Time- and Spatial-Harmonic Content in Synchronous Electrical Machines

The use of power electronics has led to a growing importance of higher time-harmonic content in electrical machines. To gain insight in phenomena related to these higher harmonics, such as noise and losses, a good understanding of the magnetic field's harmonic content is mandatory. Moreover, the development of fast and accurate, harmonic-based, analytical models requires a qualitative knowledge of the machine's time- and spatial-harmonic content. Although the harmonic content of electric machines is an extensively studied topic, previous publications tended to focus on one type of synchronous machines and often did not consider higher time-harmonic orders. This paper complements the existing theory by providing a more general approach, thereby covering machines and operating points that were not covered until now. It considers both three-phase and multi-phase machines with an odd number of phases. The winding distribution can either have an integer or a fractional number of slots per pole and per phase, and higher time-harmonic content is regarded as well. Note that the saturation is neglected. Despite its general validity, this paper succeeds at providing one simple equation to determine the machine's time-and spatial-harmonic content. Moreover, this paper also extensively discusses the physical causes of the harmonic content. The combination of this general validity, the simple result, and the insight in the physics makes that this paper is a strong tool to both study harmonic-related phenomena in electric machines and to develop harmonic-based analytical models.