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.