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This article presents a bridge between topology optimization (TO) and additive manufacturing. On the one hand, it presents an algorithm that considers the design variables as binary and then solves the problem by binary linear programming to optimize a ferromagnetic core. On the other hand, a 3-D printing process is developed to manufacture the shapes obtained by TO. Finally, these magnetic parts are characterized through electrical measurements.

Optimization using finite element analysis and the adjoint variable method to solve engineering problems appears in various application areas. However, to the best of the authors’ knowledge, there is a lack of detailed explanation on the implementation of the adjoint variable method in the context of electromagnetic modeling. This paper aimed to provide a detailed explanation of the method in the simplest possible general framework. Then, an extended explanation is offered in the context of electromagnetism. A discrete design methodology based on adjoint variables for magnetostatics was formulated, implemented, and verified. This comprehensive methodology supports both linear and nonlinear problems. The framework provides a general approach for performing a very efficient and discretely consistent sensitivity analysis for problems involving geometric and physical variables or any combination of the two. The accuracy of the implementation is demonstrated by independent verification based on an analytical test case and using the finite-difference method. The methodology was used to optimize the parameters of a superconducting energy storage device and a magnet press and the optimization of the topology of an electromagnet. The objective function of each problem was successfully decreased, and all constraints stipulated were met.

Decision-making is a crucial and difficult step in the design process of complex systems such as the hybrid powertrain. Finding an optimal solution requires the system feedback. This can be, depending on the granularity of the models at the component level, highly time-consuming. This is even more true when the system’s performance is determined by its control. In fact, various possibilities can be selected to deliver the required torque to the wheels during a driving cycle. In this work, two different design strategies are proposed to minimize the fuel consumption and the cost of the hybrid powertrain. Both strategies adopt the iterative framework which allows for the separation of the powertrain design problem and its control while leading to system optimality. The first approach is based on model reduction, while the second approach relies on improved cycle reduction techniques. They are then applied to a parallel hybrid vehicle case study, leading to important cost reduction in reasonable delays and are compared using different metrics.

Metamodels proved to be a very efficient strategy for optimizing expensive black-box models, e.g., Finite Element simulation for electromagnetic devices. It enables the reduction of the computational burden for optimization purposes. However, the conventional approach of using metamodels presents limitations such as the cost of metamodel fitting and infill criteria problem-solving. This paper proposes a new algorithm that combines metamodels with a branch and bound (B&B) strategy. However, the efficiency of the B&B algorithm relies on the estimation of the bounds; therefore, we investigated the prediction error given by metamodels to predict the bounds. This combination leads to high fidelity global solutions. We propose a comparison protocol to assess the approach’s performances with respect to those of other algorithms of different categories. Then, two electromagnetic optimization benchmarks are treated. This paper gives practical insights into algorithms that can be used when optimizing electromagnetic devices.

A multiobjective branch and bound method is presented and applied to the bi-objective combinatorial optimization of a safety transformer. New criteria are proposed for the branching and discarding. They are based on the Pareto dominance and contribution metric. The comparison with exhaustive enumeration and non-dominated sorting genetic algorithm confirms the solutions. It appears that exact and approximate methods are both very sensitive to their control parameters.

This paper compares different probabilistic optimization methods dealing with uncertainties. Reliability-Based Design Optimization is presented as well as various approaches to calculate the probability of failure. They are compared in terms of precision and number of evaluations on mathematical and electromagnetic design problems to highlight the most effective methods.

Meta-models proved to be a very efficient strategy for optimization of expensive black-box models, e.g. Finite Element simulation for electromagnetic devices. It enables to reduce the computational burden for optimization purposes. Kriging is a popular method to build meta-model. Its statistical properties were firstly used in efficient global optimization for unconstrained problems. Afterwards many extensions were introduced in the literature to deal with constrained optimization. This paper presents a comparative study of some infill criteria for constraints handling and a new strategy for parallelization of the expensive computations of models.

Reliability-Based Design Optimization (RBDO) in electromagnetic field problems requires the calculation of probability of failure leading to a huge computational cost in the case of expensive models. Three different RBDO approaches using kriging surrogate model are proposed to overcome this difficulty by introducing an approximation of the objective function and constraints. These methods use different infill sampling criteria (ISC) to add samples in the process of optimization or/and in the reliability analysis. Several enrichment criteria and strategies are compared in terms of number of evaluations and accuracy of the solution.

This paper deals with the optimal design of a direct-driven brushless DC permanent-magnet (BLDCPM) generator over a long-term wind speed cycle operation. Such a large wind speed profile causes long processing time in the search of the optimal solution, therefore a simplification method of the profile based on an original barycenter method is proposed and applied to the power losses computation of the wind energy system. As a result, the optimization methodology relies on two modeling levels different in simulation time and approach and is based on a constrained mono-objective problem with adequate optimization strategy and algorithm that aims at reducing the global system power losses for the given wind speed profile while finding the optimal geometrical and electrical features of the BLDCPM wind generator.

Three approaches are proposed for the design of a hybrid railway power substation taking into account the control of the storage system over one year. The first one is based on a piecewise linearization of the cost function and solved with linear programming. The others decompose the whole problem in two levels with lower dimensionality. Collaborative optimization solves it with a double-loop scheme while Benders decomposition allows a sequential resolution. This last gives the same solution as linear programming in about 5 times more computing time and can be used with a non-linear cost function.

Renewable energy sources and storage units’ integration in the railway power substations is an alternative solution to handle the energy consumption, due to railway traffic increase and electricity market liberalization. To integrate this technology change in the railway network, an adapted energy management system has to be established. However, when considering only energy efficiency aspects on the energy management strategy, an economical viable solution cannot be ensured. This paper proposes a supervision strategy based on multi-criteria approach including energetic, environmental and economic constraints. The energy management objectives such as reducing the network power demand, favoring local renewable consumption and ensuring storage availability are treated in different time levels. Economic aspects are first integrated in predictive mode based on forecast data. Then a supervision strategy is developed based on fuzzy logic approach and graphical tool to build it. An optimization study of the supervision strategy is proposed in order to conclude on system performance. Simulation results are discussed for different scenarios cases and the reaction of the hybrid railway power substation is detailed. Results show that this methodology can be successfully applied for hybrid systems energy management in order to improve their energy efficiency.

