Optimization of double stator PMSM with different slot number in inner and outer stators using genetic algorithm

International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 12, No. 2, Jun 2021, pp. 726~735
ISSN: 2088-8694, DOI: 10.11591/ijpeds.v12.i2.pp726-735  726
Journal homepage: http://ijpeds.iaescore.com
Optimization of double stator PMSM with different slot number
in inner and outer stators using genetic algorithm
Mohd Saufi Ahmad1
, Dahaman Ishak2
, Tiang Tow Leong3
, Mohd Rezal Mohamed4
1,3
Faculty of Electrical Engineering Technology, Univeristi Malaysia Perlis, 02600 Arau Perlis, Malaysia
2
School of Electrical and Electronic Engineering, Universiti Sains Malaysia, 14300 Nibong Tebal, Penang, Malaysia
4
University Kuala Lumpur, Malaysian Spanish Institute, Kulim Hi-Tech Park, 09000 Kulim, Kedah, Malaysia
Article Info ABSTRACT
Article history:
Received Jan 26, 2021
Revised Mar 26, 2021
Accepted Apr 20, 2021
This paper describes the performance enhancement of double stator
permanent magnet synchronous machines (DS-PMSM) based on genetic
algorithm optimization (GAO). Generally, throughout the development stage,
an analytical calculation is implemented to build the initial model of the DS-
PMSM since the analytical calculation can provide the initial parameters
based on the types and materials used in the machine design. For further
improvement, GAO might potentially be applied to provide the optimization
technique in searching the optimal motor parameters iteratively and
intelligently with specific objective functions. For this aim, a three-phase,
DS-PMSM with different number of slots between the outer and inner stators
is first designed by using analytical parameter estimation and then later
optimized by GAO. The outer and inner stators have 12-slots and 9-slots
respectively, while, the rotor carries 10 magnetic poles. Four main input
motor parameters, i.e. outer stator slot opening, outer magnet pole arc, inner
stator slot opening and inner magnet pole arc are varied and optimized to
achieve the design objective functions, i.e. high output torque, low torque
ripple, low cogging torque and low total harmonic distortion (THDv). The
results from the optimized GAO are compared with the initial motor model
and further validated by finite element method (FEM). The results show a
good agreement between GAO and FEM. GAO has achieved very significant
improvements in enhancing the machine performance.
Keywords:
Double-stator
Fractional motor
GA optimization
Permanent magnet
Synchronous motor
This is an open access article under the CC BY-SA license.
Corresponding Author:
Dahaman Ishak,
School of Electrical and Electronic Engineering
Universiti Sains Malaysia
14300 Nibong Tebal, Penang, Malaysia
Email: dahaman@usm.my
1. INTRODUCTION
Permanent magnet synchronous motors (PMSMs) are the most reliable and efficient machine that is
widely used in home appliances, automations, industrial applications and electric vehicles [1]-[2]. The
various emerging applications in PMSM are due to its high efficiency, good dynamic performance, high
torque and high-power density [3]-[5]. In the design of PMSMs, generally, the combination of slots to poles
is important in determining the types of windings to be used. Fractional slot combinations will indicate non-
overlapping windings for the motor, while non-fractional combinations will exhibit overlapping windings.
However, the fractional slot motors are more popular due to their inherently low cogging torque, short end-
windings and high fundamental winding factor [6]-[8].

