# Decomposition of the compromise objective function in the permanent magnet synchronous motor optimization

Lech Nowak (Institute of Electrical Engineering and Electronics, Poznań University of Technology, Poznań, Poland)
Łukasz Knypiński (Institute of Electrical Engineering and Electronics, Poznan University of Technology, Poznań, Poland)
Cezary Jedryczka (Institute of Electrical Engineering and Electronics, Poznan University of Technology, Poznañ, Poland)
Krzysztof Kowalski (Institute of Electrical Engineering and Electronics, Poznań University of Technology, Poznań, Poland)

ISSN: 0332-1649

Article publication date: 2 March 2015

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## Abstract

### Purpose

The purpose of this paper is to elaborate an algorithm and the computer code for the optimization of the permanent magnet synchronous motor (PMSM) including the shaft torque, the cogging torque, the total harmonic distortion factor of the back EMF and magnet volume into compromise objective function.

### Design/methodology/approach

The mathematical model of the device includes the magnetic field equations with the nonlinearity of the magnetic core taken into account. The numerical implementation is based on the finite element method (FEM) and time stepping procedure. The genetic algorithm has been applied for the optimization. The comprehensive computer code containing the FEM model and optimization procedures have been elaborated.

### Findings

Very important problem at formulating the optimization task is the choice of the functional parameters which constitute the objective and constraint functions. In the paper it has been shown that uncritical constructing the objective function could lead to irrational variants of the designed object. Authors pointed out (Knypiński et al., 2013) that connecting the shaft torque and the cogging torque simultaneously into the one compromise objective function generates ineffective operation of the optimization algorithm and often also leads to the non-optimal result.

### Originality/value

Authors proved that in case of multi-criterion objective function composed of terms which have very different impact on this function value (i.e. very diverse sensitivity of the objective function for these terms is observed) than the optimization process can be significantly distorted. Therefore, decomposition of the optimization process into two stages has been proposed. Some of the parameters (e.g. cogging torque) have been excluded from the first stage of the process. The two stage algorithm has been successfully implemented and tested on the example of PMSM machine.

## Citation

Nowak, L., Knypiński, Ł., Jedryczka, C. and Kowalski, K. (2015), "Decomposition of the compromise objective function in the permanent magnet synchronous motor optimization", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 34 No. 2, pp. 496-504. https://doi.org/10.1108/COMPEL-07-2014-0173

## Publisher

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Emerald Group Publishing Limited