In this paper, a mathematical model of a twelvephase flux-switching permanent magnet (FSPM) machine designed for high-power wind power generation is established and investigated. Firstly, the winding inductances in both stator reference frame and dq-axes reference frame are analyzed. It should be noted that, the characteristics of the twelve-phase winding inductances are different from that of its three-phase counterpart. The largest mutual-inductance is much smaller than half of the self-inductance and most mutual-inductances are negligible, which brings the benefit of improved magnetic isolation between phases and causes the twelfth order inductance matrix to be sparse. Thereafter, an accurate inductance model is established, taking account of the magnetic coupling between adjacent threephase winding sets. Finally, the flux-linkage equation, the voltage equation and the power/torque equation are derived in sequence. The effectiveness of the proposed mathematical model are verified by comparing the theoretical results with 2D finite-element analysis (FEA)-based predictions. The work in this paper lays an important foundation for the control strategy of the twelve-phase FSPM machine. Index Terms-Flux-switching permanent magnet (FSPM), mathematical model, twelve-phase, wind power generation.Manuscript