Int J Pow Elec & Dri Syst ISSN: 2088-8694 
Optimization of double stator PMSM with different slot number (Mohd Saufi Ahmad)
727
The definition of the fractional slot motors is based on the value of the number of stator slots per
rotor poles per phase, Nspp. For the fractional slot motor with concentrated windings i.e. Nspp < 1 is usually
equipped with coils that span one stator tooth pitch [9]. Additionally, there are numerous PMSM topologies
that differ in rotor structures and stator winding arrangements. Surface-mounted PM rotor with fractional
concentrated windings is merging as a promising candidate with performance advantages due to good flux-
weakening and overload capability [10]. In these machines, the coils belonging to each phase are
concentrated and wound on each stator teeth, so that the phase windings do not overlap. This is not only a
distinctive manufacturing advantage but is also conducive to higher copper packing factor, higher efficiency
and lower possibility of an interphase fault [11]-[12].
Double stator permanent magnet synchronous machines (DS-PMSM) have recently been the subject
of extensive research since they have merits such as high torque and high-power density compared to
conventional single stator PMSM [13]-[16]. In [13], the double-stator PMSM is applied for Electric Vehicles
(EVs) and is also proposed for the dual-channel magnetically integrated charger operations. Double-stator
single-rotor has been developed to reduce the cost of manufacturing in machine constructions based on the
relative positioning of both stator slots [14]. While other types of DS-PMSM have been investigated to
reduce the mechanical stress and weight based on the sizing parameters, while the power density is
unchanged [15]. In [16], the DS-PMSM is applied to the wind power generation system where the machine
deploys two spatially independent stators for cooling system.
Generally, the slot numbers of the inner and outer stator in DS-PMSM is similar. However, in this
paper, the authors propose a DS-PMSM with different numbers of slot-to-pole between inner stator and outer
stator. Although the slot numbers of outer and inner stators are different, the ratio of both stators to the rotor
is still fractional type. As a result, high winding factor is incorporated into the proposed machine design. To
evaluate the performances of DS-PMSM, numerical methods such as the finite element analysis (FEA) have
been intensively used for designing and determining the optimal configuration of PMSMs before proceeding
to fabrication and manufacture. However, manually varying the important parameters in the machine
constructions will require a longer computational time and impractical to achieve the best motor performance
[17]-[18].
The duration for designing PMSMs with specific constraints can take a long time when the trial-and-
error method is used. Determining the optimal specification related to the multiple objectives required by DS-
PMSMs is a challenging task [19]-[21]. To overcome this problem, multi-objective genetic algorithm
(MOGA) offer a viable and practical solution to undertake design and optimization problems of DS-PMSMs.
With this in mind, a three-phase, DS-PMSM with different number of slots between outer and inner stators is
developed in this paper. The combination of slot to pole in outer part is 12-slot/10-pole and in the inner part
is 9-slot/10-pole. MOGA is applied to provide the optimization process in searching the optimal motor
parameters iteratively and intelligently with specific objective functions. The objective functions are to
achieve high output torque, low torque ripple, low cogging torque and low total harmonic distortion (THD).
2. INITIAL MODEL OF DS-PMSM
The proposed DS-PMSM is a three-phase, permanent magnet (PM) machine of fractional slot type
with different slot numbers in the outer and inner stators. The chosen stator and rotor combinations are 12-
slot/10-pole for the outer stator/rotor and 9-slot/10-pole for the inner stator/rotor. The initial design of the
model is built using FEM. The objectives of the initial design are to characterize its electromagnetic
performance such as THD, cogging torque, torque ripple and output torque. This machine performance is
further optimized with GAO as discussed in the next section.
Figure 1(a) shows the construction and main parts of the proposed initial design of the three-phase
DS-PMSM which consists of 12-slot outer stator, 10-pole rotor and 9-slot inner stator. The rotor carries
surface-mounted magnets for both inner and outer surface of the rotor core. Figure 1(b) shows the phase
winding layouts in the outer and inner stators of this three-phase DS-PMSM. Double layer windings are
applied for both stators. Red color represents the phase A winding, while yellow and blue colors describe the
phase B and phase C windings respectively. Detailed dimensions of the proposed DS-PMSM initial model
are given in Table 1. Discussion for obtaining the initial dimensions is explained in motor sizing and winding
factor under Section 3.

