Direct Consideration of Eddy Current Losses in Laminated Magnetic Cores in Finite Element Method (FEM) Calculations Using the Laplace Transform

Abstract

The following article presents a computation procedure that enables us to simulate the dynamic states of electric machines with a laminated magnetic core, with direct consideration of the eddy current losses. The presented approach enables a significant reduction of the simulation process computational complexity. The verification of the obtained data correctness is based on a detailed balance of energy and power in the investigated system. The correctness of the obtained results was also confirmed by comparing them with the results included in norms that describe the losses in laminated sheets. The presented approach is based on expressing the equivalent permeability of transformer metal sheets by using RC or RL circuits. The impedances of these circuits are treated as the transmittance of Infinite Impulse Response filters (IIR) of the Laplace s variable. In this form they are implemented in direct calculations of the dynamics of electric machines based on field-circuital models, using the Finite Element Method (FEM). In this way, we present the method of including eddy current losses in laminated metal circuits of chokes or transformers, during calculations using the finite element method, with the IIR filter in the domain of the variable s of the Laplace transform. Eddy current losses are directly included in the calculation process. Therefore, they have a direct impact on the transient state waveforms. However, the use of the Laplace variable s caused an excessive increase in the number of state variables, and the overall computational efficiency of the presented method is sufficiently low so as to be used in the simulation process of electrical machine dynamic states with a relatively large number of elements in the FE Model.

Innovative Construction of the AFPM-Type Electric Machine and the Method for Estimation of Its Performance Parameters on the Basis of the Induction Voltage Shape

“…The channel made this way is supposed to provide a path for the flow of magnetic stream. The reduction of flux leakage outside the channel area, by using a coating of low magnetic permeability, is of great importance, in particular in the case of higher ripples of the magnetic field, as it limits eddy current losses that would take place in the material of rotor sheets [33]. It is of great importance, as the power of these losses conveyed in the form of heat would additionally heat the permanent magnets [34], which adversely affects their lifetime.…”

Magneto-Thermo-Structural Analysis of Power Transformers under Inrush and Short Circuit Conditions

“…The application of FEM makes it possible to analyze complex phenomena in an efficient way, such as in Gołebiowski et al [15], where the losses due to eddy currents in laminated magnetic nuclei were analyzed. However, despite the fact that FEM presented fairly coherent results, it was necessary to couple different physical phenomena in order to more accurately represent what happened in the equipment, as well as in couplings such as electromagnetic-structural, electromagnetic-thermal, and thermal-fluid, among others.…”

Analogues of the Laplace Transform and Z-Transform with Piecewise Linear Kernels

“…A discrete transform is one where the input function is a sequence and the integral is typically replaced by a summation [6,9]. Two of the most well-known and also widely used transforms are the Laplace transform [3,6,10] The Laplace transform and Z-transform have many nice properties, hence they are ubiquitous in many areas of applied mathematics and engineering [6,12,13]. Note that here for simplicity we assume that s and z are positive real numbers although they can also be considered in the complex plane.…”