Winding Configurations and AC Loss of Superconducting Synchronous REBCO Motors

We investigate effects of armature winding configurations on properties of fully superconducting synchronous motors using REBCO tapes. The effect of the configurations on ac losses in the winding tapes due to the changing transvers magnetic fields applied to the tapes in direction of perpendicular to the flat face of the tapes is important. In generally, it is effective to close winding factor to 1 for improvement of properties of motors. For the purpose, the shape of armature windings is better saddle-shaped winding than race-track winding. In this paper, numerical calculations on the properties of fully superconducting synchronous motors using REBCO tapes with 500 kW class were described. Operating temperature was 65 K. In order to demonstrate the feasibility of saddle-shaped winding, test coil with 5 turns were wound with YBCO tapes and then critical current measurements were carried out. The degradation of the properties has not observed.


Introduction
The developments of synchronous motors with REBCO tapes are ongoing [1]. The field winding without iron cores, which are wound by REBCO tapes, can produce higher magnetic flux density than the saturation magnetic flux density of iron. Therefore, it is expected that the REBCO motors can be realized lightweight and small size. In order to improve efficiencies, however, ac losses in armature windings must be reduced. A candidate of the reduction method of the ac losses is the application of scribing processed REBCO tapes and the special winding [2][3][4]. Although several studies on structures and ac losses in armature windings of rotating machines were carried out [5 -13], it has been not clarified optimum structures of motors applied both of multifilamentary REBCO tapes with scribing process and the special windings. In generally, shapes of armature windings have been race-track shapes in the design of the fully superconducting motors with REBCO tapes. In the case of the race-track shape, however, it is difficult to design to be a high winding factor, because the ends of the three-phase windings interfere with each other. In contrast, the saddle-shaped winding has more flexible at the ends of the windings than that of the race-track shape. For this reason, it is possible to assemble while avoiding contact at the coil ends. Also, the angles around the axis of the winding tapes at straight parts are possible to control. So the adjusting the direction of magnetic fields applied to the tapes to parallel to its flat face in the saddle-  Fig. 1. Hysteresis losses in the REBCO tapes are decided by perpendicular magnetic fields applied to the tape face. Therefore, it might be to reduce the perpendicular magnetic fields and ac losses in the windings by adopting the saddle-shaped windings. In this paper, numerical calculations on the properties of fully superconducting synchronous motors using REBCO tapes with 500 kW class are described. About the differences between two armature winding shapes on the transverse magnetic fields applied to the tapes in the armature windings and ac losses in their windings are explained.

Analysis method and model
In this study, hysteresis losses in the fully synchronous motors with an output power of 500 kW were calculated on the two cases of the race-track shape windings and the saddle-shaped windings. And in order to investigate influences of the short-node winding coefficient on the loss reduction effects, ac losses in the motors on three cases of coil pitches of the armature windings were calculated. In this chapter, calculation methods of losses in the motor are explained.

The calculation method of ac losses in the armature winding
In this calculation, magnetic fields distributions in the calculated model of the motor were analyses by finite element method. The analyses were calculated by using simulation software, JMAG, which is developed by JSOL Corporation. The analyses of the magnetic field distributions were not taken the electromagnetic behaviors of superconductors into account. Therefore, the permeability of the superconducting winding area was assumed to the vacuum permeability. And eddy currents in the normal conductors were not considered. So the FEM analyses were based on A-method. Ac losses in the superconducting tapes in the armature winding were calculated by following. The ac losses in REBCO tapes are determined by the magnetic fields applied to the tapes in the direction of perpendicular to the tape face. The magnetic fields, which are perpendicularly applied to the tape face in each element of REBCO winding area in the numerical model, were obtained by the simulation software mentioned above. Ac losses in superconducting windings were calculated from ac losses in each element in the FEM model. Ac losses per unit volume and cycle of applied magnetic fields were calculated by the equation of Brandt [14]. And then, whole ac losses in the superconducting winding area were obtained by volume integral of ac losses in each element. Finally, the cooling penalty is taking into account.

