FUZZY AND ANT COLONY OPTIMIZATION BASED HYBRID SOLUTION STRATEGY FOR OPTIMAL DESIGN OF INDUCTION MOTOR

118

FUZZY AND ANT COLONY OPTIMIZATION BASED

HYBRID SOLUTION STRATEGY

FOR OPTIMAL DESIGN OF INDUCTION MOTOR

C.Pitchai (Assistant Professor) P.A.Prassath (Assistant Professor)

Department of Electrical & Electronics Engineering Department of Electrical & Electronics Engineering A.S.L.Pauls College of Engineering and Technology A.S.L.Pauls College of Engineering and Technology Coimbatore, India Coimbatore, India

[email protected] [email protected]

Abstract: Design optimization of an induction motor is considered as a nonlinear multivariable constrained optimization problem. A set of twelve basic variables is identified and suitable constraints are imposed to meet the requirements of the machine. Continuous attempts have been made in the past to update the design of induction motors with a view to improve the performance characteristics and/or to reduce the cost. However, most of these attempts were basically of trial and error type in which improvements in design owed much to professional experience than to mathematical analysis. The advent of present generation of digital computers with tremendous computing rate and their ability to carry out logical decisions for facilitating the use of advanced optimization techniques in the design of electrical machines and the optimization is achieved through ant colony optimization.

Keywords:Induction motor, optimal design, ant colony optimization, low-cost implementation.

1.Introduction

:

About half of all electricity produced

globally is used in electric motors. Among the available motors, inductions motors, particularly the squirrel cage type is characterized by its simplicity, robustness and low cost, which has always made it very attractive and it has therefore captured the leading place in agricultural, domestic and industrial sectors. Electric motors have a significant impact on the environment because of the large energy flows. If the motors are poorly designed or used inefficiently, the increased losses in the motors further increase the overall power demand besides polluting the environment through additional burning of fuel. Environmental threats give electrical engineers a good reason for designing new and efficient electric motors. Even a small efficiency improvement can produce very large saving across the country and hence their design assumes great importance [1]. Basically, the design involves calculating the dimensions of various components and parts of the machine, weights, material

specifications, output parameters and performance in accordance with specified international standards. The calculated parameters may not tally with the final tested performance. Hence, design has to be frozen keeping in view the design analysis as well as the previous operating experience of such machines. Though the final design may meet all the required specifications, it need not be an optimal one as regards the weight and cost of the active materials, and certain performance aspects like efficiency, temperature rise etc. Many conflicting objectives have to be reconciled during the design. They are

(a) Higher Efficiency

(b) Lower weight for given KVA output (Kg/KVA)

(c) Lower Temperature-Rise

119

(e) Any other parameter like higher PF for induction motor

The design of Induction Motor can be formulated as an optimization problem with certain objectives besides considering various constraints. Constraints can be from technical or availability aspects. Technical constraints can be from calculation methods, available process systems, skilled labour, manufacturing facilities, machinery or tools etc. Sometimes transport facilities to site also pose problems. If suitable quality materials are not available indigenously they may have to be imported, which effects cost. If a motor is designed with an objective of maximizing the efficiency, it may not be optimum in other parameters, maybe the cost is high. A compromise is in general made under such situation that tries to satisfy all the objectives considered.Earlier, a trial and error approach is adopted in arriving at a solution which is deemed to best satisfy such conflicting requirements. The present generation of digital computers are endowed with tremendous computing capacity at reasonable cost and are capable of taking logical decisions. This has, therefore, facilitated the use of optimization techniques in the field of electrical machine design.

Optimization of the induction motor design dates back to 1960, where Veinot [2] proposed a digital computer based strategy. The minimization of the production price was the main goal in the early works [3,4]. After the oil crisis and the rise in the energy cost, some researchers, such as Buschart [5] and Diamant [6] put more effort on the optimization of the induction motor efficiency. A process was developed [2],[3], which had to start with a conventionally designed machine; furthermore the objective function had to be written in the form of a generalized positive polynomial. One advantage is that global optimum is always guaranteed [4] and that no transformation of function is needed [5]. In the Sequential Unconstrained Minimization Technique (SUMT), the constraints are again suppressed by the use of penalty factors [4], [6]. The rotating coordinate’s method

has been used [5], [7] and [8] in connection with the SUMT. It may be considered as a further development of the method of Hooke and Jeeves [6]. Artificial neural networks [7] and fuzzy logic [8] are employed in the optimal design of induction motor.

