OPTIMAL DESIGN OF SWITCHED RELUCTANCE
MACHINE USING GENETIC ALGORITHM
Ms. R.T.NAAYAGI
Dr. V.KAMARAJ
Department of Electrical and Electronics Engineering
Sri Venkateswara College of Engineering, Sriperumbudur
INDIA
Abstract: - In this paper, a novel optimization method based on Genetic algorithm (GA),
for efficient design of a Switched Reluctance Machine (SRM) is proposed. We propose
the method, which determines the typical parameters like Stator Pole Arc, Rotor Pole
Arc, Rotor Diameter and Stack Length of SRM, suitable especially for direct drives using
Genetic Algorithm (GA). Magnetic Field analysis was done using Finite Element
Analysis (FEA) based CAD package. The optimal design maximizes Flux linkage and
Torque per unit rotor volume of the SRM. The simulation results obtained highlight the
usefulness and effectiveness of the proposed strategy.
Key-Words: - Switched Reluctance Machine (SRM), Genetic Algorithm (GA),
Finite Element Method (FEM), Finite Element Analysis (FEA)
1 Introduction
In the recent past, greater emphasis is being
laid on the design of reliable, high
performance and cost effective Switched
Reluctance Machines (SRM)[1]. The
Switched Reluctance Machine, owing to its
higher torque component, has gained much
prominence and is of high significance to
the electrical community, as it is used in a
number of high profile applications, such as
in
wind
energy
applications,
starter/generator systems in gas turbine
engines, high performance aerospace
applications and other numerous high
precision applications.
For most effective and highly efficient
transfer of power from a motor to load of
any drive type, the direct drive mechanism is
found to be the most suitable. Besides this,
they require very little maintenance and
suffer only from minimal power loss. An
explicit requirement of direct drives is the
higher torque component and hence a SRM
can be effectively coupled to them to meet
this critical requirement [3].
For optimization of the machine, a magnetic
field analysis method for performance
evaluation and a suitable optimization
method to search for the optimal shape are
necessary. In this paper, we use finite
element method (FEM) for magnetic field
analysis and genetic algorithm (GA) as a
suitable optimization method due to the
following reasons:



The GA enables global optimization
because of its multipoint searching
abilities
Handling of multivariable problems
is possible and relatively simple
Algorithm is comparatively easy
2 Design by FEM
A standard SRM is modeled and simulated
for performance evaluation using FEA based
CAD
package[4].
Magnetic
field
distribution of a typical 8/6, 4 phase SRM
by finite element method is shown in figure
1 for the rated current .The flux distribution
at every part of SRM is determined for
various current excitations from 0 to 25 A.
The other parameters such as flux linkage,
electromotive force etc are also computed
accurately using FEA Based CAD package.
Based on the flux linkage value for various
stator current excitations and rotor positions,
the inductance of a stator winding can be
evaluated as a function of rotor position and
stator current .The inductance profile for
various current excitations is shown in
figure2.
2.1 Optimization using GA
Genetic Algorithm (GA) is a stochastic
optimization method, which imitates the
natural processes of adaptation to the
environment and evolution. Although GA
highly simplify these processes, in spite of
that simplicity, the GA is still well known as
an effective technique to get the most
appropriate optimization result for various
problems, which are difficult to be solved
with usual mathematical (or) deterministic
techniques [11]. The main features of GA
optimization are follows:



Because of the stochastic nature of
GA, the probability of achieving
global optimal solution is very high.
Computation of gradient of the
objective function, which must be
done for Newton method, QuasiNewton method, Gradient method
etc., is not necessary.
Multivariable problems can be
handled easily and the algorithm is
comparatively easier to implement.
The objective function to be optimized is a
constrained,
non-linear,
multivariable
function. The design variables are Stator
pole arc, Rotor pole arc [6], Rotor Diameter
and Stack Length and the parameters to be
optimized are Flux linkage, Torque per unit
rotor Volume etc.
Figure 1: Flux Plots for Aligned and
Unaligned positions
60
The objective function is defined as follows.
Inductance In mH
45
F = Maximize (F1, F2)
30
Where,
0
15
0
0
50
10
60
20
30
40 50
Angle in DEG
40
Figure 2: Inductance as a Function of rotor
30
20
10
0
position at various excitations by
FEA
F1 = Flux linkage
F2 = Torque Per Unit rotor Volume
The general expression for the torque [1]
produced by a phase is given by,
T = ∂Wc (θ,i)/∂θ│ i=constant ----- (1)
Where Wc (θ,i) is the co-energy given by,
Wc (θ,i) = ∫ ψdi
----- (2)
Where ψ is the flux linkage given by
ψ = L.i
----- (3)
2.3 Flowchart
The general expression for inductance of
SRM is the function of rotor position θ is
given by [9],
L =
Input Parameters (Initial population,
No. .of design variables, crossover
,mutation rates etc..)
