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.
A comparison between different analytical and finite-element (FE) tools for the computation of cogging torque and torque ripple in axial flux permanent-magnet synchronous machines is made. 2D and 3D FE models are the most accurate for the computation of cogging torque and torque ripple. However, they are too time consuming to be used for optimization studies. Therefore, analytical tools are also used to obtain the cogging torque and torque ripple. In this paper, three types of analytical models are considered. They are all based on dividing the machine into many slices in the radial direction. One model computes the lateral force based on the magnetic field distribution in the air gap area. Another model is based on conformal mapping and uses complex Schwarz Christoffel (SC) transformations. The last model is based on the subdomain technique, which divides the studied geometry into a number of separate domains. The different types of models are compared for different slot openings and permanent-magnet widths. One of the main conclusions is that the subdomain model is best suited to compute the cogging torque and torque ripple with a much higher accuracy than the SC model.
A demand for more efficient electrical machines with a high power density is driving the interest for high-speed permanent-magnet synchronous machines (PMSMs). However, the design of such machines is a challenging task. One of the problems is that the effect of the shielding cylinder, a conductive sleeve around the magnets, on the machine's performance has not been studied extensively. To cope with that problem the authors of this work introduce an analytical method to study the torque in high-speed PMSMs. The presented method implies dividing the torque in two components, depending on how they are produced. The method is successfully validated and an illustration of its advantages is provided.
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