 ISSN: 2088-8694
Int J Pow Elec & Dri Syst, Vol. 12, No. 2, June 2021 : 726 – 735
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Outer Stator
Outer
windings
Outer PMs
Rotor core
Inner stator
Inner
windings
Inner PMs
Phase A
Phase B
Phase C
(a) (b)
Figure 2. Construction of DS-PMSM, (a) main part, (b) 3-phase non-overlapping windings
Table 1. Parameters and dimensions for the initial model of DS-PMSM
Parameters Symbols Values
Outer Stator Slot Number Nos 12
Inner Stator Slot Number Nis 9
Rotor Pole Number 2p 10
Outer Stator Outer Radius (mm) Roso 90
Outer Stator Inner Radius (mm) Rosi 60
Inner Stator Outer Radius (mm) Riso 48
Inner Stator Inner Radius (mm) Risi 12
Rotor Outer Radius (mm) Rro 59
Rotor Inner Radius (mm) Rri 49
Outer Magnet Outer Radius (mm) Romo 59
Outer Magnet Inner Radius (mm) Romi 56
Inner Magnet Outer Radius (mm) Rimo 52
Inner Magnet Inner Radius (mm) Rimi 49
Stack Length (mm) ls 40
Outer Air-gap Length (mm) hog 1
Inner Air-gap Length (mm) hig 1
Outer Magnet Thickness (mm) hom 3
Inner Magnet Thickness (mm) him 3
Magnet Remanence (T) Br 1.12
Saturation Flux density (T) Bmax 1.6
Relative Recoil Permeability µr 1.05
Rated Speed (rpm) rm 600
Outer Stator Tooth Body width (mm) wotb 10.4
Inner Stator Tooth Body width (mm) witb 12
Outer Stator Winding Turns per coil Noc 114
Inner Stator Winding Turns per coil Nic 50
3. MOTOR SIZING AND WINDING FACTOR
In double-stator PM machine, the total area of the inner stator is inherently smaller than outer stator
because the inner stator position is inside the DS-PMSM structure. Therefore, the slot number of the inner
stator is preferably selected to be lower than that of the outer stator. This allows more space for the slot area
in the inner stator which can accommodate higher number of winding turns. To estimate the initial values of
motor dimensions and main geometric parameters, (1) to (6) are applied to determine the inner bore for outer
stator part [22].
2
4
2
osi
oso
D b b ac
D a
− − −
=
(1)
2
max max
2 2 2 1
og og
B B
k k
a
p p B B
 
 
 
 
 
= + + −
 
 
 
  
 
(2)

729
max
3
2 1 2 4
2
og
tt tt
oso oso
B
w w
k
b
p D B D

 
  
= − + − −
 
  
  
  (3)
2
1 4 tt
oso
w
c
D
 
= −  
  (4)
1
3
k =
(5)
1
r
og
og
o
om
B
B
h
h

=
−
(6)
Where Dosi is the outer stator inner diameter, Doso is the outer stator outer diameter, k is the constant for
concentrated winding, Bog is the average outer airgap magnetic flux density and Bmax is the maximum flux
density in the stator tooth. The rotor and inner stator dimensions are bound to be based on the inner bore of
outer stator size.
The magnitude of the phase back-emf is influenced by the winding factor, Kdpn. Because the double-
stator motor has two stators, the combination of each stator against the rotor is different, resulting in different
Kdpn values, namely the winding factor in the inner stator, Kdpin and the winding factor in the outer stator,
Kdpon. The derivations of Kdpin and Kdpon are given in (7) and (8), where Ns is the number of stator slots, p is
the number of rotor pole pairs, and n is the harmonics numbers. The open-circuit flux-linkage per phase,
ψphase of the inner and outer stator motor can be estimated by (9) and (10), where Ros, Ris, Bgon, Bgin, la, Np, and
ωr are the outer stator bore radius, inner stator bore radius, magnitude of outer airgap flux density, magnitude
of inner airgap flux density, motor active axial length, number of winding turns per phase, and rotor angular
speed in rad/s. Subsequently, the phase back-emf for outer and inner stators which is the rate of change of
inner and outer phase flux-linkage can be estimated by (11) and (12). The total back-emf for each phase can
be given in (13).
2
sin
dpon
s
np
K
N

=
(7)
1 2
sin 1 2cos
3
dpin
s s
np np
K
N N
 
 
   
= −
 
   
   
