| The Design of Experiments (DOE) applied to electrical systems modeled by the finite element method (FEM) has become a useful strategy to solve many optimization problems. In this paper, two direct optimization methods by DOE and 2-D FEM were applied on a Superconducting Magnetic Energy Storage (SMES) device with modular toroid coil, in order to optimize its storage capacity: the method by zooms without computation of models and the method by slidings of plans without computation of models. Two parameters that characterize the geometric torus shape were chosen to minimize the volume of the superconducting material with a maximum stored magnetic energy: the coil inner diameter ratio and the coil thickness ratio. The 2-D FEM implementation uses an equivalent rectangular cross section toroid, conserving the inductance of the system. The optimization results by the two methods are obtained with less than 2% error of objective function value and they are comparable between them and better than previous approximate values determined by simple numerical tests. |
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