research article parameter estimation of three-phase...

Research ArticleParameter Estimation of Three-Phase Induction Motor UsingHybrid of Genetic Algorithm and Particle Swarm Optimization

Hamid Reza Mohammadi and Ali Akhavan

Department of Electrical and Computer Engineering University of Kashan Ravand Street PO Box 87317-51167 Kashan Iran

Correspondence should be addressed to Hamid Reza Mohammadi mohammadikashanuacir

Received 24 July 2014 Revised 7 November 2014 Accepted 9 November 2014 Published 1 December 2014

Academic Editor Guangming Xie

Copyright copy 2014 H R Mohammadi and A Akhavan This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

A cost effective off-linemethod for equivalent circuit parameter estimation of an inductionmotor using hybrid of genetic algorithmand particle swarm optimization (HGAPSO) is proposed The HGAPSO inherits the advantages of both genetic algorithm (GA)and particle swarm optimization (PSO) The parameter estimation methodology describes a method for estimating the steady-state equivalent circuit parameters from the motor performance characteristics which is normally available from the nameplatedata or experimental tests In this paper the problem formulation uses the starting torque the full load torque the maximumtorque and the full load power factor which are normally available from the manufacturer data The proposed method is used toestimate the stator and rotor resistances the stator and rotor leakage reactances and the magnetizing reactance in the steady-stateequivalent circuit The optimization problem is formulated to minimize an objective function containing the error between theestimated and the manufacturer data The validity of the proposed method is demonstrated for a preset model of induction motorinMATLABSimulink Also the performance evaluation of the proposed method is carried out by comparison between the resultsof the HGAPSO GA and PSO

1 Introduction

Inmost of the applications inductionmotors are preferred toDCmotors because of their simple structure easy operationand also low cost maintenance and durability Recentlyadvanced control techniques such as vector control and field-oriented control (FOC)make them compete with DCmotorsin many aspects [1] The information regarding motor circuitparameters is very important for design performance evalu-ation and feasibility of these control techniques

The conventional techniques for estimating the inductionmotor parameters are based on the locked-rotor and the no-load tests However these techniques cannot be implementedeasily The main disadvantage of these techniques is that themotor has to be locked mechanically In the locked-rotorcondition the frequency of the rotor is equal to the supply fre-quency but under operating condition the rotor frequencyis about 1ndash3HzThis incorrect rotor frequency will cause bad

results for the locked-rotor test Besides in the motors withhigh power this test is impractical These problems haveencouraged the researchers to investigate alternative tech-niques for parameter estimation The problem of inductionmotor parameter estimation has been addressed extensivelyby many researchers in the past Deep bar motors wereconsidered in [2] and parameter estimation was carried outwith emphasis on leakage reactance in [3] The method offinite element analysis was employed in [4] Also parameterestimation of an induction motor using some evolutionaryalgorithms is presented in [5ndash7]

Evolutionary algorithms such as genetic algorithm (GA)and particle swarm optimization (PSO) seem to be a promis-ing alternative to traditional techniquesThe GA is a stochas-tic search procedure that mimics biological evolution byusing genetic operators [8] Like GA the PSO is initializedwith a population of random solutions Compared withGA PSO has some attractive properties It has memory

Hindawi Publishing CorporationJournal of EngineeringVolume 2014 Article ID 148204 6 pageshttpdxdoiorg1011552014148204

2 Journal of Engineering

so that knowledge of good solutions is retained by allparticles whereas in GA previous knowledge of the problemis destroyed once the new population generates [5] Howeverboth methods have strengths and weaknesses It seems thata hybrid of the GA and PSO models could lead to furtheradvances Therefore in this paper GA and PSO mergetogether to use the benefits of both methods This algorithmis named as hybrid of genetic algorithm and particle swarmoptimization (HGAPSO) There have been many technicalpapers using evolutionary algorithm for parameter estima-tion but parameter estimation of an induction motor usingHGAPSO has never been presented by now

This paper uses some nameplate or manufacturer datafor problem formulation By using the proposed method thesteady-state equivalent circuit of the motor can be estimatedIn fact the optimization problem is formulated so that theerror between calculated data using the estimated parametersand manufacturer data is minimized

