Simulink Model for PWM-Supplied Laminated Magnetic Cores Including Hysteresis, Eddy-Current, and Excess Losses

Abstract

A new implementation of an iron-loss model for laminated magnetic cores in the MATLAB/Simulink environment is proposed in this paper. The model is based on numerically solving a one-dimensional diffusion problem for the eddy currents in the core lamination and applying an accurate hysteresis model as the constitutive law. An excess loss model is also considered. The model is identified merely based on the catalog data provided by the core material manufacturer. The implementation is validated with analytical and finite-element models and experimentally in the case of a toroidal inductor supplied from a GaN FET full-bridge inverter with 5-500 kHz switching frequencies and a deadtime of 300 ns. Despite the simple identification, a good correspondence is observed between the simulated and measured iron losses, the average difference being 3.3% over the wide switching frequency range. It is shown that accounting for the skin effect in the laminations is significant, in order to correctly model the iron losses at different switching frequencies. Some differences between the measured and simulated results at high switching frequencies are also discussed. The model is concluded to be applicable for designing and analyzing laminated magnetic cores in combination with power-electronics circuits. The Simulink models are openly available.

Iron-Loss and Magnetization Dynamics in Non-Oriented Electrical Steel: 1-D Excitations Up to High Frequencies

“…According to the conductive constitutive relation (2), these two components generate an eddy-current density j, which is flowing circularly with respect to the z-axis. Because w m b, the induced electric-field component E x (x, y, t) [and, consequently, the eddy-current density j x (x, y, t)] is negligibly small compared to the component E y (x, y, t), and can be neglected [35], [36], [45], [74]. Consequently, the second term on the left hand side of (5) can be omitted, as indicated by the strikethrough.…”

“…In order to predict the iron-loss and magnetization behavior under such conditions accurately, it is indispensable to utilize a hysteresis model that is coupled directly to an eddy-current (lamination) model. This can be solved by using various approaches, where the lamination model is, e.g., based on Maxwell equations [9], [11], [23], [24], [27]- [36], [38]- [57], saturation wavefronts [58]- [60], equivalent circuits [37], [48], [61]- [63] or is included in the hysteresis model implicitly [43], [64], [65]. A comparison of different 1-D lamination models in terms of mathematical structure, implementation, computational performance, accuracy and spatial discretization can be found in [48].…”

Iron Loss Modelling of Electrical Traction Motors for Improved Prediction of Higher Harmonic Losses

“…For electrical steel laminations, the representation is often simplified to a one-dimensional problem in the direction of the lamination, with only half the lamination modelled, as schematically shown in Figure 1c. This leads to a simplified one-dimensional diffusion equation in the z-direction [8,9,13]:…”

“…A non-linear calculation methodology of the 1D problem has been derived in [8,9], by dividing the lamination in a number of layers with constant flux and current densities, as given in Equation 12:…”

“…As an alternative to the FE schemes, for solving the non-linear 1D problem, a Finite Difference (FD) approach could be used [8,9], by dividing the lamination in a number of parallel layers that exhibit constant flux and current density. Such an analysis can easily be implemented as a postprocessing operation to the main 2D FE model using standardly available dynamic solvers.…”