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Indian Streams Research Journal

KEYWORDS-

CostOptimization, Xl bit, Elitism, Tournament Selection, Roulette Wheel.

I.INTRODUCTION

Optimization is the act of obtaining the best result under given circumstances [5]. Optimization of electric machines is making trade-off between different objectives such as a particular item of performance, cost of device or quality or reliability.Optimization can be done with single objective or multi objective. In either case, optimization process shall include, if any, the constraints imposed in the system. If the optimization is done for any one of the parameters such as cost, efficiency, volume of material used, torque, starting current etc. associated with the system then it is a single objective optimization problem. If two or more of the parameters are involved in the optimization process then it is a multi objective optimization problem. In single objective optimization, the parameter of importance will be identified as objective

Abstract:

Optimisation is the process of finding an alternative with the most cost effective or highest achievable performance under the given constraints, by maximizing desired factors and minimizing undesired ones. Three-phase cage rotor induction motors are widely used in industrial drives because they are rugged, reliable and economical. In this paper an optimized design of three phase squirrel cage IM using Genetic Algorithms (GA), with cost as objective, has been considered for 11KW motors. Out of more than 140 variables concerning the electrical and magnetic circuits of the machine, eleven parameters having predominating influence on the cost and performance of the motor have been identified as basic independent variables while the other parameters are either referred in terms of the 11 parameters or treated as fixed for a particular problem. The constraint functions are expressed in terms of the equivalent circuit parameters which in turn are evaluated in terms of the eleven independent variables. The initial values of the basic variables have been chosen through calculations ensuring that no constraint has been violated. The cost function is constructed by considering the cost of electrical conducting and magnetic materials. In the optimization process using GA, a software Xl bit, used as Add-In in MSEXCEL 2007, has been used. Computer simulations have been carried out and the design has been tested with three different selection / cross over methods: Elitism, Roulette Wheel, and Tournament Selection. All the three methods produced almost identical optimized cost. It has been observed that optimization using GA results in an approximate saving of 23 % for the 11KW motor on the total cost of materials. The research work has confirmed once again the supremacy of GA in the design optimization problem, over the other conventional optimization techniques.

OPTIMISATION OF THREE PHASE SQUIRREL CAGE INDUCTION MOTOR USING GENETIC ALGORITHM

KRISHNAMOORTHY , ABIRAMI.RA AND ANITHA.A

EEEAgni college of Technology Chennai , India.

ORIGINAL ARTICLE

ISSN:-2230-7850METHODS ENRICHING POWER & ENERGY DEVELOPMENTS (MEPED'13)

th April 12 , 2013

function f(X) and optimized.Of late, the advent of high-speed digital computers has enabled the implementation of analysis, synthesis and optimization of electrical machine design to satisfy certain specification constraints. In the design of electrical machinery using computers, the concepts of two commonly acceptable approaches to machine design namely, analytical method and synthesis method were practiced initially. Thereafter, a third method, referred to as Hybrid method, combines the advantages of these methods and is widely practiced. The design of electrical machines consists essentially of the solution of many complex and diverse engineering problems and normally these problems are loosely interrelated. The aim of optimization in the design of electrical machines is to choose the best solution for a given problem from the multitude of possible solutions. The optimization process, therefore, involves the choice of various variables in such a manner that the design in regard to a particular feature is the best, and at the same time satisfies all limitations and constraints imposed on its performance. Hence, optimization is the collectiveprocess of finding a set of conditions required toachieve the best results from a given situation. Normally, the objective of study in most of the industrial problems is carried out on optimization within an economic framework. A characteristic feature of optimization in the design of electrical machines is the presence of conflicting or opposing influences e.g. cost and performance. The best design will be obtained by the compromise of important factors.Among the various types of electrical machines, Induction Motor(IM) is the most widely used in domestic,commercial and various industrial applications. The squirrel cage type of IM is characterized by its simplicity, robustness and low cost, which has always made it very attractive, and hence widely finds a leading place in industrial sectors. As a result of its extensive use in the industry, cost optimization of IM through a better design becomes a major concern.IM design optimization is a problem in non-linear programming solved by the method of Sequential Unconstrained Minimization Technique (SUMT) [6]. In SUMT, the constrained optimization problem is converted into a series of unconstrained problems in the following manner: The augmented function at the beginning of kth iteration is

k k kP (X) = F (X) + R 1/ (g i (X)), R >0 .(1)

