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Introduction
To some extent, the winding of a switched reluctance machine [SR motor] could be treated as an air‑gap winding, where the eddy currents in the conductors could be significant. This is most noticeable on the leading (“motoring”) side of a coil between the unaligned and aligned position, which is quite a complex magnetic circuit. For this reason a transient finite element analysis is desirable to verify the affect of eddy currents.

Figure 1a:Mesh of low voltage.

Figure 1b: standard voltage for SR models.

FLUX2D modelling
Eddy‑current modelling of a SR motor has some special features and requirements. In this study, two main models were created. Both represent an 8/6 SR motor; the essential difference between them is that one is for low voltage operation (4 turns per pole, 8mm squared conductors) and the other is for standard voltage operations (25 turns per pole, 2mm rounded conductors. This is shown in Figs. 1 (a) and (b). A fine mesh is required around the stator conductors for precise determination of the eddy currents and in the air gap, for satisfactory estimation of performance. There are 14,067 surface elements for the low voltage model and 15,672 surface elements for the standard voltage model. The conductors assumed a constant resistivity of copper (Ï?Cu=1.72×10-8Ωm). The control circuit is simple and uses a single pulse control, with a constant voltage source as shown in Fig. 2 (a) and (b). This circuit also provided the correct connection for the series‑connected conductors; because of the large number of conductors in Fig 2 (b) only one phase was simulated.

Figure 2a: Electric circuit of low voltage

Figure 2b: Standard voltage SR models.

Simulation
It was anticipated that the p.u. eddy current loss will be much higher in the low voltage model by virtue of its large conductors. The transient FE magnetic analysis included rotor movement. Waveforms and performance obtained from FLUX 2D and compared to SPEED PC-SRD – the results are shown in Table 1. The PC-SRD model has more phase turns but the current was adjusted to produce the same torque.

Table 1: Main parameters of the analytical and FE models.
Low voltage SR model
The phase current waveforms are shown in Fig. 3 (a). This is the mean current across a conductor. The highest distortion of current density was in the surface conductors of the coil on the rotor side and, more significantly, on the motoring side. The loss factor (= total loss / DC loss) was found to vary between 1.38 and 9.15 per period. Fig. 3 (b) shows the current density distribution across the conductors on the motoring side. The view is from top right corner on the motoring side of the coil.

Figure 3a: Current waveforms.

Figure 3b: 3Ddistribution of current density for low voltage model.

Standard voltage SR Model
In this case, when the radius of a conductor was significantly smaller than the skin depth, the variation of losses was not so severe and is kept below 9 percent per period. The maximum value of the loss factor was 1.09. The torque waveform and current density distribution are shown in Fig. 4. As can be observed, the current density is practically uniform, except for the outer conductors. This is in contrast to the thick square conductors for the low voltage model.

Figure 4a: Torque waveform.

Figure 4b: 3D distribution of current density for standard voltage model.

Conclusion
The eddy‑current loss is high in the low voltage SR model with thick conductors. According to the finite‑element results, the difference between maximum and minimum loss was almost 600% with a loss factor of about 9. Thus precise calculation of eddy currents is essential otherwise they could lead to the insulation failure and burning of the winding as well as poor performance. It was also computed that the losses due to eddy currents do not exceed about 9% of the DC loss for conductors with a radius of about one quarter of the skin‑depth.

This article is reproduced with permission of the authors, Martin Klauz and David Dorrell from the SPEED Laboratory.