40620130101004

Journal of Electrical Engineering & Technology (JEET) ISSN 2347-422X (Print), ISSN
2347-4238 (Online), Volume 1, Issue 1, July-December (2013)
25
GENETIC OPTIMIZATION OF CONSTRUCTION PARAMETERS OF
AN ASYNCHRONOUS MACHINE
H.Ladaycia, A, Boukadoum, M. Mordjaoui
ABSTRACT
In this paper, we present a classical model of cage induction motor design (IM) with
constant voltage and frequency supplies. The method of genetic algorithm has been adapted
in order to optimize his conception and improve his performances, in the occurrence his
efficiency. Our objective is to minimize losses of the induction motor that appear as a
nonlinear function, in account of equality constraints and inequality constraints. For that we
give an arranged formulation to the induction motor design optimization.
Key words: Design optimization, asynchronous machine, genetic algorithm
I. INTRODUCTION
The level of prosperity of a community is related to its capability to produce goods
and services. But producing goods and services is strongly related to the use of energy in an
intelligent way.
Electrical energy, measured in kWh, represents more than 30% of all used energy and
it is on the rise. Part of electrical energy is used directly to produce heat or light (in
electrolysis, metallurgical furnaces, industrial space heating, lighting, etc.). Intelligent use of
energy means higher productivity with lower active energy and lower losses at moderate
costs.
The induction motor has been, intensively, studied and described in the literature
during several decades. They are employed in great quantity in different applications and
have a significant impact on the consumption of electricity. Consequently, their design takes
a great importance.
Activities of research have been intensified to improve the efficiency of the induction
motor. The replacement of low efficient motors with those having a higher efficiency can be
a significant resource for the optimization of the power consumption [2] - [3]. This can be
also carried out by improving dimensioning of the motor (machine) at the time of its design.
This is the goal of this work. The design, the dimensioning and the optimization of the motor
are essential in order to minimize the losses and to improve the efficiency and the other
performances of the machine.
JOURNAL OF ELECTRICAL ENGINEERING & TECHNOLOGY
(JEET)
ISSN 2347-422X (Print)
ISSN 2347-4238 (Online)
Volume 1, Issue 1, July-December (2013), pp. 25-36
© IAEME: http://www.iaeme.com/JEET.asp
JEET
© I A E M E

26
II. DESCRIPTION OF THE PROBLEM
The electric motor constitutes the fundamental structural element of a drive system.
The alternating current drives are, today, widely used. They can, from now on, provide
dynamic performances as good as those of the traditional drives (direct current machine),
while being more robust and of less maintenance. Among the alternating current machine, the
squirrel cage induction motor which is characterized by its simplicity and its robustness. This
motor is used, today, in the whole range of power as well as for current industrial
applications.
The design of the induction motor was an interesting sector as reflected in the literature on
the improved design [4] - [8]. Being a nonlinear problem, the design of an induction machine
for a given objective function requires considerable efforts by formulating the problem and
by finding an adapted solution, which implies many iterative procedures. The design
optimization of an induction machine employs a suitable technique of nonlinear optimization
[4]:
 define, clearly, the objective or quantity to be optimized (such as the cost, the weight, the
output … etc).
choose, Judiciously, parameters of the design (variable).
 specify, intelligently, the constraints.
In the literature, concerning the problems of the optimal construction of the induction
machine, several mathematical models of optimization were employed to determine the
parameters affecting more the objective function and the constraints function and their
breaking values. Optimal construction is formulated as a nonlinear problem in [1] & [4].
The authors describe the optimization methods which treat the problem with simple
objective function such as the technique of sequential quadratic minimization without
constraints. The use of these methods has disadvantages, since convergence is, excessively,
difficult and they converge, frequently, towards a local optimal point [9]. In addition, in [9]
the authors consider the optimal construction of the induction machine as a nonlinear
programming multi objective problem. The solution of such a problem is, usually, calculated
by combining the objective functions in only one function. Several techniques are suggested
to solve the multi-objective problem: method of weighting, the aggregation of the objectives
using fuzzy logic … etc. These methods have difficulties encountered at the time of the
resolution of a multi-criterion problem. They are, in addition to the presence of constraints,
related to the properties of the functions to be optimized. The various methods of multi-
criterion optimization and the difficulties encountered in the latter are presented in detail in
the reference [10].
III. GENETIC ALGORITHM
It is in the beginning of 1960s, that John Holland of the University of Michigan
started to be interested in what was going to become genetic algorithm GA [11]. His works
found a first result in 1975 with the publication of the article: Adaptation in natural and
artificial system [11] & [12]. Holland pursued 2 principal goals:
Highlight and explain thoroughly the process of adaptation of natural systems.
Designing artificial systems (ie software) that have important properties of natural
systems