In the next sections the set of equations for problem for-mulation is introduced Also a short description of GA andPSO and a more detailed explanation of HGAPSO are pro-vided The validity of the proposed method is tested by usinga preset model of induction motor in MATLABSimulinkAlso the performance evaluation of the proposed methodis carried out by comparison between the results of theHGAPSO GA and PSO

2 Problem Definition

An induction motor can be modeled by using a steady-state equivalent circuit The parameter estimation problem isformulated as a least squares optimization problem so thatthe objective function is the minimization of the deviationbetween the estimated and the nameplate data The problemformulation for a three-phase induction motor is describedbelow

The problem formulation uses the manufacturer datasuch as the starting torque the full load torque themaximumtorque and the full load power factor The proposed methodis used to estimate the stator and rotor resistances thestator and rotor leakage reactances and the magnetizingreactance in the steady-state equivalent circuit of the motorIn Figure 1(a) the steady-state equivalent circuit model of athree-phase inductionmotor is shown It should be noted thatthe rotor parameters have been referred to as the stator sideAlso it is assumed that the core-losses are negligible

For problem formulation Thevenin equivalent circuitproposed in IEEE standard 112 is used as shown in Figure 1(b)The problem formulation and objective function are as fol-lows

1198911=1198701199051198771015840119903119904 [(119877th + 119877

1015840

119903119904)2

+ (119883th + 1198831015840

119903)2

] minus 119879fl (mf)

119879fl (mf)

1198912=1198701199051198771015840119903 [(119877th + 119877

1015840

119903)2

+ (119883th + 1198831015840

119903)2

] minus 119879st (mf)

119879st (mf)

1198913=1198701199052 [119877th + radic119877

2

th + (119883th + 1198831015840

119903)2

] minus 119879max (mf)

119879max (mf)

1198914

=cos (tanminus1 ((119883th + 119883

1015840

119903) (119877th + 119877

1015840

119903119904))) minus 119901119891fl (mf)

119901119891fl (mf)

(1)

where 119877119904is the stator resistance 1198771015840

119903is the rotor resistance

which has been referred to as the stator side 119883119904is the stator

leakage reactance 1198831015840119903is the rotor leakage reactance which

has been referred to as the stator side119883119898is the magnetizing

reactance and 119904 is the slip Also it is assumed that119883119904is equal

to1198831015840119903 The other variables are introduced as follows

119881th =119881ph119883119898

119883119904+ 119883119898

119877th =119877119904119883119898

119883119904+ 119883119898

119883th =119883119904119883119898

119883119904+ 119883119898

119870119905=31198812th120596119904

(2)

where 119881ph is input phase voltage 119881th is Thevenin voltage119877th and119883th are Thevenin resistance andThevenin reactancerespectively 120596

119904is angular velocity and 119870

119905is the constant

coefficient Also ldquomfrdquo index is used for themanufacturer dataso that 119879st(mf) 119879fl(mf) and 119879max(mf) are the manufacturervalues of the starting torque full load torque and maximumtorque respectively Also 119891

1 1198912 and 119891

3are error between

the calculated andmanufacturer value of the full load torquestarting torque and maximum torque respectively Also 119891

4

is error between the calculated andmanufacturer value of thefull load power factor

The objective function using aforementioned equations isdefined as follows

119865 = 11989121+ 11989122+ 11989123+ 11989124 (3)

3 Evolutionary Methods

The proposed HGAPSO method is a combination of the GAand PSO to form a hybrid algorithm This hybrid algorithmuses the benefits of the two well defined methods andproduces the better results In this section basic concepts ofthe GA and PSO and also HGAPSO are introduced

31 Genetic Algorithm Genetic algorithm is a computationalmodel and evolutionary process that solves optimizationproblems by imitating the behavior of populations duringgenerations and based on the theory of evolution It mimicsbiological evolution by using genetic operators [9] It assumesthat the solution of a problem is an individual and canbe represented by a set of parameters Genetic algorithminvestigates the search space from the points it has to bias thesearch towards the best point This algorithm is a stochasticsearch method and has shown that the answer is appropriatefor problems where there are many global minimums orsearch space is extensive A positive value generally calledfitness value is used to measure the degree of ldquogoodnessrdquo

