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This paper aims to study unstructured-partial element equivalent circuit (PEEC) method for modelling electromagnetic regions with surface impedance condition (SIBC) is proposed. Two coupled circuits representations are used for solving both electric and/or magnetic effects in thin regions discretized by a finite element surface mesh. The formulation is applied in the context of low frequency problems with volumic magnetic media and coils. Non simply connected regions are treated with fundamental branch independent loop matrices coming from the circuit representation.

Because of the use of Whitney face elements, two coupled circuits representations are used for solving both electric and/or magnetic effects in thin regions discretized by a finite element surface mesh. The air is not meshed.

The new surface impedance formulation enables the modeling of volume conductive regions to efficiently simulate various devices with only a surface mesh.

The propagation effects are not taken into account in the proposed formulation.

The formulation is original and is efficient for modeling non simply connected conductive regions with the use of SIBC. The unstructured PEEC SIBC formulation has been validated in presence of volume magnetic nonconductive region and compared with a SIBC FEM approach. The computational effort is considerably reduced in comparison with volume approaches.

This paper aims to present the mathematical formulations of a magnetic inverse problem for the electric arc current density reconstruction in a simplified arc chamber of a low-voltage circuit breaker.

Considering that electric arc current density is a zero divergence vector field, the inverse problem can be solved in Whitney space W² in terms of electric current density J with the zero divergence condition as a constraint or can be solved in Whitney space W¹ in terms of electric vector potential T where the zero divergence condition naturally holds. Moreover, the tree gauging condition is applied to ensure a unique solution when solving for the vector potential in space W¹. Tikhonov regularization is used to treat the ill-posedness of the inverse problem complemented with L-curve method for the selection of regularization parameters. A common mode approach is proposed, which solves for the reduced electric vector potential representing the internal current loops instead of solving for the total electric vector potential. The proposed inversion approaches are numerically tested starting from simulated magnetic field values.

With the common mode approach, the reconstruction of current density is significantly improved for both formulations using face elements in space W² and using edge elements in space W¹. When solving the inverse problem in space W¹, the choice of the regularization operator has a key role to obtain a good reconstruction, where the discrete curl operator is a good option. The standard Tikhonov regularization obtains a good reconstruction with J-formulation, but fails in the case of T-formulation. The use of edge elements requires a tree-cotree gauging to ensure the uniqueness of T. Moreover, additional efforts have to be taken to find an optimal regularization operator and an optimal tree when using edge elements. In conclusion, the J-formulation is to be preferred.

The proposed approaches are able to reconstruct the three-dimensional electric arc current density from its magnetic field in a non-intrusive manner. The formulations enable us to incorporate a priori knowledge of the unknown current density into the solution of the inverse problem, including the zero divergence condition and the boundary conditions. A common mode approach is proposed, which can significantly improve the current density reconstruction.

Thin conducting sheets are used in many electric and electronic devices. Solving numerically the eddy current problems in presence of these thin conductive sheets requires a very fine mesh which leads to a large system of equations, and it becomes more problematic in case of higher frequencies. The purpose of this paper is to show the numerical pertinence of equivalent models for 3D eddy current problems with a conductive thin layer of small thickness e based on the replacement of the thin layer by its mid-surface with equivalent transmission conditions that satisfy the shielding purpose, and by using an efficient discretization using the boundary element method (BEM) to reduce the computational work.

These models are solved numerically using the BEM and some numerical experiments are performed to assess the accuracy of the proposed models. The results are validated by comparison with an analytical solution and a numerical solution by the commercial software Comsol.

The error between the equivalent models and analytical and numerical solutions confirms the theoretical approach. In addition to this accuracy, the computational work is reduced by considering a discretization method that requires only a surface mesh.

Based on a hybrid formulation, the authors present briefly a formal derivation of impedance transmission conditions for 3D thin layers in eddy current problems where non-conductive materials are considered in the interior and the exterior domain of the sheet. BEM is adopted to discretize the problem as there is no need for volume discretization.