F(X) is the cost function. The sigma term, called the penalty term, is to ensure that during the minimization process no constraint is violated. Optimization algorithms can be classified into two categories: Deterministic and Stochastic. The deterministic algorithms seek the minimum point by using the gradient of the objective function. The algorithm efficiency depends on several factors, e.g., starting point, accuracy of the descent direction evaluation, and method used to execute the line search as well as the stopping criteria. The algorithm in general searches a point of local optimum, which could also be the global optimum if the function is unimodal. The drawbacks of the deterministic methods are the need of the gradient evaluations and lack of guarantee on obtaining the global optimum [9]. This is not exactly the desired behaviour necessary for an optimization algorithm, which generally requires high probability of finding the global optimum and fast convergence speed. The direct search methods of conventional optimization methods are usually deterministic while the GAs, invented by John Holland, is stochastic in nature. The stochastic algorithms have the following advantages:

Gradient evaluation is not requiredHigh probability of finding global optimum is achievedInitial position is independent of the solution.

GA mimics the principles of natural genetics and natural selection to constitute search and optimization procedure. It is a problem solving method that uses genetics as its model of problem solving. The wide range of applications that have appeared since the arrival of the techniques proves that GA, indeed, is a powerful in solving complicated problems the way nature does [4]. However it has a disadvantage of requiring highest number of objective function computations than that of the deterministic method [13]. The genetic algorithm implementation steps are shown as follows

Step 1: Define parameter and objective function Step 2: Generate first population at randomStep 3: Evaluate population by objective functionStep 4: Test convergence. If satisfied then stop else continue.Step 5: Start reproduction process (Selection, Crossover, and Mutation)Step 6: New generation. To continue the optimization, return to step 3.


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RELATED WORKS

A powerful tool for the optimal design of induction motor, an Evolutionary Algorithm, which uses binary encoding, Roulette wheel selection, single-point crossover, bit mutation, and elitism has been carried out [11]. The results obtained for a realistic device such as the induction motor presented substantiate the usefulness of evolutionary optimization methods in electromagnetic device.

In the Design Optimization of Electric Motors by Genetic Algorithm [2], binary encoding has been used. A comparison between GA and classical hill-climbing direct-search method has been performed. This comparison showed the GA to carry out more iterations than conventional techniques. However, the GA is able of finding global optimum and avoiding local, being the major advantage of the GA compared to more classical techniques. Another property of the GA is that there is no need for a good initial point to start the optimization from. The choice of setting process parameters, like crossover probability and mutation rate has been explored and the findings support the previous discussed effects these parameters have on the performed search.

In the Design optimization of three-phase induction motors by using genetic algorithm [3], torque of the motor has been chosen as the objective function.The design is based on binary encoding, Roulette wheel selection, single-point crossover, bit mutation and it has been observed that the Gas offer advantages over other approaches.

In recent years, GA has been recognized as a potent tool in design optimization of electrical machinery [3]. GA improves the performance by finding the global optimum [13]. In the most general sense, GA-based optimization is a stochastic search method that involves the random generation of potential design solutions and then systematically [7] evaluates and refines the solutions until a stopping criterion is met [1]. Each iteration consists of selection, reproduction, evaluation and replacement.

In the recent works connected with Gas in the design optimization of Electrical Machinery, it has been observed that the GA locate the global optimum region faster than the conventional direct search optimization techniques [10,12]

MATERIALS AND METHOD

The aim of this paper is to give a further contribution in the optimized design of a three phase IM with cost as objective function. GA having feature of a unique search is then used for optimization process. In this paper, design optimization of three phase IM has been presented with cost as objective function (Single objective optimization), for 11kw motors. The specifications of 11kw motor designed are as follows: Input Voltage 440 V, 50Hz., 3-Phase; No. of Poles 6; 1000 rpm; star connected; Stator steel, Rotor -copper .

IM design optimization is a problem in non-linear programming. A general non-linear programming problem can be stated mathematically as given in Eq. (2).

Find X = (X , X , X ) such that 1 2 nF(X) is a minimum & g i(X) 0 for i = 1..n (2)

X is a set of independent variable concerning the electrical and magnetic circuits of the machine. Out of more than 140 variables concerning the electrical and magnetic circuits of the machine, only some have a predominating influence on the cost and performance of the motor [8]. In the design under consideration, 11 parameters which have a predominating influence on the cost and performance of the motor are considered as independent variables. Other parameters are either referred in terms of these 11 parameters or treated as fixed for a particular problem. All lengths are expressed in metres and air gap flux density in Tesla. The constraint functions are expressed in terms of the equivalent circuit parameters which in turn are expressible in terms of the eleven independent variables. The initial values of these variables have been chosen through calculations ensuring that no constraint has been violated. The function to be minimized is formed by considering the cost of electrical conducting and magnetic materials. The design procedure followed conventionally has been adopted. The motor design procedure consists of a system of non linear equations which evaluates the various parameters associated in the design without violating the constraints imposed. The initial values of basic variables & the constraints imposed in the design are given in Table 1 and Table 2 respectively.

