Partial Electrical Equivalent Circuits and Finite Difference Methods Coupling; Application to Eddy Currents Calculation for Conductive and Magnetic Thin Plates

Abstract

This paper presents a new integro-differential coupling between partial equivalent electrical circuits (PEEC) and finite difference method (FDM) taking into account the magnetization effect. This coupling is intended for thin plates having simultaneously significant conductive and magnetic properties in the presence of exciting coils of complex topologies. These cases exist in eddy current nondestructive testing (ECNDT), eddy current separation, induction or levitation melting devices, and more other applications. The choice of FDM, is in relation with rectangular surfaces generated by numerical meshes leading to mathematical integrations of magnetic and electrical quantities with independent variables, unlike more complicated forms of surfaces generated by finite element method (FEM) or others. Fully successful analytical expressions have been realized and implemented in overall coupling process. The PEEC method is mainly used to calculate the magnetic field applied to the nodes of the plate from different inclined polygonal coils. The results of magnetic field and eddy current distributions on thin plates are presented, and parts of them are compared with those realized by Flux 3D software.

Metrology and Measurement Systems

“…From measured and analytical results, we can observe the periodicity of magnetic quantities developed by such applications. With these results, we can decide on the placement of the metal pieces to be heated and predict the shapes and the values of induced eddy currents (some results were published by our team on this subject [35]). On other hand, the analytical approach developed by us represents a good way for the optimization process and inverse problem analysis because all the expressions obtained are in direct relation with dimensions and physical parameters.…”

Real‐Time Frequency Adaptive Tracking Control of the WPT System Based on Apparent Power Detection

“…where Z(ω) is the output impedance of the inverter at the corresponding angular frequency ω. Combining equations ( 6)-( 8), the input current of the inverter can be expressed as follows: In (9), ∅(Z(ω x )) is the impedance angle of the inverter output impedance at angular frequency ω x .…”

“…To ensure that the WPT system operates at the resonant frequency point, there are three main control methods: coil topology optimization [8][9][10], dynamic compensation tuning [11][12][13], and frequency tracking. Compared to the other two methods, frequency tracking control is widely used in systems due to its easy implementation and fast response [14][15][16][17][18][19][20][21].…”