Journal of Engineering 3

Iph RsjXs jX

998400

r

VphjXm

R998400

r

s

(a)

Iph Rth jXth jX998400

r

VphR

998400

r

s

(b)

Figure 1 (a) One phase steady-state equivalent circuit model of a three-phase induction motor (b)Thevenin equivalent circuit of inductionmotor

of the chromosome for solving the problem and this valueis closely dependent on its objective value The objectivefunction of a problem is an important source providing themechanism for evaluating the status of each chromosome Ittakes the chromosome as input and produces a number orlist of numbers such as objective value as a measure to thechromosomersquos performance This is a main link between thealgorithm and the system [10]

32 Particle Swarm Optimization The PSO is a stochas-tic optimization method which uses swarming behaviorsobserved in flock of birds In fact the PSO was inspired bythe sociological behavior associated with swarms The PSOwas developed by Kennedy and Eberhart in 1995 as a newheuristic method [11] Each particle in the PSO algorithm isa potential solution for the optimization problem and keepstrack of its coordinates in the problem space and tries tosearch the best position through flying in a multidimensionalspace which are associated with the best solution (called bestfitness) it has achieved so far called ldquopbestrdquo Another ldquobestrdquovalue called ldquogbestrdquo that is tracked by the global version ofthe particle swarm optimizer is the overall best value andits location is obtained so far by each particle in the swarmEach particle is determined by two vectors in119873-dimensionalsearch space the position vector and the velocity vector [12]Each particle investigates its search space through previousexperience its present velocity and the experience of theneighboring particles The PSO concept is the change in thevelocity of each particle toward its pbest and gbest positionsin each iteration In the PSO acceleration of each particle isweighted by a random term [13] The PSO is a history-basedalgorithm such that in each iteration particles use their ownbehavior associated with the previous iterations

33 Hybrid of Genetic Algorithm and Particle Swarm Opti-mization Since GA and PSO both work with a population ofsolutions combining the searching abilities of both methodsseems to be an excellent approach PSOworks based on socialadaptation of knowledge and all particles are considered to beof the same generation On the contrary GA works based onevolution from generation to generation so that the changesof individuals in a single generation are not consideredHowever GA and PSO have strengths and weaknesses [14]

In comparison with GA the information sharing mech-anism in PSO is significantly different In GA chromosomes

Start

Random population

Fitness evaluation of all individuals

Stopping criteria

Yes

Enhancement(PSO)

NoFind the best half (elites)

and discard others

New population (enhanced elites and offspring)

Offspring

Crossover and mutation

End Best individuals

Tournament selection

Figure 2 The block diagram of the HGAPSO algorithm

share information with each other so that whole populationmoves like a one group towards an optimal area

In PSO only ldquopbestrdquo and ldquogbestrdquo give out the informationto other particles It is a one-way information sharing mech-anism However PSO does not have genetic operators likecrossover and mutation On the contrary in PSO particlesupdate themselves with the internal velocity Also theyhave memory which is important for the algorithm Bymerging GA and PSO together the produced algorithm hasmemory and genetic operators like crossover and mutationConsequently the new algorithm avoids the weaknesses ofGA and PSO at the same time

Therefore in this paper GA and PSO merge togetherto benefit from the advantages of both genetic algorithmand particle swarm optimization This algorithm consists offour main operators enhancement selection crossover andmutation [15]

In Figure 2 the flowchart of the HGAPSO method isshown In each iteration of the algorithm the fitness valuesof all the individuals in the population are calculated Ifthe calculated fitness values are within the acceptable rangethe algorithm can be stopped Otherwise the top-half bestperforming ones are marked and named as elites Instead


Table 1 Original data of the test motor

Capacity (HP) 5Voltage (V) 460Current (A) 49252Frequency (Hz) 60Number of poles 4Full load slip 0021Starting torque (Nm) 1192629Maximum torque (Nm) 149082Full load torque (Nm) 196730Starting current (A) 831818Full load power factor 089

of reproducing these top individuals directly to the nextgeneration as GA does elites will be increased The enhance-ment operation tries to imitate the maturing phenomenon inthe nature where individuals will become more suitable tothe environment after learning knowledge from the societyFurthermore by using these enhanced elites as parents thegenerated offspring will achieve better efficiency than thosebred by original elites [16]