Figure 1.
Armature windings arrangements and direction of the magnetic fields applied to the winding tapes in the armature windings. The right and the left sides represent the race-track shape winding and the saddle-shaped one, respectively. In case of saddle-shaped one, it is possible to adjust the direction of magnetic fields applied to the tapes to parallel to its flat face.  Figure 2 shows the analysis of 2D models. In these analyses, the 2D infinite-long model is applied. As shown in Fig. 2, the analysis was carried out on the four-pole machine. All analysis has been carried out on the condition that the load angle is 45 degree. Table 1 shows the parameters of 2D FEM analysis. Parameters of the analysis are as follows: The output power of the motor is 500 kW. The rotating speed is 1800 rpm. Gap magnetic flux density, Bg, varied from 1.0 T to 2.5 T. The same model was used in

Yoke
Armature winding Field winding Vacuum heat-insulating Shaft  both cases of the race-track shape winding and saddle-shaped one. In order to check the effect of the short-node winding coefficient, the analysis was carried out on the coil pitches of the armature winding of 30, 60, 90 degrees, which correspond to short-node winding coefficients of 0.5, 0.867, 1.0, respectively. In this paper, magnetic loadings are dominant in order to suppress ac losses in armature windings. As shown in Table 2, ampere-turns of armature and fields windings are different about 10over 100 times. So applied magnetic fields to the armature windings are decided mainly by magnetic fields produced from the fields winding.

Results of analysis
In this chapter, the results of FEM analysis and ac loss calculations are explained. Firstly, perpendicular magnetic flux density applied to the flat face of the REBCO tapes in the armature windings in cases that coil pitch of 30, 60, 90 degrees are explained. Also, then ac losses in each case are shown. Figure 3 shows distributions of perpendicular magnetic flux density applied to the REBCO tapes in the armature windings when the coil pitch of the armature windings is 90 degree, i.e., the short-node

Race-track
Perpendicular magnetic flux density Coil pitch 90 coefficient is 1.0. In every case of Bg, these results clearly show that perpendicular magnetic flux density in case of the saddle-shaped windings are smaller than that in the case of race-track windings, over the whole winding area. The maximum values of perpendicular magnetic flux density in the saddle-shaped windings are half of the values in case of the race-track windings. Figure 4 shows the maximum perpendicular magnetic flux density in the armature windings. The reduction ratios are 45 -50 %. Figure 5 shows the comparison of ac losses in the armature windings in case that coil pitches are 30, 60, 90 degrees, at Bg is 1.0 T. Ac losses in the armature windings were calculated by using the magnetic fields distributions shown in Figure 4. The calculation methods of ac losses in the armature windings have been explained in section 2.1. It is clear that ac losses in the saddle-shaped winding are smaller than that of race-track windings. The maximum loss reduction effect is obtained in case of coil pitch of 90 degree. Because the angle between the flat face of the REBCO tapes and applied magnetic fields direction decrease as the coil pitch decrease. The larger ac losses in case of small coil pitch are estimated. This reason is that winding volume of the armature windings increase as the short-node coefficient decrease. In addition, ac losses increase as short-node coefficient decrease. This reason is that the winding volume of the armature windings increases as the short-node winding coefficient decrease.

Conclusions
Numerical calculations on the properties of fully superconducting synchronous motors using REBCO tapes with 500 kW class were carried out. The transverse magnetic fields applied to the tapes in the armature windings on two winding shapes, race-track shape windings and saddle-shaped windings and ac losses in their windings were investigated. Results show as follows: The perpendicular magnetic fields applied to the flat face of the winding tapes smaller in the saddle-shaped windings than race-track shape. As a result, ac losses in saddle-shaped windings are smaller than that of race-track windings. The loss reduction effects increase as short-node winding coefficient increase.