Novel Non-Linear Transient Path Energy Method for the Analytical Analysis of the Non-Periodic and Non-Linear Dynamics of Electrical Machines in the Time Domain

This paper proposes a novel analytical method for the analysis of the dynamics of electrical machines. The method is applied to the analysis of complex permanent magnet (PM)-type magnetic contactors (MCs), which exhibit strong magnetic non-linearities and a high portion of stray and leakage magnetic fluxes. The latter means that the analysis of PM-type MCs using traditional magnetic equivalent circuit (MEC) methods is impossible, thus requiring computationally expensive and time-consuming finite element analysis (FEA). To overcome the limitations of traditional MECs, the magnetic field distribution in PM-type MC is studied in great detail, and a novel non-linear dynamic MEC (ND-MEC) method is proposed. The accuracy of the ND-MEC method is comparable to that of FEA which is achieved by accounting for non-linear effects and dynamic changes in the magnetic flux distribution using a novel stray path elliptical function. Furthermore, the applicability of the ND-MEC is extended to the time domain by combining it with the time difference method (TDM). The complete method, referred to as the non-linear transient path energy method (NT-PEM), combines the ND-MEC, TDM, and a path energy method for the calculation of electromagnetic forces. The validity of the NT-PEM is verified by comparing it with 3D FEA and experimental results obtained from a PM-type MC prototype. The NT-PEM is a fast and inexpensive alternative to FEA, which is particularly advantageous when many designs must be analyzed and optimized while reducing analysis costs. The proposed method can also be applied to the analysis of emerging technologies dealing with multiphysics coupled problems, as in the case of smart materials.