Employing the Magnetic Coenergy for Precise Torque Ripple Calculation from Flux Linkages

Output torque is one of the most important quantities when describing an electric machine. The calculation of the fundamental torque from flux linkages is well-known. However, a machine’s output torque typically also shows a ripple component due to spatial harmonics. Describing this ripple component directly with flux linkages is difficult. Alternatively, finite element analysis (FEA) typically calculates the torque using energy-based methods like virtual displacement. Since FEA models are not available for every machine (especially from a typical user’s perspective), this work calculates torque solely from measured flux linkages by calculating the magnetic coenergy first. It is demonstrated that this method suits permanent-magnet-free machines especially well and is consequently applied to a synchronous reluctance machine. Research considering flux linkage identification including saturation and spatial harmonics has advanced sufficiently to accurately determine flux linkages from measurement. Therefore, this work uses measured flux linkages to calculate coenergy and torque.