Mathematical Model and Vector Control of SPMSM Considering Eddy Current and Hysteresis Effects Based on Vector Magnetic Circuit Theory

The traditional mathematical models of surface-mounted permanent magnet synchronous motor (SPMSM) usually ignore the influences of the eddy current and hysteresis effects due to the fact that there is no appropriate parameter to quantitatively characterize these effects. However, with the increase of operating frequency of the SPMSM and switching frequency of the converter, their influences are becoming increasingly serious and have to be considered. The vector magnetic circuit (VMC) theory contains three basic magnetic circuit parameters, i.e., reluctance, magdutance, and hysteretance, which respectively characterize the magnetization, eddy current effect, and hysteresis effects in the magnetic circuit, and provide a new prospective for motor control to consider the eddy current and hysteresis effects. Therefore, based on the VMC theory, this paper establishes the mathematical model of the SPMSM by proposing a R-L coordinate transformation to consider eddy current and hysteresis effects in the iron core, but keep the d- and q- axis equations decoupled. Consequently, based on the proposed mathematical model, the novel i_d = 0 vector control of SPMSM is designed. Simulation and experimental results show that compared with the traditional i_d = 0 vector control, the novel i_d = 0 vector control has higher current control accuracy, better steady state and dynamic performances.