EngOpt 2008 - International Conference on Engineering Optimization Rio de Janeiro, Brazil, 01 - 05 June 2008. Mixed-variable optimal design of induction motors including efficiency, noise and thermal criteria J. Le Besnerais 1 , A. Fasquelle 1,2 , V. Lanfranchi 3 , M. Hecquet 1 , and P. Brochet 1 1 Laboratoire d’Electrotechnique et d’Electronique de Puissance (L2EP), Ecole Centrale de Lille, Cit´ e Scientifique, 59651 Villeneuve d’Ascq, FRANCE (e-mail:jean.le besnerais@centraliens.net) 2 Laboratoire de M´ ecanique et d’Energ´ etique (LME), Universit de Valenciennces, Le Mont Houy, 59313 Valenciennes, FRANCE (e-mail: aurelie.fasquelle@ec-lille.fr) 3 Laboratoire d’Electrom´ ecanique de Compi` egne (LEC), Universit´ e de Technologie de Compi` egne, 60200 Compi` egne, FRANCE (e-mail: vincent.lanfranchi@utc.fr) 1. Abstract Squirrel cage induction motors design requires making numerous trade-offs, especially between its audible electromagnetic noise level, its efficiency and its material cost. However, adding the vibro- acoustic and thermal models to the usual electrical model of the motor drastically increases the simulation time. A finite element approach is then inconceivable, especially if the model has to be coupled to an evolutionary optimization algorithm. A fast simulation tool of the variable-speed induction machine, based on electrical, mechanical, acoustic and thermal analytical models, has therefore been elaborated. It has been validated at different stages with both tests and finite element method (FEM) simulations. This model is then coupled to a mixed-variable constrained Non-dominating Sorting Genetic Algorithm (NSGA-II) with a stochastic repair algorithm. Some global optimizations with respect to several objectives (noise level, efficiency and material cost), including thermal constraints, are finally presented, and several convenient visualizations of multi-dimensional solutions are presented. 2. Keywords: Multi-objective optimization, multi-physics modelling, induction machine, thermal nodal network, acoustic noise. 3. Introduction Squirrel-cage induction machines are widely used in the industry for their easy manufacturing and robustness. For instance, variable-speed induction motors are particularly present in electrical transport systems such as subways and trains. Their design variables are principally sized by the constraint to produce a given torque at a given speed, with the highest efficiency and, of course, fulfilling some mechanical and thermal constraints. A proper motor cooling is essential for subways, as they are continuously subjected to starting and breaking cycles. With the climbing raw materials market, material cost has become another influential factor on the design process besides torque, temperature and efficiency. The environmental impact of the motor is also gaining increasing attention: in addition to the minimization of electricity consumption, the acoustic comfort of train passengers and frontage residents has to be ensured. While the aerodynamic sources of noise (fans) can be reduced by reducing the motor temperature, the magnetic noise issue, mainly due to Maxwell air-gap forces which make the stator vibrate in the audible range [1, 2, 3], has to be tackled in a different way. The problem of induction motor optimal design has received much attention since the beginning of computer science [4, 5, 6, 7, 8]. Indeed, many trade-offs have to be made: for example, a smaller air-gap improves the efficiency, but increases the magnetic sound power level ; increasing the stator height of yoke to diameter ratio generally lowers magnetic vibrations [9], but it heightens material cost, and with a fixed motor size, it decreases the available output torque and highers rotor temperature [8]. Nevertheless, dealing with both noise and thermal criteria in an induction motor optimal design process has never been done. When treating several conflicting objectives, using Pareto-optimality-based algorithms like the recent Non-dominated Sorting Genetic Algorithm (NSGA-II) [10] is notably fitted to the industrial framework: 1