Electromagnetic modelling of switched reluctance machines exploiting flux tubes

Abstract

A new and computationally efficient algorithm for the design and analysis of switched reluctance machines is proposed. At the heart of the rapid analysis and design methodology is the reduced order computational method based on a flux tube model which has been refined, extended and formalised. The new flux tube method is a combination and important extension of the existing flux tubes and tubes-and-slices modelling techniques used for quantifying magnetic fields in electromechanical devices. The new method is applied to translating and rotating switched reluctance machine topologies in order to obtain the flux-linkage maps for the machines. Original analytically derived numerical error analysis of the improved flux tube method is presented which shows that the numerical accuracy afforded by the method is high despite the fact that the method is classed as a reduced order computational method. It is demonstrated how the improved model enables consistent and accurate analysis and design optimization of switched reluctance machines. The new technique is also validated against finite element simulation results.

Instead of manually laborious geometry based analytical derivations; an automatic generation of cubic splines is introduced to model the magnetic flux using the improved flux tube method. The improved flux tube method exploits cubic-spline approximations for construction of constant flux lines in the magnetic and non-magnetic parts of electromechanical devices. To make the magnetic field modelling of the devices practical the saturation effects of ferromagnetic materials are included in the cubic-spline based flux tube method. Furthermore, the new flux tube method enables, in principle, the modelling of the magnetic leakage flux effects that are important from the machine performance
results accuracy point of view. It is shown that in order to account for the leakage flux effects it is necessary to assume and construct probable, yet representative, leakage flux paths which are not known beforehand. An argument is put forward to support the assumption that the assumed probable leakage flux paths, even if approximate, will accurately account for the majority of leakage flux effects in the device. In order to perform rapid initial design search and optimization of switched reluctance machines the improved flux tube method was combined with the genetic algorithm based multi-objective optimization.

The flux-linkage functions pertinent to a particular optimized switched reluctance machine topology obtained from the improved flux tube method indicate that the method offers good accuracy compared to finite element based analysis, but with significantly improved computational efficiency. It is demonstrated that the new modelling technique can accurately capture the important magnetic saturation and leakage flux effects occurring in the modelled machine parts. Furthermore, the new flux tube method is seen to be computationally efficient and reduces ambiguity and number of parameters used to define flux tubes in the electromagnetic devices. Pareto fronts obtained from the multi-objective genetic algorithm based optimization of a selected number of distinct topology switched reluctance machines indicate that the new flux tube method leads to the accurate and consistent estimation of these Pareto fronts. The proposed analysis and design approach based on flux tubes is applicable to translating and rotating switched reluctance machines of various topologies and therefore enables rapid design search and optimization of novel topologies.

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Identifiers

ORCID for Jan Sykulski: orcid.org/0000-0001-6392-126X

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