  (8)
( )
,
1,3,5,..
1
2 cos
phase os p a osi gon dpon
n
N l R B K np
np
 

=
=  
(9)
( )
,
1,3,5,..
1
2 cos
phase is p a iso gin dpin
n
N l R B K np
np
 

=
=  
(10)
( )
,
1,3,5,..
2 sin
phase os p a osi r gon dpon r
n
EMF N l R B K np t
 

=
=  
(11)
( )
,
1,3,5,..
2 sin
phase is p a iso r gin dpin r
n
EMF N l R B K np t
 

=
=  
(12)
, ,
phase phase os phase is
EMF EMF EMF
= +
(13)
4. OPTIMIZATION TECHNIQUE
Genetic algorithm (GA) is one of the artificial intelligent optimization methods. GA begins the
optimization process with a set of random chromosomes. Population-based GA is the basis of the survivor of
the most powerful individual and transmission of its genetic characteristic to the next generations [23]. The

 ISSN: 2088-8694
730
algorithm operates on three simple genetic operators called selection, crossover and mutation. The selection
is carried out using the fitness function, and these operators are applied to obtain better population
generation. During the selection, the ‘parent’ individuals aimed at producing ‘child’ chromosomes are
chosen. The fitness value determines which chromosomes to survive and generate the population of the next
generation [24]. Crossover’s main objective is to ensure that the genes are shared and that the children inherit
the parent’s genes. The mutation operator replaces a gene with another gene in the same chromosome.
Mutation helps the population to achieve variety and diversity. The selection process, crossover and mutation
will continue until some form of convergence criterion has been met or by a fixed number of generations
[25]. Flow chart of the genetic algorithm optimization (GAO) is shown in Figure 2 which displays the overall
procedures of optimization and evaluation processes.
(a) (b)
Figure 2. Flow chart of GA optimization, (a) overall process, (b) one evaluation process
5. OBJECTIVE FUNCTIONS
The design optimization of DS-PMSM in this paper is based on the multi-objective functions from
GA optimization. Four objective functions are considered, i.e. to have lowest total harmonics distortion of
line back-emf, F1; to have lowest cogging torque, F2; to have lowest torque ripple, F3; and to have highest
electromagnetic torque, F4. The optimization results will be in vector form for each objective function and
can be simplified as indicated in (14). Magnitude with the minimum values of these function will be
considered in a group of high performances from the input parameters created by GA process. The Pareto-
chart is applied to identify the best motor parameters that give the best motor performances.
ℱobj = [ ℱ1, ℱ2, ℱ3, ℱ4’]min (14)
6. OPTIMIZED PARAMETERS
Figure 3 illustrates the DS-PMSM motor parameters. There are two types of geometric parameters
in DS-PMSM described as either fixed or variable parameters. The fixed parameters are labelled in black
colour, while the variable parameters are labelled in red colour. The variable parameters will become the
input parameters which can be varied based on the GAO selection in order to achieve the multi-objective
functions. Due to the importance of magnetic flux density in both air-gaps, then four parameters near the
outer and inner air gap regions will be optimized, i.e. inner magnet pole arc, αi; inner slot opening, bi; outer
magnet pole arc, αo; and outer slot opening, bo. These variable input parameters have lower and upper
boundaries as given in Table 2.
Start
Obtain initial
Population
Xi = [x1,x2,...xn]
Check constrains,
Evaluate objective functions,
Fobj = [F1,F2,...Fk]
Genetic Algorithm operators
(Selection, crossover & mutation)
New offspring evolution and
displacement
Iteration
number
Create next evaluation
End
Yes
No
One evaluation process
Current generation:
The individuals at start
Parents:
Number of individuals
Mating pool:
Children:
Pareto front:
Number of survivors
Merged individuals:
*Current generation
*Children
*Survivors from
Pareto Front
Next
Generation

