International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) V...
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) V...
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) V...
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) V...
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) V...
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) V...
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) V...
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Cost and performance optimization of induction motor using genetic

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Cost and performance optimization of induction motor using genetic

  1. 1. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 2, March – April (2013), © IAEME443COST AND PERFORMANCE OPTIMIZATION OF INDUCTIONMOTOR USING GENETIC ALGORITHM TECHNIQUEA. S. Sindekar1, A. R. Agrawal21Dept.of Electrical Engineering, Govt. College of Engineering, V.M.V. Road, Amravati,India2Dept.of Electrical Engineering, Govt. College of Engineering, V.M.V. Road, Amravati,IndiaABSTRACTThis paper presents three different optimal designs of induction motor. The optimallydesigned motor is compared with classically designed motor, having same ratings. GeneticAlgorithm is used for optimization and three objective functions namely efficiency, torqueand cost are considered. The motor design procedure consists of a system of non-linearequations, which gives induction motor characteristics, motor performance, magnetic stressesand thermal limits. Genetic Algorithms (GAs) give satisfactory results in the designoptimization of electrical machinery, it has been observed that the GAs locate the globaloptimum region faster than the conventional direct search optimization techniques.Nowadays optimization of induction machine is making trade-off between differentobjectives such as a particular item of performance, cost of machine or quality or reliability.Keywords: Optimization Technique, Genetic Algorithm, Induction Motor.1. INTRODUCTIONInduction motors have always played and will continue to play an important role inthe industry due to their simple structure, robustness [7, 11] and high reliability. It hasbecome a kind of demand by both the users and the manufacturers to optimize the design toimprove the performance in terms of efficiency, torque and reduce the active material whichcomprises cost of the induction motor. Because the optimization of induction motor design ishighly nonlinear mix-discrete constrained multivariable problem, the conventionalINTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING& TECHNOLOGY (IJEET)ISSN 0976 – 6545(Print)ISSN 0976 – 6553(Online)Volume 4, Issue 2, March – April (2013), pp. 443-449© IAEME: www.iaeme.com/ijeet.aspJournal Impact Factor (2013): 5.5028 (Calculated by GISI)www.jifactor.comIJEET© I A E M E
  2. 2. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 2, March – April (2013), © IAEME444optimization methods, are not effective. On the other hand genetic algorithm showsremarkable effects and is being widely used for solving the optimization problems forelectrical machines and other electromagnetic devices. If the standard non-linearprogramming (NLP) techniques were to be used in this case, then they would becomputationally very expensive, time consuming and inefficient. GA’s have been renownedas an important tool in design optimization of electrical machinery in recent years. One of themost important advantage of the GA over the standard NLP techniques is that it is able tofind the global minimum, instead of a local minimum. Another advantage is that it does notrequire derivative of the function, which is not always easily obtainable or may not evenexist. The aim of this paper is to give a further contribution in the optimum design of threephase induction motor in manufacturing process; using three objective functions, namely cost(C), efficiency (E) and torque (T). A design sheet has been developed for a particular three-phase squirrel-cage type induction motor. An induction motor of 2.2 kW, 400 V, 1500synchronous r.p.m. is chosen for comparison with three optimally designed motors [12].Same motor rating (basic specification) is used for three optimal designs and sameperformance limits (constraints) are considered for all three designs. Advantages anddisadvantages of each design are then briefly discussed.2. BASICS OF GENETIC ALGORITHMGenetic Algorithm is a random search method [10] which involves stochasticgeneration of several valid design solutions and then systematically validates and refines thesolutions until a stopping criterion is met. There are three fundamental operators whichcomprise in the search process of genetic algorithm: selection, crossover, and mutation.Following are the steps to implement GA:Step 1: Define all parameters involved and form objective functionStep 2: Generate first population at randomStep 3: Check and validate population on the basis of fitness value of objective functionStep 4: Test the solution. If satisfied then stop else continue.Step 5: Apply all GA operators (Selection, Crossover, and Mutation)Step 6: New generation is obtained, to continue the optimization return to step 3.Selection: Selection is a process in which individual chromosomes (combination ofparameters) are selected according to their fitness value. The selection probability [1] can bedefined byPj = F (xi) / ∑ iF (xi)Where Pj is probability of selection of certain individual string and F (xi) is objectivefunction.Crossover: This is the most powerful genetic operator. There are two types of crossover,single-point crossover and multi point crossover. Usually single-point crossover is used.Following is an example of single-point crossover; crossover point is selected between thefirst and the last bits of the parent chromosome. The binary code which is to the right of thecrossover point of Parent1 goes to Offspring2 [1] and Parent2 passes its code to Offspring1.
