application of ant colony optimization algorithm for...

International Journal of Mechatronics, Electrical and Computer Technology

Vol. 4(13), Oct, 2014, pp. 1674-1690, ISSN: 2305-0543

Available online at: http://www.aeuso.org

© Austrian E-Journals of Universal Scientific Organization

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Application of Ant Colony Optimization Algorithm for Optimal

Design of Squirrel Cage Induction Motor

Behzad Alizadeh1* and S. Asghar Gholamian2

1Master Student, Babol University of Technology

2Assistant of Electrical, Babol University of Technology

*Corresponding Author's E-mail: [email protected]

Abstract

Low efficiency and high volume are one of the major disadvantages of induction

motors. In recent decades, for determined motor power output, the motor dimension is

reduced, and so efficiency is the upside. The main purpose of design of an induction motor

is obtaining the physical dimensions of all parts of the motor to satisfy the customer. This

paper proposes the optimal design of a three-phase induction motor for increased efficiency

and reduces the volume. In this paper, the motor has been optimized by ant colony

optimization algorithm because it offer maximum efficiency and minimum size. A multi-

objective optimization is performed in this paper for optimum dimensions of the motor

using ant colony optimization algorithm.

Keywords: Ant colony algorithm, Optimization, Induction motor, Squirrel cage.

1. Introduction

Two kinds of secondary windings of rotor in induction motors are wound-rotor and

squirrel cage rotor. In recent years, squirrel cage Induction motors used most widely in

industry. Low efficiency, high volume, low power factor and high startup current is the

major disadvantages of this type of motor. by small changes in rotor, the startup

characteristics of the motor can be significantly improved [1].This motor due to the ease of

operation, high reliability, cost-saving, easy to work and maintenance, sturdy structure and

mailto:[email protected]


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low noise are used more than other motors. The role of this motor in industry is increased

with the expansion of controlled speed drives [4]. In the last decades for fixed output

power, the volume is reduced thereby the efficiency the trend is upward. The main purpose

of induction motor design is getting physical dimensions of all parts of this machine for

customer satisfaction. a design requires the following: Dimensions of the stator core and its

winding details, design of the rotor detail and Executive features. Optimum design of

squirrel cage induction motor has gained great attention in recent years [11].

For example, Similar works have been done in this case is as : a systematic optimal design

algorithm to design the shape of rotor slot to get a special speed-torque characteristic in

three-phase squirrel cage induction motor for the application to motor operated valve

actuator. The developed method consisted of three steps: design based on equivalent circuit

method utilizing multi-objective formulation, selection of the strongly influential geometric

parameters of rotor slot and precise design based on FEM. The validity of the suggested

design method has demonstrated through applications to rotor slot design of three-phase

induction motor to achieve a NEMA class D speed-torque characteristic. Through design

applications with two types of rotor slot, the developed design method is proven to give an

optimal shape of rotor slot for a desired speed-torque characteristic. It is found that the

multi-objective optimization algorithm based on ECM, even by itself, is very effective for

an optimal shape design of rotor slot to get a desired speed-torque characteristic. In This

paper is used the Gaussian multi-objective particle swarm optimization algorithm to get a

proper Pareto-front for achieving the best characteristic of the motor [7].

In the other paper about the optimization design of the squirrel cage induction motor, it is

presented a novel method for multi objective design and optimization of three phase

induction machines. In this case, the proposed method had more efficient than traditional

design methods because it found an optimal design with no heuristic approaches or design

iterations. The optimal design results are verified by FEA. The results provided useful


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insight for the drive system designers. PSO and GA algorithms has compared in this paper

with the aim of finding which algorithm is more suitable for motor design optimization.

The results indicated the PSO and GA both had the ability to find the correct optimal

solution, but PSO had a better performance in finding the global optima. Also, in terms of

the computational efficiency, PSO had a lower performance degrading with a smaller

population size and higher robustness to its running coefficients. The comparison results

provided that PSO should be preferred over GA particularly when computational tine is a

limiting factor [10].

In the other work done in 2013, the impact of the rotor slot number selection on the

induction motors is examined as firstly, analytical equations reveal the spatial harmonic

index of the air gap magnetic flux density, connected to the geometrical features and the

saturation of the induction motor then, six motors with different rotor slot numbers are

simulated and studied with FEM. the stator was identical in all motors. the motors are

examined under time-harmonic analysis at starting and at 1440 rpm. their electromagnetic

characteristics, such as electromagnetic torque, stator current, and magnetic flux density,

are extracted and compared to each other. the analysis reveal that the proper rotor slot

number selection has a strong impact on the induction motor performance [8].

in the other work with title of Establishment of the optimal constructive dimensions for the

asynchronous motors with rotor in cage, it indicates that The optimal design solves the

actual problems of the producers of electrical machines like reducing the consumption of

energy, obtaining of superior operating characteristics and also perspective demands

regarding the diminishing of the operating cost. Thus to the optimized motor reported to the

real one, the total cost decreased by %9.04, and if compared with unfavorable variant, it

follows a decrease of %26.5 [3].

