This paper describes the modeling of a permanent magnet synchronous machine by using lumped models. Designing electrical machines necessarily involves several fields of physics, such as electromagnetics, thermics, mechanics and acoustics. Magnetic, electrical, electronic and thermal parts are represented by lumped models, whereas vibro-acoustic and mechanical parts are represented by analytical models. The aim of this study is to build a design model of a permanent magnet synchronous machine for traction applications. Each model is parameterized in order to optimize the machine. The method of taking into account saturation and movement is described. These fast, lumped models make it possible to couple the software used with optimization tools. Simulation results are presented and compared with the finite element method and the experiments performed.