An isoparametric approach to model ferromagnetic hysteresis including anisotropy and symmetric minor loops

Modelling hysteresis behaviour is an essential task in transient analysis of electrical machines. A curve fitting approach based on isoparametric elements is proposed in this work. A hysteresis loop is split into sub-curves and each sub-curve has been modelled in terms of a second degree polynomial using three data points. Thus the model requires few data points to model a complete loop. The model equations can be easily derived using predefined shape functions of an isoparametric element without using any curve fitting algorithms. The proposed approach has been applied to model hysteresis data of two different materials, namely, grain-oriented (GO) laminations and soft magnetic composites (SMC). Symmetrical minor loops of GO materials with magnetization along any arbitrary direction are modelled for the first time. The calculated results are in close agreement with measured values. Compared to existing methods, the proposed technique in this paper is simple to understand and computationally efficient.