Optimal design of transient eddy current systems driven by voltage source

The structure and the characteristics of an optimal design procedure of electromagnetic devices are examined and the three different approaches to design sensitivity derivation are reviewed. For the shape design problems of the transient eddy current systems driven by voltage sources, the design sensitivity is derived in an explicit form to the design variables using the finite element algebraic system equation and the adjoint variable method. The original state variable equation is an initial value problem, but the adjoint variable equation is derived as a terminal value problem. Both equations are solved using a time-stepping finite element method. As a numerical example, the coil-positioning problem of an induction heating system is tested and the proposed algorithm is validated.