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Table 1: Independent Variables and their Initial Values

Table 2: Constraints Imposed

The function to be minimized is F, formed by considering the cost of electrical conducting and magnetic materials. For cost calculations, cost of Iron (Steel) and Copper have been taken as Rs. 50 and Rs.520 per Kilogram respectively. F is the summation of costs of Stampings, Stator Copper and Rotor Materials. In the design optimization process using GA, software Xl bit [14], used as Add-In in MSEXCEL 2007, has been used. It is GA based optimization software mimicking the evolution of life. It is known that this evolution of life operates on chromosomes. GA using simple manipulations ofchromosomes such as encoding and reproduction mechanism has proved to be very effective in

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Description

Motor

Rating 11Kw

Basic

variable

Initial

Values

Stator Bore Diameter X1 0.254

Stator Stack Length X2 0.133

Depth of Stator slot X3 0.029

Width of Stator slot X4 0.0085

Depth of Stator core X5 0.03

Depth of Rotor slot X6 0.013

Width of Rotor slot X7 0.013

Air gap flux density X8 0.45

End ring depth X9 0.015

End ring width X10 0.01

Air gap length X11 0.00057

Motor Rating 11Kw

Constraints Magnitude

Starting Current = 66A

Starting Torque = 42 N m

Pull-out Torque = 150 N m

Full Load Slip = 0.05

Full Load

Temperature Rise = 80 C

Full Load Power

Factor = 0.85


optimization applications. It is widely used in image processing, criminal suspects' recognition, job shop optimization etc.

Actual steps of this algorithm are:

An initial population of random solutions is created.A fitness value is then assigned to each individual based on its evaluation to the current problemIndividuals or Chromosomes with a higher fitness values are selected to parent new solutions during reproductionThe new off-springs are then set to replace the old, thus a generation is completed.Return to step b to d until the population is converged.Prior to running this optimization software, Cost function and the constraints are set in the respective fields and the test set up is adjusted according to the needs.

The procedure carried out is described in the following steps..

Step 1: Calculation of Initial values of the independent variables Step 2: Evaluation of Equivalent Circuit ParametersStep 3: Evaluation of ConstraintsStep 4: Check for constraint violation. If any constraint is violated go to step 1.Step5: Enter the test Set up (population, generation, mutation rate etc), in the software Xl bit to the requirements. Also choose the type of selection and cross over method to be adopted.Step 6: Carry out the optimization process using the software Xl bit

The test setup used (refer step 5) is as follows: Population: 100, Generation: 50 (up to 250 considered), Variable type: Non Integer, Crossover Rate: 0.7, Mutation rate: 0.002 and Fitness Scale: Linear Normalize. To ensure meaningful results, variation of the basic variables has been restricted in the range of 0.9 to 1.1, compared to their initial values [14]. The design has been tested with three different selection / cross over methods: Elitism, Roulette Wheel, and Tournament Selection. Screen display of the optimization set up in Xl bit is shown in Fig. 1

The generated report at the end of the GA optimization process is given in Fig. 2

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Fig1: optimization setup


Figure 2 Generated report at the end of the optimization process

RESULTS AND DISCUSSIONS

Computer simulated results have been tabulated for analysis. Optimized results of basic variables are shown in Table 3. Optimized costs of each material used and total cost are shown in Table 4. (All Costs in Rs.).

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Target Cell: 41400.84273

Population 100

Generation 350

Crossover % 0.7

Crossover Method Elitism

(Recommended)

Mutation Rate 0.000002 Fitness Scaling Linear Normalize Best Fitness 1.995859916

Least Fit 1.9955415

Basic

Variables

11Kw Motor

Initial Value

Selection / Cross Over Methods

Elitism Tournament Selection Roulette Wheel

X1 0.254 0.2413 0.2286 0.2317

X2 0.133 0.1197 0.133 0.1267

X3 0.029 0.0261 0.0261 0.0261

X4 0.0085 0.00765 0.00765 0.00765


Analysis of Results:It has been found that the design tested with three different selection / cross over methods, Elitism, Roulette Wheel, and Tournament Selection, produced almost identical optimized cost. From the simulated results, it has been observed that due to the optimization process, the cost of the motor has reduced to 77 % of the initial cost, thereby saving approximately 23 % on the cost of materials for the 11 Kw motor. The research work has confirmed once again the supremacy of GA in the design optimization problem, over the other conventional optimization techniques.

