Physically motivated and analytical prototype functions are proposed to approximate the nonlinear flux linkages of nonlinear synchronous machines (SMs) in general; and reluctance synchronous machines (RSMs) and interior permanent magnet synchronous machines (IPMSMs) in particular. Such analytical functions obviate the need of huge lookup tables (LUTs) and are beneficial for optimal operation management and nonlinear control of such machines. The proposed flux linkage prototype functions are capable of mimicking the nonlinear self-axis and cross-coupling saturation effects of SMs. Moreover, the differentiable prototype functions allow to easily derive analytical expressions for the differential inductances by simple differentiation of the analytical flux linkage prototype functions. In total, two types of flux linkage prototype functions are developed. The first flux linkage approximation is rather simple and obeys the energy conservation rule for “symmetric” flux linkages of RSMs. With the gained knowledge, the second type of prototype functions is derived in order to achieve approximation flexibility necessary for SMs with permanent (or electrical) excitation with “unsymmetric” flux linkages due to the excitation offset. All proposed flux linkage prototype functions are continuously differentiable, obey the energy conservation rule and, as fitting results show, achieve a (very) high approximation accuracy over the whole operation range.

中文翻译：

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同步电机中磁链近似的分析原型函数


提出了物理激励和分析原型函数来近似非线性同步电机（SM）的非线性磁链；特别是磁阻同步电机 (RSM) 和内置永磁同步电机 (IPMSM)。这种分析功能不需要庞大的查找表（LUT），并且有利于此类机器的优化操作管理和非线性控制。所提出的磁链原型函数能够模拟 SM 的非线性自轴和交叉耦合饱和效应。此外，可微的原型函数允许通过对解析磁链原型函数的简单微分来容易地导出微分电感的解析表达式。总共开发了两种类型的磁链原型函数。第一个磁链近似相当简单，并且遵循 RSM“对称”磁链的能量守恒规则。利用所获得的知识，推导了第二种类型的原型函数，以便实现具有永久（或电）励磁且由于励磁偏移而具有“不对称”磁通链的 SM 所需的近似灵活性。所有提出的磁链原型函数都是连续可微的，遵循能量守恒规则，并且如拟合结果所示，在整个操作范围内实现（非常）高的逼近精度。