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What is new in this work is the generic capabilities of the proposed analytical model of permanent magnet machines associated with a novel deterministic global optimization method. That allows to solve some more general inverse problem of designing. The analytical approach is powerful to take into account various kinds of constraints (electromagnetical, thermal, etc.). The inverse problem associated with the optimal design of actuators could then be formulated as a mixed‐constrained optimization problem. In order to solve these problems, interval Branch and Bound algorithms which have already proved their efficiency, have made it possible to determine some optimized rotating machines.

In this work, a method to design a slotless permanent magnet machine (SPMM) based on the joint use of an analytical model and deterministic global optimization algorithms is addressed. The purpose of this study is to propose to include torque ripples as an extra constraint in the optimization phase involving de facto the study of a semi-infinite optimization problem.

Based on the use of a well-known analytical model describing the electromagnetic behavior of an SPMM, this analytical model has been supplemented by the calculus of the dynamic torque and its ripples to carry out a more accurate optimized sizing method of such an electromechanical converter. As a consequence, the calculated torque depends on a continuous variable, namely, the rotor angular position, resulting in the definition of a semi-infinite optimization problem. The way to solve this kind of semi-infinite problem by discretizing the rotor angular position by using a deterministic global optimization solver, that is to say COUENNE, via the AMPL modeling language is addressed.

In this study, the proposed approach is validated on some numerical tests based on the minimization of the magnet volume. Efficient global optimal solutions with torque ripples about 5% (instead of 30%) can be so obtained.

The analytical model does not use results from the solution of two-dimensional field equations. A strong assumption is put forward to approximate the distribution of the magnetic flux density in the air gap of the SPMM.

The problem to design an SPMM can be efficiently formulated as a semi-infinite global optimization problem. This kind of optimization problems are hard to solve because they involve an infinity of constraints (coming from a constraint on the torque ripple). The authors show in this paper that by using analytical models, a discretization method and a deterministic global optimization code COUENNE, this problem is efficiently tackled. Some numerical results show that the deterministic global solution of the design can be reached even if the step of discretization is small.

This paper aims to propose a novel direct method for indefinite algebraic linear systems. It is well adapted for sparse linear systems, such as those of two-dimensional (2-D) finite elements problems, especially for coupled systems.

The proposed method is developed on an example of an indefinite symmetric matrix. The algorithm of the method is given next, and a comparison between the numbers of operations required by the method and the Cholesky method is also given. Finally, an application on a magnetostatic problem for classical methods (Gauss and Cholesky) shows the relative efficiency of the proposed method.

The proposed method can be used advantageously for 2-D finite elements in stepping methods without using a block decomposition of matrices.

This method is advantageous for direct linear solving for 2-D problems, but it is not recommended at this time for three-dimensional problems.

The proposed method is the first direct solver for algebraic linear systems proposed since more than a half century. It is not limited for symmetric positive systems such as many of direct and iterative methods.

This paper demonstrates how the 3D edge element method can be applied to the analysis of permanent magnet motors. The edge element method using the vector magnetic potential has been used. Special attention has been paid to the analysis of systems with inhomogeneously magnetized permanent magnets. The magnets are not skewed and are mounted on a cylindrical laminated rotor. Calculations have been performed for different magnet widths and different distribution of the magnetization vector. Brushless motors with radially and inhomogeneously magnetized magnets have been compared.

The purpose of this paper is to present two optimization methodologies based on interval branch‐and‐bound algorithm.

These techniques decrease the total time of computation, even in spite of discrete nature of some of the design variables. Computational experiments performed on multivariable optimization problem reveal great accuracy and technical validity of developed approaches. As an example, the optimal design of the induction machine (IM) was treated, where the aim was to find the set of the most efficient and, at the same time, cheapest in the manufacturing configurations.

In this paper, two approaches were developed for resolving the problem of optimal design of IM with discrete variables. The strategy of constructing the meta‐models is utilized and put in practice. The methods show relatively high efficiency and robustness of obtained results.

These approaches are the core technics of the developed industrial application, which help identify the set of optimal configurations of IM with the criteria of optimality such as total cost of manufacturing and the efficiency of IM.

An approach for electrical machines design by using a software which links the sizing procedure to the magnetic field computation is presented in this paper. After reviewing the principles of an electrical machine general design, the process of the development and the use of a special link between the dimensions data and the magnetic field computation is described. The whole solution procedure is conducted automatically. Any change on the machine dimensions can be made and the sequence of the CAD tasks can be prepared and run automatically without any user intervention. The whole procedure is applied to a comparative study of different structures of permanent magnets synchronous motors.