Optimal design with the finite element models is often expensive in terms of the computation time. The space-mapping technique allows benefiting both the fast calculation of the coarse model and the accuracy of the fine one. In this paper, an n-level output space-mapping algorithm is proposed. The results show that the proposed algorithm allows saving computation time compared to traditional 2-level output space mapping algorithm

We present an optimization problem that requires the modeling of a multirate system composed of subsystems with different time constants. We use waveform relaxation method (WRM) in order to simulate such a system, but computation time can be penalizing in an optimization context. Thus, we apply output space mapping (OSM) that uses several models of the system to accelerate optimization. WRM is one of the models used in OSM.

Multi-objective optimization with 3D finite element model is a complex and time consuming process. Output space-mapping techniques allow having an affordable computation cost with a minimum number of computationally expensive FEM evaluations. In this paper, a three-level adapted output space-mapping technique is proposed to assist two-objective optimization problems. Three models having different granularity and describing the same device are used jointly in the optimization process. The results for the safety isolating transformer show that the proposed algorithm allows saving a substantial amount of computation time compared to the classical two-level output space-mapping technique.

Optimal design with finite element model is often expensive in terms of computation time. The output space mapping technique allows benefiting both the rapidity of the analytical model and the accuracy of the finite element model. In this paper, a three-level output space-mapping technique is proposed to reduce the computation time. Three models having a different granularity and describing the same device are used jointly within the optimization process. Proposed strategy is applied for solving the optimal design problems of two electromagnetic devices. Results show that three-level output space mapping strategy allows saving a substantial computation time compared to the classical two-level output space-mapping.

This paper shows two interesting results in multidisciplinary optimization. The first one is a comparison study of a single phase transformer optimization process using three multidisciplinary design optimization formulations. A comparison using analytical models was made on convergence rates and computing time. The second one shows the benefits of using multidisciplinary optimization formulations within output space-mapping technique in order to reduce its computing time once more and to allow parallelization of computations. 3D finite element models are used in this second part

The optimal design of electromagnetic devices needs to address two particular aspects: 1) the use of accurate tools and 2) the limited time budget affected to this task. In order to respond to these issues, two low evaluation budget multiobjective optimization techniques — efficient global optimization (EGO) and output space mapping (OSM) — are investigated in this paper with regard to a biobjective optimization benchmark. The device to be optimally sized is a low-voltage safety isolating transformer, represented through two levels of modeling: 1) coarse (analytical model) and 2) fine (numerical 3-D FEM). The biobjective character of the problem is accounted for by OSM through an epsilon-constraint technique. A transformation technique is set up with EGO by considering the constraints as an additional objective function in order to handle the constraints of the initial optimization problem. The biobjective comparison of the two techniques on the transformer benchmark is discussed.

The optimization of electromagnetic devices by direct use of finite element models is computationally expensive. This paper presents two effective surrogate-assisted optimization algorithms: Output Space Mapping and Efficient Global Optimization which are employed with regard to a minimum number of finite element model evaluations. A parallel between both algorithms is made through a single phase safety isolating transformer optimization problem using 3D finite element models.

Multi-objective optimizations by means of 3-D finite element models result in very high computation burden. To have an affordable computation cost, the output space-mapping technique is applied with a new method where the scalar correction of the model outputs is replaced by a set of corrective functions. This method is used for the bi-objective optimization of a transformer and allows finding the complete Pareto optimal set in less than two days on a laptop.

In order to optimize the design of an enclosed induction machine of railway traction, a multiphysical model is developed taking into account electromagnetic, mechanical and thermal flow phenomena. The electromagnetic model is based on analytical formulations and allows calculating the losses. The thermal flow modeling is based on an equivalent thermal circuit which has the feature to consider the flow structure inside the machine. In this way, a numerical study has been carried out to evaluate this internal flow structure depending on the rotational speed. The results of the multi-physical model are confronted with experimental results.

In this paper, traction system design in carried out with a multilevel optimization technique called Target Cascading. This methodology is based on a hierarchical breaking down and allows solving a problem with multiple parallel optimizations. The large-scale system design problem is usually decomposed into several linked optimization subproblems according to project organization structure. Target Cascading gives a new approach to formulate and to solve the complex system design optimization problem in the electrical field. The problem formulation is more suitable to this kind of problem than conventional methods because it is closer to a work organisation of design engineers.

The optimal design method is applied to a complex system design. It replaces trial-and-error process, often performed by engineers, while ensuring the system optimality. A surrogate model is used in order to accelerate the optimization process when the simulation time is high. A hybrid optimization algorithm is proposed allowing a compromise between global and local search. The optimization of tram traction system is presented as an application of this method.

In this paper, traction system design in carried out with a multilevel optimization technique called Target Cascading. This methodology is based on a hierarchical breaking down and allows solving a problem with multiple parallel optimizations. The large-scale system design problem is usually decomposed into several linked optimization subproblems according to project organization structure. Target Cascading gives a new approach to formulate and to solve the complex system design optimization problem in the electrical field. The problem formulation is more suitable to this kind of problem than conventional methods because it is closer to a work organisation of design engineers.

The optimal design method is applied to a complex system design. It replaces trial-and-error process, often performed by engineers, while ensuring the system optimality. A surrogate model is used in order to accelerate the optimization process when the simulation time is high. A hybrid optimization algorithm is proposed allowing a compromise between global and local search. The optimization of tram traction system is presented as an application of this method.

In this paper, target cascading methodology is presented and adapted to improve its convergence in the case of the optimisation design of an electric system. With target cascading, the overall system problem is decomposed into sub-problems, which are solved separately and coordinated via conjoint targets. The methodology allows solving complex problem with strong interactions.

This paper presents a new method to handle discrete or mixed constrained optimization problems based on a high-fidelity 3D finite element computational model. The original idea aims to combine branch-and-bound method that is enabling to ensure a global optimal solution and space-mapping techniques that allow to speed-up the optimization procedure by aligning a fine model and a coarse model. These algorithms are applied to design optimally a safety isolating transformer with categorical and integer design variables.

The optimal design method is applied to a complex system design. It replaces trial-and-error process, which is often performed by engineers, while ensuring the system optimality. The surrogate model is used in order to accelerate the optimization process when the simulation time is high. A hybrid optimization algorithm is proposed allowing a compromise between global and local search. The optimization of tramway traction system is presented as an application of this method.

Particle swarm optimization (PSO) and ant-colony optimization (ACO) are novel multi-agent algorithms able to solve complex problem, as for example, multi-level optimization problems. By consequence, it would seem wise to compare their performances before adapt them for such problems. For this purpose, both algorithms are compared together and with Matlab’s GA in term of accuracy of the solution and computation time. In this paper the optimization is applied on the design of a brushless DC wheel motor that is known as a nonlinear multimodal benchmark.