27
GA are algorithms of exploration based on the mechanisms of the natural selection
and genetics. They use both the principles of the survival of the best structures adapted and
the pseudo-random exchanges of information, to form an algorithm of exploration which has
some of the characteristics of human exploration. With each generation, a new whole of
artificial creatures "of the character strings" is created by using parts of the best elements of
the preceding generation, thus of the innovating parts, on the occasion. Although they are
based on the principle of the chance, GA are not purely random. They exploit, effectively,
information obtained, previously, to speculate in the position of new points to explore, with
the hope to improve the performance [13].
GA seeks the extrema of a function defined on a space of data to use it; one must have the 5
following elements [14]:
Tab 1. Genetic biological analogy / GA [15].
genetic algorithms biological organisms
- Coding of solutions
- Elementary constitutive block
encoding
- Set of potential solutions
- Criterion to be optimized
- Iterations of the procedure
- Individual (represented by their
chromosomes)
- gene
- population
- Adaptation of the individual to his
environment
- generations
An electric machine (EM) can be described as a complex system of parameters. By
changing a parameter to improve some performances, naturally, another will change in the
negative direction. It is therefore not possible to optimize the design of an EM by optimizing
one parameter at a time. One solution is to use the model of the EM and use it to find a set of
parameters that give the machine the desired properties [16]. In this present work, the energy
losses of induction motor (IM) will be minimized by GA using the approach based on the loss
model (steady state). The performance evaluation of IM involves estimating the parameters
of the equivalent circuit of the latter. They are required to calculate the different
characteristics of the machine. The analytical model described in [1] presents empirical data
and formulas, characterized by their ease of implementation, their malleability and the speed
with which it provides results. It is very often used in the early stages of the design to provide
a preliminary geometry or compare the relative performance of different structures and
machine technologies[17].The main steps of the model used to design the IM are shown in
Figure 1.

28
Fig 1. The design algorithm [1].
A. Application of GA to the optimization of construction parameters
1) Design variables
In our case, the choice of the design variables is based on author’s experiment of the
IM design in order to obtain values for the five parameters of the equivalent circuit in T fig 2.
To calculate the performances of the studied machine, the design variables are given in table
2 (Appendix).
stK1+
No
Yes
Step 7
Computation of losses,
the nominal slip &
efficiency
Step 8
Computation of power factor,
starting current and torque,
breakdown torque
&temperature rise
Is performances
satisfactory
Step 2
Sizing the electrical &
magnetic circuits
Step 1
Design specs electric &
magnetic loadings
End
Step 5
Computation of
magnetization current
Step 6
Computation of
equivalent circuit electric
Step 3
All construction and geometrical data are known and
slightly ajusted
Step 4
Verification of electric &
magnetic loadings

29
Fig 2. The T equivalent circuit [1].
2) Definition of the constraints
as specified constraints, nominal slip is:
0284.0
PPPP
P
S
supmvAln
Al
n =
+++
= (1)
The nominal selected power-factor is:
0.83
ηI3V
P
cos
n1nph
n
==nϕ (2)
The ratio breakdowns torque/rated torque:
2.5
T
T
t
en
bk
bk ≤= (3)
The ratio starting torque/ rated torque:
1.75
T
T
t
en
LR
LR ≤= (4)
The ratio starting current/rated current:
6
I
I
i
1n
LR
LR ≤= (5)
Temperature rise given :
80θC0 ≤ [o
C] (6)
The limited stator magnetic induction in the yoke:
1.7Bcs ≤ [T] (7)
3) Objective function
In order to obtain a high motor efficiency, the objective function is defined by the sum
of the various losses of the machine presented by the formula (7). The mechanical ventilation
and additional losses are considered constant

