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This paper presents a method to analyse electrical machines considering simultaneously the electromagnetic field, electric circuit, control loop, movement and skewing effects. The major contribution of this work leans on its generality, i.e. it can be applied to electrical machines connected to static converters submitted to any control laws, avoiding an a priori analysis. Simulation results of a three‐phase Brushless AC (BLAC) motor fed by a PWM converter is presented as well as a comparison of simulation and experimental results obtained using a two‐phase‐on converter were also presented.

To develop a sub‐domain perturbation technique for efficiently modeling moving systems in magnetodynamics with a magnetic field h‐conform finite element (FE) formulation.

A reference problem is first solved in a global mesh excluding some moving regions and thus avoiding the inclusion of their meshes. Its solution gives the sources for a sequence of perturbation problems with the supplementary moving magnetic and conductive regions. Each of these sub‐problems requires an appropriate proper volume mesh of the associated moving region and its surrounding region, with no need of interconnection. The solutions are transferred from one problem to the other through projections of source fields between meshes.

The consideration of sub‐problems and associated sources, in a sequence of perturbation problems, leads to a significant speed‐up of the repetitive solutions in analyses of moving systems. A free movement in any direction can be considered with no need of remeshing.

When working with the perturbation fields, the volume sources can be limited to the moving regions, what allows for homogeneous perturbation boundary conditions and reduces the computational efforts for projecting and evaluating the sources. The curl‐conformity of the unknown magnetic field is preserved during the whole process thanks to the use of edge FEs for both the magnetic field and the intermediate source quantities. The sub‐problem approach also gives an easy way to directly express the time derivatives in moving frames.

To provide a numerical technique for the quick and simple determination of the switching time instants for field‐circuit coupled problems with switching elements.

3D magnetic vector potential formulation coupled to an electrical circuit with switching elements, for example, diodes, is presented. The change of the state of the switching elements is implemented as a modification of the model topology.

Since every step of the singly diagonally implicit Runge‐Kutta methods delivers not only the solution of this time step but also its stage derivatives, they can be efficiently employed to construct a dense‐output‐based interpolation polynomial, with their roots approximating the switching time instants.

This paper presents a computationally cheap interpolation approach for quick and accurate determination of switching time instances for field‐circuit coupled problems with switching elements. The proposed technique can be successfully incorporated into software packages designed to model coupled problems of different nature, where sudden changes of quality may take place.

The magnetic field strength measurement in a rotational single sheet tester (RSST) is quite difficult to achieve. In fact, flux leakage perturbs the field sensors as well as the homogeneity in the sample area. This paper seeks to present a 3D finite element (FE) model of an RSST taking into account a vector hysteresis model. The use of such model allows analyzing with accuracy the magnetic behavior of the system.

A vector hysteresis model, which is based on a general vectorization of the scalar Jiles‐Atherton model, is incorporated in a 3D FE code, with vector potential formulation.

The vector hysteresis model is validated by comparison with rotational experimental results. A good agreement is observed between calculations and measurements.

This paper shows that a classical scalar hysteresis model can be extended to take into account the magnetic vector behaviour and can be included in a 3D FE code. The methodology for the hysteresis including in the FE formulation is shown. This is useful for the design and analysis of an RSST prototype, improving the measurement techniques.

An original and easy‐to‐implement method to take into account movement (motion) in the 2D harmonic balance finite element modelling of electrical machines is presented. The global harmonic balance system of algebraic equations is derived by applying the Galerkin approach to both the space and time discretisation. The harmonic basis functions, i.e. a cosine and a sine function for each nonzero frequency and a constant function 1 for the DC component, are used for approximating the periodic time variation as well as for weighing the time domain equations in the fundamental period. In practice, this requires some elementary manipulations of the moving band stiffness matrix. Magnetic saturation and electrical circuit coupling are considered in the analysis as well. As an application example, the noload operation of a permanent‐magnet machine is considered. The voltage and induction waveforms obtained with the proposed harmonic balance method are shown to converge well to those obtained with time stepping.

This paper deals with the two‐dimensional finite element analysis in the frequency domain of saturated electromagnetic devices coupled to electrical circuits comprising nonlinear resistive and inductive components. The resulting system of nonlinear algebraic equations is solved straightforwardly by means of the Newton‐Raphson method. As an application example we consider a three‐phase transformer feeding a nonlinear RL load through a six‐pulse diode rectifier. The harmonic balance results are compared to those obtained with time‐stepping and the computational cost is briefly discussed.

The paper seeks to develop dual 3D finite element (FE) formulations for modeling both inductive and capacitive effects in massive inductors, in particular micro‐coils. The paper aims to build circuit relations relating the voltages and the currents in such inductors to be used in circuit coupling.