This paper describes a new methodology for using artificial neural networks (ANN) and finite element method (FEM) in an electromagnetic inverse problem (IP) of parameters identification. The approach is used to identify unknown parameters of ferromagnetic materials. The methodology used in this study consists in the simulation of a large number of parameters in a material under test, using the FEM. Both variations in relative magnetic permeability and electric conductivity of the material under test are considered. Then, the obtained results are used to generate a set of vectors for the training of generalized radial basis function neural networks (RBFNN). Finally, the obtained neural network (NN) is used to evaluate a group of new materials, simulated by the FEM, but not belonging to the original dataset. The reached results demonstrate the efficiency of the proposed approach.

The design of electric machines is often expressed in term of optimization problems with continuous parameters, seldom with discrete ones. However, these continuous problems are in the second part of the design process and often limited to the fine tuning of some parameters corresponding to the structure selected in the first part. There is a lack of decision tools for the choice of the structure and materials. In this stage, the parameters are mainly discrete and non-classable. Moreover, the production in very small series practiced by some small and medium firms must be necessarily supported by standards. It is thus a question of choosing among a great but finished number of solutions rather than to optimize some dimensions finely. Two analytical models and two finite element models are built and compared in terms of accuracy and computation time. They can be used as a benchmark to compare algorithms for multi-level and combinatorial optimizations. The discrete optimization of the transformer is done using branch and bound methods. The multi-level optimization is performed using one analytical model and the 3D FE model jointly thanks to the space-mapping techniques.

The paper presents a comparison between sinusoidal and trapezoidal waveforms in order to reduce the torque ripple and the power to grid fluctuation for large direct-drive PM wind generator. Trapezoidal waveform brings 28% higher power density but also two major drawbacks: necessity to vary the DC bus voltage and requirement for an additional filter on the DC bus.

The sequential quadratic programming (SQP) and genetic algorithms (GA) are finely tuned on the optimal design of a brushless DC wheel motor. Combining both methods, a hybrid approach is tested. Multiobjective optimizations are performed using Nondominated Sorting Genetic Algorithm (NSGA-II), Strength Pareto Evolutionary Algorithm (SPEA2), and a variable weighted sum of objectives with the sequential quadratic programming. The Pareto fronts are compared in term of accuracy, uniformity, and coverage criteria using some quality indicators.

In order to increase the power capability of direct-drive PM wind generators with respect to established quality criteria like the electromagnetic torque and the power transferred to the grid, a polyphased multi-star system is studied. The influence of the number of stars, their phase shift and the waveform of the electromotive force are investigated. The possible configurations, i.e. the numbers of magnets and slots, are found and compared.

L’article présente une démarche de conception qui aboutie à la réalisation d’un moteur synchrone et à son intégration dans une pompe étanche pour fluides corrosifs. La machine synchrone à flux axial est proposée et sa construction dans le cadre de petites et moyennes séries est simplifiée. Pour cela, une structure à bobinages concentrés et à encoches droites est retenue. Les différentes configurations entre le nombre de pôles et de dents sont présentées. L’étape de dimensionnement analytique est détaillée et permet de sélectionner la configuration la mieux adaptée à l’application. Une dernière étape de modélisation éléments finis permet de valider les hypothèses faites lors du dimensionnement analytique et aide également au choix de la configuration la plus appropriée. Il apparaît clairement que l’utilisation des bobinages concentrés dans les structures à flux axial conjugue compacité et facilité de fabrication.

An analytical model of an electric machine is built for optimal design. This model is useful in the first steps of the design process as many parameters are unknown and have to be set under rigorous constraints. The optimal design of a brushless DC wheel motor is detailed, including sizing equations. At the moment, some benchmarks exist to compare optimisation methods but they use finite element models. As no optimisation method is universally better, the proposed problem will highlight those well fitted to analytical models.

Specificities of optimal design problem in electromagnetic are emphasized. To overcome the revolting difficulties met with the classical stochastic methods, a new tabu search algorithm for global optimization of multimodal functions with continuous variables is presented and used for solving some of this kind of electromagnetic optimization problems such as Bruhless DC motor, SMES optimization and die mold press. It is compared favorably with Hu’s tabu search and universal tabu search methods

The optimisation of two electromagnetic devices is carried out by means of various stochastic and deterministic methods, which are then compared. Their respective advantages and disadvantages are pointed out. A complementarity between the stochastic and deterministic methods is highlighted and leads to a mixed strategy combining global optimisation, accuracy and respect of the constraints.

In this paper, several ways to reduce the manufacturing cost of permanent magnet brushless direct current motors are explored. Actually, the most promising way seems to be a modular structure with axial flux, rolled metal sheet, straight slots and concentrated windings. Rules for optimality are presented and applied to transform a distributed winding into a concentrated one. All combinations of the number of poles with the number of teeth are explored and the five most interesting configurations are detailed. A calculation sheet is derived from the specifications, and gives the performances, the temperatures, the price and the bulk of the motor. It is validated using finite element analysis at no-load, locked rotor, and full-load. An optimization process is used to minimize the cost with respect to technical constraints. A prototype is built and shows good agreement between measurements and specifications. Moreover, the photos of axial flux motors with concentrated and distributed windings, side by side, emphasize the possible reduction in the manufacturing cost of the stator.

A new tabu search algorithm for global optimization of multimodal functions with continuous variables is presented. The taboo list contains all points and a prohibited zone around each point that depends on the value of the objective function and decreases as the number of iteration increases. The numerical results obtained by solving problems 22 and 25 of the TEAM workshop demonstrate the speed effectiveness of the proposed method. It is compared favorably with other tabu search, genetic algorithm, and simulated annealing.

In this paper, a new stop criterion is proposed for genetic algorithms using a response surface fitted on the best individuals. This criterion is tested on a superconducting magnetic energy storage optimization and compared with stop criteria found in the literature that are reviewed and detailed.

The problem addressed here is to improve the efficiency of a brushless DC motor while respecting constraints on weight, size and demagnetization current. Genetic algorithms are used to solve this problem since they have been proved to be a good method of searching for the global optimum and dealing with the numerous variables

In this paper, an optimization method, based on fractional experimental design, is proposed and applied to the design of a brushless DC motor. Taguchi’s methodology and a limited number of finite element simulations are used to build an approximation of the cost function of an optimization problem. This approximation allows to quickly locate the global optimum.

