Power Density Paper

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Genetic Algorithm Based Power Density

Optimization of Radial Flux PMBLDC motorAmit N. Patel1, Nirav Patel2, Pranay Patel2 Institute of Technology, Nirma University, Ahmedabad

[email protected] [email protected] 2 [email protected]

Abstract — This paper presents Genetic Algorithm based

optimal design procedure for Radial flux PMBLDC motor.

Fitness function considered for the algorithm is power

density of motor. Power density of the motor is output

apparent power per unit volume of the motor. Aim is to

maximize the power density using GA based optimization

technique. Air gap flux density (Bg), Slot loading (Is),

Length of air gap (lg), Aspect ratio (Ar) and Split ratio (Sr)

are selected as design variables. At the end, FEM (Finite

Element Method) is used to validate optimized design

obtained from the algorithm.

Keywords —

Genetic Algorithm (GA), Finite Element

Method (FEM), Radial flux PMBLDC motor, Computer

Aided Design (CAD).

I. I NTRODUCTION

Permanent Magnet Brushless DC (PMBL DC) motors have

become popular because of various improvements made on

permanent magnets, power electronic devices and increasing

need to develop cheaper, lighter and energy efficient motors.

PMBLDC motors are used in selected areas of industry where

high efficiency, less weight and desired performance are

strongly required. PMBLDC motor designed using

conventional design procedures may not give desired

performance. However, performance of such motors can be

enhanced using design optimization techniques. In this paper,

2.2 kW, 230 V, 1450 rpm radial flux PMBLDC motor isselected to illustrate GA based design optimization technique.

At first, motor is designed using developed computer aided

design (CAD) program [4]. Then, motor design is optimized

using GA based optimization process [3] [7]. At last, FEM

(Finite Element Method) is used to verify obtained optimized

design.

II. DESIGN OF R ADIAL FLUX PMBLDC MOTOR

Design process of radial flux PMBLDC motor includes

main four steps i.e. calculation of main dimensions, statordesign, rotor design and calculation of performance

parameters [1] [2]. Flow chart of CAD program for designing

the motor is shown in Figure1. It contains all the design stagesstated above. In addition to that, two correction loops are

introduced in the program. Inner loop is for correcting

assumed air gap flux density (Bg (assumed)) so that error between

calculated Bg and Bg (assumed) is within tolerable limit (e1).

Similarly, outer loop is inserted to reduce the difference (e 2)

between calculated efficiency (η) and assumed initial

efficiency (ηint).

FIG.1 Flowchart of CAD of Radial Flux PMBLDC motor

Stacking factor (K st), winding factor (K w), stator teeth

flux density (Bst), stator yoke flux density (Bsy), rotor yoke

flux density (Bry), leakage factor (K l), and specific iron losses(Wsi) are various assumed parameters considered in CAD

program.

Accept user inputs for motor rating, type of material, fixed

parameters and assumed initial efficiency (ηint)

Calculate main dimensions

Design of stator: stator slot, stator coreand winding dimensions,

Calculate length of magnet (lm),Design of rotor: rotor core, magnet

size

Calculate air- gap flux density (Bg)

Calculate ΔBg = Bg - Bg (assumed)

Is

ΔBg < e1?

Increase

lm

Decrease

ηint

Calculate performance parameters: phaseinductance, resistance, losses, weight and effi. (η)

Calculate Δη = η – ηint

Is

Δη < e2?

End

Yes

Start

No

Yes

No


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Bg Is lg Ar Sr Fitness value

FIG. 2 String representation

III. GENETIC ALGORITHM

GA is one of the most powerful and reliable optimization

tools which is used in various engineering design problems.

This technique uses Darwin’s principle “Survival of the

fittest” to optimize particular fitness function. In figure 2

string representation is shown. It contains one value from each

design variable and fitness value calculated from those

variables. Several strings combine together to form a

population. Five design variables are selected with appropriate

range for algorithm.

Air gap flux density (B g ): 0.5-0.9 T

Electrical slot loading ( I s): 100-400 ALength of air gap (l g ): 0.3-1 mm

Motor aspect ratio ( Ar ): 0.3-1.4

Motor split ratio (Sr ): 0.3-0.7

The method is further divided into four operators that are

explained as follows and flowchart for the same is shown infigure 3.

A. Generate population

This operator randomly generates population from available

ranges of design variables. Each chromosome in the

population is randomly generated to ensure diversity within

the population. Only one of the strings from the entire

population is taken from the initially developed CAD

program.

B. Selection The string which has highest value of objective function

is assigned fitness “2”, others are given “1” and st ring withlowest value is given “0” fitness. String with lowest fitness

value is discarded from the population and string with highest

fitness is retained with multiple copies.

