This paper presents a methodology that allows taking advantage of the geometrical periodicity of electrical machines together with the modeling of rotor motion. It enables by means of the discrete Fourier transform (DFT) to reduce the large-scale system obtained from the finite-element model to several smaller independent subsystems, allowing a shortening of the computational time. Due to DFT properties, the computational time can be more reduced especially when we consider the inter-dependence of the spectral components under either balanced or unbalanced supply condition. In addition, a further reduction is possible in the case of balanced regimes where the distribution of the eventual numerical solution is governed by a limited number of prevailing harmonics.