**1. Introduction**

304 MATLAB – A Fundamental Tool for Scientific Computing and Engineering Applications – Volume 1

*Transactions on*, vol.29, no.9, (September 1982), pp. (624-633)

pp.(2103-2112)

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> In this chapter, we present a new approach for modeling the non-linear inductances by an analytic expression under the MATLAB-SIMULINK® code.

> The current representation of these nonlinear inductances under MATLAB-SIMULINK® based on the introducing point by point (by a Lookup Table bloc in SIMULINK) [3]-[7] the values of Ф (i) deduced from the values of the magnetizing curve B-H and the geometric parameters of the corresponding portion of the magnetic circuit.

> This new approach is based on a determination of analytic expressions of the non liner inductances deduced by a new analytic fitting of the nonlinear B-H curve. We have validate this new approach using the high voltage circuit of the power supply for magnetrons simulated by MATLAB-SIMULINK® code at the nominal state using the ferromagnetic material SF19. The comparison between experimental and simulated currents and voltages shows that the simulation curves match nearly with the experimental measurements (an error approximately one percent: 1%) [6].

> This approach allowed us to give a general equivalent model for an eventual HV power supply (single and three phases) of the microwaves generators with N magnetrons (N = 1, 2,... ….10) for the industrial applications. In other words, we were able to modeling a HV transformer (single and three phases) with magnetic shunts able to supplying N magnetrons on its secondary. Thus, to define a general strategy for multicriteria optimization of this HV power supply with N magnetrons. This approach can also solve many problems of modeling, simulation and optimization of the electrics machines in general [8].

> To summarize, this chapter is organized as follows. In the second section, we remind of the actual modeling of the nonlinear inductances under MATLAB-SIMULINK code. Section III presents the new model based on a hybrid method of fitting the magnetizing curve B-H in

order to derive analytic expressions of the nonlinear inductances. In the last one a conclusion.
