Optimal design of electrical machines : mathematical programming formulations

Sonia Cafieri (1) , Leo Liberti (2) , Frédéric Messine (3) , Bertrand Nogarède (3)

1 MAIAA - ENAC - Laboratoire de Mathématiques Appliquées, Informatique et Automatique pour l'Aérien
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
3 ENSEEIHT - Ecole Nationale Supérieure d'Electrotechnique, d'Electronique, d'Informatique, d'Hydraulique et de Télécommunications

The optimal design of electrical machines can be mathematically modeled as a mixed-integer nonlinear optimization problem. We present six variants of such a problem, and we show, through extensive computational experiments, that, even though they are mathematically equivalent, the differences in the formulations may have an impact on the numerical performances of a local optimization solver used to solve it. We first consider the optimization problem as a continuous problem, then we discuss how to deal with an integer variable. We conclude by solving the mixed-integer problem via a deterministic global optimization solver.

Mots clés: analytical model; electrical machine; formulation; local optimization; inverse problem; mixed integer non-linear programming; design; deterministic global optimization

Domaines: Optimisation et contrôle [math.OC]

Sonia Cafieri, Leo Liberti, Frédéric Messine, Bertrand Nogarède. Optimal design of electrical machines : mathematical programming formulations. COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 2013, 32 (3), pp 977-996. ⟨10.1108/03321641311305863⟩. ⟨hal-00934665⟩