30
supmvferAlC0 PPPPPPertes ++++=∑ (8)
C0P represent the stator winding losses, they are calculated by :
2
1nsC0 I3RP = (9)
AlP refer to the cage rotor losses( S = Sn’ nominal slip’ ), they are calculated by:
( ) 2
1n
2
Ir
2
rnnSrAl IK3RIR3P == (10)
The mechanical ventilation losses are considered as:
2Ppour0.012PP nmv
== (11)
The additional losses are defined as fraction of the nominal power of the machine according
to standard NEMA:
n
2
sup P10P −
= (12)
The losses in the core ferP are made of fundamental losses
1
ferP and additional losses
(harmonics)
s
ferP . The total losses in the iron core are:
s
fer
1
ferfer PPP += (13)
The fundamental core losses occur only in the teeth and the back iron ( t1P , y1P ) of the stator
as the rotor (slip) frequency is low
( 2f < (3 à 4) [Hz]). An empirical equation for the fundamental losses in the stator teeth is
given by [1]:
ts
1.7
ts
1.3
1
10tt1 GB
50
f
PKP 





≈ (14)
Where 10P is the specific losses in [W/kg] at 1[T] and 50 [Hz] & tK accounts for core loss
augmentation due to mechanical machining (stamping value depends on the quality of the
material, sharpening of the cutting tools, etc.). tsG Is the stator tooth weight given by:
( ) Fe0swstssironts LKhhhbNγG ++= (15)
The stator back iron (yoke) fundamental losses:
y1
1.7
cs
1.3
1
10y1y GB
50
f
PKP 





= (16)
yK Takes care of the influence of mechanical machining and the yoke weight y1G is [1] :
( )[ ] Fe
2
csout
2
outirony1 LK2hDD
4
π
γG −−= (17)

31
So, the fundamental iron losses 1
ferP is:
y1t1
1
fer PPP += (18)
The flux pulsation loss in the core teeth constitutes the main components of stray losses














+





⋅≈ −
tr
2
prpr
1
1
sts
2
psps
1
1
r
4s
fer GBK
p
f
NGBK
p
f
N100.5P
(19)
ts
ps
B2.2
1
K
−
≈ (20)
tr
pr
B2.2
1
K
−
≈ (21)
( ) gc2ps B1KB −≈ (22)
( ) gc1pr B1KB −≈ (23)
The rotor teeth weight trG is:
tr
21
rrFeirontr b
2
dd
hNLKγG 




 +
+= (24)
The design optimization program structure of induction motor is shown in figure 3
4) RÉSULTATS & DISCUSSION
The genetic process minimizes the loss of the machine, represented by the objective
function, while satisfying the other criteria of the design. The best design is saved for each
successive initial population to converge to the optimal solution. Figure 4 shown this fact. In
addition, the genetic algorithm seems to converge asymptotically to the accurate solution, as
the number of the initial population increases. After 100 initial populations of 50 generations
(iterations), the best designs are given at the end of algorithm execution.
Figure 5 & 7-8 represent efficiency-speed, current-speed and torque-speed
characteristics, respectively, of the initial and optimal design. According to figures 5 - 6, we
note a small improvement of the efficiency for the optimized design as shown in figure 6
(zoom of the characteristic). This justifies the smallest value of the objective function
obtained by the optimization problem. In figure 7, we can see that the inrush current is
different for the 2 designs. The highest variation is carried out by the optimized design

32
Fig 3. GA program structure of the process design optimization
This result shows the variation effects of dimensions of the rotor slots on the current.
Because, the variation of these parameters influences, directly, on the stator and rotor
reactances, as well as on rotor resistance which are essential parameters for the estimate of
the current. According to figure 8, the starting torque of the optimized design is larger than
that of the initial motor. Consequently, it shows a better execution for greater loads
Yes
Showing best
resultsEn
Specification of constants
construction data, areas,
constraints, number of
generations, etc...
Generation of population
- Calculate the parameters dependent on
design variables
- Calculate the objective function
- Calculate the constraint functions.
Selection, crossover, mutation
Début
No
Save the best
Number of
maximum
populations
Yes
No Number of
maximum
generation