The aim of this paper is to model time‐harmonic problems in unbounded domains with coils of complex geometry and ferromagnetic materials.

The approach takes the form of a coupling between two integrals methods: the magnetic moment method (MMM) and the partial element equivalent circuit (PEEC) method. The modeling of conductor system is achieved thanks to PEEC method while the MMM method is considered for the magnetic material.

The paper shows how to use the MMM/PEEC coupled method to model a problem comprising conductors and ferromagnetic materials and compare its results with the FEM and the FEM/PEEC coupling.

The two methods PEEC and MMM are well‐known. The innovation here is coupling these methods in order to take advantages from both methods. Moreover, the performances of this coupling are studied in comparison with others (FEM, FEM/PEEC coupling).

To synthesize equivalent circuit obtained from reduced order model of large scale inductive PEEC circuits.

This paper describes an original approach for reducing and synthesizing large parasitic RLM electrical circuits coming from inductive Partial Element Equivalent Circuit (PEEC) models. The proposed technique enables the re-use of the reduced order model in the time domain circuit simulation context.

The paper shows how to use a synthesis method to realize an equivalent circuit issued from compressed PEEC circuits.

The coupling between methods PEEC and a compressed method as Fast Multipole Method (FMM) in order to reduce time and space consuming are well-known. The innovation here is to realise a smaller circuit equivalent with the original large scale PEEC circuits to use in temporal simulation tools. Moreover, this synthesis method reduces time and memories for modelling industrial application while maintaining high accuracy.

This paper deals with the problem of magnetization identification. We consider a ferromagnetic body placed in an inductor field. The goal of this work is, from static magnetic field measurements taken around the device, to obtain an accurate model of its magnetization. This inverse problem is usually ill‐posed and its solution is non‐unique. It is then necessary to use mathematical regularization. However, we prefer to transform it to a better posed one by incorporating our physical knowledge of the problem. Our approach is tested on the magnetization's identification of a real ferromagnetic sheet.

This paper aims to compute the magnetic stray field created by faulty electrical machines.

This paper proposes two approaches to compute the magnetic stray field created by faulty electrical machines. The first one presents a homogenized FEM method. The second one is based on a combination of an analytical expression for the magnetic field in the machine air gap with an integral method.

The studies show good agreement and demonstrate the reliability of the approach.

Two models developed in this paper originally used to compute the stray magnetic field of electrical machines. They can contribute to develop new tools for fault monitoring.

A conveyor device is studied with the aim to reduce the friction between the inner surface of the beam and the chain. The lower is the friction between the chain and the beam, the lower is the surface wear. The magnetic repulsion force among permanent magnets (PMs) placed on the beam and on the chain is utilized to reduce friction. The paper aims to discuss these issues.

The considered magnetic suspension is realized with PMs in repulsive configuration; it is designed by solving a constrained optimization problem, with reference to the geometry of the 90° horizontal bend FlexLink WL322 conveyor. Flux density field and its gradient are evaluated using volume integral equation method, allowing to calculate the forces acting on the chain and the stiffness of the magnetic suspension.

The magnetic suspension prototype was manufactured and tested. The experimental and calculated values of the forces acting on the chain compares well. A stable horizontal equilibrium of the chain was obtained during both static and dynamical tests.

The quasi-static model used neglects the dynamical interactions among the elements of the chain, the PMs and loads weight during motions and the eddy current losses in the aluminium beam. However the dynamical tests on the prototype show that the chain motion is regular up to the nominal velocity all along the conveyor with the exception of the trailing edge of the 90° curve.

The tests on the prototype show the possibility of a removal or at least a reduction of the friction force between the chain and the inner side of the beam by means of a passive magnetic suspension. As a consequence a reduction of noise and vibrations and an increase of the mean-time-to-failure is expected.

Prototype testing shows that the unavoidable vertical instability of the magnetic forces has no practical consequence since, reducing the allowed vertical gap, the chain is stabilized by the gravitational force.