Mathematical and Computational Applications, Vol. 11, No. 3, pp. 193-3, 6. Association for Scientific Research DESIGN OPTIMIZATION OF INDUCTION MOTOR BY GENETIC ALGORITHM AND COMPARISON WITH EXISTING MOTOR Mehmet Çunkaş a, and Ramazan Akkaya b a Department of Electronics and Computer Education, Selçuk University, Konya, 475, TURKEY b Department of Electrical and Electronics Enineerin, Selçuk University, Konya, 431, TURKEY mcunkas@selcuk.edu.tr Abstract-This paper presents an optimal desin method to optimize three-phase induction motor in manufacturin process. The optimally desined motor is compared with an existin motor havin the same ratins. The Genetic Alorithm is used for optimization and three objective functions namely torque, efficiency, and cost are considered. The motor desin procedure consists of a system of non-linear equations, which imposes induction motor characteristics, motor performance, manetic stresses and thermal limits. Computer simulation results are iven to show the effectiveness of the proposed desin process. Key words-desin optimization, induction motor, enetic alorithm 1. INTRODUCTION Induction motors are the most widely used in domestic, commercial and various industrial applications. Particularly, the squirrel cae type is characterized by its simplicity, robustness and low cost, which has always made it very attractive, and it has therefore captured the leadin place in industrial sectors. As a result of its extensive use in the industry, induction motors consume a considerable percentae of the overall produced electrical enery. The minimization of electrical enery consumption throuh a better motor desin becomes a major concern. Many practical optimization problems in optimization of the electromanetic devices have mixed (continuous and discrete) variables and discontinuities in search space. If the standard non-linear prorammin (NLP) techniques were to be used in such cases, then they would be computationally very expensive and inefficient. Some applications utilizin the standard NLP techniques include the desin optimization of induction motor [1,]. In recent years, GA s have been reconized as potent tools in desin optimization of electrical machinery [3-6]. One of the most important advantaes of the GA over the standard NLP techniques is that it is able to find the lobal minimum, instead of a local minimum, and that the initial attempts with different startin point need not be close actual values. Another advantae is that it does not require the use of the derivative of the function, which is not always easily obtainable or may not even exist, for example, when dealin with real measurements involvin noisy data. The aim of this paper is to ive a further contribution in the optimum desin of a three phase induction motor in manufacturin process, usin three objective functions, namely torque (T), cost (C) and efficiency (E). Genetic Alorithm havin feature of a unique search [7,8] was then used for optimization processes. A desin packae has
194 M. Çunkaş and R. Akkaya been developed specifically for a three-phase squirrel-cae type induction motor. Threephase squirrel-cae type induction motor havin specifications 3 hp,38v, star connected, 4 pole, is chosen for comparison with three optimally desined motors. The basic specifications of these desins are similar and the same constraints are imposed upon the desin process. Performance characteristics of the existin motor and three optimum desins are plotted on the same plane for comparison. Advantaes and disadvantaes of each desin are then briefly discussed. It was observed that the cost optimization procedure was sensible, and the performance results obtained were promisin.. PROBLEM DEFINITION AND DESIGN APPROACHES The used equivalent circuit model of the motor is shown in Fiure 1. The model is popular and well understood amon enineers and, despite its shortcomins, offers reasonably ood prediction accuracy with modest computational effort. This model is basically a per phase representation of a balanced poly-phase induction machine in the frequency domain, comprisin six elements, or model parameters. The six impedances are stator resistance R 1, stator leakae reactance X σ1, manetizin reactance X σm, coreloss resistance R m, rotor leakae reactance X σ, and rotor resistance R. In this paper, the approaches and methods used to calculate the motor performances are based on the works of [9,1]. Fiure 1. Equivalent circuit model of induction motor To apply the GA approach, an objective function has to be defined to evaluate how ood each motor desin is. This objective function may include all the eometrical dimensions of the motor and a lare subset of constraints (eometrical constraints) have to be formulated to ensure the physical feasibility of the motor. These objective functions are iven in the followin. First objective function: The cost will be minimized. The cost variable consists of the laminations cost, copper cost, rotor-end-rin cost, and the core punchin cost, which are used as the objective function of the optimization [11]. The weiht of iron, W Fe, is L1SFDoPfe WFe =, (1) 4 the weiht of the stator windin, W sw, is W sw = L1S1A1mf ewpsw, () and the weiht of the rotor conductors, W rw, is