A car alternator with claw poles is typically a 3D device because its shape is not axi-symmetrical nor XY-symmetrical. A 3D finite element model can be useful to simulate the thermic behavior of the machine but is rarely available. In this paper, it is shown that a 2D simulation can fit even if all the thermal phenomenon relating to the missing direction are neglected. The alternator have been modeled in two different sections to show their respective reliability. Moreover, thermal hybrid conductivities have been defined to take into account the succession of the different materials in the missing direction.

In this paper, Powell’s conjugated directions method is used to optimize the teeth and magnet shapes of a brushless direct current (BDC) wheel motor. The aim of optimization is to have the most constant electromotive force (e.m.f.) at no-load during the phase conduction with a value equal to the half of the lower voltage supply. The e.m.f. is computed using a finite element model (FEM). The FEM and Powell’s method are integrated in an optimization loop in order to find the best shape for the BDC motor. A comparison between Powell’s conjugated directions method and the conjugated gradient method is carried out. It shows the superiority of the conjugated direction method that doesn’t need the gradient of the objective function.

This paper presents the shape optimization of a switched reluctance motor (SRM) using a finite element model and several deterministic methods. Firstly, the experimental design method is used to determine the SRM shape that produces the higher static torque, then a shape sensitivity analysis is carried out beyond the feasible triangle limits. Secondly, deterministic methods are compared on SRM dynamic optimization with regard to motor performances and the number of finite element simulations needed. The optimized motor shape and transistor drive allow a high torque without a large current peak.

Une éolienne synchrone à aimants permanents, flux axial et attaque directe est conçue au moyen d’un modèle multi physiques, multi niveaux et multi échelles. Les bobinages concentrés offrent de nombreux avantages pour les machines polyphasées. Les différentes configurations sont décrites et classées. Une optimisation multi objectifs permet de trouver la meilleure possible et propose même un ensemble de compromis au concepteur.

Les auteurs proposent une approche pour l’enseignement de la modélisation numérique des machines électriques statiques avec le logiciel Opera2D. Elle est appliquée depuis 3 ans aux élèves ingénieurs en dernière année de l’Ecole des Hautes Etudes Industrielles de Lille (H.E.I.). La démarche pédagogique repose sur une série de travaux pratiques (T.P.) qui sont précédés par un cours magistral. Tout au long des séances, le parallèle entre les méthodes analytiques et la méthode des éléments finis est fort pour mettre en évidence les avantages et inconvénients de chaque méthode.

This paper presents an application of Evolutionary Computation (EC) to the benchmark of the safety isolating transformer problem. The benchmark adopts multidisciplinary optimization strategies, namely the multidisciplinary feasible (MDF) and the individual discipline feasible (IDF) formulations. The benchmark meets the requirements of engineers and scientists working with machine design problem, such as in the first part of the design process that is the choice of structure and materials. The EC methods employed in this paper are based on Evolutionary Algorithms (EAs), namely two variants of Differential Evolution (DE), two variants of Hybrid Adaptive DE (HyDE) and the Vortex Search (VS). The results showed in this paper suggest that EA methods are competitive with the classical optimization method, the sequential quadratic programming (SQP). Among the developed EAs, HyDE-DF is able to obtain better values than SQP on a significant battery of trials.

The motivation of this communication is to test a method for computing the gradient of a quantity of interest for an electromagnetic device modeled by finite elements method (FEM). The gradient is a key ingredient in many important tasks: sensitivity analysis, robust design, design optimization and reliability analysis. It can be computed efficiently using the adjoint method, its advantage is not only reducing the computational cost of computing the gradient compared to different methods (e.g. finite difference) but also handling the numerical noise that could appear when re-meshing in the case of finite elements analysis.

Meta-models proved to be a very efficient strategy for optimization of expensive black-box models, e.g. Finite Element simulation for electromagnetic devices. It enables to reduce the computational burden for optimization purposes. Kriging is a popular method to build meta-model. Its statistical properties were firstly used in efficient global optimization for unconstrained problems. Afterwards many extensions were introduced in the literature to deal with constrained optimization. This paper presents a comparative study of some infill criteria for constraints handling and a new strategy for parallelization of the expensive computations of models.

Reliability-Based Design Optimization (RBDO) in electromagnetic field problems requires the calculation of probability of failure leading to huge computational cost in the case of expensive models. Three different types of RBDO approaches using kriging surrogate model are proposed to overcome this difficulty by introducing an approximation of the objective and of the constraints. These methods use different infill searching criteria to add new samples in the process of optimization or/and in the reliability analysis. The enrichment criteria and the best suited enrichment strategies are discussed in this communication. These approaches are compared in terms of number of evaluations and accuracy of the solution.

This paper reports on the modelling of a direct-driven brushless DC permanent-magnet (BLDCPM) generator to be used in micro-wind turbine applications for long-term wind-speed profiles. Three models are investigated and confronted in precision and computation time. For power loss calculation of BLDCPM generator operating under large time-scale wind-speed fluctuations, an original barycenter method is applied.

In this paper a multiobjective branch and bound method is presented and applied to the bi-objective combinatorial optimization of a safety transformer under constraints. The comparison with exhaustive enumeration and non-dominated sorting genetic algorithm confirms the solutions. It appears that exact and approximate methods are both very sensitive to their control parameters.

This paper presents the design of a Hybrid Railway Power Substation by collaborative and multilevel optimizations. The principles of both approaches are detailed such as their advantages and drawbacks. Their computing time and convergence are compared on the HRPS optimization problem.

This paper compare different probabilistic optimization methods dealing with uncertainties. Methods of Robust Design Optimization (RDO), Reliability-Based Design Optimization (RBDO) and Reliability-Based Robust Design Optimization (RBRDO) are presented and the approaches to calculate the moments and probability of failure are introduced. Then mathematical and electromagnetic design problems are tested to show the effectiveness of these methods.

Because of the rail network development, power demand of railway power substation (RPS) becomes increasingly important. The integration of renewables energies could compensate this need and reduce pollution. Nevertheless the known intermittency factor of these energies makes difficult to estimate the amount of produced power. By introducing a storage device, the hybrid RPS (HRPS) may operate without the grid and could ensure a good power quality. The storage device should be accurately used according to the consumed power, the produced power and the evolution of prices fixed by power supplier. To enhance the design of HRPS, the energy management strategy should be suitable in the long term. However, a high number of unknowns is induced by these temporal variables and thereby two different formulations are investigated within the linear programing. By taking into account economical aspects, the optimal design of each source and the energy management strategy are known for a time step of ten minutes during one year.

Two model order reduction approaches are applied to reduce the computational time of a quasistatic finite element problem. Both methods are compared on an academic example.