The paper highlights the process of electric vehicles optimal design as an inverse problem and presents the global constrained optimization as the best way to solve it.

The electric vehicle optimal design is carried out by a new approach. It consists an electric vehicle design model managed by constrained optimization techniques. It includes sizing models for all drive train components and a vehicle dynamic model build in a new “design way” as an energy‐based model using the response surface methodology. The sensitivity of first simple sizing models can be evaluated by the experimental design method, giving information about the most important part of the model that must be improved.

The result shows the superiority of the constrained optimization technique that treats simultaneously the global optimization and the model adjustment. This method of simultaneous resolution is much more powerful than the successive resolution of each subproblem. The proposed “design approach” used for electric vehicle optimal design offer a large potential in the field of the complex systems design.

The electric vehicle design process is treated on a vehicle design model based on a design approach. It allows determining the drive train components specifications for imposed vehicle performances, taking into account the dynamic model of the vehicle and all components interactions. Furthermore, considering fine components sizing models, the components can be sized taking into account the whole system behavior in an optimal global design.

This paper aims to propose a method to evaluate the information obtained on harmonics calculations and to estimate the precision of results using finite element method for an innovative motor topology in which some well-known meshing rules are difficult to apply.

The same magnetostatic problem is solved with several mesh sizes using both scalar and vector potentials magnetics formulations on a complex topology, an axial claw pole motor (ACPM). The proposed method lies in a comparison between the two weak formulations to determine what information is obtained on harmonics calculations and to estimate its precision. Moreover, an original mesh method is applied in the air gap to improve the numerical results.

The precision on harmonics calculations using finite element method on an ACPM is estimated. For the proposed motor and mesh, only the mean value (even with large mesh) and the first harmonic (with fine mesh) of torque are calculated with a good accuracy. This results confirm that the non-respect of the meshing rules have a strong impact on the results and that scalar and vector potentials magnetics formulations do not give exactly the same results. Before using torque harmonics values in vibration calculations, a finite element model has to be validated by using both fomulations.

This method is time-consuming and only applied on an ACPM in this work.

The axial claw pole motor, for which the classic meshing rules cannot be applied, is a complex topology very under-studied. To improve the calculation of space harmonics, the authors proposed to split the airgap into four parts. Then in the two central parts, the meshing step of the structured mesh is equal to the rotating step.

Analytical models are often used in the first steps of the design process. They are associated with optimisation methods to find a solution that fulfil the design specifications. In this paper, the analytical model of an electric motor is built and proposed as a benchmark to highlight the optimisation methods the most fitted to analytical models.

This paper studies the optimal design of a brushless DC wheel motor. First, the analytical model is presented. Each equation used for the sizing is described, including the physical phenomenon associated, the hypotheses done, and some precautions to take before computing. All equations are ordered to ease their resolution, due to a specific procedure which is then described. Secondly, three optimisation problems with an increasing number of parameters and constraints are proposed. Finally, the results found by the sequential quadratic method point out the special features of this benchmark.

The constraint optimisation problem proposed is clearly multimodal as shown in the results of one deterministic method. Many starting points were used to initialise the optimisation methods and lead to two very different solutions.

First, an analytical model for the optimal design is detailed and each equation is explained. A specific procedure is presented to order all equations in order to ease their resolution. Secondly, a multimodal benchmark is proposed to promote the development of hybrid methods and special heuristics.

The purpose of this paper is to present a method for computing voltage spikes endured by the insulation of the first coils of high-temperature (HT°) synchronous machines fed by PWM inverters that deliver fast-fronted voltage pulses.

The transient state following each steep edge is computed by SPICE using the global high-frequency (HF) equivalent circuit of the motor winding. This equivalent circuit is automatically built using the proposed elementary coil model. Two inorganic HT° technologies are compared: the first one uses a round copper wire insulated by a thin ceramic layer and the second one is made with an anodized aluminum strip.

The winding made with an anodized aluminum strip, which has a higher turn-to-turn capacitance, yields a better voltage distribution between coils of the machine.

The elementary coil equivalent circuit is computed from impedance measurements performed on an elementary coil. Another starting point could be developed with an FE analysis to determine the parameters of the HF equivalent circuit, which would avoid the need for a prototype coil before the machine design.

For inorganic motors, the insulation layers have poorer electrical characteristics compared with standard organic ones. Therefore, the computation of voltage spikes distribution along the coils of each phase represents a major issue in the design of HT° machines.

The presented approach is a step toward the design of HT° (400-500°C) actuators fed by PWM inverters based on fast SiC electronic switches.