Desin Optimization of Induction Motor by Genetic Alorithm 195 πw a (D r (D r w r ) Wrw = Prw + SA b (L w a ), (3) The punchin cost C p is estimated as % of the total cost. Thus the total manufacturin cost or also objective function is expressed as follows: C = W Fe + (W + W )Cu + C, (4) total Fe cos t sw rw cos t Second objective function: The full load torque will be maximized. It should be noted that the objective function is defined as: 6 Vs R Tn = m, (5) πn1 R s R1+ τ 1 + ( X1+ τ 1 X ) s where the τ 1 is the correction factor, the n 1 is the synchronous speed. Third objective function: The rated efficiency will be maximized, and the objective function is defined as: Pout η =, (6) P + P input out Table 1 shows the practicable domains and the resolution for the desin parameters. To obtain an acceptable desin, the desin parameters need to be bound between upper and lower limit values. In the case presented here, ten desin parameters, some of which is used in literature and affect induction motor s first order basic eometry is chosen. Table 1 Desin parameters and their limit values Desin parameter Description Lower limit Upper limit Number of bit x 1 Number of turns per phase 6 96 1 x Stator iron lenth (cm) 15 3 1 x 3 End-rin width (mm) 15 3 1 x 4 Stator interior diameter (cm) 18 5 1 x 5 Stator slot heiht (mm) 18 38 8 x 6 Stator slot width (mm) 7 1 8 x 7 Air-ap (cm).4.65 1 x 8 Bride thickness of rotor closed.5.5 8 slot (cm) x 9 Rotor bar diameter (mm) 6 1 8 x 1 Stator exterior diameter (cm) 3 38 8 p 3. AN OVERVIEW OF GENETIC ALGORITHM In the most eneral sense, GA-based optimization is a stochastic search method that involves the random eneration of potential desin solutions and then systematically evaluates and refines the solutions until a stoppin criterion is met. There are three fundamental operators involved in the search process of a enetic alorithm: selection, crossover, and mutation. The enetic alorithm implementation steps are shown as follows: Step 1: Define parameter and objective function (Initializin) Step :Generate first population at random Step 3: Evaluate population by objective function
196 M. Çunkaş and R. Akkaya Step 4: Test converence. If satisfied then stop else continue. Step 5: Start reproduction process (Selection, Crossover, Mutation) Step 6: New eneration. To continue the optimization, return to step 3. Genetic alorithm that produces ood results in many practical problems is composed of the followin three operators: Selection: Selection is a process in which individual strins are selected accordin to their fitness. The selection probability can be defined by P = F(x ) F(x (7) i j i i ) Where P j is selection probability and F(x i ) is objective function. Crossover: This is the most powerful enetic operator. One of commonly used methods for crossover is sinle-point crossover. As shown in the followin examples, a crossover point is selected between the first and the last bits of the chromosome. Then binary code to the riht of the crossover point of chromosome 1 oes to offsprin and chromosome passes its code to offsprin 1. This operation takes place with a defined probability P c that statistically represents the number of individuals involved in the crossover process. Chromosome Chromosome 1 Crossover Point = 11 11 = 11111 Offsprin Offsprin 1 = 11 1 = 1111 11 Mutation: This is a common enetic manipulation operator, and it involves, the random alteration of enes durin the process of copyin a chromosome from one eneration to the next. Raisin the ratio of mutations increases the alorithm s freedom to search outside of the current reion of parameter space. Mutation chanes from a 1 to a or vice versa. It may be illustrated as follows. 111 1111 4. IMPLEMENTATION OF THE OPTIMAL DESIGN PROCEDURE The formulation of the objective function is the followin: F(x) P( (x),r) If F(x) P( (x),r) > ' j j F (x) =, (8) If F(x) P( j (x),r) Where, F (x) is the objective function as the motor material cost, efficiency or torque, and moreover r is the penalty coefficient that is related to the value of objective function. The penalty function, P ( j (x), r), are expressed with respect to the type of inequality used. By means of exterior penalty function, constrained problems are converted to unconstrained problems by removin constraints. Accordin to constraints, penalty function is defined as followin; r [max(, j)] j= 1,...6 j P ( j(x),r) =, (9) r [min(, j)] j= 7,8 j Accordin to Eq. (8), it is noticed that when the constraint inequality is satisfied, the penalty function becomes inactive. In the feasible reion, the aumented objective function emphasizes the larer constraint violations and the optimization search tries to
