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The aim of this paper is to propose an approximate technique for the reconstruction of magnetic-field distribution in the proximity of unknown sources. The method is based on two nested optimization algorithms--the external one is responsible for the definition of the geometry of the equivalent-source system, while an internal procedure based on least-square minimization is used to identify the currents of the sources. The goal is to minimize the deviation between the reconstructed and actual field. It is shown that under magnetic quasi stationary conditions, the proposed approach is able to reconstruct the field distribution of a complex 3-D environment as medium-voltage/low-voltage substations. The main limitation is the availability of magnitude and phase of the measured magnetic field. This information is not usually provided by standard probes but can be obtained by a proper measurement setup. The proposed technique allows accurate reconstruction of the magnetic field even in the case of many sources without requiring their accurate geometrical description and is suitable for the evaluation of stray fields and the design of magnetic shielding. Index Terms--Identification, magnetic fields, equivalent-source system.

This paper presents a methodology to study nonlinear electromagnetic phenomena inside ferromagnetic pieces where eddy currents are driven by an external supply source in the medium frequency range. The proposed methodology takes, as reference, a nonlinear time-harmonic solution of the iron part and then identifies, by means of an optimization procedure, the magnetic permeability values of an equivalent layered linear material which would give the same value of Joule losses of the nonlinear case. This approach has been applied to a test configuration obtaining good results. Index Terms--Induction heating, nonlinear time-harmonic eddy currents, optimization.

The paper presents a two-stage approach to solve a class of nonlinear 3-D eddy current problems with high saturation, typical of induction heating processes. The proposed method separates the problem of heavy nonlinearity from the complexity of the geometry, by resorting to a 1-D fast nonlinear solver which is coupled with a linear 3-D solver. Under certain hypotheses on the geometry, the approach is shown to be effective and accurate. Comparison with a commercial 3-D nonlinear code are provided. Index Terms--Induction heating, magnetoquasistatic, nonlinear ac model.

In any industrial installation, power electric systems generate extremely low frequency magnetic fields. Field amplitude values must fulfill the limits related to health effects or to disturbances on electromagnetic devices, and a shielding system is sometimes necessary. The design of magnetic field shields requires the simulation of the sources and of the shields in order to evaluate the main parameters like geometry, material, and position with respect to sources. An alternative approach is proposed in this paper which requires one to measure a spatial distribution of the magnetic field amplitude. Actual field sources are simulated by means of suitable simplified sources handled by analytical relations. An identification process of measured magnetic fields is performed using a genetic algorithm applied to the simplified source system. The simplified system is a suitable combination of three-phase sources, and it seems able to create a realistic magnetic field distribution in both space and time. This paper presents the proposed method and its application to the design of a conductive shielding to reduce the leakage fluxes of a three-phase transformer without enclosure. The magnetic field to be shielded is evaluated with a simple 3-D model of a transformer constituted by three windings in air with current values deduced from the equivalent magnetomotive force which is considered the actual source. Unshielded fields on a plane region are used to identify the simplified source, and the effects of a conducting aluminum shielding are compared using actual and simplified sources. The influence of some parameters of the simplified sources on the results is discussed. Finally, the application for the design of a magnetic field shielding in real substation is presented. Index Terms--Identification of sources, magnetic field, shielding.

Force computation in magnetostatic structures is approached by surface integration of Maxwell stress tensor. Two formulations based on the cell method are presented: the first one with volume discretization and the second one with a hybrid integral scheme. A case with permanent magnets where experimental values of force are available is used as benchmark for comparison of both accuracy and computational cost of the two approaches. Index Terms--Cell method, Green function, hybrid formulations, magnetic forces.

We have applied a multiobjective combinatorial optimization (MOCO) based on a vector immune system (VIS) algorithm to determine the optimal sequence of parallel cables in a multiconductor three-phase system. We build the objective function in a way that minimizes the magnetic stray field and the current unbalance of a bunch of rectilinear power cables. Our principal aim is to extend and verify the ability of the VIS algorithm to solve combinatorial problems represented by nonlinear objectives that are not usually solved in MOCO problems. Index Terms--Artificial immune systems, combinatorial optimization, current sharing, magnetic stray field, multiobjective optimization, parallel cables.