33
Fig 4. Objective function evaluated in each iteration.
Fig 5. Efficiency - speed characteristic after optimization.
Fig 6. Zoom of the efficiency - speed characteristic after optimization.
0 20 40 60 80 100
608.215
608.22
608.225
608.23
608.235
608.24
608.245
608.25
608.255
Minimisation de la fonction objective : Ptot = 608.2151 [W]
Nombre de populations initiales
Valeurminimaledelafonctionobjectivetrouvée[W]
0 200 400 600 800 1000 1200 1400 1600 1800
-40
-20
0
20
40
60
80
100
Vitesse [rpm]
Rendement[%]
Moteur initial
Moteur optimisé
1735 1740 1748.88 1755 1760 1765 1770 1775
86.5
87
87.5
88
88.5
89
89.5
Vitesse [rpm]
Rendement[%]
Moteur initial
Moteur optimisé

34
Fig 7. Stator current-speed characteristic after optimization
Fig 8. Électromagnétic torque-speed characteristic after optimization.
IV. CONCLUSION
In this work, we are interested in the design of a 5.5 [kW] squirrel cage induction
motor supplied by 460 [V] with the GA approach. The improvement of the efficiency is not
significant because the method used at the beginning of dimensioning is an already optimized
method. This does not lead to considerable improvements. Values of the various
characteristics: starting torque, maximum torque, starting current … etc are satisfactory. In
addition, the choice of somme variables affect, directly, the improvement. However, other
variables have no effect on the objective function. The use of GA gave acceptable results
with a significant reduction in the rotor teeth weight of 21.6%.
REFERENCES
1. I. Boldea & S. Nasar, “The induction machine handbook”, Electric Power
Engineering series, CRC Press LLC, Boca Raton, London, New York, Washington,
2002.
2. P. Pillay, V. Levin, P. Otaduy, J. Kueck, “In-situ induction motor effeciency
determination using the genetic algorithm”, IEEE Transactions on Energy
Conversion, Vol. 13, No
4, December 1998.
3. Kh. Banan, M. B. B Sharifian, J. Mohammadi “Induction motor efficiency
estimation using genetic algorithm”, University of Tabriz, Transactions on
Engineering, Computing and Technology v.3 pp 271-275,, December 2004.
0 200 400 600 800 1000 1200 1400 1600 1800
0
10
20
30
40
50
60
70
80
Courant[A] Vitesse [rpm]
Moteur initial
Moteur optimisé
0 500 1000 1500 2000
0
20
40
60
80
100
120
Vitesse [rpm]
Couple[N.m]
Moteur initial
Moteur optimisé

35
4. L. Shridhar, B. Singh, C. S. Jha, B. P. Singh, S. S. Murthy “ Design of an energy
efficient motor for irrigation pumps operating under realistic conditions”, IEE Proc.
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. 6, November 1994.
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a finite element method”, Thèse de Doctorat, Helsinki University of Technology
Laboratory of Electromechanics, Helsinki, Electrical Engigneering series No
. 84,
Finland, 1996.
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for cage induction motors”, IEEE Transactions on Industry Applications, Vol. 32, No
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3, May / June 1996.
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their comparison with a typical industrial motor”, Journal of Computers and Electrical
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. 3, pp.
193-203, 2006.
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évolutionnaire multicritère”, Thèse de Doctorat, Institut National Polytechnique de
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Décembre 2007.

36
ANNEXE
Tab. 2 - Design variables of the optimization problem of a squirrel cage
induction motor
Variables Domaines de définition Units
Stator external diameter outD 188.5D180 out ≤≤ [mm]
Rotor tooth height rh 25h7 r ≤≤ [mm]
Rotor tooth width trb 5.9b5 tr ≤≤ [mm]
Rotor notch width maximal 1d 6.5d5 1 ≤≤ [mm]
Rotor notch width minimal 2d 1.7d1 2 ≤≤ [mm]
Tab. 3 - Data of the asynchronous machine
Denomination Symbols Values Units
Nominal voltage
1phV 460 [V]
Speed of synchronism
1n 1800 [tr/mn]
Fréquence d’alimentation
1f 60 [Hz]
Phase numbers m 3
Nombre de phase m 3
Nominal power-factor
ncosϕ 0.83
Nominal effeciency
nη 0.895

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