The aim of this paper is to show how SMES devices, if arranged with mo
re than two magnetic dipoles, can perform better. The analysis is carr
ied out either considering or not the presence of a ferromagnetic shie
ld, In the latter case a shape optimization of the iron shield is perf
ormed using a combined stochastic/deterministic method. The paper show
s bow advantages can be taken by evaluating the sensitivity matrix of
the iron shape optimization by means of a Lagrangian formulation of th
e Maxwell's equations.