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Rosi
Roso
Riso
Rro
Rri
Romo
Romi
Rimo
Rimi
log
lig
bo
αo
αi
bi
Figure 3. DS-PMSM motor with main parameters
Table 2. Boundaries of four input parameters for GAO
Parameters αi (°) bi (mm) αo (°) bo (mm)
Minimum 24 1.5 24 1.5
Maximum 36 3 36 3
7. RESULTS AND DISCUSSION
DS-PMSM motor is initially applied with 50 turns per coil for the inner stator and 114 turns per coil
for the outer stator. A sinusoidal phase current of 6 A peak current is excited into both inner and outer stator
windings. The initial motor model generates 2.82% THDv, 0.247Nm cogging torque, 4.94% torque ripple
and 21.50Nm output torque. The proposed DS-PMSM motor is then optimized by GAO, and the multi-
objective functions are set as Fobj expressed in (14). Four input variables for the GAO process are chosen as
listed in Table 2. After 30 generations of GA, the optimized process has approached to the optimal solution.
Each solution candidate of the population is decoded into a set of machine parameters.
To distinguish the best motor parameters, two pareto charts are created to tabulate the four objective
functions as shown in Figure 4 and Figure 5. In the figure legends, “GA” means the genetic algorithm
optimization. “Initial” means the output from the initial motor parameters as given in Table 1. The
optimization process should fulfill the four objective functions, i.e. lowest line back-emf THDv, lowest
cogging torque, lowest torque ripple and highest output torque. As can be seen, a group of the best motor
performance is identified in the square dotted line. From this group, the best selected point is chosen with the
output performance of 2.17% THDv, 0.178Nm cogging torque, 4.29% torque ripple and 21.32Nm output
torque as shown by a red color in both Figure 4 and Figure 5. The selected point has their own optimized
machine parameters where the inner slot opening bi, inner magnet arc αi, outer slot opening bo and outer
magnet arc αo as listed in Table 3.
Figure 4. THDv-torque ripple vs cogging torque Figure 5. THDv-torque ripple vs output torque
Table 3 shows the input parameters for the DS-PMSM motor with output performance for initial
model and the optimized model from GAO. Referring to tab GA-Initial (%), after GA optimization, the
machine achieves 23.0% reduction in total harmonic distortion of line back-emf THDv, 27.9% reduction in
cogging torque, 13.2% reduction in torque ripple and almost the same output torque. Clearly, the optimized

 ISSN: 2088-8694
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DS-PMSM machine has an improved performance after being subjected with GAO process. The optimized
machine shows results with lower THDv, low cogging torque, low torque ripple but similar output torque.
Table 3. Initial and optimized parameters with output performance of DS-PMSM
Parameters Initial GA GA - Initial (%)
Inner magnet arc, αi [°] 36 33.8 -6.1
Inner slot opening, bi [mm] 2 2.9 45.0
Outer magnet arc, αo [°] 36 33.3 -7.5
Outer slot opening, bo [mm] 2 1.5 -25
Magnet height, hm [mm] 3 3 0
Airgap thickness, bg [mm] 1 1 0
Outer stator radius, Rso [mm] 90 90 0
Coil slot area, Ac [mm2
] 171.3 171.3 0
Harmonic distortion, THDv [%] 2.82 2.17 -23.0
Cogging torque, Tcog [Nm] 0.247 0.178 -27.9
Torque ripple, Tripple [%] 4.94 4.29 -13.2
Average output torque, Tavg [Nm] 21.5 21.3 -0.9
8. FURTHER VALIDATION OF OPTIMIZED MACHINE MODEL
To compare the motor performance and its accuracy from GAO in designing DS-PMSM, the
optimal machine parameters are built to confirm its performance in FEM. Figure 6 (a) and Figure 6 (b)
illustrate the magnetic flux density distribution under no-load condition before and after optimized
respectively. Before optimization, the peak flux density in stator teeth is about 1.56T, and after being
optimized, the flux density is slightly reduced to 1.54T due to smaller magnet pole arc at inner and outer
magnets.
(a) (b)
Figure 6. Magnetic flux density distribution, (a) initial model, (b) best model from GA
The line back-emf, cogging torque and electromagnetic torque waveforms from the initial model
and optimized model of DS-PMSM are compared and evaluated. After GAO, the shape of the back-emf
waveform is more sinusoidal compared to the initial model due to the decrement of the THDv percentage as
shown in Figure 7 (a) for phase back-emf and Figure 7 (b) for line back-emf. Figure 8 (a) shows the cogging
torque waveforms which clearly indicates a significant reduction of cogging torque after GAO. The
optimized DS-PMSM from GAO also produces smaller torque ripple which can contribute to lesser machine
vibration and noise. The average output torque is not much affected before and after the optimization which
is a good merit. The optimized motor also achieves reduction in torque ripples as shown in Figure 8 (b).