Railway traffic increases and electricity market liberalization constrain the railway actors to consider new solutions to handle energy consumption. Hence, a technology change in the railway electrical systems is considered through the integration of renewable energy sources and storage units. In this context, a relevant methodology is proposed here for optimal design and operation analysis of railway hybrid power substations. This method is useful for the analysis and improvement of future railway power network efficiency.

The modeling of a multirate system -formed by components with heteroge- neous time constants- can be done using fixed-point method. This method allows a time- discretization of each subsystem with respect to its own time constant. In an optimization process, executing the loop of the fixed-point at each model evaluation can be time consum- ing. By adding one of the searched waveform of the system to the optimization variables, the loop can be avoided. This strategy is applied to the optimization of a transformer.

Railway traffic increases and electricity market liberalization constrain the railway actors to consider new solutions to handle the energy consumption. Hence, a technology change in the railway electrical systems is considered through the integration of renewable energy sources and storage units. In this context, a relevant methodology is proposed here for optimal design and operation analysis of railway hybrid power substations. This method is useful for the analysis and improvement of future railway power network efficiency.

For the optimization of a component from a multirate system, the article presents benefits of the joint use of several models for the optimization and of fixed-point strategy for the modeling. Thus, space mapping allows reducing time computation of an optimization process by limiting the number of evaluations of time consuming models. In the case of multirate problems, these models can be modeled by Waveform Relaxation Method to provide an additional time saving.

In the communication, the WRM and the POD techniques are applied to study a transformer supplied by a power converter. The transformer is modeled by Finite Element Method. A reduced model of the transformer provided by the POD tech- nique is used to couple the power converter and the transformer using the WRM technique.

The optimal design of electromagnetic devices needs to address two particular aspects: the use of accurate tools, and the limited time budget affected to this task. In order to respond to these issues, two low evaluation budget multi-objective optimization techniques - Efficient Global Optimization (EGO) and Output Space Mapping (OSM) - are investigated in this paper with regard to a bi-objective optimization benchmark. The device to be optimally sized is a low-voltage safety isolating transformer, represented through two levels of modeling: coarse (analytical model) and fine (numerical 3D FEM). The bi-objective character of the problem is accounted for by OSM through an epsilon-constraint technique. A transformation technique is set up with EGO, by considering the constraints as an additional objective function, in order to handle the constraints of the initial optimization problem. The bi-objective comparison of the two techniques on the transformer benchmark is discussed.

The optimal design of electromagnetic devices needs to address two particular aspects: the use of accurate tools, and the limited time budget affected to this task. In order to respond to these issues, two low evaluation budget multi-objective optimization techniques - Efficient Global Optimization (EGO) and Output Space Mapping (OSM) - are investigated in this paper with regard to a bi-objective optimization benchmark. The device to be optimally sized is a low-voltage safety isolating transformer, represented through two levels of modeling: coarse (analytical model) and fine (numerical 3D FEM). The bi-objective character of the problem is accounted for by OSM through an epsilon-constraint technique. A transformation technique is set up with EGO, by considering the constraints as an additional objective function, in order to handle the constraints of the initial optimization problem. The bi-objective comparison of the two techniques on the transformer benchmark is discussed.

Optimal design in engineering is often constrained by a limited budget of time. The simulation models used in each field offer a good substitute for the real process to be designed, but the evaluation time of such a model is very high. In this paper a surrogate assisted multi-objective optimization algorithm is applied to solve the problem of optimal sizing of a super capacitor pack on board a tramway. The results are compared to those obtained using the NSGA-II algorithm.

This paper presents an ecodesign approach of an auxiliary transformer used by a railway traction using a bi-objective optimization method. Amongst the objectives, one is to minimize environmental impacts. Three criteria are tested: the global warming potential, the total energy for the life cycle, and Impact 2002+ that is an aggregation of impacts. The results obtained by the different criterions are compared to show their influence on the dimension parameters of the transformer and the mass of its active parts

Ce papier propose différentes approches introduisant l’éco-conception dans la procédure d’optimisation des dispositifs électromagnétiques. Les évaluations des indicateurs d’impact de toutes étapes du cycle de vie sont obtenues par le logiciel EIME (Environmental Information and Management Explorer) utilisant la méthodologie de l’Analyse du Cycle de Vie (ACV). L’idée de la première approche est d’évaluer tous les impacts environnementaux des quatre étapes (fabrication, distribution, utilisation et valorisation) de l’ACV d’un dispositif électromagnétique. La comparaison des impacts de chaque étape permet les arbitrages. La deuxième approche est d’établir un modèle environnemental qui est directement utilisé dans une optimisation multi-objectif. Ce modèle surrogate est construit en utilisant la méthode des plans d’expériences (DoE) et le logiciel EIME. Ce modèle d’impact est ensuite combiné avec des modèles économique et thermo-électromagnétique. Des algorithmes d’optimisation multi-objectif fournissent le front de Pareto. Une des machines électriques les plus utilisées, un transformateur de sécurité, est considéré comme un benchmark pour tester ces deux approches de l’éco-conception. Sa conception actuelle sert de référence.

In this paper, traction system design in carried out with a multilevel optimiza- tion technique called Target Cascading. This methodology is based on an object- based decomposition and allows solving the problem with parallel optimizations. The large-scale system design problem is usually decomposed into several linked subproblems according to project organization structure. Target Cascading gives a new approach to formulate and to solve the complex system design optimization problem. The problem ormulation is more suitable to this kind of problem than conventional method.

Multi-objective combinatorial optimization problems are typically of engineering design problems. Such hard optimization problems require very long computational times, regardless of the chosen solving method: exact or approximated. In this paper, multi-objective combinatorial optimization algorithms based on combining exact methods and Branch-and-Bound global procedures which seek good solutions at a reasonable computational cost are proposed. They are applied to a safety transformer design problem and provide Pareto optimal fronts.

Analytical Target Cascading (ATC) is a hierarchical multi-level design methodology. According to the state of the art, it is conrmed that for problems with unattainable targets, strict design consistency cannot be achieved with nite weighting factors. Then a new formulation is proposed to improve the ATC convergence. The weighted sum of deviation metric is transformed into a multi-objective formu- lation. An original optimization problem with a single global optimal solution is used as a benchmark. Thereafter an optimal design of tram traction system is used as an application example in the aim to demonstrate the robustness of the algorithm.

