Vector magnetic circuit analysis of silicon steel sheet parameters under different frequencies for electrical machines

Silicon steel sheets (SSSs), serving as the principal constituent of the magnetic circuit in electric machines, necessitates precise modelling and accurate computation using magnetic circuit theory as a prerequisite for analysing the characteristics of electric machines. Nevertheless, the conventional magnetic circuit theory, limited to a single reluctance component, fails to address the phase relationship between magnetomotive force and magnetic flux, and inadequately represents the magnetic flux distribution observed under high-frequency conditions. Consequently, the existing magnetic circuit model for SSSs remains imperfect in its current state. Fortuitously, the advent of magductance has effectively addressed these challenges. Building upon magductance, this study deduces the fundamental laws and theorem within the vector magnetic circuit theory. Subsequently, a distributed parameter vector magnetic circuit model for the SSSs is constructed, accompanied by the derivation of expressions pertaining to its reluctance and magductance. The authors propose the transfer function composed of reluctance and magductance parameters, successfully resolving the phase between the magnetic circuit vectors, the magnetic flux distribution, and the magnetic circuit loss under different frequencies for SSSs. Finally, experimental findings affirm the efficacy and validity of the distributed parameter vector magnetic circuit model for SSSs. The proposal of vector magnetic circuit theory opens a whole new door for the analysis, computation, and optimisation of electric machines.