Desin Optimization of Induction Motor by Genetic Alorithm 197 reduce these violations to zero. This would result in pushin the search into the feasible desin reion. Within this reion all the constraints are satisfied and the optimization approach attempts to move the desin into its best optimum solution. However, in the electrical machine problem, the orders of manitude of the various constraints are much different from one to another. Therefore, to have meaninful converence criteria, constraint functions need to be normalized with respect to the specified objective function. This is necessary to ensure that constraints with hiher values do not dominate over others. The normalized constraint functions in the penalty function are developed as shown in the followin. b j ref b j j norm (x) =, j=1,,..8, (1) b where j ref j b is the value calculated from the current evaluation whereas b j is the expertdefined constant as shown in Table. Table Inequality constraints Rated slip, s ( b 1 =.5) Stator yoke flux density, Rotor yoke flux density, Stator teeth flux density, Stator slot fillin factor, Startin current to a rated current ratio, B ( b = 1.6) sy B ( b 3 = 1.6) ry B ( b 4 = ) f st F ( b 5 =.69) I I ( b 6 = 7) start Power factor, Cosφ ( b 7 =.8) Pull-out torque to a rated torque ratio, p n n T T ( b 8 = 1.9) The main purpose for imposin the constraint b j is to have the final desin for practically feasible and acceptable. In eneral, the constraints are decided upon with reat care takin into consideration the availability of materials, customers requirements and manufacturin standards. In the present work, in Table, also referred to as the motor specifications and their constraint values are considered. Constraint values of variables can be expressed by followin inequality. 1 1 (x) Bsy b 3 (x) Bry b3 4 (x) Bst b 4 (x) = s b (x) = F b 5 f 5 6 (x) = Istart I n b8 7 (x) Cosϕ b7 8 (x) = Tp Tn b6 = = = (11) = In Eq.(11), there are two different conditions of inequality constraint. Let us explain these conditions. First condition: It is not iven permission that some constraints (as j (x), j=7,8) are the lower level. For example, hih values for power factor are desired for ood performance in induction motor. If the expert-defined constraint for power factor as shown in Table were.8, then anythin less than that would be a violation.
198 M. Çunkaş and R. Akkaya Second condition: It is not iven permission that some constraints (as j (x), j=1,..6) are the upper level. For example, stator yoke flux density may not exceed certain values on account of iron losses. If the expert-defined constraints for stator yoke flux density as shown in Table was 1.6, then anythin more than that would be a violation. If a constraint for these conditions are violated, then the correspondin values of violation as defined in Eq. (9), are introduced into the calculation of P( j (x),r) in Eq. (8) If a constraint is not violated for these conditions, then the correspondin P( j (x),r) becomes zero, implyin that there is no penalty associated with these constraints. The software developed for the desin optimization of the induction motor was prepared usin Delphi hih level prorammin lanuae. This software can analyze and optimize motors or evaluates the cost and performance of desin. Parameters of the motor or materials can be easily modified to investiate their effect on performance. Selection type and optimization type (torque, cost etc.) can be selected dependin on user. The GA optimization alorithm was based on a roulette wheel selection, sinle point crossover, bit mutation, and elitism Fiure. The flow chart for desin optimization process The flow chart of the desin optimization procedure is depicted in Fiure. Each block consists of number subroutines. Execution of the proram starts with the performance specifications such as the initial motor desin variables, the number of enerations, population size, crossover rate, and mutation rate. Population size, number of enerations, crossover rate and mutation rate can be selected dependin on user. Each