  3. 3. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 2, March – April (2013), © IAEME445Point of crossoverParent1 = 0010010 101Parent2 = 0101011 100Offspring1 = 0010010 100Offspring2 = 0101011 101Mutation: This is a common genetic shuffling operator, which involves the stochasticalteration of genes [2] during the process of copying a chromosome from one parent to itsoffspring. The mutation operator should be used because, mutation increases algorithm’sfreedom to search outside the current region of parameter space. Mutation changes from a“0” to a “1” or vice versa. It may be illustrated as follows:110001010 › 1100000103. PROBLEM FORMULATIONa) Objective functionsAs mentioned earlier there are three objective functions, cost of the motor, efficiencyof the motor and torque of the motor.i) Objective function for costTotal cost of motor [3, 8] is addition of copper material cost, iron materialcost, fabrication cost and laminating cost. Lamination cost for low and mid range motors isaround 150% of total active material cost and fabrication cost is around 25% of total motorcost. For formulation purpose only cost of active material (addition of copper cost and ironcost) is used as a function. The cost of copper or iron depends on its weight and weightdepends on the volume. Volume is a function of area and length. Iron weight and copperweight is multiplied by per kg rate of Rs.50 and Rs.450 respectively, thus cost objectivefunction is written as:Cost of active material [fun(y)] = [(weight of iron * 50) + (weight of copper * 450)]ii) Objective function for efficiencyEfficiency is the ratio of output and input of the motor [4]; so mainly we needto calculate the output and all losses such as copper losses, iron losses and friction andwindage losses. Moreover for considering the additional losses such as harmonic losses,pulsation losses, 0.5 is deducted from the equation for efficiency. So the required objectivefunction will be:Efficiency [fun(y)] =outputoutput + lossesEfficiency [fun(y)] =PW×1000ሺPW×1000ሻ+total loss×100 - 0.5
  4. 4. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 2, March – April (2013), © IAEME446iii) Objective function for torqueThe objective function is given by:Torque at full load [fun(y)] =rotor input × 602× π×NsWhere Ns is synchronous speed in r.p.m. and rotor input is the addition of rotor output,friction and windage losses and rotor copper losses. Thus we need to calculate theseparameters with MATLAB program.bሻbሻbሻbሻ Design variables:Practically there are many parameters in induction motor design which can beconsidered as design variables. Some key independent variables are selected and are assignedfrom X1 to X13 with their upper and lower bounds [9].Table 1: Design Variablesc) Inequality constraintsSome key performance parameters [5] are considered with their upper and lowerbounds [9] as inequality constraints. The performance parameters are taken as constraintsonly to have a practical optimal design (feasible design), which has an optimal value of theconsidered objective function with all the performance parameters within the specified limits.Table 2: Performance Constraints (limits)Variable Parameter UpperlimitLowerlimitX1 Stator turns per phase 480 400X2 Length of stator core (m) 0.13 0.11X3 Diameter of stator core (m) 0.110 0.105X4 Stator slot height (mm) 20 15X5 Stator tooth width (mm) 6 3X6 Depth of rotor slot (mm) 10 9X7 Width of rotor slot (mm) 8 6X8 Actual diameter of stator conductor (mm) 0.96 0.90X9 Area of each rotor bar (mm2) 45 43X10 Depth of end ring (mm) 11 8X11 Thickness of end ring (mm) 9 7X12 Depth of rotor core (mm) 18 15X13 Length of air gap (mm) 0.35 0.29Variable Parameter UpperlimitLowerlimitb1 Efficiency (%) 85 80b2 Power factor 0.9 0.8b3 Full load slip (%) 6 3b4 Rotor bar current density (A/mm2) 6 4b5 Stator current density ( A/mm2) 5 3.9b6 Starting current (A) 19 15b7 Starting torque (N-m) 17 14
  5. 5. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 2, March – April (2013), © IAEME4474. EXECUTION OF PROBLEMClassical design of induction motor is carried out with MATLAB. Simple program iswritten for obtaining all the required design parameters. The values of all three objectivefunctions are calculated without applying any optimization technique (classically). Geneticalgorithm tool box is used to optimize the objective functions of cost, efficiency and torque.The fitness function (objective function) is written as @name of m. file in which function issaved, then the total number of variables used is mentioned in the next row and finally thelinear inequalities are written in the matrix form.5. RESULTSIn table 3 values of all design variable, for classical design, efficiency optimization,cost optimization and torque optimization is given. Table 4 shows, values of all performanceparameter for all three optimization and classical design. Both the tables give a comparativeevaluation of all results obtained.Table 3: Comparative values of design variableTable 4: Comparative values of performance parameterVariable Parameter ClassicaldesignEfficiencyoptimizationCostoptimizationTorqueoptimizationX1 Stator turns per phase 416 408 433 440X2 Length of stator (m) 0.125 0.123 0.120 0.120X3 