International Journal of Advanced Engineering Technology
E-ISSN 0976-3945
Research Article
GA BASED OPTIMAL DESIGN OF THREE PHASE
SQUIRREL CAGE INDUCTION MOTOR FOR ENHANCING
PERFORMANCE
1
1
S.S.Sivaraju and 2 N. Devarajan
Address for Correspondence
Department of Electrical and Electronics Engineering, RVS College of Engineering and Technology,
Coimbatore, Tamilnadu, India.
2
Department of Electrical and Electronics Engineering, Government College of Technology, Coimbatore,
Tamilnadu, India.
ABSTRACT
In this paper, optimal design of three phase squirrel cage induction motor to improve efficiency and power factor and to
reduce total loss for variable load application is proposed. It has compared conventional and optimally designed same rating
of 10hp (7.5kW) motor. The motor is designed and optimization using Genetic Algorithm and the simulation results are
presented. The Genetic Algorithm is used for optimization and five objective functions namely Stator Copper Loss, Rotor
Copper Loss, Stator Iron Losses, Efficiency, and Power Factor are considered. The importance of this work is highlighted by
the recent concerns about the need to achieve energy savings in the industry and in the territory sectors. The motor design
procedure consists of a system of non-linear equations, which imposes induction motor characteristics and motor
performance. This is very useful to optimize the power factor, losses and efficiency of the induction motors.
KEYWORDS: Induction Motor, Genetic Algorithm, SCL, SIL, RCL, Efficiency, Power Factor, Loss
I. INTRODUCTION
The squirrel-cage Induction motors are 90% used in
various industrial, domestic and commercial
applications [1, 2]. Particularly, the squirrel cage type
is simplicity, robustness and low cost, which has
always made it very good-looking, and has therefore,
captured the leading place in industrial sector. The
average load factor of electric motors in both
industrial and tertiary sectors is estimated to be less
than 60% [3]. However, in some industrial sectors,
the average load factor for some motor power ranges
can be as low as 25% [3,4].Individual motors in those
ranges have even lower load factors. Because the
motor load factor is an average of motor load during
a period (e.g. motor duty-cycle period), the motor
load can alternate between values lower and higher
than the motor load factor. As a result of its extensive
use in the industry, induction motors consume a
considerable percentage of the overall production of
electrical energy. The minimization of electrical
energy consumption through a better motor design
becomes a major concern. The problems in the
optimization of the electromagnetic devices are
mixed (continuous and discrete) variables and
discontinuities in search space. In this paper, we have
modeled the optimal design of an induction motor as
a nonlinear multi-objective optimization problem and
described three different methods for its solution.
When a multi objective problem is treated, each
objective conflicts with one another and unlike a
single objective optimization, the solution to this
problem is not a single one, but a family of solutions
known as the Pareto-optimal set. Among these
solutions, the designer should find the best
compromise, taking into proper account the attributes
and characteristics of the handled problem. If the
standard non-linear programming (NLP) techniques
[2, 3, 4 and 5] were to be used in such cases, then
IJAET/Vol.II/ Issue IV/October-December, 2011/202-206
they would be computationally very expensive and
inefficient. Some applications utilizing the standard
NLP techniques include the design and control
parameter optimization of induction motors [6, 7, 8,
and 9]. In recent years, GAs has been recognized as
potent tools in design optimization of electrical
machinery [3, 10]. One of the most important
advantages of the GA over the standard NLP
techniques [5] is that it is able to find the global
minimum, instead of a local minimum, and that the
initial attempts with different starting points need not
be close to actual values. Another advantage is that it
does not require the use of the derivative of the
function, which is not always easily obtainable or
may not even exist. For example, when dealing with
real measurements involving noisy data, the
efficiency and power factor improvement [1, 2, 6, 8,
and 9] is mainly considered. The aim of this paper is
to give a further contribution in the optimum design
of a three phase induction motor with efficiency and
power factor improvement, using the five objective
functions, namely Stator Copper Loss (SCL), Rotor
Copper Loss (WRCL), Stator Iron Losses (SIL), Full
Load Efficiency ( η ), and Full Load Power Factor
(P.F). Genetic Algorithm having the feature of a
unique search [12, 13] was then used for optimization
processes. A design package has been developed
specifically for a three-phase squirrel-cage type
induction motor. As per our literature survey, many
proposals based on multi objective approaches for the
electrical machines design have been uncounted [1],
[2]. In this paper, three methods are described and
employed for the design optimization of three-phase
induction motors, when conflicting objectives are
chosen. In this paper a conventional three phase
squirrel-cage
type
induction
motor
with
specifications 10 hp (7.5kW), 400V, star connected
International Journal of Advanced Engineering Technology
and 4 poles is chosen for comparing with our
optimally designed motor.