A circuit relation involving a unique voltage and complementary inductive and capacitive currents is defined for each inductor. The inductive circuit relation is first classically obtained by a FE magnetodynamic model. Then, the capacitive relation is obtained through a FE electric model, using sources evaluated from the first model. The conformity is defined on one hand for the magnetic flux density and the electric field, and on the other hand for the magnetic field and the electric flux density. Mixed FE, i.e. nodal, edge and face elements, are used to satisfy each chosen conformity level for the unknown fields and to naturally define the involved global quantities, i.e. the voltages, currents and charges.

This contribution points out the interest of satisfying conformity properties for the coupled magnetic and electric problems. An accurate computation of these effects is obtained in the critical frequency range of their strong interaction. In addition, the complementarity of dual solutions gives the possibility to estimate the discretisation error.

The mathematical and discretisation tools for any wished conformity level are unified for naturally coupling magnetic and electric problems. The global quantities basis functions involved in the FE circuit relations benefit from a significant support reduction, which facilitates their evaluation and gives them direct physical interpretations.

This paper aims to develop a methodology for progressive finite element (FE) modeling of transformers, from simple to complex models of both magnetic cores and windings.

The progressive modeling of transformers is performed via a subproblem (SP) FE method. A complete problem is split into SPs with different adapted overlapping meshes. Model refinements are performed from ideal to real flux tubes, one-dimensional to two-dimensional to three-dimensional models, linear to nonlinear materials, perfect to real materials, single wire to volume conductor windings and homogenized to fine models of cores and coils, with any coupling of these changes.

The proposed unified procedure efficiently feeds each SP via interface conditions (ICs), which lightens mesh-to-mesh sources transfers and quantifies the gain given by each refinement on both local fields and global quantities, with a clear view on its significance to justify its usefulness, if any. It can also help in education with a progressive understanding of the various aspects of transformer designs.

Models of different accuracy levels are sequenced with successive additive corrections supported by different adapted meshes. The way the sources act at each correction step, up to the full models with their actual geometries, is given a particular care and generalized, allowing the proposed unified procedure. For all the considered corrections, the sources are always of IC type, thus only needed in layers of FE along boundaries, which lightens the required mesh-to-mesh projections between subproblems.

Improperly fitted parameters for the Jiles–Atherton (JA) hysteresis model can lead to non-physical hysteresis loops when ferromagnetic materials are simulated. This can be remedied by including a proper physical constraint in the parameter-fitting optimization algorithm. This paper aims to implement the constraint in the meta-heuristic simulated annealing (SA) optimization and Nelder–Mead simplex (NMS) algorithms to find JA model parameters that yield a physical hysteresis loop. The quasi-static B(H)-characteristics of a non-oriented (NO) silicon steel sheet are simulated, using existing measurements from a single sheet tester. Hysteresis loops received from the JA model under modified logistic function and piecewise cubic spline fitted to the average M(H) curve are compared against the measured minor and major hysteresis loops.

A physical constraint takes into account the anhysteretic susceptibility at the origin. This helps in the optimization decision-making, whether to accept or reject randomly generated parameters at a given iteration step. A combination of global and local heuristic optimization methods is used to determine the parameters of the JA hysteresis model. First, the SA method is applied and after that the NMS method is used in the process.

The implementation of a physical constraint improves the robustness of the parameter fitting and leads to more physical hysteresis loops. Modeling the anhysteretic magnetization by a spline fitted to the average of a measured major hysteresis loop provides a significantly better fit with the data than using analytical functions for the purpose. The results show that a modified logistic function can be considered a suitable anhysteretic (analytical) function for the NO silicon steel used in this paper. At high magnitude excitations, the average M(H) curve yields the proper fitting with the measured hysteresis loop. However, the parameters valid for the major hysteresis loop do not produce proper fitting for minor hysteresis loops.

The physical constraint is added in the SA and NMS optimization algorithms. The optimization algorithms are taken from the GNU Scientific Library, which is available from the GNU project. The methods described in this paper can be applied to estimate the physical parameters of the JA hysteresis model, particularly for the unidirectional alternating B(H) characteristics of NO silicon steel.

This paper seeks to develop a sub‐domain perturbation technique to efficiently calculate strong skin and proximity effects in conductors within frequency and time domain finite element (FE) analyses.

A reference eddy current FE problem is first solved by considering perfect conductors. This is done via appropriate boundary conditions (BCs) on the conductors. Next the solution of the reference problem gives the source for eddy current FE perturbation sub‐problems in each conductor then considered with a finite conductivity. Each of these problems requires an appropriate volume mesh of the associated conductor and its surrounding region.

The skin and proximity effects in both active and passive conductors can be accurately determined in a wide frequency range, allowing for precise losses calculations in inductors as well as in external conducting pieces.

The developed method allows one to accurately determine the current density distributions and ensuing losses in conductors of any shape, not only in the frequency domain but also in the time domain. Therefore, it extends the domain of validity and applicability of impedance‐type BC techniques. It also offers an original way to uncouple FE regions that allows the solution process to be lightened, as well as efficient parameterized analyses on the signal form and the conductor characteristics.