CONCLUSION

From the results it is observed that GA is better than the conventional optimization techniques. In recent years, GA has been recognized as potent tool in design optimization of electrical machinery. Further progress in the research work combining conventional Optimization techniques and GA approach may produce better results for the design optimization problem under consideration. The optimization process has been carried out with a single objective function, i.e., cost as objective. Parameters other than cost my also be considered and optimized. Further, multi-objective optimization may also be carried out with suitable changes in the objective function.

REFERENCES

[1]Abdelhadi, B., A. Benoudijit, and N. Nait, 2004, Identification of Induction machine parameters using a new adaptive genetic algorithm, Electric power components and systems, vol. 32(8), pp. 767 784, doi: 10.1080/15325000490466645.[2]Bianchi, N., and S. Bolognani, 1998, Design optimization of electric motors by genetic algorithm, IEEE Proc. on electrical power appliances. Vol. 145, pp. 475-483, doi: 10.1049/ip-epa:19982166 [3]Cunkas, M., R. Akkaya, and O. Bilgin, 2007, Cost optimization of submersible motors using a genetic algorithm and a finite element method, Int. J. of Advanced Manufacturing Technology, vol. 33, pp. 223-

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X5 0.03 0.02926 0.03 0.03

X6 0.013 0.0117 0.0117 0.0117

X7 0.006 0.0057 0.0054 0.006

X8 0.45 0.4917 0.4921 0.4916

X9 0.015 0.0135 0.0165 0.015

X10 0.01 0.009 0.01099 0.01

X11 0.00057 0.000627 0.00063 0.000629

Description

11Kw Motor Cost with Initial Values in Rs.

Selection / Cross Over Methods

Elitism Tournament Selection Roulette Wheel

Cost of Steel 3017.73 2439.55 2444.37 2374

Cost of Copper 52054 39989.04 39465.71 39226

Total Cost 55072 42428.6 41910.08 41600 % of Initial total cost 100 % 77.04% 77.04 % 77.04 %


232, doi: 10.1007/s00170-006-0458-x.[4]Mohammed, O.A., 1997, GA optimization in electric machines, Proc. IEEE Conf. on Electric machines and drives, pp. TA1/2.1-TA1/2.6, doi: 10.1109/IEMDC.1997.604194.[5]Ramarathnam, R., B.G. Desai, and V. Subbarao, 1971, Optimization of polyphase induction motor design A nonlinear programming approach., IEEE Trans. on Power Apparatus and Systems, vol. 90, pp. 570-579. doi: 10.1109/TPAS.1971.293060.[6]Rao, S.S., 2009, Engineering optimization, John Wiley & sons.[7]Sareni, B., L. Krahenbuhl, and A. Nicolas, 2000, Efficient Genetic algorithms for solving hard constrained optimization problems,. IEEE Trans. on Magnetics, vol. 36, pp. 1027-1030, doi: 10.1109/20.877616.[8]Sawhney, A.K., 2005, A course in Electrical Machine Design, 5th ed., Dhanpat Rai & Co. [9]Thangaraj, C., S.P. Srivastava, and P. Agarwal, 2009, Energy Efficient control of Three- Phase Induction Motors - A Review, International Journal of Computer and Electrical Engineering , vol.1, pp. 61-70, http://www.ijcee.org/papers/010.pdf[10]Uler, G.F., O.A. Mohammed and C.S. Koh, 1995 Design optimization of electrical machines using genetic algorithms, IEEE Trans. on Magnetics, vol. 31, pp. 1932-1935, doi: 10.1109/20.376437.[11]Wieczorek, J.P., O. Gol and Z. Micahalewicz, 1998, An evolutionary algorithm for the optimal design of induction motors, IEEE Trans. on Magnetics, vol. 34, pp. 3882-3887, doi: 10.1109/20.728298[12]Wurtz, F., M. Richomme, J. Bigeon and J.C. Sabonnadiere, 1997, A few results for using genetic algorithms in the design of electrical machines, IEEE Trans. on Magnetics, vol. 33, pp. 1982-1985, doi: 10.1109/20.582656.[13]Yong-Hwan, O.H., T.K. Chung,, M.K Kim, and H.K Jung, 1999, Optimal design of electric machine using Genetic algorithms coupled with Direct method, IEEE Trans. on Magnetics, vol. 35, pp. 1742-1745, doi: 10.1109/20.767366.[14]Xl bit software, www.xlpert.com/wxl%20bit.htm.

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