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The purpose of this paper is to use different model order reduction techniques to cope with the computational effort of solving large systems of equations. By appropriate decomposition of the electromagnetic field problem, the number of degrees of freedom (DOF) can be efficiently reduced. In this contribution, the Proper Generalized Decomposition (PGD) and the Proper Orthogonal Decomposition (POD) are used in the frame of the T-Ω-formulation, and the feasibility is elaborated.

The POD and the PGD are two methods to reduce the model order. Particularly in the context of eddy current problems, conventional time-stepping algorithms can lead to many numerical simulations of the studied problem. To simulate the transient field, the T-Ω-formulation is used which couples the magnetic scalar potential and the electric vector potential. In this paper, both methods are studied on an academic example of an induction furnace in terms of accuracy and computational effort.

Using the proposed reduction techniques significantly reduces the DOF and subsequently the computational effort. Further, the feasibility of the combination of both methods with the T-Ω-formulation is given, and a fundamental step toward fast simulation of eddy current problems is shown.

In this paper, the PGD is combined for the first time with the T-Ω-formulation. The application of the PGD and POD and the following comparison illustrate the great potential of these techniques in combination with the T-Ω-formulation in context of eddy current problems.

This paper compares six reliability-based design optimization (RBDO) approaches dealing with uncertainties for a simple mathematical model and a multidisciplinary optimization problem of a safety transformer to highlight the most effective.

The RBDO and various approaches to calculate the probability of failure are is presented. They are compared in terms of precision and number of evaluations on mathematical and electromagnetic design problems.

The mathematical example shows that the six RBDO approaches have almost the same results except the approximate moment approach that is less accurate. The optimization of the safety transformer highlights that not all the methods can converge to the global solution. Performance measure approach, single-loop approach and sequential optimization and reliability assessment (SORA) method appear to be more stable. Considering both numerical examples, SORA is the most effective method among all RBDO approaches.

The comparison of six RBDO methods on the optimization problem of a safety transformer is achieved for the first time. The comparison in terms of precision and number of evaluations highlights the most effective ones.

In this communication, the Preisach and Jiles‐Atherton models are studied to take hysteresis phenomenon into account in finite element analysis. First, the models and their identification procedure are briefly developed. Then, their implementation in the finite element code is presented. Finally, their performances are compared with an electromagnetic system made of soft magnetic composite. Current and iron losses are calculated and compared with the experimental results.

The purpose of this paper is to find out how uncertainties in the characterization of magnetic materials propagate through identification and numerical simulation to the computation of iron losses in electrical machines.

The probabilistic uncertainties in the iron losses are modelled with the spectral approach using chaos polynomials. The Sobol indices are used for the global sensitivity analysis. The machine is modelled with a 2D finite element method and the iron losses are computed with a previously developed accurate method.

The uncertainties propagate in different ways to the different components of losses, i.e. eddy current, hysteresis, and excess losses. The propagation is also different depending on the investigated region of the machine, i.e. Stator or rotor teeth, yokes, tooth tips.

The method does not account for uncertainties related to the manufacturing process, which might result in even larger variability.

A major implication of the findings is that the identification of iron loss parameters at low frequencies does not affect the loss variability. The identification with high-frequency measurement is very important for the rotor tooth tips. The variability in the excess loss parameters is of low impact.

The presented results are of importance for the magnetic material manufacturers and the electrical machine designers. The manufacturers can plan the measurement and identification procedures as to minimize the output variability of the parameters. The designers of the machine can use the result and the presented procedures to estimate the variability of their design.

To take account of the uncertainties introduced on the magnetic properties during the manufacturing process, the present work aims to focus on the stochastic modelling of iron losses in electrical machine stators.

The investigated samples are composed of 28 slinky stators, coming from the same production chain. The stochastic modelling approach is first described. Thereafter, the Monte‐Carlo sampling method is used to calculate, in post‐processing, the iron loss density in a PMSM that is modelled by the finite element method.

The interest of such an approach is emphasized by calculating the main statistical characteristics associated to the losses variability, which are Gaussian distributed for A and Ω formulations.

The originality of the approach is due to the fact that the global influence of the manufacturing process (cutting, assembly, …) on magnetic properties of the considered samples is taken into account in the way of computing the iron losses.

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.

This paper presents a method of coupling magnetostatic potential formulations with electrical circuits for the 3D FEM. Allowing for the current density distribution in stranded conductors, two vectors N and K are introduced. A systematic method of decomposing both vectors in Whitney’s element spaces is suggested. This method can be used for coils with a complex shape. As an example of application a three‐phase transformer is studied.

Classically the magnetic material models are considered with a deterministic approach. Nevertheless, when submitted to the fabrication process, the magnetic core properties are negatively impacted and may be subject to variability during the process. This variability can be of such importance that the performances of the final device (electrical machine) will also present a noticeable variability. The aim of this research is to develop a stochastic model of the magnetic behaviour law of slinky stators used in claw pole generators. The proposed methodology is general and can be applied to other physical properties of electrical devices.

The approach is based on a methodology that uses experimental data and a statistical description of the magnetic properties. To that end, a set of samples issued from the same chain of assembly is considered. The hysteresis model is then developed by accounting for the parameter correlation structure.

It is found that the magnetic hysteresis properties of the studied samples can be modelled by means of statistical tools applied to the parameters of the hysteresis model. The dependency of the parameters can also be accounted for a more accurate modelling.

The paper proposes a statistical approach and a methodology that are applied to the hysteresis modelling accounting for the variability of the magnetic properties. The developed model can be further used in a numerical tool to represent the impact on the performances of electrical devices that are subject to the fabrication process variability.

Mechanical stress can heavily affect the magnetic behaviour law in ferromagnetic materials. This paper, aims to take into account the effect of mechanical stress into a hystreresis model. This model is implemented in a finite element analysis code and tested in the case of a simple system.

A simple extension of the classical Preisach model is proposed, in which a function linked to the Preisach density is parameterized using the mechanical stress as a supplementary parameter. The methodology is based on experimental measurements for identifying the required function. As a first approach, a linear interpolation is used between the measurements in order to have a continuous evolution of the magneto‐mechanical behaviour. This model has been tested in the case of a steel sheet in which width is not constant in order to obtain a non‐uniform distribution of stress and magnetic flux density.

The model can predict the magneto‐mechanical behaviour with a good accuracy in the case of tensile stress. Implementation of the model in finite element analysis has shown that the model can predict the behaviour of steel sheet subject to a non‐uniform stress distribution.

This paper shows that a classical hysteresis model can be extended to take into account the magneto‐mechanical behaviour. This is useful for the design of electrical machines which are subject to non‐negligible mechanical stress.