In theHGAPSO the GA operations are performed on theenhanced elites achieved using PSO In order to select parentsfor the crossover operation in the HGAPSO the selectionscheme is used Two enhanced elites are selected and theirfitness values are compared together to select the one withbetter fitness as a parent [16]

In the next step two offspring are created by applyingcrossover on the parent solutionsThe final step in the geneticoperator is mutation This step can generate a new geneticdescendant in the population to maintain the populationrsquosvariety in the society After performing the GA operators theoffspring and the enhanced elites from PSO the new popula-tion and their fitness values are evaluated and compared inorder to select the elites for the next generation

4 Simulation Results

To validate the proposed HGAPSO method for parameterestimation this algorithm is tested on a 5 HP three-phaseinduction motor in MATLABSimulink preset models TheHGAPSO results are compared with the original parametersof the MATLAB model The original data of the test motorare given in Table 1 Also a comparative study between theresults of the HGAPSO GA and PSO is done to verify theeffectiveness of the proposed HGAPSO method The errorsbetween the calculated and original values of the startingtorque maximum torque full load torque and full loadpower factor in three methods are given in Table 2 Thesimulation results which are given in Table 2 show that theHGAPSO has lesser error than GA and PSO and thus theaccuracy of the proposedHGAPSOmethod is better thanGAand PSO

010

20

40

60

80

100

120

Real curve using original dataEstimated curve using GA dataEstimated curve using PSO dataEstimated curve using HGAPSO data

Slip

Roto

r cur

rent

09 08 07 06 05 04 03 02 01

Figure 3 The rotor current versus slip curve using GA PSO andHGAPSO data

0

20

40

60

80

100

120

140

160

180

200

220


Torq

ue

01Slip

09 08 07 06 05 04 03 02 01

Figure 4 The torque versus slip curve using GA PSO andHGAPSO data

The steady-state equivalent circuit parameters obtainedusing HGAPSO GA and PSO methods for the test motorare presented in Table 3 The results show that all of theparameters obtained using HGAPSO are closer to originalparameters and the HGAPSO has lesser error than GA andPSO

The rotor current characteristics versus slip using param-eters obtained by the GA PSO and the HGAPSO are shownin Figure 3 It can be seen that estimated rotor current curve


Table 2 Starting torque maximum torque full load torque and full load power factor calculated by GA PSO and HGAPSO

Torque and power factor Original value GA PSO HGAPSOCalculated data Error () Calculated data Error () Calculated data Error ()

119879st 1192629 1240018 397 1210186 147 1192300 minus003119879max 149082 1540410 333 1511170 137 1491226 0027119879fl 196730 198227 076 198136 071 197877 058PFfl 089 091 225 091 225 090 112

Table 3 The results of the parameter estimation by GA PSO and HGAPSO

Parameters Original value GA PSO HGAPSOEstimated data Error () Estimated data Error () Estimated data Error ()

119877119904

1115 10291 minus77 11029 minus109 11229 0711198771015840119903

1083 10304 minus486 10351 minus442 10741 minus0821198831199041198831015840119903



0 10 20 30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Iterations100

Best

cost

times10minus3

Figure 5 Convergence diagram of GA

using parameters obtained by GA and PSO has differencecompared to the real curve while estimated curve usingparameters obtained by the HGAPSO is very close to thereal curve As shown in this figure accuracy of the proposedHGAPSO method is excellent

Also torque characteristics versus slip using parametersobtained by the GA PSO and the HGAPSO are shown inFigure 4 It can be seen that estimated torque curve usingparameters obtained by GA and PSO has a little differencecompared to the real curve while estimated curve usingparameters obtained by the HGAPSO is very close to realcurve

The performance of the optimization method in termsof the fitness value for GA PSO and HGAPSO is shown inFigures 5 6 and 7 respectively It can be seen that the fitnessvalue reduces over the iterations and converges to aminimum

0 10 20 30 40 50 60 70 80 902

3

4

5

6

7

8

Iterations100

Best

cost

times10minus3

Figure 6 Convergence diagram of PSO

value It should be noted that the convergence speed of theHGAPSO is faster than GA and PSO