Diameter of stator core (m) 0.105 0.1055 0.105 0.109X4 Stator slot height (mm) 17 15 15 19.98X5 Stator tooth width (mm) 3.9 3 3 3X6 Depth of rotor slot (mm) 9.3 10 9 10X7 Width of rotor slot (mm) 6.8 6 6.057 7X8 Actual diameter of conductor (mm) 0.95 0.936 0.91 0.90X9 Area of each rotor bar (mm2) 44 44.56 43 43X10 Depth of ring (mm) 10 8 8 10.99X11 Thickness of ring (mm) 8 9 7 7X12 Depth of rotor core (mm) 17 17 16 16.21X13 Length of air gap (mm) 0.3 0.31 0.29 0.314Parameter ClassicaldesignEfficiencyoptimizationCostoptimizationTorqueoptimizationEfficiency (%) 81.3 83.93 80.5 79.9Power factor 0.829 0.865 0.81 0.89Full load slip (%) 5.6 3.06 3.04 3.009Rotor bar current density (A/mm2) 4 4.50 4.001 4.003Stator current density (A/mm2) 3.9 3.95 3.89 4.08Starting current (A) 18.86 18.37 19 17.68Full load torque (N-m) 15 14.89 15.06 15.25Starting torque ( N-m) 15 14.80 15.04 15.25Active material cost (INR) 2600 2570 2348 2630
  6. 6. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 2, March – April (2013), © IAEME4486. CONCLUSIONOptimization of all three objective functions is carried out with the help of GAtoolbox which gives effective and fast results in comparison with the MATLAB GA program.At the time of optimization many constant parameters can also be taken into consideration asdesign variables or performance parameters. Apart from the three objective functions chosenin this paper, power factor can also be considered as an objective function for maximization.With respect to the results shown in table 3 and table 4, following conclusions can be drawn:1. Active material cost is reduced by almost 10% with all the performance parameterswithin their specified limits.2. Almost 3% increase is seen in efficiency as compared to the classically designedmotor that to with a better cost. It can be further increased by improving the qualityof active material used.3. Full load torque goes up by almost 2% with torque optimization, with the highestcost and lowest efficiency amongst all four.4. All three optimal designs obtained can be fabricated (assembled) by using the framesize ‘D100L’, which is a standard frame size for this rating.5. Diameter of stator core and length of stator changes slightly in all three optimaldesigns; however the same frame size can be used.6. In efficiency optimized design, stator turns per phase are less than that of theclassical design which will slightly affect the loading capacity of the motor. Thisproblem can be resolved either by making new stator stampings according to the newdimensions obtained or by slightly increasing the actual diameter of conductor used.Making new stator stamping is affordable only when there is a bulk order of motormanufacturing.7. In cost and torque optimized designs, stator turns per phase are greater than that ofthe classical design those can be accommodated in the same slots of stampings byslightly decreasing the diameter of conductor.8. There are minor changes in the width and depth of rotor slot in all the three optimaldesigns. This results into change in the starting torque of the motor. End ring currentis not investigated.REFERENCES[1] Mehmet Cunkas and Ramazan Akkaya, “Design Optimization of Induction Motor byGenetic Algorithm and Comparison with Existing Motor”, Mathematical andComputational Application, Vol. 11, No. 3, pp 193-203, 2006[2] Li HAN, Hui LI, Jingcan LI, Jianguo ZHU, “Optimization for Induction Motor Designby Improved Genetic Algorithm”, Australasian Universities Power EngineeringConference, pp 26-29 September 2004[3] Shivendra Prakash Verma, “Design Optimization of 7.5 Kw, 4 Pole, 3-Phase, 50 HzInduction Motor Employing Genetic Algorithm / Improved Genetic Algorithm UsingSweep Frequency Response Analysis”, MIT International Journal of Electrical andInstrumentation Engineering Vol. 1, No. 2, Aug. 2011, pp 108-115 ISSN 2230-7656©MIT Publications.[4] S. Ghozzi, K. Jelassi, X. Roboam, “Energy optimization of induction motor drives”,IEEE conference on industrial technology, 2004
  7. 7. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 2, March – April (2013), © IAEME449[5] J. Faiz, M.B.B. Sharifian, “Optimal design of three phase induction motors and theircomparison with a typical industrial motor”, Int. J. of Comp. and Elect. Engg. Eng.27:133-144, 2001[6] X. Liu, G. R. Slemon, “An Improved Method of Optimization for ElectricalMachines”, IEEE Trans. On energy conversion, Vol. 6, no. 3, pp 492-496, sep. 1991[7] C.G. Veinott, Theory and Design of Small Induction Motors, McGraw-Hill, NewYork, 1959.[8] M. Ramamoorty, “Computer Aided Design of Electrical Equipment”, Affilated EastWest Press Private Limited, New Dehli, 1987, pp 1 -4, 86-94[9] A Shanmugasundaram, G Gangadharan, R Pillai, “Electrical Machine Design DataBook” New Age International Pvt. Ltd., New Dehli, 2001[10] D.E. Goldberg, “Genetic Algorithms in Search, Optimization, and Machine Learning”,Addison Wesley, New York, 1989.[11] S.J. Chapman, “Electric machinery and power system fundamentals”, McGraw-Hill,New York, 2002.[12] A. K. Sawhney, “A Course in Electrical Machine Design”, Dhanpat Rai and Sons,New Delhi, 5th Edition, 1991, pp 10.1-10.97, 22.1-22.7.

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