The finite element models used in electrical engineering are very time consuming. For example, one simulation of a safety isolating transformer with a 3D magneto-thermal coupled model requires 2hours. The multi-objective optimization problem of this device has two conflicting objectives: minimize the total mass, and maximize the efficiency. In order to build the Pareto optimal set, two algorithms: Non-dominated Sorting Genetic Algorithm (NSGA II) and Adaptive Weighted Sum method using the Sequential Quadratic Programming (AWS-SQP) are often used. NSGA-II is a population-based multi-objective evolutionary algorithm. AWS-SQP is still and may always remain the most frequently used approach. This method consists on the association of each objective function with a weighting coefficient and optimizes the weighted sum of the objectives. In this way, the developers of AWS, Kim and Weck (2004 and 2005), proposed to change the weights adaptively and imposed additional inequality constraints to find the concave parts of the Pareto front. Unfortunately, both algorithms require a very high number of model evaluations what is not compatible with 3D FE models. Then, in order to reduce the computational time and increase the accuracy of the Pareto optimal set the space-mapping technique (SM) is used. SM allows aligning “coarse” model and “fine” model responses. In this case study, the coarse computationally cheaper model is a lumped mass (LM) model, and the fine computationally expensive model is the 3D FE model. In this paper, SM is combined with the both multi-objective optimization algorithms. Both optimal Pareto set are compared such as the time required building them. A special attention is taken on the way to align both model responses on the whole Pareto optimal set.

Optimal design of electrical devices is usually performed by means of analytical models. But only 3D finite element models can ensure high fidelity modeling and realistic optimization. However, their computational cost can make the optimization a daunting task. Here, we combine space-mapping technique and multi-objective optimization to improve computational efficiency, making then the 3D finite element an effective optimization tool.

Continuous decreasing in price of permanent magnet attracts many industries to invest in the development of permanent magnet synchronous motor, especially in traction application because of its high efficiency and compactness. In this paper a design of Surface-Mounted Permanent Magnet (SMPM) synchronous motor has been studied. The optimal design of SMPM motor can be achieved by applying a global design process and the multiobjective optimization.

Space-mapping optimization techniques allow to align low-fidelity and high-fidelity models in order to reduce the computational time and increase the accuracy of the solution. The main idea is to build an approximate model from the difference of responses between both models. Therefore the optimization process is computed on the surrogate model. In this paper, some recent approaches of space-mapping techniques such as aggressive-space-mapping, output-mapping and manifold-mapping algorithms are applied to optimize a safety isolating transformer. The electric, magnetic and thermal phenomena of the device are modelled by an analytical model and a 3D finite elements model. It is considered as a benchmark for multi-level optimization to test different algorithms.

In much system design there is a hierarchy of decision-makers and decisions are taken at different levels in this hierarchy. The engineering system optimization problem is a complicated task because of the interactions between sub-systems and also between engineering domains e.g. mechanical, electrical, and thermal. Many engineering teams are involved in this design process. Unfortunately, to now there is no universal methodology for solving such hard problems. As ant-colony optimization (ACO) is a novel multi-agents method, it’s used to solve multi-level optimization problems. Contrary to genetic algorithms, ACO draws inspiration from the collaborative behavior of certain ants. ACO is a global optimization method that is considered as a population based stochastic optimization techniques. The adaptations required to ACO for obtaining the trade-off between multiple disciplinary, and how ACO is behaving to obtain effective solutions to a multi-level optimization problem are discussed. For this purpose, two original optimization problems with a single global optimal solution are used as benchmarks. According to the state of art and the Analytical Target Cascading (ATC) formulation, those original problems can be decomposed into one system-level sub-problem and two subsystem-level sub-problems. Thereafter, ACO is used to solve this Bi-level optimization problem. The ACO results are compared to those obtained by the Bi-level ATC dual coordination algorithm.

The optimization problem of a safety isolating transformer is presented. This benchmark meets the requirements of engineers and scientists working with discrete and non-classable design variables, such as in the first part of the design process during the choice of structures and materials (embodiment design). It is dedicated to highlight the most efficient multi-level and combinatorial optimization methods. Two models are given. The first one is based on 3D FEA and gives a good accuracy with a huge computation time. The second is an analytical model that may speed-up the optimization process. http://l2ep.univ-lille1.fr/come/benchmark-transformer.htm

In this paper, two combinatorial algorithms are compared for the optimization of a safety isolating transformer. The first one is a Branch-and-Bound method using partial enumeration to arrive at the solution and the second one is a genetic algorithm with a specific coding. To speed-up the optimization, a coarse model is used during the bounding process of the Branch-and-Bound method.

The optimization problem of a safety isolating transformer is presented. This benchmark meets the requirements of engineers and scientists working with discrete and non-classable design variables, such as in the first part of the design process during the choice of structures and materials (embodiment design). It is dedicated to highlight the most efficient multi-level and combinatorial optimization methods. Two models are given. The first one is based on 3D FEA and gives a good accuracy with a huge computation time. The second is an analytical model that may speed-up the optimization process. http://l2ep.univ-lille1.fr/come/benchmark-transformer.htm

In this paper, two combinatorial algorithms are compared for the optimization of a safety isolating transformer. The first one is a Branch-and-Bound method using partial enumeration to arrive at the solution and the second one is a genetic algorithm with a specific coding. To speed-up the optimization, a coarse model is used during the bounding process of the Branch-and-Bound method.

In this paper, the design of a safety isolating transformer by means of an analytical “coarse” model and a finite element “fine” model is presented. Since the accurate model has typically an excessive computational cost, space-mapping techniques are used. The idea of space-mapping techniques is to align the coarse and the fine model responses in order to speed up the optimization procedure. The aggressive space-mapping algorithm and an output space-mapping algorithm are applied and compared with sequential quadratic programming method for the constrained optimization problem of the transformer. This optimization problem provides a benchmark to compare algorithms for multi-level optimization.

The paper points out a rational methodology to design electric or hybrid drive trains components taking into account the whole system by a global approach. The aim of this global approach is to assure an optimal global solution, all components being simultaneously and conjointly designed to obtain the best adaptation to the desired system specifications. This general methodology is used to design a wheel traction motor, as a component of the global system of an electric kart drive train.

A new tabu search algorithm for global optimization of multimodal functions with continuous variables is proposed and described. The taboo list contains all points and a prohibited zone around each point that is determined using heuristic rules. Its numerical performances are investigated on the optimal design of a die press with electromagnet for orientation of magnetic powder. The proposed algorithm is faster in finding the global optimum compared with other stochastic methods.

