三角函数的开关磁阻电机磁链解析模型

Analytical model of flux-linkage for switched reluctance motor with trigonometric function

针对现有高精确度开关磁阻电机磁链解析模型在转矩计算时过于复杂的问题,根据由磁链与转子位置曲线的对称特性,提出了一种基于三角函数的新型开关磁阻电机磁链解析模型。模型中与转子位置相关的磁链用最高次谐波数为4次的傅立叶级数表示,各谐波项的系数由一个6阶多项式表示。误差分析表明,模型计算出的磁链与转矩与通过有限元方法获取的数据匹配良好,达到现有解析模型的精确度,同时大幅减少瞬时转矩的计算开销。系统仿真和实测结果表明,在斩波控制与角度控制两种模式下,仿真和实测结果具有很好的一致性;在基于72 MHz主频的ARM Cor-tex M3内核CPU中运行磁链和转矩计算软件,其执行时间分别为60μs和187μs。

The computation of torque based on existed high accuracy analytical models of the flux-linkage of switched reluctance motor （SRM） is complicated. To solve this problem, an analytical model with trig- onometric functions is presented, considering the symmetry characteristics of flux-linkage versus rotor po- sition curves. In this proposed model, the flux-linkage depending on the rotor position was represented by a Fourier series whose highest harmonic order is 4. The coefficients of the harmonic terms were formulated by 6-order polynomials. The error analysis results show that the flux-linkage and torque calculated with the proposed model well match that obtained through finite element analysis （FEA）. The calculation cost of torque based on the proposed model decreases significantly, and the accuracy of the proposed model is as high as the existed analytical models. System simulation results show good agreements with the experi- mental results when SRM operates on current-chopping-control mode and angular-position-control mode. The running time of calculation of flux-linkage and torque are 60μs and 187 μs, respectively, which is operated in an ARM Cortex M3 core CPU with 72 MHz frequency.