C. Crossover

This operator interchanges two different strings from particular population at random and this leads to generation of

two new different strings. In other words, it creates diversity

in population though there are multiple copies of same strings.

D. MutationMutation operator brings sudden and random changes in

a string selected at random in given population. This operatorsis incorporated in algorithm because in natural selection

process, mutation sometimes brings positive change leading to

generation of better string.

IV. POWER DENSITY OPTIMIZATION

In this optimization process, power density of the motor is

considered as fitness function for GA. Power density of motor

is output power of motor per unit volume. At first, only two

design variables Bg and Is are considered and optimized values

FIG. 3 Flowchart for main Genetic algorithm.

TABLE 1 Optimum power density of designed motor

Design variables Optimum Power Density

(W/m3) x 106

Bg ,Is 1.3134

Bg ,Is, lg 1.3259

Bg ,Is, lg, Ar 1.3463

Bg ,Is, lg, Ar, Sr 1.3725

TABLE 2 Optimized design parameters

Design variable Optimized Value

Air gap flux density B g (T) 0.82

Electrical slot loading I s (A) 294

Length of air gap l g (mm) 0.6

Motor aspect ratio Ar 0.68

Motor split ratio Sr 0.55

of variables as well as power density is found out. Then no. ofdesign variables are increased and same process is carried out.

From the result (Table 1) it is observed that as no. of design

variables increase optimum power density also increases.

Table 2 shows optimum values of design variables. Figure 4shows plot of power density versus no. of generations.Comparison of various flux densities and average motor

torque for CAD and GA based designs is shown in Table

3.Optimum design parameters obtained from GA are used to

carry out FEM analysis in order to validate optimized design.

Results obtained from FEM are then compared with GA

results. Figure 5 shows per unit relative comparison of bothGA and FEM results for 2.2 kW motor. Figure 6 shows flux

density plot of designed PMBLDC motor.

Start

Accept user inputs for No. of generations and population size

Generate initial population from

given range of design variables

Carry out selection process on population

Carry out crossover process on population

Carry out mutation process on population

Algorithmending

criteria

No

End

Yes


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FIG. 4 Power Density v/s no. of generations

TABLE 3 Comparison of CAD and GA based designs

CAD based

design

GA based

designCAD FEM GA FEM

Average Torque(N-m) 14.48 14.4 14.48 14.5

Air gap flux density(T) 0.73 0.76 0.78 0.795

Stator core flux density(T) 1.3 1.4 1.3 1.45

Stator teeth flux density(T) 1.8 1.86 1.8 1.9

Rotor core flux density(T) 1.1 1.16 1.1 1.15

.

FIG. 5 Comparison of GA and FEM result with respect to CAD result

FIG. 6 Flux density profile of designed motor

V. CONCLUSION

Design optimization procedure of radial flux PMBLDC

motor is presented in this paper using Genetic Algorithm.Fitness function taken for GA is power density of the motor.

Aim is to maximize power density up to possible value.

Maximum power density indicates that motor will run at

maximum power with least volume. Finite element method

(FEM) was carried out to confirm the methodical optimized

design. Results of FEM indicated that the results of analytical

optimization agree with those obtained by FEM.

VI. R EFERENCES

1. D.C. Hanselman , Brushless Permanent Magnet

motor design. New York, McGraw-Hill, 1994.

2. J.R.Handershot and T.J.E Miller , Design of Brushless

Permanent Magnet motors, Oxford, U.K, 1994.

3. Reza Ilka, Ali Roustaei Tialki, Hossein Asgharpour-

Alamdari, Reza Baghipour, “Design optimization of

Permanent Magnet-Brushless DC motor using Elitist

Genetic Algorithm with Minimum loss and Maximum

Power Density”, IJMEC, January-2014.

4. Parag R. Upadhyay and K.R.Rajagopal, “FE analysis

and CAD of Radial Flux Surface Mounted Permanent

Magnet Brushless DC Motors”, IEEE Transactions

on Magnetics, vol.41, no. 10, October 2005. 5. Parag R. Upadhyay and K.R.Rajagopal , “Genetic

Algorithm based design optimization of permanentmagnet brushless dc motor”, Journal of applied

physics 97,10Q516 (2005) 6. N. Bianchi, S. Bolognani, “Brushless DC motor

design: an optimization procedure based on genetic

algorithms”, in Proc. International Conference on

Electrical Machines and Drives, UK, 1997, pp. 16-20.

7.

J.L. Hippolyte, C. Espanet, D. Chamagne, C. Bloch,

and P. Chatonnay, “Permanent Magnet Motor

Multiobjective Optimization Using Multiple Runs Of

An Evolutionary Algorithm”, 2008 IEEE Vehicle

Power and Propulsion Conference, Harbin, China.

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