In recent years, Evolutionary Algorithms (EA’s) such genetic algorithm, evolutionary programming, particle swarm optimization etc have been applied in solving IM design problems as they exhibit a high rate of global convergence across the broad spectrum of optimization problems. Since the search progress is based on function evaluations, no gradient evaluation is required [9,10,11].

2.

Formulation Of An Induction Motor Design Problem:The

main objectives of the optimal design of the induction motor are enhancement of efficiency and minimisation of material cost while satisfying various constraints on torque, current, power factor, temperature rise, slip, etc. The design problem can mathematically be formulated as a bi-objective optimization problem as

Min









₁



(

1





)



₂

(3.1) Subject to

02

.

0

50

13

9

.

0

9

.

0

5

.

3













f m sr sr mr

S

I

PF

T

T



(3.2)

Where



₁



1

(

1





)

120



: efficiency of the motor

t

C

: total annual motor cost



: trade-off parameter that represents relativeimportance between the objectives

There are several control parameters that are to be adjusted to obtain the optimal design of the induction motor. In this thesis, the following twelve parameters are heuristically chosen as decision variables, as the remaining variables are identified to have insignificant effect on the performance of the motor.

1. Bore diameter,

D

2. Stator slot depth,

h

_s

3. Rotor slot depth,

h

_r

4. Stator slot width,

b

_s

5. Rotor slot width,

b

_r

6. Rotor slot opening depth ,

h

_r1

7. Rotor slot opening width ,

b

_r1

8. Stator core depth ,

h

_sc

9. Rotor core depth ,

h

_rc

10. Air gap length ,



11. Average air gap flux density,

B

_g

12. Stator current density,

j

_s .

The performance in respect of efficiency and net cost, required for computing the objective of Eq. (3.1) and the various constraints of Eq. (3.2) can be evaluated from the chosen design variables through the following set of equations.

3. Derivations:

Output equation:

HP



k

L

D

h

s

b

B

g

J

s (3.3) where

p

pf

N

k

fk

k



9

.

35

_{ws ss s}

10

3

/

Annual Iron Material Cost, Ci

Ci





c

i

(

M

isc



Mist



Mi

rc



M

irtt



M

irtb

)

_(3.4)

Where

]

)

(

[

)

(

88

.

0

]

)

(

[

88

.

0

)

2

(

88

.

0

]

)

(

[

88

.

0

)

2

(

88

.

0

1 1 1 1 1 r r r r r r r i i rtb r r r r r i i rtt rc r r rc i i rc s s s s i i ist sc s sc i i sc i

b

N

h

h

D

h

h

L

k

w

Mi

b

N

h

D

h

L

k

w

Mi

h

h

D

h

L

k

w

Mi

b

N

h

D

h

L

k

w

M

h

h

D

h

L

k

w

M











































Ann

ual Copper Material Cost,

C

_c

C

c



C

c

(

M

sc



M

b



M

er

)

_(3.5) where c i m j r r r r sr c er r r r r sr c b s s s ss c sc

C

C

C

p

k

h

h

N

b

D

k

w

M

h

h

N

b

L

k

w

M

L

P

D

N

b

h

k

w

M



















)

/(

)

(

9

.

1

)

(

02

.

1

]

)

/

(

72

.

4

0635

.

0

[

1 1 Annual

Iron Loss Cost,

C

_ip

C

ip





C

p

(

p

isc



p

ist

)

(3.6)

121

Annual Copper Loss Cost,

C

_cp

C

cp



c

p

(

P

sc



P

b



P

er

)

(3.6) where

)

/

(

)

(

)

/

(

)

/

(

2 2 2 c er er r j er c b r r b c sc s s sc

w

M

k

k

j

P

w

M

j

P

w

M

j

P

r













Annual Friction and Windage Loss Cost,

C

_fp

f p fp

c

p

C





(3.8) Where 2 3

)

/

(

661

D

L

f

P

P

_f



Annual Stray Loss Cost,

C

_sp

C

sp





c

p

p

s (3.9) where sp fp cp p p s

C

C

C

C

C

HP

P











0

.