Also in the other work is examined using of the parameterisation in the study of the

geometric redesign of the rotor slots on a cage induction motors so that has been described


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a strategy to parameterise geometrically the rotor slot shape. A magnetodynamic model of

FEM was developed in order to obtain new performance curves. the results was obtained

from an industrial 90 KW , 4- Pole three double squirrel cage motor in order to improve

performance of the motor at starting by redesigning the rotor slot shape. the described

strategy shows an easy way to implement the redesign of the rotor slot shape without

manufacture additional cost. In this work, has outlined the capability of the actual

computing tools based on 2D finite elements coupled to electrical circuit model taking into

account 3D effects, as well as the external supply voltage sources [11].

Also the other paper was focused on the method on improving squirrel cage induction

motor efficiency. In this work, The first discussion presented the main importance of

efficient motors and its drive systems. These are partly conceptual, partly concerning

circuit topology and current commutation technique. The second discussion optimization of

SCIM efficiency using intelligent techniques which are of particular interest. The third

discussion describes the energy efficiency of SCIM standards and most effect motor

parameters on SCIM efficiency [6].

The other paper focused on design, development of Six Phase Squirrel Cage Induction

Motor and its Comparative Analysis with Equivalent Three Phase Squirrel Cage Induction

Motor Using. it shown that the torque of six phase induction motor is more and found to be

approximately more than equivalent three phase motor. Also Efficiency of six phase

induction motor is more than that of equivalent three phase induction motor [13].

In this paper, it is presented an optimal design of three-phase squirrel cage induction motor

for having optimal size and efficiency. the aim of this paper is to optimize a sample of such

motor. For this purpose, ant colony optimization algorithm is applied which is a new

optimization algorithm and it has not been used for optimum design of such motors yet.

Optimization is performed with an objective function which is a combination of maximum

efficiency and minimum size. The rest of paper is classified as follow:


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Firstly, design process is presented in section 2. Then, a case study is presented for further

investigation of the design methodology. After that, optimum design of three-phase squirrel

cage induction motor is carried out in section 3. Finally, paper is concluded.

2. Squirrel cage induction motor design

The motor rating, stator current in phase, number of stator slots, air gap flux, turns

of stator winding and stator induced voltage in phase is calculated as follows [1,4]:

VA (1)

VA (2)

A

(3)

(4)

wb

(5)

(6)

v (7)

where S is the motor rating in voltamperes, Pout is the motor output in wattage, η is

the efficiency, PF is power factor, B av is magne`tic flux density, ac is the specific

electrical loading in amperes per meter, kws is winding factor, L is the motor length in

meters, D is the stator bore diameter in meters, ns is the rated speed in revolutions per

second, Is is the stator current in phase, Vph is the stator voltage in phase in volts, P is

number of poles, q is the number of stator slots per pole per phase, Ss is the number


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of stator slots, φ is air gap flux/p, L i is the real length of the motor in meters, τps is the

stator pole pitch, Nph is number of stator turns/phase, Es is the stator induced voltage

in phase in volts and f is frequency in hertz [1,4].

2.1. Stator slot design

Using the following equation, it obtained the area of stator slot. Current density in the

stator windings of a standard induction motor can be considered from 3 to 6 Ampere/mm2

[1].

mm2 (8)

m2

(9)

The small induction motors use the semi-closed slots. fill factor of this slot is considered

about 0.4. In the above equations, Zss is the number of stator conductors, Acs is total stator

copper area, Kfill is fill factor of stator slot, as is the conductor cross-section of the stator

and Ass is the stator slot area. dss1 & dss2 are the Stator slot depths in two parts 1 and 2, so by

using the following equations, the depth of each stator slot can be achieved [1,2]:

[

( )( )] ( ) m

(10)

In the above equation, w2ss is width of bottom of stator slot, wsd is width of stator

trapezoidal slot, and dss stator slot depth [7]. Using the following equation, the

resistance of stator winding / phase is achieved [1,5]:

Ω (11)


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In the above equation, Lmts is medium length of double-layer winding. ρs is Specific

resistivity of stator conductor and rs resistance of stator in phase[1,9].

