## 3 Characteristic Analysis of the Flux-Controllable NI HTS FSM
### Flux-Regulation Characteristics of the Proposed FSM  
The flux-regulation characteristics were analyzed by means of a transient motion analysis. With the FEM, the no-load magnetic field distributions and flux contours of the proposed machine with different MMF levels of the additional field windings were analyzed. Figure 17 shows the magnetic field distributions according to the MMF of the additional field windings. In this analysis, the excitation current of the NI HTS field coil was maintained at 100 A, while the MMF of the additional field winding was changed. Figure 17c presents the magnetic field distribution and flux contour under only NI HTS field coil excitation. Figure 17a,b show the field distributions with negative regulation current levels of 20 A and 10 A, respectively. Correspondingly, Figure 17d,e show the field distributions with positive regulation current levels of 20 A and 10 A. These figures show that as the regulation current increases, the magnitude of the magnetic field density in the FSM also increases.  
Figure 16: Phase voltage and line current in resistance-load condition due only to the NI HTS field coil.  
Figure 17: Flux vector contour and magnetic field distribution according to the magneto-motive force (MMF) of the additional field winding: (**a**) \(-\)4 kA-T, (**b**) \(-\)2 kA-T, (**c**) 0 kA-T, (**d**) 2 kA-T, and (**e**) 4 kA-T.  
Figure 18 shows the flux linkage of the phase C armature winding under different regulation current levels. The regulation current was maintained at zero until 14 milliseconds, and the regulation current was applied to the additional field winding after 14 milliseconds. By controlling the regulation current, the flux linkage of the armature winding can be regulated. When the NI HTS field coils and additional field windings work together, a flux-regulation operation is achieved. Figure 19 compares the no-load voltage waveforms under different regulation modes at 1000 rpm. For solely the NI HTS field coil excitation mode, the peak value of the no-load voltage is approximately 770 V. The peak values in the maximum negative regulation current, and the positive regulation current, are 410 and 980 V, respectively. By applying MMF of \(-\)20 kA-T, the amplitude of the no-load voltage can be reduced by nearly 53%, from 770 V to 410 V. By applying MMF of 20 kA-t, the amplitude of the no-load voltage can be increased by 27%, from 770 V to 980 V. Figures 20 and 21 correspondingly show the phase voltage and phase current waveforms at the rated operation condition. In this case, the armature winding coils were connected to a resistance load. The simulation results confirm that the output power of the FSM in the negative regulation mode can be reduced to approximately 6.7 kW. On the other hand, in the positive regulation mode, the output power of the FSM is approximately 36.2 kW, which is increased by 180%, compared to that in the solely NI HTS field coil excitation mode. Figure 22 shows the torque curve according to the MMF of the additional field winding. From these simulation results, it is confirmed that the torque of the machine in the positive regulation mode is approximately 4700 N-m, which is increased by 210%, compared to that of the solely NI HTS field coil excitation mode.  
Figure 18: Flux linkage of Phase C according to the MMF of the additional field winding.  
Figure 19: No-load voltage of Phase C according to the MMF of the additional field winding.  
Figure 20: Phase voltage of Phase C in the resistance-load condition according to the MMF of the additional field winding.