Desin Optimization of Induction Motor by Genetic Alorithm 199 desin parameter and penalty limits for penalty function can be varied within its domain. Then desin parameter of the stator and rotor layout is calculated. This is followed by optimization process such as the selection, crossover, mutation and specification of the constraints. The desin is evaluated for every individual of a population. The alorithm terminates after testin the specified converence and optimum desin achievin. At this point, the desiner is offered the option to view the performance analysis for the proposed desin. If the optimization are satisfied, then the desin optimization process must be stop, otherwise continue the GA optimization process. The desiner can improve the value of objective function reviewin constraint specifications. 5. THE RESULTS AND DISCUSSION Table 3 shows the values for the ten desin parameters for each optimization. Accordin to the results in Table 3, the alorithm has returned an acceptable solution every time, which is indicated by a ood value for objective with no constraint violations. Other variables of the induction motor are in turn reported in Table 4. Table 3.The desin parameter values obtained after optimization Desin parameter EM T E C Number of turns per phase 7 66 66 78 Stator iron lenth (cm) 19.54.544 4.813 17.41 End-rin width (mm) 5 3.48 7.74 9.395 Stator interior diameter (cm).381 1.87 1.196 Stator slot heiht (mm) 33 5.59 6.78 9.45 Stator slot width (mm) 1 11.75 1.647 11.98 Air-ap (cm).4.53.649.46 Rotor slot path (cm).5.9.96.481 Rotor bar diameter (mm) 8.8 9.71 7.988 9.137 Stator exterior diameter (cm) 37 34.83 34.17 34.1 EM: Existin motor T: Torque optimization E: Efficiency Optimization C: Cost Optimization Table 4. Comparison of the different desins and simulation results EM T E C Full load torque (Nm) 138.7 147.89 137.1 139.91 Pull-out torque (Nm) 33.51 41.67 377.36 359.8 Startin torque (Nm) 74.345 119.45 16.55 93.33 Power factor.875.88.85.864 Efficiency (%) 88.91 89. 9.98 86.5 Cost ($) 48 486 513 36 Full load current (A) 4.95 45.67 4.9 43.31 Startin current (A) 176.3 9.45 8.53 197.83 Stator tooth flux density (T) 1.3 1.5 1.95 1.768 Rotor tooth flux density (T) 1.6 1.59 1.478.3 Stator yoke flux density (T) 1,185 1.8 1.31 1.53 Rotor yoke flux density (T) 1.31 1.18 1.84 1.477 Air ap flux density (T).63.584.544.691 Rotor current density (A/mmP P) 5.74 4.95 6.38 5.77 Temperature (P PC) 75 75 75 75 Stator slot fillin factor.636.566.68.649 EM: Existin motor T: Torque optimization E: Efficiency Optimization C: Cost Optimization
M. Çunkaş and R. Akkaya Accordin to these results in Table 4, while achievin performance improvements, the cost of the motor is reduced by about 5%, which is a important reduction. Moreover, startin torque and pullout torque are desirably increased. On the other hand, a small decrease in efficiency and power factor is observed from the results. An essential remark here is that temperature rise of the motor is not known initially. Therefore, a fix value is iven to the proram. Accordin to these results, it can be said that GA is suitable for motor desin and can reach successful desins with lower cost, hiher torque, and hiher efficiency than the existin motor while satisfyin almost every constraint. 4 36 Torque[Nm] 3 8 4 16 T C M EM E 1 8 4 15 3 45 6 75 9 15 1 135 15 Speed [rpm] (a) Current [A] 5 175 15 15 1 T EM 75 C E 5 M 5 15 3 45 6 75 9 15 1 135 15 Speed [rpm] (b)
Desin Optimization of Induction Motor by Genetic Alorithm 1 1,9 Power Factor,8,7,6,5,4,3,,1 T C M EM E 15 3 45 6 75 9 15 1 135 15 Speed [rpm] (c) 1 Efficiency [%] 9 T EM 8 C E 7 M 6 5 4 3 1 15 3 45 6 75 9 15 1 135 15 Speed [rpm] Fiure 3 Performance Characteristics; a) Torque-speed, b) Current-speed, c) Power factor-speed and d) Efficiency-speed curves. (EM: Existin motor, T: Torque optimization, E: Efficiency Optimization, C: Cost optimization, M: Measured results) (d) Fiure 3 depicts examples of performance characteristics of an existin desin and three optimum desins as a function of the speed. Accordin to Fiure 3(a) startin torque of three optimum desins are always larer than that of the existin motor. Therefore, it exhibits better performance for larer loads. The full load torque at the cost and efficiency desin is approximately equal while bein the reater at the torque-based desin. When Fiure 3(b) is investiated, it can be seen that the startin current of the