The optimization of superconducting magnetic energy storage (SMES) is performed by means of different stochastic methods: genetic algorithms, genetic algorithms with response surface, simulated annealing, improved simulated annealing, tabu search and new tabu search. An analytical comparison among them is performed. Finally, results on different methods are discussed.

This paper gives an overview of some stochastic optimization strategies, namely genetic algorithms, simulated annealing and tabu search, applied as a technique of system design for electrical engineering problems. A comparison among them is performed and results are discussed on a constrained optimization problem.

The different design steps of an electric wheel motor are reported from specifications, technological choices, different modeling and also the set-up of an optimization process that is performed using numerical algorithms. The design methodology is presented. The contribution of numerical methods is emphasized and comparisons with measurements are reported. Wheel motors are particularly attractive since there is no gear between the motor and the wheels. This way, the number of mechanical transmission element is greatly reduced.

The different design steps of an electric wheel are reported from specifications, technological choices, different modeling and also the set-up of an optimization process that is performed using numerical algorithms. The design methodology is presented. The contribution of numerical methods is emphasized and comparisons with measurements are reported.

This paper shows how the Design of Experiments Method and particularly the Responses Surface Methodology builds polynomial models of various responses, when studying an electrical device. These polynomials are included in a global analytical design model simulating then various situations. Obvious optimization are then realized.

An optimisation software is designed on a finite element model for the description of electromagnetic systems. The optimisation process is derived from the experimental design method because this method possesses many advantages for the designer. Then, two optimisation methods are tested on two different electric motors, a brushless synchronous motor and a switched reluctance motor. Both allow to find a good optimum and to obtain information on the response sensitivity.

The design and optimization of electromagnetic devices are very complex and their solutions require a good knowledge of the studied devices and a long development time. So it is important to find tools that lead to the best device in the shorter time. We propose to use an electronic-magnetic coupled finite element model with optimization methods to solve the design problem of a switched reluctance motor. Several optimization methods are compared with regard to the motor performances and the number of finite element simulations needed.

We study a switched reluctance motor with six stator poles and four rotor poles. Straight forward parameters are Br the rotor pole arc and Bs the stator pole arc. Our aim is to determine Br and Bs to improve the motor performances. An analytic approach leads to define an area of the plan (Br,Bs) called feasible triangle where the motor produces an unidirectional torque. However, this approach does not allow to find the optimal choice neither its sensitivity. We propose an approach that combines a finite element simulation with an optimization based on experimental design method to avoid the uncertainties of the analytic approach.

Nous nous intéressons à la mise au point d’un moteur à réluctance variable à double saillance avec quatre pôles statoriques et deux pôles rotoriques. Etant donnée la simplicité du capteur de position, le démarrage est particulièrement délicat. De même, pour mettre au point une commande robuste bien adaptée à la géométrie de la machine, il faut pouvoir tenir compte de la complexité de la loi de commande des interrupteurs. Ainsi, nous avons enrichi un modèle éléments finis couplé électrique-magnétique avec un couplage mécanique et amélioré le couplage électronique. Pour valider notre modèle, nous simulons le démarrage du moteur, puis, nous nous en servons pour tester la robustesse de la commande.

The design of a switched reluctance motor with four stator poles and two rotor poles is investigated. Because of the position sensor simplicity, the starts are especially difficult, so that the transistor drive must includes suitable commands that shall be precisely designed. We have upgraded an electric-magnetic coupled finite element model with a mechanical coupling and improved the electronic coupling in order to simulate the motor start and test the design of the set control-converter-machine.

The design of a switched reluctance motor with four stator poles and two rotor poles is investigated. Because of the position sensor simplicity, the starts are especially difficult, so that the transistor drive must includes suitable commands that shall be precisely designed. We have upgraded an electric-magnetic coupled finite element model with a mechanical coupling and improved the electronic coupling in order to simulate the motor start and test the design of the set control-converter-machine.

Trois approches sont proposées pour la conception par optimisation d’une sous-station ferroviaire hybride en considérant sa commande sur un horizon temporel d’une année. La première est basée sur une linéarisation par parties de la fonction coût et une résolution par programmation linéaire. Les deux autres décomposent le problème complet en deux niveaux de moindre dimensionnalité. L’optimisation collaborative le résout par une approche avec deux boucles imbriquées alors que la décomposition de Benders permet une résolution découplée séquentielle. Cette dernière donne la même solution que la programmation linéaire en environ cinq fois plus de temps mais présente l’avantage de pouvoir être utilisée avec une fonction coût non linéaire.

Cet article présente le problème d’optimisation d’un transformateur de sécurité. Ce problème à variables discrètes et non classables peut être utile à l’élaboration de nouvelles méthodes d’optimisation combinatoire, multi-niveaux et multi-objectif sous contraintes. Sa vocation est donc de server de benchmark. Des premiers résultats d’optimisation sont comparés dans le cas multi-objectif avec les méthodes Sequential Quadratic Programming (SQP) et Non-Dominated Sorting Genetic Algorithm (NSGA-II), dans le cas multi-niveaux avec des techniques de Space-Mapping (SM), et dans le cas combinatoire avec la méthode Branch-and-Bound (BB) et un algorithme génétique (GA). Deux modèles thermo-électromagnétiques sont établis : le premier est un modèle éléments finis 3D (MEF), le deuxième est un modèle analytique. Un site internet a également été réalisé. Il rassemble les informations utiles en vue de tester le benchmark ainsi que les premiers résultats d’optimisation présentés dans cet article. Il permettra à la communauté scientifique de capitaliser leurs résultats et de comparer les méthodes d’optimisation. http://l2ep.univ-lille1.fr/come/benchmark-transformer.htm

Un modèle de pré-dimensionnement d’un moteur à courant continu, aimant permanent, bobinage concentré et commutation électronique est présenté. Il peut être employé dans les premières étapes de la conception et fournit les dimensions géométriques à partir du cahier des charges. Les équations dimensionnantes sont présentées en précisant les phénomènes physiques pris en compte et les conditions d’application. Une analyse de la structure du système d’équations obtenues permet d’en faciliter la résolution. Pour finir, le modèle a été mis sous la forme de trois cahiers des charges pouvant servir de benchmarks pour des méthodes d’optimisation.

Une nouvelle méthode de recherche taboue pour l’optimisation globale de fonctions multimodales avec des paramètres continus est présentée. La liste taboue contient tous les points générés ainsi qu’une zone autour de chaque point dont la taille dépend de la valeur de la fonction objectif et du numéro d’itération. Appliquée à l’optimisation d’une bobine supraconductrice pour le stockage d’énergie et d’une presse à aimants, cette méthode démontre son efficacité et sa rapidité. Elle est comparée avec les méthodes des algorithmes génétiques, du recuit simulé, de la recherche taboue de Hu et la recherche taboue universelle.