005

(

746

/



)

Annual energy loss cost,

C

_e

C

_e



c

_e

(

T

C

_p

/



c

_p

)

(3.10)

Total Annual Cost,

C

_t

C

t



C

m



C

p



C

e (3.11)

Maximum to Full-load Torque Ratio,

T

_mr

)]

cos

1

(

[sin

1

/

)

1

(

1

[



₂



₂2



₂



₂2





₂







S

s

s

s

S

Tmr

(3.12)

Starting to Full-Load Torque Ratio,

T

_sr

2

(

)

/[(

1

){sin

2

(

1

cos

)}]

2

2

1















S

S

s

s

T

_sr

(3.13)

Starting to Full-Load Current Ratio,

I

_sr

















/

2

)

[

(

/

2

)]

cos

(

1 2 12

2 2 2 1 2

1











sr

I

(3.14) Where 1

tan

2

s





Full-Load Power Factor,

pf

pf



(



1

/

2

)

sin



(3.15)

Full-Load Efficiency,







[

746

HP

/(

746

HP



P

t

)]



0

.

005

(3.16) Where

Pf

P

P

P

P

P

P

_t



_isc



_ist



_sc



_b



_er



Maximum Temperature Rise,



_m

)]

4

/(

)

2

)(

(

)

/

(

)

/

/[(

)}]

/(

{

[

2 2 scv v o sci sco o sc is m

c

n

D

D

c

L

D

c

L

Do

L

L

L

p

p























(3.18)

ACO based solution strategy:

122

Fig.3.1 Representation of an Ant

Cost Function:

The objective of the induction motor design is to maximise efficiency and minimise annual production cost while satisfying various constraints given by Eq. (3.2). The parameters’ lower and upper limits are taken care of by enforcing these limits while generating values for the decision variables. But the constraints of Eq. (3.2) are handled through a penalty function approach. Penalty terms are incorporated in the cost function and are set to increase the cost depending on the magnitude of the violation. The cost function is therefore formed by augmenting the problem objective function and the constraints using a penalty factor



as

Minimise



























i i i

g

x

COST



₁

(

1



)

₂



(

)

(3.18) Where

)

(

x

g

_i =

i

thconstraint of Eq. (3.2)

A larger value in the range of several hundred has been chosen

for



_i. During the search process, if the constraint is not

satisfied for a random ACO solution point, the mismatch is

multiplied by the large



_i value and is reflected in the COST function. This will consequently increase the cost function value and the ACO will alter the ant towards the optimal solution point that minimises the COST.

Stopping Criteria: The process of generating new ants can be

terminated either after a fixed number of iterations or if there is no further significant improvement in the global best solution.

4

.

Results And Discussions:

The proposed method (PM) has been applied on a 1200 HP, 50 Hz, 2000 V, 4 pole squirrel cage induction motor. The optimal solution obtained by the PM is given in Table 4.1. The performances of the PM are compared with that of the existing method (EM) suggested in Ref. [12] with a view to illustrate its superiority in Table 4.2. This table provides efficiency, material cost, power loss and energy loss. The analysis of this table clearly indicates that the PM offers higher efficiency and lower cost compared to that of the existing approach.

The parameters of various constraints considered in the design problem are listed in Table 4.3. This table also indicates the respective lower and upper limits. It is observed from this table that none of the constraints violate the respective limits. The convergence characteristics of the PM is shown in Fig 4.1. It is clear from this figure that the algorithm converges quickly to the global best solution.

The PM is very effective in designing the induction motor and can be applied for the design of induction motor with different capacities.