5 Conclusion

In this paper hybrid of genetic algorithm and particle swarmoptimization method for parameter estimation of a three-phase induction motor using steady-state equivalent circuitmodel has been proposed This problem is formulated asa nonlinear optimization problem The feasibility of theproposedHGAPSOmethod is shown by evaluation on a 5HPpresetmodel of three-phase inductionmotor inMATLAB Byanalyzing the parameter estimation results it can be seen thatthe parameter estimation using HGAPSO gives better resultsthan GA and PSO The comparison between the HGAPSOGA and PSO results shows that the estimation errors using


0 10 20 30 40 50 60 70 80 902

3

4

5

6

7

8

Iterations100

Best

cost

times10minus3

Figure 7 Convergence diagram of HGAPSO

HGAPSO are comparatively lesser than those obtained usingGA and PSO Also the convergence speed of the HGAPSO isfaster than GA and PSO

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] K S Huang W Kent Q H Wu and D R Turner ldquoParameteridentification for FOC induction motors using genetic algo-rithms with improved mathematical modelrdquo Electric PowerComponents and Systems vol 29 no 3 pp 247ndash258 2001

[2] P Castaldi and A Tilli ldquoParameter estimation of inductionmotor at standstill with magnetic fluxmonitoringrdquo IEEE Trans-actions on Control Systems Technology vol 13 no 3 pp 386ndash400 2005

[3] FTherrien LWang J Jatskevich andOWasynczuk ldquoEfficientexplicit representation of AC machines main flux saturationin state-variable-based transient simulation packagesrdquo IEEETransactions on Energy Conversion vol 28 no 2 pp 380ndash3932013

[4] BOuyangD Liu X Zhai andWMa ldquoAnalytical calculation ofinductances of windings in electrical machines with slot skewrdquoin Proceedings of the 19th International Conference on ElectricalMachines (ICEM rsquo10) pp 1ndash6 September 2010

[5] V P Sakthivel R Bhuvaneswari and S Subramanian ldquoMulti-objective parameter estimation of induction motor using par-ticle swarm optimizationrdquo Engineering Applications of ArtificialIntelligence vol 23 no 3 pp 302ndash312 2010

[6] A I Canakoglu A G Yetgin H temurtas and M TuranldquoInduction motor parameter estimation using metaheuristicmethodsrdquo Turkish Journal of Electrical Engineering amp ComputerSciences vol 22 pp 1177ndash1192 2014

[7] M A Awadallah ldquoParameter estimation of inductionmachinesfrom nameplate data using particle swarm optimization and

genetic algorithm techniquesrdquo Electric Power Components andSystems vol 36 no 8 pp 801ndash814 2008

[8] D E Goldberg Genetic Algorithms in Search Optimization andMachine Learning Addison-Wesley 1989

[9] F Filho H Z Maia T H A Mateus B Ozpineci L M Tolbertand J O P Pinto ldquoAdaptive selective harmonic minimizationbased on ANNs for cascade multilevel inverters with varyingDC sourcesrdquo IEEE Transactions on Industrial Electronics vol60 no 5 pp 1955ndash1962 2013

[10] F J Lin and P K Huang ldquoRecurrent fuzzy neural network usinggenetic algorithm for linear induction motor servo driverdquo inProceedings of the 1st IEEE Conference on Industrial Electronicsand Applications (ICIEA rsquo06) pp 1ndash6 Singapore May 2006

[11] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 December 1995

[12] H Taghizadeh and M T Hagh ldquoHarmonic elimination ofcascade multilevel inverters with nonequal dc sources usingparticle swarm optimizationrdquo IEEE Transactions on IndustrialElectronics vol 57 no 11 pp 3678ndash3684 2010

[13] M Clerc and J Kennedy ldquoThe particle swarm-explosion sta-bility and convergence in a multidimensional complex spacerdquoIEEE Transactions on Evolutionary Computation vol 6 no 1pp 58ndash73 2002

[14] T Back and H P Schwefel ldquoAn overview of evolutionaryalgorithms for parameter optimizationrdquo IEEE Transactions onEvolutionary Computation vol 1 no 1 pp 1ndash23 1993

