Mathematical Modeling of a 12-Phase Flux-Switching Permanent-Magnet Machine for Wind Power Generation

In this paper, a mathematical model of a 12-phase flux-switching permanent magnet (FSPM) machine designed for high-power wind power generation is established and investigated. First, the winding inductances in both the stator reference frame and the $dq$-axes reference frame are analyzed. It should be noted that the characteristics of the 12-phase winding inductances are different from those 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 12th-order inductance matrix to be sparse. Thereafter, an accurate inductance model is established, taking account of the magnetic coupling between adjacent three-phase winding sets. Finally, a flux-linkage equation, a voltage equation, a power equation, and a torque equation are derived in sequence. The effectiveness of the proposed mathematical model is verified by comparing the theoretical results with 2-D finite-element-analysis-based predictions. The work in this paper lays an important foundation for the control strategy of the 12-phase FSPM machine.