733
(a) (b)
Figure 7. Back-emf waveforms, (a) phase back-emf, (b) line back-emf
(a) (b)
Figure 8. Motor performance, (a) cogging torque waveform, (b) output torque waveform
9. CONCLUSION
This paper has described the optimization technique on the performance of a three-phase, DS-
PMSM machine in which the slot numbers of inner stator and outer stator are different. The improvement of
the machine performance using genetic algorithm optimization has been intensively investigated and
compared using 2D FEM. Four motor parameters are optimized i.e. inner slot opening, inner magnet arc,
outer slot opening and outer magnet arc. The multi-objective functions are to have lower THDv, lower
cogging torque, lower torque ripple and higher output torque. The pareto chart is used to tabulate the
potential motor performance for certain optimized motor parameters. Pareto chart also provides the freedom
to choose the suitable motor performance based on multi-objectives set earlier. The optimized DS-PMSM
having 12 slots for the outer stator, 10 poles for the rotor and 9 slots for the inner stator motor has managed
to reduce THDv, cogging torque and torque ripple, while maintaining the average output torque. The results
from FEM have also confirmed the accuracy of the motor performance from GAO in designing the DS-
PMSM machines.
ACKNOWLEDGEMENTS
The authors would like to sincerely thank Universiti Sains Malaysia for the financial support in this
research work from RUI Grant Scheme under project number1001/PELECT/8014027.
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BIOGRAPHIES OF AUTHORS
Mohd Saufi Ahmad received the B.Eng. and M.Sc. in Electrical & Electronic
Engineering from Universiti Sains Malaysia in 2007 and 2011, respectively. He is
currently lecturer with the School of Electrical System Engineering, Universiti Malaysia
Perlis, Perlis, Malaysia. His current research interests include electrical machines and
drives.
Dahaman Ishak received the B.Sc. degree in electrical engineering from Syracuse
University, Syracuse, NY, USA, the M.Sc. degree in electrical power from the University
of Newcastle Upon Tyne, Newcastle upon Tyne, U.K., and the Ph.D. degree from the
University of Sheffield, Sheffield, U.K., in 1990, 2001 and 2005 respectively. He is
currently an Associate Professor with the School of Electrical and Electronic Engineering,
Universiti Sains Malaysia, Penang, Malaysia. His current research interests include
electrical machines and drives, power electronic converters and renewable energy.
Tiang Tow Leong received the B. Eng. (Hons.) degree in electrical engineering, the
M.Sc. degree in power systems and energy conversion, and the Ph.D. degree in electrical
machines and drives from Universiti Sains Malaysia, in 2009, 2012, and 2017,
respectively. He is currently a Senior Lecturer at Faculty of Electrical Engineering
Technology, Universiti Malaysia Perlis (UniMAP). His current research interests include
optimisation design of permanent magnet synchronous machine.
Mohd Rezal Mohamed received the BEng (Hons) degree in electrical and electronics
engineering and the MSc in electronic engineering from the Universiti Putra Malaysia,
Serdang, Selangor, Malaysia in 2002 and 2008 respectively. He obtained the PhD degree
in electrical machines and drives from Universiti Sains Malaysia, Penang, Malaysia in
2019. He is currently a senior lecturer at the Electrical, Electronics, and Automation
Section, Universiti Kuala Lumpur, Malaysian Spanish Institute, Kulim, Kedah, Malaysia.
His current research interests include design of permanent magnet synchronous machines
and electric vehicles.

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