Optimization of modular toroid coil geometry of a superconducting Magnetic Energy Storage device using design of experiments and FEM

The Superconducting Magnetic Energy Storage (SMES) system is a modern and expensive technique for storage of electricity through the magnetic energy in superconducting short-circuited coil. An optimized configuration must reduce as much as possible the volume of the superconducting material. In this paper is proposed an optimized solution of modular toroid coil geometry of SMES device using design of experiments (DOE) and finite element method (FEM). DOE is a rational realization of a series of real experiments a priori expensive and therefore it fits to the electromagnetic simulations (virtual experiments). Applied to the electrical systems modeled by FEM, it becomes a basic tool for optimization problems. Two geometric parameters characterizing the torus shape were chosen to determine the optimal configuration of the coil geometry of a SMES device for an optimized storage capacity. The ratio of maximum stored magnetic energy and the minimum volume of superconducting material was set as objective function. To solve it, the method of zooms without computation of models was used. The 2-D FEM implementation uses an equivalent rectangular cross section toroid, conserving the inductance of the system. The optimization results are obtained with less than 1% error. Comparison with previous numerical tests was made.