E-ciency often constitutes the main goal in the design of a power system because the minimization of power losses in the magnetic components implies better and safer working conditions. The primary source of losses in a magnetic power component is usually associated with the current driven by the wire, which ranges from low to medium frequencies. New power system tendencies involve increasing working frequencies in order to reduce the size of devices, thus reducing costs. However, optimal design procedures involve increasingly complex solutions for improving system performance. For instance, using litz-type multi-stranded wires which have an internal structure to uniformly share the current between electrically equivalent strands, reducing the total power losses in the windings. The power losses in multi-stranded wires are generally classifled into conduction losses and proximity losses due to currents induced by a magnetic fleld external to the strand. Both sources of loss have usually been analyzed independently, assuming certain conditions in order to simplify the derivation of expressions for calculating the correct values. In this paper, a unifled analysis is performed given that both power losses are originated by the electromagnetic flelds arising from external sources where the wire is immersed applying the decomposition into transversal magnetic (TM) and transversal electric (TE) components. The classical power losses, the so called conduction and proximity losses, can be calculated considering the TM modes under certain conditions. In addition, a new proximity loss contribution emerges from the TE modes under similar conditions.

https://www.jpier.org/PIER/pier123/06.11091909.pdf

TM-TE Decomposition of Power Losses in Multi-Stranded Litz-Wires Used in Electronic Devices

The application of boundary integral equations (BIE's) for the analysis of linear induction devices with rotational symmetry is considered. One-dimensional Fredholm integral equations are derived for the tangential field components at the boundary of a conducting medium with constant scalar conductivity and permeability excited by a time-harmonic azimuthal current source. The important special case of a short right circular conducting cylinder (magnetic or nonmagnetic) coaxial with one or more short coils is treated in detail. The explicit form of the kernels and the numerical solution technique are presented. Numerical results are presented for typical induction heating applications where the load length as well as the coil length are finite. Results are also presented for the magnetostatic problem of finding the demagnetization factors for short magnetic rods. In each case the results are compared with published results and the accuracy and efficiency of the proposed approach are demonstrated.

Boundary integral equations analysis of induction devices with rotational symmetry

Influence of workpiece height on the induction heating process

The use of boundary integral equation methods for the solution of some electromagnetic field problems are discussed. Boundary integral formulations using simple-layer potentials, and Green's formula, are explained. Readers are drawn to the similarity of discretization methods in use. Some salient features of the boundary element method are presented in review fashion. References are made to sample applications in a few problem areas. The paper concludes with a discussion that attempts to relate boundary integrals to partial differential methods.

Application of boundary integral equation methods to electromagnetics

Purpose – To provide a selective bibliography for researchers and graduate students who have an interest in induction processes applied to the electromagnetic processing of materials.Design/methodology/approach – The objective is to provide references that identify seminal, early work, and references that represent the current state of the art. References are listed in categories that cover the broad range of induction modeling and application issues.Findings – A brief overview of the key areas in induction processing of materials is provided, but greater emphasis and space is devoted to the references provided.Research limitations/implications – The middle years of each topic area are not covered.Practical implications – A very comprehensive coverage of material is provided to those with an interest in induction processing of materials.Originality/value – This paper fulfils an identified information/resources need.

State of the art of numerical modeling for induction processes

The problem considered is that of evaluating the induced fields and the power loss in a long conductor with arbitrary cross-section placed in a time-harmonic transverse magnetic (TM) field. Hitherto, the problem has been analysed by numerically solving the governing differential equations or a volume-type integral equation. The paper presents a new approach which uses Helmholtz single-and double-layer potentials to derive integral equations which relate the values of the axial current density and the tangential magnetic field at the surface of the conductor. These are two coupled Fredholm integral equations with weakly singular kernels. As an example, the eddy-current losses in a rectangular conductor placed in a uniform magnetic field are computed, and the results arecompared with previous ones. The proposed approach has two salient advantages. First, by reducing the dimensions of the problem by one, the computation time is considerably reduced. Consequently, many problems that are beyond the practical limit of previous approaches can be easily handled. Secondly, both magnetic and nonmagnetic conductors can be handled.

T.H. Fawzi

Papers

Use of surface integral equations for analysis of TM-induction problem