[15] C-F Juang ldquoA hybrid of genetic algorithm and particle swarmoptimization for recurrent network designrdquo IEEE Transactionson Systems Man and Cybernetics Part B Cybernetics vol 34no 2 pp 997ndash1006 2004

[16] K DebMulti-Objective Optimization Using Evolutionary Algo-rithms John Wiley amp Sons New York NY USA 2001

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RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



so that knowledge of good solutions is retained by allparticles whereas in GA previous knowledge of the problemis destroyed once the new population generates [5] Howeverboth methods have strengths and weaknesses It seems thata hybrid of the GA and PSO models could lead to furtheradvances Therefore in this paper GA and PSO mergetogether to use the benefits of both methods This algorithmis named as hybrid of genetic algorithm and particle swarmoptimization (HGAPSO) There have been many technicalpapers using evolutionary algorithm for parameter estima-tion but parameter estimation of an induction motor usingHGAPSO has never been presented by now

This paper uses some nameplate or manufacturer datafor problem formulation By using the proposed method thesteady-state equivalent circuit of the motor can be estimatedIn fact the optimization problem is formulated so that theerror between calculated data using the estimated parametersand manufacturer data is minimized

In the next sections the set of equations for problem for-mulation is introduced Also a short description of GA andPSO and a more detailed explanation of HGAPSO are pro-vided The validity of the proposed method is tested by usinga preset model of induction motor in MATLABSimulinkAlso the performance evaluation of the proposed methodis carried out by comparison between the results of theHGAPSO GA and PSO

2 Problem Definition

An induction motor can be modeled by using a steady-state equivalent circuit The parameter estimation problem isformulated as a least squares optimization problem so thatthe objective function is the minimization of the deviationbetween the estimated and the nameplate data The problemformulation for a three-phase induction motor is describedbelow

The problem formulation uses the manufacturer datasuch as the starting torque the full load torque themaximumtorque and the full load power factor The proposed methodis used to estimate the stator and rotor resistances thestator and rotor leakage reactances and the magnetizingreactance in the steady-state equivalent circuit of the motorIn Figure 1(a) the steady-state equivalent circuit model of athree-phase inductionmotor is shown It should be noted thatthe rotor parameters have been referred to as the stator sideAlso it is assumed that the core-losses are negligible

For problem formulation Thevenin equivalent circuitproposed in IEEE standard 112 is used as shown in Figure 1(b)The problem formulation and objective function are as fol-lows

1198911=1198701199051198771015840119903119904 [(119877th + 119877

1015840

119903119904)2

+ (119883th + 1198831015840

119903)2

] minus 119879fl (mf)

119879fl (mf)

1198912=1198701199051198771015840119903 [(119877th + 119877

1015840

119903)2

+ (119883th + 1198831015840

119903)2

] minus 119879st (mf)

119879st (mf)

1198913=1198701199052 [119877th + radic119877

2

th + (119883th + 1198831015840

119903)2

] minus 119879max (mf)

119879max (mf)

1198914

=cos (tanminus1 ((119883th + 119883

1015840

119903) (119877th + 119877

1015840

119903119904))) minus 119901119891fl (mf)

119901119891fl (mf)

(1)

where 119877119904is the stator resistance 1198771015840

119903is the rotor resistance

which has been referred to as the stator side 119883119904is the stator

leakage reactance 1198831015840119903is the rotor leakage reactance which

has been referred to as the stator side119883119898is the magnetizing

reactance and 119904 is the slip Also it is assumed that119883119904is equal

to1198831015840119903 The other variables are introduced as follows

119881th =119881ph119883119898

119883119904+ 119883119898

119877th =119877119904119883119898

119883119904+ 119883119898

119883th =119883119904119883119898

119883119904+ 119883119898

119870119905=31198812th120596119904

(2)

where 119881ph is input phase voltage 119881th is Thevenin voltage119877th and119883th are Thevenin resistance andThevenin reactancerespectively 120596

119904is angular velocity and 119870

119905is the constant

coefficient Also ldquomfrdquo index is used for themanufacturer dataso that 119879st(mf) 119879fl(mf) and 119879max(mf) are the manufacturervalues of the starting torque full load torque and maximumtorque respectively Also 119891

