Impact of speed ripple on the back-Emf waveform of permanent magnet synchronous machines

Permanent Magnet Synchronous Machines (PMSMs) are frequently used in industry due to their high efficiency and favorable dynamic properties. Mechanical limitations and design considerations cause several harmonics in the flux and back-emf of these machines. The back-emf harmonics can be measured on the machine terminals if no stator current is present and the neutral point is accessible. The measured harmonics can then be included in a mathematical model of the machine. This measurement is often done for a constant speed. However, when a speed ripple is present, several new harmonics are introduced in the flux and back-emf. Although the existence of this phenomenon is intuitively clear, it has not yet been investigated in detail and no method exists to calculate these additional harmonics. Nevertheless, the impact of a speed ripple on the back-emf can become significant in some applications. Therefore, in this paper, a mathematical model is presented which allows to accurately calculate the additional back-emf harmonics in the presence of speed ripples. Also, it provides more insight in the interaction between speed ripples and harmonics. The mathematical model is extensively validated by means of simulations and experiments