Optimisation multi-critères et multi-physique d'aérogénérateurs à aimants permanents à flux axial

This study deals with the optimization and design of direct driven Axial Flux Permanent Magnet Synchronous Generators (AFPMSGs) for small wind turbines application. The project was financed by the French ministry of research and technology. The investigated system consists of an AFPMSG sandwiched between the wind turbine and a 3-phase uncontrolled rectifier connected to an inverter via a buck-boost converter. The battery charging system ensure power continuity in case of outage while the set of solid state converters is essential for the energy management since the wind speed is not constant and always shows fluctuations. The system is modeled as a non-linear multi-objective optimization problem based on the Pareto approach using the Genetic algorithms optimization technique where a special attention was given to the generator since it is the key for a successful overall performance. As in all electric machines, the magnetic field is the medium for the energy conversion. An accurate mathematical model to calculate the exact distribution of the magnetic field is therefore of particular importance in order to predict with great accuracy the global electrical quantities (back emf, torque, etc.). In this context, the proposed analytical model is based on the resolution of the two-dimensional Laplace's and Poisson's equations derived from the set of Maxwell's equations in magnetostatics. The problem is formulated in cylindrical coordinates and solved by means of separation of variables technique for each sub domain (magnets, air-gap and slots). The analytical results for field distributions all show excellent agreement with those obtained from the finite element analysis. The discrepancy between the analytical approach and the numerical one is very small. This model thus yields to quick results while requiring much less computation time and is readily available and suitable during the preliminary design stage when integrated into an optimization strategy. A thermal model and a mechanical model were also included to predict the machine's hot-spot temperatures and control the rotor disc deflection respectively. Simulated under Matlab/Simulink environment, the aforementioned models are merged to form a compact single one which is then coupled with an optimization technique combining the GENECOP (Genetic Algorithm for Numerical COstrainted Problems) serving as a code for handling the different system constraints and the SPEA-II (Strength Pareto Evolutionary Algorithm) designed to find the set of the compromise non-dominated solutions known as Pareto-optimal solutions. This algorithm has proven to be well suited for real-world engineering optimization problems with multiple objectives. The multiple objective function can be formulated as follows: minimize the weight of the machine's active parts while maximizing its efficiency, minimize simultaneously the volume of the permanent magnets and the total RI² losses, etc... Among the fixed parameters during the optimization process we can list the rotor outer diameter, the number of phases, the number of slots, the maximum allowable induction in the magnetic circuit, etc... while the bounded optimization variables are classified as follows: the rotor disc inner diameter, the permanent magnets height, the permanent magnets remanence, the air-gap length, the slot opening factor, the slot depth, the number of turns/phase, the current density, the pole opening factor, the cogging torque magnitude, the rotor disc deflection level and the winding and permanent magnets temperature. These design parameters are constrained to vary in the feasible region of the search space reflecting different electrical, thermal or mechanical limits. The optimization strategy takes also into account the wind speed by extracting the appropriate generator rotational speed corresponding to a maximum captured power available at the main shaft. The information can be obtained from the curves provided by the turbine manufacturer. In this study, the 10kW wind turbine characteristics were taken from Bergey Windpower co. (BWC) the American leader in the manufacturing of small wind turbine. Finally, the implemented optimization code evaluates at each iteration a feasible potential solution and constructs the curve of the optimal trade-off solutions where each point represents an optimized generator having its own electromechanical characteristics. The decision maker can then choose the most appropriate solution according to the current situation.Nous avons abordé, dans ce travail, la problématique posée par la conception des machines synchrones à aimants permanents à flux axial (MSAPFA) intégrées dans un système éolien de petite puissance. Les objectifs ont été de mettre au point une méthodologie générale de dimensionnement et le développement d'une méthode de modélisation de MSAPFAs par le calcul analytique des champs à partir du formalisme de Maxwell. Le défi de cette modélisation demeure toujours le compromis à faire entre temps de calcul et précision des résultats. Un outil d'analyse analytique issu de la résolution des équations de Maxwell par la méthode de séparation des variables dans les différentes régions de la machine, a donc été développé. Un modèle thermique nodale de la structure de MSAPFA est ensuite mis au point. La construction de ce modèle conduit à un système d'équations algébriques linéaires dont la solution nous renseigne sur la température aux nœuds sensibles de la machine. Ce modèle thermique est suivi par un modèle mécanique qui s'appuie sur les expressions proposées par le modèle de Young permettant ainsi de contrôler la déflexion des disques rotoriques en choisissant la bonne épaisseur de ces derniers à partir des efforts axiaux. Ces trois modèles constituent le modèle dimensionnant multi-physique de la machine. Pour l'optimisation non linéaire, un algorithme génétique d'optimisation multi-contrainte (GENOCOP) associé un algorithme d'optimisation multi-objectif (SPEA_II) sont choisis. C'est une méthode élitiste qui utilise une archive externe pour le stockage des solutions Pareto et effectue sa mise à jour au fur et à mesure des générations. Le couplage du SPEA_II avec le GENOCOP nous a permis de développer le code d'optimisation OPTIMSAP implémenté sous Matlab et dédié au dimensionnement des machines électriques. Le code d'optimisation OPTIMSAP développé a été enfin utilisé pour le dimensionnement d'un système aérogénérateur de 10 kW à base d'une machine synchrone à aimants permanents à flux axial couplée à un redresseur à diodes suivi d'un hacheur dévolteur et débitant sur un banc de batteries de 120V en parallèle avec une charge de consommation