Optimization of fractional-slot permanent magnet synchronous machine using analytical sub-domain model and differential evolution
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Date
2019-08-01
Authors
Mohd Rezal Mohamed
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Abstract
Today's industrial trend requires designers to build electric machines with
shorter design time and to have better performance. However, the modelling of
Permanent Magnet Synchronous Machine (PMSM) using Finite Element Method
requires longer computational burden and each time machine parameters are
changed, the designers need to build another new design and it is relatively timeconsuming.
Analytical Sub-Domain model is able to overcome this problem due to
its faster computational time compared with Finite Element Method (FEM) and
Magnetic Equivalent Circuit (MEC). In order to reduce the repetitive and redundancy
works, the optimization tool is deployed to solve this problem. Three multi-objective
optimizations based on Analytical Sub-Domain (ASD) and Differential Evolution
Algorithm (DEA), Analytical Sub-Domain (ASD) and Particle Swarm Optimization
(PSO), Analytical Sub-Domain (ASD) and Genetic Algorithm (GA), for fractionalslot
Permanent Magnet Synchronous Machines (PMSM) are formulated, computed
and optimized. Then, the optimized fractional-slot Permanent Magnet Synchronous
Machine (PMSM) performance is validated using the 2-D Finite Element Method
(FEM). Two three-phase fractional-slot PMSM models are studied i.e. 6-slot/4-pole
and 15-slot/10-pole in which the magnet thickness, air gap length, magnet arc to
pole-pitch ratio, slot opening, and stator inner radius are the selected machine
parameters to be optimized. The objective functions of the optimization model are: to
have the lowest cogging torque, to have the lowest total harmonics distortion of phase back-emf, to have the highest output torque, and to have the highest efficiency.
From the results obtained, the Analytical Sub-Domain Differential Evolution
Algorithm (ASDEA) has better optimization technique capability compared with
Analytical Sub-Domain Particle Swarm Optimization (ASPSO). ASDEA is 48.2 %
faster computational time than Analytical Sub-Domain Genetic Algorithm (ASGA)
for 6-slot/4-pole PMSM and 71.5 % faster computational time than ASGA for 15-
slot/10 pole PMSM. The optimized 6-slot/4-pole PMSM design has 95.5 %
efficiency, 0.5491 Nm output torque, 86.3 W output power, 9.9 % total harmonics
distortion of phase back-emf, and 0.1566 Nm torque ripple. While the optimized 15-
slot/10-pole PMSM has 93.71 % efficiency, 4.72 Nm output torque, 296.22 W output
power, 5.39 % total harmonics distortion of phase back-emf, and 0.47 Nm torque
ripple. The cogging torque is further minimized when the rotor of the optimized
PMSM models is skewed with a selected skewing angle. The optimized 6-slot/4-pole
PMSM is skewed with 30° mech. resulting 4.9 mNm cogging torque. While the
optimized 15-slot/10-pole PMSM is skewed with 12° mech. resulting 7.7 mNm
cogging torque.