1 1198912 and 119891

3are error between

the calculated andmanufacturer value of the full load torquestarting torque and maximum torque respectively Also 119891

4

is error between the calculated andmanufacturer value of thefull load power factor

The objective function using aforementioned equations isdefined as follows

119865 = 11989121+ 11989122+ 11989123+ 11989124 (3)

3 Evolutionary Methods

The proposed HGAPSO method is a combination of the GAand PSO to form a hybrid algorithm This hybrid algorithmuses the benefits of the two well defined methods andproduces the better results In this section basic concepts ofthe GA and PSO and also HGAPSO are introduced

31 Genetic Algorithm Genetic algorithm is a computationalmodel and evolutionary process that solves optimizationproblems by imitating the behavior of populations duringgenerations and based on the theory of evolution It mimicsbiological evolution by using genetic operators [9] It assumesthat the solution of a problem is an individual and canbe represented by a set of parameters Genetic algorithminvestigates the search space from the points it has to bias thesearch towards the best point This algorithm is a stochasticsearch method and has shown that the answer is appropriatefor problems where there are many global minimums orsearch space is extensive A positive value generally calledfitness value is used to measure the degree of ldquogoodnessrdquo


Iph RsjXs jX

998400

r

VphjXm

R998400

r

s

(a)


r

VphR

998400

r

s

(b)






Start

Random population


Stopping criteria

Yes

Enhancement(PSO)


and discard others


Offspring

















010

20

40

60

80

100

120


Slip

Roto

r cur

rent

09 08 07 06 05 04 03 02 01


0

20

40

60

80

100

120

140

160

180

200

220


Torq

ue

01Slip

09 08 07 06 05 04 03 02 01










119877119904

1115 10291 minus77 11029 minus109 11229 0711198771015840119903




0 10 20 30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Iterations100

Best

cost

times10minus3





0 10 20 30 40 50 60 70 80 902

3

4

5

6

7

8

Iterations100

Best

cost

times10minus3



5 Conclusion



0 10 20 30 40 50 60 70 80 902

3

4

5

6

7

8

Iterations100

Best

cost

times10minus3





References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Iph RsjXs jX

998400

r

VphjXm

R998400

r

s

(a)


r

VphR

998400

r

s

(b)






Start

Random population


Stopping criteria

Yes

Enhancement(PSO)


and discard others


Offspring

















010

20

40

60

80

100

120


Slip

Roto

r cur

rent

09 08 07 06 05 04 03 02 01


0

20

40

60

80

100

120

140

160

180

200

220


Torq

ue

01Slip

09 08 07 06 05 04 03 02 01










119877119904

1115 10291 minus77 11029 minus109 11229 0711198771015840119903




0 10 20 30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Iterations100

Best

cost

times10minus3





0 10 20 30 40 50 60 70 80 902

3

4

5

6

7

8

Iterations100

Best

cost

times10minus3



5 Conclusion



0 10 20 30 40 50 60 70 80 902

3

4

5

6

7

8

Iterations100

Best

cost

times10minus3





References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















010

20

40

60

80

100

120


Slip

Roto

r cur

rent

09 08 07 06 05 04 03 02 01


0

20

40

60

80

100

120

140

160

180

200

220


Torq

ue

01Slip

09 08 07 06 05 04 03 02 01










119877119904

1115 10291 minus77 11029 minus109 11229 0711198771015840119903




0 10 20 30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Iterations100

Best

cost

times10minus3





0 10 20 30 40 50 60 70 80 902

3

4

5

6

7

8

Iterations100

Best

cost

times10minus3



5 Conclusion



0 10 20 30 40 50 60 70 80 902

3

4

5

6

7

8

Iterations100

Best

cost

times10minus3





References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















119877119904

1115 10291 minus77 11029 minus109 11229 0711198771015840119903




0 10 20 30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Iterations100

Best

cost

times10minus3





0 10 20 30 40 50 60 70 80 902

3

4

5

6

7

8

Iterations100

Best

cost

times10minus3



5 Conclusion



0 10 20 30 40 50 60 70 80 902

3

4

5

6

7

8

Iterations100

Best

cost

times10minus3





References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 10 20 30 40 50 60 70 80 902

3

4

5

6

7

8

Iterations100

Best

cost

times10minus3





References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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