2.2. Rotor design

Satisfactory and acceptable performance of the machine is realized when the

number of rotor slot is 15 to 30 percent smaller than the number of stator slots. By

reference to the total resistance of the rotor to the stator, the following relations are

used [1, 5]:

Ω

(12)

Ω

(13)

Ω

(14)

In the above equations, Sr is number of rotor slots, ab is sectional area of rotor

bars, ρr is rotor specific resistance, rb is total resistance of the cage bars, aer is

sectional area at the end of each loop, Der is diameter end loop resistance, rer is

resistance of both end rings, KR is correction factor ring and r'r is total of cage

winding resistance that is referenced to stator part. slot depth and thickness of the

rotor core is obtainable from the following relations [1, 4]:

m

(15)

(16)

In the above equations, D'r is inner diameter of the rotor, dsr is rotor slot depth, w2sr is

width of the rotor slot, dcr is rotor core thickness and w2sr is width of the bottom slot of the


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rotor. Figure 1 shows the motor rotor slot. To find the volume of a squirrel cage induction

motor, the following equation is used [4,2]:

(17)

Figure 1: The shape of the rotor slot [8]

2.3. Losses and Efficiency calculation

Total losses in the motor are obtained using the following formulas [2,4]:

W

(18)

( )

(19)

(20)

(21)

In the above equations, PCU,b is copper losses in the rotor bars , PCU,er is total losses of the

copper end rings, Kwv is windage losses factor, Pwv is windage losses , Pstray is additional

losses , Ph.cs is losses of stator core hysteresis cycle , Pe.cs is stator core eddy current losses ,


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Ph.ts is hysteresis cycle losses in stator teeth, Pe.ts is stator teeth eddy current losses, Pno load is

no-load losses and Ploss is the total motor losses [4]. After calculating the total losses of

squirrel cage induction motor, the motor efficiency can be achieved using the following

equation. As shown Figure 2, Flowchart of the proposed design for Squirrel Cage Induction

Motor [9].

(22)

3. Optimization

3.1. Ant colony algorithm

Ant colony algorithm is inspired by studies and observations on the ant colony. these

studies have shown that ants are social insects that live in colonies and their behavior is in

order to further the survival a part of it the colony survival. one of the most important and

interesting ants ' behavior, their behavior for finding the shortest path between food

sources. This type of behavior of ants is an intelligent that have concentrated scientists

today. Termites indicate itself exert specific activities for building of nests. Initially,

hundreds of termites moving randomly. Each termite Upon reaching the small space above

the ground will begin salivating and his saliva soaked their soil . Therefore, make small

balls of soil with their saliva . Despite the completely random nature of this behavior, the

result is a somewhat regular basis [11].

At this stage in a limited area of a small mound of dirt miniature balls soaked in saliva is

formed. After this , all miniature hills cause the termites to treat other symptoms. In the

hills, as a sign of termites act. Upon reaching the hills, each termite will start producing

balls with its saliva with high energy. This causes the miniature hills become a kind of

column. This behavior continues until it reaches a certain height of each column. Now

termites show in the third act from itself. If not to be other column close of the current


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column, leave this column immediately Otherwise they start connecting columns and

building nests. It can be observed the behavior differences of the Social intelligence of

human and the intelligence of the masses in the nest building [11].

In this article, the fourth parameters for the optimization are the number of stator poles,

electric and magnetic special loading and the ratio of stator length to diameter. the

flowchart of this algorithm has shown in figure 3.

Figure 2: The design flowchart of squirrel cage induction motor [1,7]


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3.2. Results of optimization

In this paper, for instance, a 3700-watt squirrel cage induction motor 50 Hz and rated

voltage of 400 V is applied. As mentioned, the objective function of this paper is maximum

efficiency and minimum size. ACO algorithm parameters are given in Table 1. the results

of optimization of this motor are given in Table 2. In Figures 4 to 6 is shown the optimal

function changes in this algorithm. Then The changes in various parameters of the motor

with optimized functions are shown in Table 3.

So Fitness 1 : F1 = η , Fitness 2 : F2 = Vol and Fitness 3 : F3 = αF1+βF2 that α and β

objective functions factors for achieving to the optimal solution. The parameters of the

algorithm are as follows:

Table 1: ACO parameters

α β ni np ne q z

1 1 45 50 15 0.7 1

In above table, ni is the number of iteration, z is the standard deviation factor, q is

intensification factor, np is the number of population ants, ne is the number of elite ants and

α and β are the coefficients of Simultaneous optimization of size and efficiency in the ant

colony optimization for normalization purpose [12].


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Figure 3: Results of optimization with various objective functions [11]

Table 2: results of optimization [12]

Optimal function Efficiency (%) Volume

(Cm3)

The Efficiency function 88.57 2329

The volume function 86.26 2189

Efficiency & volume function 87.42 2254


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Figure 4: Changes in Efficiency of the ACO algorithm

Figure 5: Changes in volume of the ACO algorithm


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Figure 6: Simultaneously Changes in volume & Efficiency of the ACO algorithm