The used equivalent of the motor is shown in Figure
1. The model is popular and well understood among
engineers and, despite its shortcomings, offers
reasonably good prediction accuracy with modest
computational effort. This model is basically a per
phase representation of a balanced poly-phase
induction machine in the frequency domain,
comprising six elements, or model parameters. The
six impedances are stator resistance R1, stator leakage
reactance X01, magnetizing reactance X0m, core loss
Resistance Rm, rotor leakage reactance X02, and rotor
resistance R2. In this paper, the approaches and
methods used to calculate the motor performances are
based on the works of [15].
E-ISSN 0976-3945
3. To Optimize the Stator Iron Loss
SIL = Wt *Wtk + Wc *Wck
Wt
Wc
Wtk
Wck
- Weight of the stator teeth
- Weight of the stator core
- Losses in stator tooth portion W/kg
- Losses in stator core W/kg
4. Full Load Efficiency
1000 P o
η=
*100
1000 Po + SCL + W RCL + SIL + WF
Where as
P0
- Power in KW
SCL - Stator Copper Loss in W
WRCL- Rotor Copper Loss in W
SIL
- Stator Iron Losses in W
WF
- Friction losses in W
5. Full Load Power Factor
Rs + G4
PF =
(Rs + G 4 )2 + ( X
{
s
+ G5 )2
}
Where as
RS
- Stator Resistance in Ohm
Xs
- Average air gap flux density (wb / m2)
G4, G5 - Magnetizing constants
Fig.1 of induction motor
Choice of L/ τ in induction motor
For minimum cost L/ τ = 1.5 to 2
For good power factor L/ τ = 1.0 to 1.25
For good efficiency L/ τ = 1.5
To apply the GA approach, an objective function has
to be defined to evaluate how good each motor
design is. This objective function may include all the
geometrical dimensions of the motor. A large subset
of constraints (geometrical constraints) has to been
overcome to ensure the physical feasibility of the
motor. These objectives functions are as follows.
II. The Objective Functions
The design optimization of electric motors requires a
particular attention in the choice of the objective
function that usually concerns economic or
performance features. This problem is represented by
the multi objective approach. Then, we have
considered
the
following
multi
objective
formulations:
1. To Optimize the Stator Copper Loss
SCL = 3I 2ph ( Rs )
IPH
RS
- Phase Current in Amps
- Stator Resistance in Ohms
2. To Optimize the Rotor Copper Loss
WRCL =
ρr
S2
Ib
De
Lr
P
ρ r S 2 I b2
ab
( Lr +
2 De
)
p
- Constant (.021)
- No. of rotor slots
- Rotor bar current in Amps
- Mean end ring diameter in mm
- Length of the core in m
- No. of poles
IJAET/Vol.II/ Issue IV/October-December, 2011/202-206
III. An Overview of Genetic Algorithm
In the most general sense, GA-based
optimization is a stochastic search method that
involves the random generation of potential design
solutions and then systematically evaluates and
refines the solutions until a stopping criterion is met.
There are three fundamental operators involved in the
search process of a genetic algorithm: selection,
crossover, and mutation.
Selection: Selection is a process in which individual
strings are selected according to their fitness. The
selection probability can be defined by
Pj =
F(Xi )
∑ i F(Xi )
Where as
Pj is selection probability
F(xi) is objective function.
Crossover: This is the most powerful genetic
operator. One of commonly used methods for
crossover is single-point crossover. As shown in the
following examples, a crossover point is selected
between the first and the last bits of the chromosome.
Then binary code to the right of the crossover point
of chromosome1 goes to offspring2 and
chromosome2 passes its code to offspring1. This
operation takes place with a defined probability Pc
that statistically represents the number of individuals
involved in the crossover process.
Mutation: This is a common genetic manipulation
operator, and it involves, the random alteration of
genes during the process of copying a chromosome
from one generation to the next. Raising the ratio of
mutations increases the algorithm’s freedom to
search outside of the current region of parameter
International Journal of Advanced Engineering Technology
space. Mutation changes from a “1” to a “0” or vice
versa. It may be illustrated as follows.
110000010 _ 110001010
Motor Design Variables
• Ampere conductors/m
• Ratio of stack length to pole pitch
• Stator slot depth to width ratio
• Stator core depth (mm)
• Average air gap flux densities (wb/m2)
• Stator winding current densities (A/mm2)
• Rotor winding current densities (A/mm2)
• Maximum stator tooth flux density,wb/m2
• Full load efficiency, %
• No load current, pu
• Full load power factor
The above mentioned motor design variables are all
automatically varied and finally optimal design
values are obtained.
VI. Design Optimization process.
The flow chart of the design optimization procedure
is depicted in Fig. 2. Each block consists of number
of subroutines. The Execution of the program starts
with the performance specifications such as the initial
motor design variables, the number of generations,
population size, crossover rate, and mutation rate
Population size, number of generations, crossover
rate and mutation rate can be selected depending on
the user. Each design parameter and penalty limits for
penalty function can be varied within its domain.
Then design parameter of the stator and rotor layout
is calculated.