M. Çunkaş and R. Akkaya motor increase in respect of existin motor for three optimum desins. The hihest variation of current is obtained for the torque-based desin and the lowest variation is for the existin motor. Accordin to Fiure 3(c), a small increase is observed in the power factor at torque-based desin. However, other desins are a decrease, which is acceptable that the reactive power consumption of the motor is suitable. When the Fiure 3(d) is examined it can be said that the efficiency of the motor is approximately the same at existin motor and at the torque-based desin while decreasin at cost-based desin. Furthermore the motor efficiency was considerably increased at the efficiencybased optimization. On the other hand, an important reduction in the cost of the motor was obtained in respect of existin motor at cost-based optimization. The cost of the torque-based desin is almost similar to that of the existin desin, but the efficiency-based desin has larer cost. Comparison of four desins indicates that in eneral, efficiency optimization is the most expensive one. If the decrease at the power factor and the efficiency isn t taken into consideration, it can be said that cost-based desin is better than the other one, resultin in a ood performance reardin the cost of different component and their dependencies on reion, manufacturer and time. The performance of the optimized motor is seen to be improvin respectably when compared with the existin motor. 6. CONCLUSION This paper has compared three different optimally desined three-phase squirrel-cae induction motors with an existin motor of the same ratin. An optimization technique based on GAs has been applied to the desin of 3 hp three-phase induction motor. A packae proram that analyzes and optimizes induction motors and evaluates the cost and performance of the desins has been developed. Comparison of the final optimum desins with the existin desin indicates that the ain of the proposed performance is even better than expected. In this instance, hiher startin and pullout torques, larer efficiency and finally a lower cost for induction motor desins can be pointed out. While achievin performance improvements, the cost of the motor is reduced by about 5%, which is an important result. The optimum cost-based desin is the best in this respect, reardin the cost of different components and their dependencies on reion, manufacturer and time. List of symbols Cu cost cost of unit weiht of copper; D e stator diameter at centers of stator slots; D o stator outer diameter; D r rotor diameter; Fe cost cost of unit weiht of iron; f ew end windin factor; L 1, L axial lenth of stator and rotor, respectively; m number of phase; P fe density of the iron sheet; P sw, P rw density of stator and rotor conductors, respectively; P lcu total copper losses of stator and rotor; total iron losses; P lfe
Desin Optimization of Induction Motor by Genetic Alorithm 3 s SF S 1, S w a, w r slip; stackin factor; number of stator and rotor slot, respectively; rotor end rins axial and radial width, respectively; REFERENCES 1. R Fci, E.F. Fuchs, H. Huauh, Comparison of two optimization techniques for the desin of a three-phase induction motor desin, IEEE Trans on Enery Conv.;4(4):651-9, 1989.. J. Faiz, M.B.B. Sharifian, Optimal desin of three phase induction motors and their comparison with a typical industrial motor. Int. J. of Comp. and Elect. En. 7:133-144, 1. 3. G.F. Üler, O.A. Mohammed, C.S. Koh,. Utilizin enetic alorithms for the optimal desin of electromanetic devices, IEEE Trans. on Manetics, Vol. 3, No. 6, pp. 496-498, 1994. 4. N. Bianchi, S. Bolonani, Desin optimization of electric motors by enetic alorithm. IEE Proc. Electr. Power Appl., 145: 475-483, 1998. 5. J.P. Wieczorek, Ö. Göl, Z. Michalewicz, An evolutionary alorithm for the optimal desin of induction motors. IEEE Trans. On Manetics, Vol. 34 No.6, pp. 388-3887, 1998. 6. M. Çunkaş, R. Akkaya., O. Bilin, Cost optimization of submersible motors usin a enetic alorithm and a finite element method, Int. J. of Adv. Manuf. Tech., in press, 6. 7. D.E. Goldber, Genetic Alorithms in Search, Optimisation, and Machine Learnin, Addison Wesley, New York, 1989. 8. Z. Michalewicz, Genetic alorithms + Data Structures = Evolution Prorams, nd ed., Spriner-Verla, New York, 1994. 9. S.J. Chapman, Electric machinery and power system fundamentals, McGraw-Hill, New York,. 1. C.G. Veinott, Theory and Desin of Small Induction Motors, McGraw-Hill, New York, 1959. 11. J. Faiz, M.B.B. Sharifian, A. Keyhani, A. Proca, Performance comparison of optimally desined induction motors with aluminum and copper squirrel-caes, Elect. Mach. and Power Sys, 8:1195-17,.