# PRACTICAL USE OF MODELING TECHNIQUES IN THE TEACHING OF POWER ELECTRONICS

Design and modeling of ferrite inductors plays an important role in the study of power electronics systems. This is not an easy task as the materials used in this area, in particular ferrites, present a nonlinear behaviour (hysteresis, saturation and losses in the core). Circuit modeling and simulation is useful for the teaching of power electronics as the use of these softwares helps students understand the aforementioned nonlinear physical phenomena, which are generally difficult to assimilate.

In this paper we present a modeling procedure step by step which is valid to simulate inductors with a ferrite core. The procedure is valid for undergraduate and postgraduate students of power electronics and related subjects and includes the construction and design of the magnetic components, simulation and modeling, and experimental measurements. The procedure uses different standard softwares and modeling techniques and it is valid for modeling and simulating various ferrite inductors excited by sinusoidal and square waveforms.

We present a procedure that uses different programming and modeling techniques: a Computer Aided Design program (AutoCAD), a Finite Element Analysis program (Maxwell), two scientific calculus programs for the numerical solving of derivatives and integrals (Origin and Matlab), a numerical simulation program (Simulink) combined with Matlab and finally an electronic circuit simulation program (PSIM). Through this technique a student can see how these softwares can be used jointly to solve an electronic component modeling and simulating procedure.

The objective is to obtain the voltage, current and power waveforms (v(t), i(t) and p(t)) of the inductor with a ferrite core corresponding to its serial electric circuit, consisting of two nonlinear parameters: inductance L as a function of the excitation current I (L-I curve) and core resistance R as a function of the rms current Irms and frequency (R-Irms curve). The process begins with the construction of the inductor (ferrite core and a coil former on which a copper wire is wound) and the measuring of the magnetic properties of the core (B-H curve being B and H the magnetic fields as a function of I). Next, the students use AutoCAD to design the inductor in 2D or 3D. These designs are introduced into the Maxwell software and the boundary and adaptative meshing conditions as well as the excitation level (voltage and current) are assigned. Adaptative meshing consists in making a finer mesh at the spatial points that are more irregular, such as corners and regions with irregular borders. Then students run the Maxwell Finite Element Analysis program and obtain the magnetic B and H fields as a function of I, and the R-Irms curve. Using the program Origin and through integration of the B field, the Φ-I curve is obtained and from this the L-I curve is derived by differentiating Φ with respect to I. In the last phase, students use three programs (Matlab, PSIM and Simulink) jointly in order to obtain the waveforms.

One of the advantages of this procedure for the students is a simultaneous and efficient use of several commercial softwares in the context of an experimental environment, which helps motivate them and increases their level of interest as it shows the practical application of the theoretical concepts involved in power electronics. This procedure is being tried successfully on undergraduate students doing their final project.