E-ISSN 0976-3945
Fig. 3. Optimization process (GA)
At this point, the designer is offered the option to
view the performance analysis for the proposed
design. If the optimization is satisfied, then the
design optimization process must be stopped,
otherwise the GA optimization process should be
continued show in the fig.3. The designer can
improve the value of objective function reviewing
constraint specifications.
Table 1:Results Comperetion
VI. THE RESULTS AND DISCUSSION
Table 1 shows the values for the ten design
parameters for each optimization. According to the
results in Table 1, the algorithm has returned an
Description
Diameter of Stator in mm
Length of Stator in m
Ratio L/tove
Outer diameter of stator in mm
Stack length in m
Stator depth to width
Stator core depth
Average air gap flux density
(wb/mm2)
Stator winding current density A/mm2
Rotor winding current density A/mm2
Stator Iron Losses (SIL) in watts
Rotor Copper Loss (WRCL) in watts
Stator Copper Loss (SCL) in watts
Total Loss in watts
Full Load Efficiency
Full Load Power Factor (P.F)
Fig. 2 Flow Chart for Design Optimization
Process.
This is followed by optimization process such as the
selection, crossover, mutation and specification of the
constraints. The design is evaluated for every
individual of a population. The algorithm terminates
after testing the specified convergence and optimum
design achieving.
IJAET/Vol.II/ Issue IV/October-December, 2011/202-206
Normal
Design
0.0817
0.5398
1.3423
0.1499
2.7632
4.05493
4.23895
2.5769
Optimal
Design
0.09482
0. 56853
1.52700
0. 15541
3.0552
4.2067
3.97515
2.78329
5.83
5.83
4.3756
65.8761
147.673
217.924
84.176
0.8432
7.039
7.023
1.6903
43.6206
133.482
203.740
93.0987
0.96178
acceptable solution every time, which is indicated by
a good value for objective with no constraint
violations. According to these results the achieving
performance improvements show in fig.6 and fig 7.
The conventional motor design displays poor
efficiency, low power factor and higher losses show
in the fig 4 and fig.5. This is because in the
conventional motor design variables are manually
selected but in the proposed GA based optimal
design, the design variables are automatically varied
to find the optimal solution. Hence the optimally
International Journal of Advanced Engineering Technology
designed three phase squirrel cage induction motor
attains higher efficiency, better power factor and low
losses.
Fig.4. Efficiency as a function of percentage of
load for normal design
Fig.5. Power factor as a function of output
power for normal design
Fig.6. Maximum Power factor as a function of
output power for optimal design
E-ISSN 0976-3945
three-phase squirrel-cage induction motor. A package
program that analyzes and optimizes induction
motors and evaluates the performance of the designs
has been developed. Comparison of the final
optimum designs with the existing design indicates
that the gain of the proposed performance is even
better than expected. The presented paper can
contribute significantly to the loss reduction and
improve the efficiency and power factor in electricmotor-driven systems in both industrial and tertiary
sectors. While achieving performance improvements,
the operating cost also is reduced. Further work is
needed to assess the impact of the increase of the
stator-winding connection change frequency on the
life time of both motor and contactors by using
extreme machine learning, which should be
accounted for the economical analysis.
List of symbols
P0
WSCL
WRCL
WSIL
WF
IPH
Rs
EPH
f
KW
X1
X2
X3
X4
X5
X6
X7
L
D
P
ρr
Ib
S2
Ig
dsr
asr
Lr
De
ab
S1
dss
Wt
Wc
Wst
Li
OD
P.F
- Power in kW
- Stator Copper Loss in watts
- Rotor Copper Loss in watts
- Stator Iron Losses in watts
- Friction losses in watts
- Phase Current in Amps
- Stator Resistance in Ohm
- Voltage per phase in Volts
- Frequency in Hz
- Winding factor
- Ampere conductors/m
- Stack length / pole pitch ratio
- Stator Slot Depth to Width
- Stator core depth in cm
- Average air gap flux density (wb / m2)
- Stator winding current density (A/mm2)
- Rotor winding current density (A/mm2)
- Length of the armature in mm (stator)
- Diameter of stator in mm
- No. of poles
- Constant (0.021)
- Rotor bar current in Amps
- No. of rotor slots
- Radial Air Gap Length in m
- Depth of the Rotor Slots
- Rotor slot area m2
- Length of the core in m
- Mean end ring diameter in mm
- Rotor bar area m2
- No. of stator slots
- Depth of Stator slot
- Weight of the stator teeth
- Weight of the stator core
- Mean Stator Tooth Width in mm
- Length of the core in m
- Outer Diameter of Stator in mm
- Full Load Power Factor
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Fig.7. Efficiency as a function of percentage of
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VII. CONCLUSION
This paper has compared optimally designed threephase squirrel-cage induction motors with an existing
motor of the same rating. An optimization technique
based on GAs has been applied to the design of 10 hp
IJAET/Vol.II/ Issue IV/October-December, 2011/202-206
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E-ISSN 0976-3945
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