Initial SRM Design using FEM
2Np2µ0 r1lα
__________ + Lu
----- (4)
g
Using typical values of 4 phase SRM,
L =
[0.1143(θ - θx) + Lu ]
Define Objective Function
Setting the Constraints
----- (5)
Choose the GA
optimization Techniques
Torque per unit rotor Volume
Solve
(T/V) =
2
Nr Bs (λ- 1)qβrg
_______________________
----- (6)
Modify the limits
and iterations
2∏2 µ0 r1
Where Bs = Flux density at maximum
Flux linkage
Yes
Obtain the Design Variables
λ=aligned/unaligned inductance
ratio
q = Total number of phases
g = air gap
r1 = rotor diameter
3 Results and Inferences
Parameter
Conventional
Design
Rotor pole
arc
Stator pole
arc
Rotor
diameter
Stack
length
32 deg
Optimal
Design
using GA
29.2 deg
28 deg
26.8 deg
37 cm
34 cm
50.5 cm
46.5 cm
The Constraint conditions are given by [5],
0 <βr ≤αr; 0 < βs < αs
βr > βs,2π/Nr – βr > βs
where,
αr = Rotor Pole Pitch
αs = Stator Pole Pitch
βr = Rotor Pole Arc
βs = Stator Pole Arc
Equations are framed in accordance with [1]
2.2. Parameters Used
GA Parameters
Number of Design variables
Number of chromosomes
Cross over rate (in % )
Mutation rate (in % )
Maximum generation
:
:
:
:
:
Hass the
function
converged?
No
4
10
60
10
500
From the above results, we can observe that
the simulated SRM has rotor diameter and
stack length dimensions, which are 7.5 %
and 8.54 % lesser than the corresponding
actual sizes of a standard 8/6 pole, 4-phase
machine, which is that achieved by the
optimal design.
4 Conclusion
In this optimal design methodology, Rotor
pole arc, Stator pole arc, Rotor diameter and
Stack length of SRM are taken as design
variables. Based on the Genetic Algorithm,
an improvement in performance has been
effected, by way of increase in Torque and
decrease of primary size, thereby the weight
of SRM has been accomplished. Power
density of the machine is improved by
18.9 %, which is significant for direct drive
applications. The simulation results obtained
so far are encouraging and they demonstrate
better performance than that reported in [2],
using analytical approaches.
References:
[1] T.J.E. Miller, “Optimal Design of
Switched Reluctance Motors”, IEEE
Transactions on Industrial Electronics,
Vol.19, No.1, Feb.2002.
[2] Stephane Brisset and Pascal Brochet,
”Optimization of Switched reluctance
motors using deterministic methods
with static and dynamic Finite Element
Simulations”, IEEE Transactions on
Magnetics, Vol.34, No.5, Sept. 1998.
[3] Jurgen Reinert, Robert Indeoka,
Marous Menne, Rik W.De.Doncker,
“Optimizing performance in
Switched Reluctance Drives”, IEEE
Industry Applications Magazine,
July/August 2000.
[4] Dr. V.Kamaraj, “Modeling and
Simulation of SRM using Magnet 6.0”,
Proceedings of the 5th International
Conference on Power Electronics
and Drives, PEDS 2003, Singapore.
[5] K.R.Rajagopal, “Optimum pole arcs for
SRM for higher torque with reduced
ripple”, IIT, Delhi.
[6] Koichi Koibuchi, “A Basic study for
optimal design of SRM by FEM”, IEEE
Industry Applications, 1997.
[7] Young Ahn Kwon, “Computation of
Optimal Excitation of a SRM using
Variable Voltage”, IEEE Industry
Applications, 1998.
[8] R.Krishnan et al., ”Design Procedure for
Switched Reluctance Motors”, IEEE
Trans. on IA, Vol.24, No.3, 1988,
pp 456-461.
[9] Miller T.J.E, and McGLIP.M, ”Non
Linear theory of the Switched
Reluctance Motor for rapid
computer aided design”, IEE
Proc.B 1990, 137(6), pp337-347.
[10] Arumugam,D. A.Lowther, R.Krishnan
and J.F.Lindsay, ”Magnetic Field
Analysis of a Switched reluctance
Motor using a two dimensional finiteElement model”, IEEE Trans.on
Magnetics, Vol.MAG-21, No.5,
pp1883-1885, Sept.1985.
[11] GoldBerg, David E,”Genetic algorithms
in Search Optimization and Machine
Learning “, Addison Wesley, 2000.
[12] T.J.E Miller, ”Switched Reluctance
Motors and their Control”, Magna
Physics, Calendran Press, 1993.