Table 3: Specifications of the engine to optimize with separation of the objective functions

parameter Volume & Efficiency volume Efficiency

Bav (T) 0.6 0.6 0.6

ac (A/m) 24800 25000 24798

u 1.42 0.8 1.665

p 2 2 2

Ss 24 24 24

Sr 18 18 18

L (mm) 219.3 189.2 243.63

Li (mm) 208.3 179.7 231.4

D (mm) 55.93 60.2 53

tps (mm) 87.85 94.6 83.3

φ (wb) 0.011 0.0102 0.0116

Zss (turns) 960 1008 888

Nph (turns) 160 168 148


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Es (V) 370.3 370.2 371.1

Lg (mm) 0.4215 0.4134 0.4274

ωts (mm) 4.05 4.6 3.7

dcs (mm) 15.4 15.8 13.9

dss (mm) 14.64 14.8 14.4

ω2ss (mm) 8.85 9.3 8.5

Lmts (m) 0.81 0.7866 0.8543

rs (Ω) 2.543 2.555 2.444

Dr (mm) 55.08 59.4 52.21

rb (Ω) 0.0028 0.0023 0.0034

Der (mm) 49.93 54.2 47

rer (Ω) 0.00008 0.00008 0.00008

R ‘r (Ω) 2.392 2.167 2.46

rm (Ω) 2001 1972 2044

ωtr (mm) 3 3.2 2.8

dsr (mm) 6.8 6.7 7

dcr (mm) 10.71 12 10

ω2sr (mm) 6.6 7.1 6.3

ω1sr (mm) 0.4 0.6 0.3

X0 (Ω) 1.407 1.671 1. 142

Xz (Ω) 0.0001 0.0001 0.0001

X 1 (Ω) 2.643 2.813 2.341

X’r (Ω) 0.772 0.7359 0.8931

Xm (Ω) 133.9 142.9 122


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Conclusion

The main goal of this paper is optimal design of a three-phase squirrel cage induction

motor to increase efficiency and reduce the volume. For this purpose, the motor has been

optimized by ant colony optimization algorithm offers maximum efficiency and minimum

size. Design procedure was examined with a case study. when the efficiency is the

objective function, the optimization design leads to a induction motor with 88.57% and

when the volume is the objective function, the optimization design leads to a induction

motor with 2189 cobic meters and when the both of size and efficiency are the multi

objective function, it indicates 1.15% Increase in total loss and 2.97% Increase in the motor

volume in the ant colony optimization. Future works may be devoted to the optimization of

squirrel cage induction motor with new optimizing algorithm or with other objective

functions.

References

[1] Essam S.Hamdi, "Design of small electrical machines", wiley publisher, (1994).

[2] Fernando j.t.e. Ferreira and Aníbal T. de Almeida, "Induction motor downsizing as a low-cost strategy to

save energy", Journal of Cleaner Production 24,(2012), pp. 117-131.

[3] Ion vlad,Aurel campeanu,Sorin enache and Gabriela petropol, "Establishment of the optimal constructive

dimensions for the asynchronous motors with rotor in cage", No. 35,(2011), ISSN 1842-4805.

[4] A. K. Sawhney, "A Course in Electrical Machine Design", CBS publisher, (1984).

[5] Jacek F. Gieras, Fellow, IEEE and Juha Saari, "Performance Calculation for a High-Speed Solid-Rotor

Induction Motor" , IEEE transactions on industrial electronics, vol.59, no. 6,( 2012).

[6] Ramdan Razali, Ahmed N Abdalla1, Ruzlaini Ghoni1 and C. Venkatases haiah, "Improving squirrel cage

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1129 - 1140.

[7] Dianhai Zhang, Chang Soon Park and Chang Seop Koh, "A new optimal design method of rotor slot of

three-phase squirrel cage induction motor for NEMA class D speed-torque characteristic using multi-objective

optimization algorithm", IEEE transactions on magnetics, Vol. 48, No. 2, (2012).


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[8] Konstantinos N. Gyftakis and Joya Kappatou, "The Impact of the Rotor Slot Number on the Behaviour of

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[9] Swati sharma, Vijay Bhuria and Divya rai, "Efficiency Optimization technique for Induction Motor with

implementation of Fuzzy Logic", Volume 2, Issue 5, (2012), ISSN 2250-2459.

[10] Yao duan. Member, IEEE, and Ronald G. Harley, Fellow, IEEE, "A Novel Method for Multiobjective

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[11] R.H. Engelmann and W.H. Middendorft, "Handbook of Electric Motors", New York, Marcel Dekker,

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[12] Marco Dorigo and Thomas Stützle, Ant Colony Optimization, A Bradford Book The MIT Press

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Massachusetts Institute of Technology.

[13] Dr. Archana Nanoty , Dr. A.R.Chudasama, "Design, Development of Six Phase Squirrel Cage Induction

Motor and its Comparative Analysis with Equivalent Three Phase Squirrel Cage Induction Motor Using Circle

Diagram",International Journal of Emerging Technology and Advanced Engineering, Volume 3,(2013), Issue 8.

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