123

0 10 20 30 40 50 60 70 80 90

1.2 1.22 1.24 1.26 1.28 1.3 1.32x 10

4

Generation

S

c

o

r

e

Mean Score Best Score

Figure 4.1 Convergence characteristics of the PM

Table 4.1 Optimal design parameters obtained by the PM

Design Parameters Optimal Values

D

0.5557

g

B

0.4238

s

j

3.8950xl06



0.0015

s

h

0.0391

s

b

0.0128

sc

h

0.1148

r

h

0.0137

r

b

0.0095

rc

h

0.1052

1

r

h

0.0016

1

r

b

0.0031

Table 4.2 Comparison of the Results of the PM with EM

Performance EM PM

Efficiency 94.3% 96%

Material

Iron Copper Total

227.66 85.01 312.67

157.52 65.79 223.31

Power loss

Iron Copper Friction + wind Stray Total

39.77 95.04 62.11 27.74 224.67

46.072 81.83 74.65 28.425 157.335

Energy loss Total 4920.29 5058.5

Total Annual

Cost 6835.08 5519.165

124

Parameter Value offered by

the PM Limits

pf

0.982 >=0.9

mr

T

5.791 >=3.5

sr

I

13.069 <=13

sf

0.015 <=0.02

sr

T

1.310 >=0.9

m



23.083 <=50

Summary: The results in terms of design parameters,

efficiency, material cost and annual energy loss cost of a 1200 HP induction motor have been presented in this chapter. It has been found that the PM is very effective in designing the induction motor.

5.Conclusion: An elegant strategy involving ACO has been

developed for the design of induction motor in this thesis. The enhancement of efficiency and reduction of net annual cost have been considered as the main objectives of the design problem. Various constraints on torque, current, temperature rise, slip and power factor have been included in the design problem. The ACO searches for optimal solution by minimizing a COST that comprises the bi-objectives and the penalized constraints. In the light of the fact that the PM is able to offer a robust solution in terms of higher efficiency and lower annual energy cost that is better than that of the existing methods, the PM acclaims its supremacy and will go a long way in nurturing its role in motor manufacturing industries.

The present study opened up new avenues for further work in the following directions.

 The problem may be solved by considering other objectives such as lowering temperature rise, improving power factor etc.

 The proposed strategy may be modified to search for a best compromise solution that is nearer to the best of the individual objectives.

 The performance may be studied by plotting pareto front through solving the problem with different trade-off parameter values in the objective function.

6.References:

[1]. K M Visnu Moorthy (2008) .“ Computer aided design of electrical machines”, B S Publications.

[2]. C.G. Veinott (1957). “Induction Machinery Design Being Revolutionized by The Digital Computer”, AIEE, Trans on Power Apparatus and Systems, Vo1.75, pp. 1509-1516.

[3]. G.L. Godwin (1959). “Optimum Machine Design by Digital Computer”, AIEE, Trans on Power, Apparatus and Systems, Vo1.78, pp. 478-488.

[4]. O.W. Andersen (1967). “Optimum Design of Electrical Machines”, IEEE Trans on Power Apparatus and Systems, Vol.pas-86, N0.6, pp. 707-711.

[5]. R. Buschart (1979).“Motor Efficiency”, IEEE Trans on Industry Application,Vol.lA-l5, N0.5, pp. 507-510. [6]. P. Diamant (1981). “The High Efficiency Induction

Machine of 1980’s.Part 2”, IEEE Trans on Power Apparatus and Systems, Vol.pas- 100, NO. 12, pp. 4969-4973.

[7]. K. ldir and L. Chang (1998). “Improved Neural Network Model for Induction Motor Design”, IEEE Trans on Magnetics, Vo1.34, N0.5, pp. 2948-295 I . [8]. J.T.Park, C.G.Lee, M.K.Kim and H.K. Jung (1997).

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[9]. D.H. Cho, H.K. Jung and C.G. Lee (1999). “Induction Motor Design for Electric Vehicle Using a Niching Genetic Algorithm”, Electric Machine and Drives International Conference IEMD’99, pp. 290-292,. [10]. M.V.k. Chari, and P. Silvester (1971).“Finite-Element

Analysis of Magnetically Saturated D-C Machines”, IEEE transactions on power system.

[11]. G.Fuat Üler, O.A Mohamed and Chang-Seop.Koh (2008-2011).“Design optimization of electrical machines using genetic algorithms”, IEEE Transactions on Magnetics, Vol. 31, No 3, 1995, pp.

[12]. Lucian Tutelea and Ion Boldea(2010). “ Induction motor electromagnetic design optimization Hooke jeeves method versus genetic algorithms”,IEEE international journal on optimization of electrical and electronic equipment,OPTIM .

[13]. Mehmet cunkas and ramazan akkaya (2006). Design optimization of induction motor by genetic algorithm and comparision with existing motor vol 11,no.3,pp,193-203.

[14]. M R feyzi and H V Kalankesh (2003). “Multi-objective optimization of induction motor slot design using finite element method”,IEEE transaction on magnetics. [15]. Giampaolo liuzzi, Stefano lucidi, Francesco parasiliti