Nous décrivons une méthode d’optimisation avec contraintes utilisant les algorithmes génétiques. Cet algorithme est appliqué pour maximiser le rendement d’un moteur Brushless DC tout en respectant des contraintes techniques.

Les différentes étapes du dimensionnement d’un moteur roue sont détaillées en allant du cahier des charges, des choix technologiques et des différentes modélisations jusqu’à la mise en place d’un procédé d’optimisation construit avec des méthodes numériques. La méthodologie d’optimisation est présentée. L’accent est mis sur la contribution des méthodes numériques et la comparaison avec les performances mesurées sur le prototype.

Cet article présente l’étude et la conception d’un moteur roue pour un véhicule électrique. Le cahier des charges du moteur est présenté et conduit à un choix technologique pour l’ensemble moteur-convertisseur-commande : moteur à courant continu sans collecteur et onduleur triphasé bidirectionnel avec régulation du courant. Un modèle éléments finis permet de parfaire le dimensionnement en prenant en compte le flux de fuite et la saturation magnétique. Ensuite, une simulation dynamique du moteur et de son convertisseur valide le dimensionnement.

Cet article présente l’étude et la conception d’un moteur-roue pour un véhicule solaire participant à la course « World Solar Challenge ». Le cahier des charges du moteur ainsi que les particularités de la course et du véhicule sont présentés et conduisent à un choix technologique pour l’ensemble moteur-convertisseur-commande : moteur à courant continu sans collecteur et onduleur triphasé bidirectionnel avec régulation du courant. Une méthode de dimensionnement analytique du moteur est utilisée avec la technique des plans d’expériences pour optimiser le rendement du moteur. Auparavant, un modèle éléments finis permet de parfaire le dimensionnement en prenant en compte le flux de fuite et la saturation magnétique. Ensuite, une simulation dynamique du moteur et de son convertisseur valide le dimensionnement.

Les problèmes de conception et d’optimisation des dispositifs électromagnétiques sont très complexes et leur résolution nécessite une grande connaissance des dispositifs étudiés ainsi qu’une longue durée d’étude. Il est donc intéressant de trouver des méthodes qui conduisent au meilleur dispositif dans un délai d’étude minimum. Nous proposons d’associer la méthode des éléments finis avec les méthodes d’optimisation pour résoudre les problèmes de conception des dispositifs électromagnétiques. Ces méthodes seront appliquées à l’optimisation d’un moteur à réluctance variable à double saillance.

Moteur électrique pour la propulsion des bateaux N° de publication : 2 796 775, N° d’enregistrement national : 99 09559, date de mise à disposition du public du brevet d’invention : 17 août 2001. Exploité par la société PROPELEC, créée à cette occasion.

Transportation is responsible for 24% of the total greenhouse gases (GHG) emission worldwide. Thus, the rolling stock industry makes efforts to improve the performances of trains and to reduce their environmental impacts. A railway traction system is considered as a complex system. Its design problem is a complicated task requiring many designers and experts as well as an efficient industrial management. A complex system can be referred to as a system that is composed of several interacting subsystems and components. This system involves many technical disciplines and many human factors as the system is operated in a specific environment by users. Three sources of complexity can be identified: - interactions between subsystems and/or components constituting the system - interactions between disciplines describing physical or non-physical phenomena - interactions between the system and the environment in which the system operates Optimization helps the designer in this complicated task by providing methodologies and techniques that can be drawn on 3 axes: - multi-granularity, i.e. using models with different accuracies and computing time - multi-physics, i.e. managing the interactions between disciplines and/or components - multi-level, i.e. propagating targets and constraints from system to components These tools are applied to the design of railway drivetrains by optimization. The applications are the design of a super-capacitor storage system onboard to reduce GHG and cost, the optimal tradeoff between mass and efficiency of a main transformer and its PWM rectifier, and the design of a railway powertrain that is composed of several interacting subsystems and components.

Le but de ce stage est la modélisation par la méthode des éléments finis du moteur asynchrone Leroy Somer LS180 à encoches droites. La modélisation s’est faite sur l’application MV2DYN, qui permet de traiter les problèmes magnétiques bidimensionnels plans, et notamment les problèmes magnétodynamiques où les courants ne sont pas constants et où certaines pièces de la géométrie sont en mouvement de rotation. Cette application intègre également la résolution simultanée d’un circuit extérieur comportant des éléments passifs et actifs tels que des diodes et transistors. Afin de comparer le pas-à-pas dans le temps à la magnétodynamique complexe, j’ai effectué également la modélisation du LS180 avec le logiciel FLUX2D version 6.55, au sein du centre de calcul de la Direction des Etudes et Recherches d’EDF à Clamart. De plus, des mesures ont été effectuées sur le LS180 à encoches droites au centre d’essai de la DER à Saint Denis sur plusieurs cas d’utilisation. Ce rapport se propose donc de présenter, dans une première partie, la conception, étape par étape, d’un outil de résolution des problèmes de magnétodynamique en pas-à-pas dans le temps. Ensuite nous verrons les différentes étapes de la modélisation du LS180 pour les deux méthodes magnétodynamiques, autant du point de vue de l’utilisateur que de celui des hypothèses physiques et des méthodes de résolution.

Nous étudions un moteur à réluctance variable à double saillance avec quatre dents statoriques et deux dents rotoriques dont les deux phases sont câblées en demi-pont asymétrique. Son nombre de phase étant faible, le démarrage pose problème et nécessite l’élaboration d’une loi de commande complexe pour compenser la simplicité du capteur de position constitué d’une roue dentée et d’une fourche optique. Un modèle éléments finis couplé électronique-magnétique-cinématique est alors construit, validé puis utilisé pour résoudre les problèmes liés au démarrage. De plus, les cotations de la géométrie du moteur et les instants de commutation des interrupteurs doivent être déterminés pour satisfaire au mieux le problème de conception formulé au moyen d’un cahier des charges. Une méthodologie est proposée pour résoudre les problèmes de conception des dispositifs électromagnétiques. Elle consiste, dans un premier temps, à exprimer le problème de conception dans un formalisme mathématique puis, dans un deuxième temps, à appliquer des méthodes d’optimisation pour le résoudre. L’outil qu’est le modèle éléments finis et la méthodologie de résolution du problème de conception sont ensuite utilisés conjointement pour l’optimisation d’un moteur à réluctance variable à double saillance.