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

Abstract

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.INDEX TERMS Magnetic contactor, magnetic equivalent circuit (MEC), nonlinear dynamics, permanent magnets, stray flux modeling.

Analysis of Nonlinear Dynamics of Permanent Magnet Magnetic Contactor via Novel Computationally Efficient Analytical Method Considering Stray and Leakage Fluxes

“…The ND-MEC, as well as other nonlinear MEC methods, requires (6) to be evaluated iteratively, minimizing error in flux density [24]. However, it was found that the original permeability correction significantly increases computational costs, particularly when high accuracy is required.…”

“…Equation 7was empirically derived as part of this study. For the complete description of µ c update routine, the reader is referred to [24] and the reference therein.…”

“…However, Sheikh-Ghalavand et al and Yeo and Ro proposed the modeling of stray and leakage paths using circular arcs [26], [27]. Furthermore, Robertson et al [28], [29] and Janssen et al [30] and Tang et al [31], as well as Ravaud et al [32] and Babic and Akyel [33], proposed the use of an elliptical-like functions to model the interaction between the PM and coil, whereas Gabdullin and Ro recently proposed an algebraic representation for an elliptical flux path function that could be conveniently combined with MEC analysis for the purposes of stray flux calculation [24].…”

“…where k e is 0.5 or 0.25, depending on the type of elliptical arc that depends on the magnetic field distribution [24]. A s.av is an average cross-sectional area of the flux tube in a stray region that depends on the shape of the flux tube.…”

Electrodynamic Contact Bounce Induced by Fault Current in Low-Voltage Relays

“…Other ongoing research focuses on controlling the contact closing process by means of electromagnetic coil energy control [18,19]. Another approach is to use FEM methods for non-linear dynamic analysis of electrical machines in the time domain [20]. These studies are focused on controlling the electromagnetic coil and electrical contacts at make and do not address the topic of effects of electrodynamic bounce of contacts.…”