Time- and Spatial-Harmonic Content in Synchronous Electrical Machines

Abstract

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 didn't consider higher time-harmonic orders. This work complements the existing theory by providing a more general approach, thereby covering machines and operating points that weren't 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 saturation is neglected. Despite its general validity, the work succeeds at providing one simple equation to determine the machine's time-and spatial-harmonic content. Moreover, the work 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 work is a strong tool to both study harmonic-related phenomena in electric machines and to develop harmonic-based analytical models.

Analysis of Stator/Rotor Pole Combinations in Variable Flux Reluctance Machines Using Magnetic Gearing Effect

“…(b) 6s/(7, 11)r, 12s/ (10,14)r, 18s/ (17,19)r and 24s/20r VFRMs have higher average output torque than their counterparts with the same stator slot number, which reveals the conclusion that the stator slot and rotor pole number should be close to each other to achieve the highest output torque.…”

“…As proved in [16], the modulated MMFs of armature and field currents are identical to their corresponding MMFs in terms of harmonic order and corresponding rotating speed, albeit with modified harmonic magnitude due to the modulation effect of stator slot effect. In this case, the spatial harmonic content of modulated MMF can be easily deduced from winding theory [17].…”

Computational-Time Reduction of Fourier-Based Analytical Models

“…Moreover, the harmonic content of synchronous electric machines can be predicted. An extensive discussion on this prediction is presented in [10]. This section is limited to a brief introduction on the topic so that the results can be used in Section V. There are four aspects that define the machine's harmonic content; the permanent magnets, the stator currents, the winding distribution and the machine's geometry.…”

“…It was shown in [10] that, if the machine's winding is determined using the SOS, it contains ςmτ slot groups (also known as phase belts). Where ς = 1 or ς = 2, depending on whether Ns τ is odd or even.…”

“…Two techniques to reduce the FB model's computational effort are considered in this work; simplifying the geometry and applying a qualitative analysis of the machine's time-and spatial-harmonic content. That analysis was performed by the authors in [10]. The results are validated using a Finite-Element Model (FEM).…”