are many designs which satisfied the design criteria but there exists unique values for the core thickness core leg width and window height which yielded mini
18. ng factor is about 0 95 e The cost of most mass produced equipment is proportional to the equipment weight or mass A reasonable estimate of this cost is about 4 4 dollars kg e A typical current density in transformer winding is about two amperes per square millimeter e In designing the coils an allowance must be made for the space between the conductors and for the thickness of the insulation on the conductors In typical transformers the conductors themselves will only occupy about half of the available window area Thus a typical space factor is about 0 5 The PC based program is intended for designing the following classes of transformers Single phase core type Single phase shell type The core and coils of the two transformer types modeled by the program are shown in Figs 2 and 3 respectively As with any design procedure a number of assumptions are made bale eee StL 4 d St 1 Pis s plp s slp gt c 28 P fe ol c s Je Fig 2 Geometry of a core type transformer c 2s 2p c In designing both transformers the following assumptions are made The cores have been proportioned so that the flux density is uniform throughout the core The low voltage coil has been wound closest to the core The high voltage coil has been wound over the top of the low voltage coil The number of turns are rounded to the nearest integer Temperature is uniform The transformer operates at
19. riables as the output from the program is a reflection of their chosen inputs Consequently for a particular design alternative the computer program could not manipulate their inputs to give a better design Instead careful analysis of the output files for different inputs revealed trends which are used to develop a systematic or a more logical approach towards arriving at the best design After progressing thus far they acknowledged the fact that the program has made their design process simpler as the data it generated would have consumed several more hours of their time if they had calculated it manually for each design alternative Accordingly it is on this level of interaction with the program that students strategize input files analyze and interpret the output Then further manipulate one or two variables while keeping others fixed to optimize the design In this way the design is successively built upon or synthesized by the student until a final satisfactory design is achieved After completing all the calculations the students realized that there are only four independent variables which they could have manipulated to obtain the best design These independent variables were flux density B the core thickness T core leg width C and the window height H All four variables affected specifications which are critical in meeting the design criteria 7 0 Design Optimization of Core Type Transformer 7 1 Initial Design The initial desi
20. tionale 1 to minimize designing time 2 its accuracy and capabilities and 3 it represents state of the art engineering The approach is surprisingly simple and efficient 2 0 Typical Design Information During the first design session the transformer specifications are presented Apparent power rating 25KVA Primary voltage rating Vp 2500V Secondary voltage rating Vs 250V Excitation current of the transformer cannot exceed 2 of the full load current Copper to core loss ratio must remain within 1 2 and 2 69 e Maximum efficiency occurs between 75 and 100 of the full load A magnetic data for a typical 60Hz power transformer is also provided A core magnetization curve is shown in Fig 1 5 18 8 16 6 14 4 12 E S042 2 2 Z Z m 10 m 10 8 8 6 6 4 4 10 100 1 000 10 000 ma 0 1 1 10 Magnetizing Force RMS Ampere Turns Per Meter Watts Per Pound P a Magnetizing force b Core loss Fig 1 Core magnetization curve Proceedings of the 2004 American Society for Engineering Education Annual Conference amp Exposition Copyright 2004 American Society for Engineering Education ZvZe 6 bed The following information about the transformer is provided to the students as well 5 e A typical stacki
21. tions there must be a trade off between flux density and cost 8 0 Design Alternatives Since the design constraints such as are within the specified limits students narrowed their selection down to the economics of the various design alternatives The optimum design is obtained after meticulously analyzing the output data A number of design alternatives are produced to judge the performance of the transformer design However for brevity only the following four design alternatives are reported in this paper with a peak flux density of 1 3 Tesla and are given in Figs 4 7 5 0 2 i T 0 15 2 S g 0 3 0 05 oO R 0 0 T T T p Design 1 Design2 Design 3 Design 4 Design 1 Design2 Design3 Design 4 Fig 4 Comparison of cu core loss ratio Fig 5 Comparison of excitation current 97 700 96 600 500 g 95 400 S 94 8 300 ti 93 epo 92 100 0 914 Design 1 Design 2 Design3 Design 4 Design 1 Design 2 Design 3 Design 4 Fig 6 Comparison of transformer efficiency Fig 7 Cost comparison In design alternative 1 values for T 0 135m C 0 05m and H 0 08m produced a satisfactory excitation current but the copper to core loss ratio is too excessive and there is an increase in the transformer cost as well This design satisfied the excitation current requirement but the copper to core loss ratio is too large and exceeds the specifications In order to fin
22. ze Paper Award in October 2002 Mohamed F Chouikha received his Ph D degree in Electrical Engineering from The University of Colorado in Boulder in 1988 Since 1988 he has been with Department of Electrical Engineering at Howard University where he is currently a Professor and Chair of Electrical and Computer Engineering Department His research interests include multimedia signal processing and communications Image processing and image analysis and intelligent systems application Donatus Cobbinah was born in Accra Ghana He received the B Sc degree in Electrical Engineering with honors from the University of Science and Technology Kumasi Ghana in 1997 He is currently working towards the M S degree in Electrical Engineering at Howard University Washington DC His current interests include research and development of intelligent systems and high performance servo drives and their related knowledge based control schemes Abdul R Ofoli S 02 received the B Sc degree in Electrical amp Electronic Engineering 1999 from Kwame Nkrumah University of Science and Technology KNUST Kumasi Ghana in 1999 From 1999 to 2000 he worked as a teaching research assistant at the Electrical Engineering department in KNUST He is currently a graduate student Master s candidate at Howard University His research interests are in the areas of power systems and intelligent controls Proceedings of the 2004 American Society for Engineering Educ
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