In this paper, an induction heating system composed of two partly coupled coils connected to a double half-bridge resonant inverter is deeply analyzed. Induction coils are electrically characterized by their electrical equivalents, usually a series RL circuit, where the inductance is determined by the magnetic energy stored in the system and the resistance is associated with the power dissipated in the load, generally, a metallic workpiece. The aim of this work is to obtain the electrical equivalent of an inductor system with two concentric coils used in domestic cookers by means of computational methods, in order to be included into the models used in computational aided electronic tools to simulate the time-domain behavior of the associated electronics. The multiple-coil system is characterized with a frequency-dependent impedance matrix, where the diagonal terms are the impedance of each isolated coil, and the nondiagonal terms are coupling impedance components describing the mutual coupling between coils. The impedance matrix is calculated with finite-element analysis tools, and equivalent passive networks are proposed to perform time-domain simulation with a good accuracy in the frequency range of interest. The proposed system has been experimentally verified, obtaining accurate time-domain waveforms and output power calculation.

Computational Modeling of Two Partly Coupled Coils Supplied by a Double Half-Bridge Resonant Inverter for Induction Heating Appliances

We present a new method for the evaluation of the per unit length (p.u.l.) internal impedances of solid and hollow conductors. Our method is semianalytical, and takes into account the proximity effect arising from currents mutually induced by nearby conductors which, in turn, modify their internal current density distribution and, hence, their impedance. We eventually apply the developed method to the case of a three-core cable and we calculate the voltages induced in its screens by a lightning current.

An Improved Method for the Calculation of the Internal Impedances of Solid and Hollow Conductors With the Inclusion of Proximity Effect

A procedure is presented for the efficient computation of multiwire shielded cable parameters. In order to reduce the calculation time, a special technique Is used to calculate the magnetic field using Bessel functions. The skin and proximity effects are taken into account in a frequency range where displacement currents can be neglected. The results obtained with the present model were compared successfully with those obtained by the FEM. >

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Multiwire shielded cable parameter computation

It is pointed out that adaptive methods using hierarchal triangles can automatically determine a good distribution of free parameters for the finite-element analysis of microwave and optical devices. Such methods avoid repeated mesh refinement; instead, they vary the polynomial order of the elements in different parts of the mesh. A simple yet effective method for hierarchal adaptation for high-frequency finite-element analysis is developed and evaluated. A simple wavelength criterion was shown to yield an effective initial distribution of degrees of freedom for the adaptive analysis of the microwave and optical devices considered. >

Adaptive finite elements analysis of microwave and optical devices using hierarchal triangles

This paper presents a numerical procedure for the calculation of the polynomial chaos (PC)-expansion coefficients for the per-unit-length capacitance and inductance matrices of wire structures affected by random parameter variability. According to the recent literature results, these coefficients in turn allow the generation of electrical circuit models for stochastic cables. The procedure is based on the twofold expansion of the nonuniform and stochastic charge distributions on the wire boundaries in terms of both Fourier and PC expansions. A stochastic Galerkin method allows to cast the problem in terms of a deterministic system of equations, whose solution provides the unknown coefficients. The proposed methodology is validated via the generation of statistical models for wire structures with random parameters, whose probabilistic responses are compared against the results of Monte Carlo simulations.

Numerical Calculation of Polynomial Chaos Coefficients for Stochastic Per-Unit-Length Parameters of Circular Conductors

The authors describe an application of the finite-element method to the computation of the parameters per unit length of shielded and multiphase cables. Recently developed techniques were used in the domain of the solution of unbounded problems and adaptive mesh refinement. Comparison with analytical results illustrates the efficiency of the proposed techniques in terms of computation times and accuracy. >

New techniques in FEM field calculation applied to power cable characteristics computations

The use of the impedance boundary condition in a finite element formulation is presented for high-frequency axisymmetric problems. The method has the following advantages: (a) a gain in discretization time; (b) a smaller system to be solved and thus a gain in computer memory; and (c) a gain in total computation time. >

The impedance boundary condition applied to the finite element method using the magnetic vector potential as state variable: a rigorous solution for high frequency axisymmetric problems

A. Raizer

Papers

New techniques in FEM field calculation applied to power cable characteristics computations

The impedance boundary condition applied to the finite element method using the magnetic vector potential as state variable: a rigorous solution for high frequency axisymmetric problems