## 2 Machine Structure Operating Principle and Design of the Flux-Controllable NI HTS FSM
### Design of the Flux-Controllable FSM
However, \(R_{C}\) for the straight section in a racetrack coil depends on the Lorentz force induced by the excitation current. Because the Lorentz force dissipates as the coil current is instantly decreased to zero, \(R_{C}\) is not at all affected by the Lorentz force during a sudden charge [32; 42]. Therefore, it is more appropriate to calculate the \(R_{C}\) of the NI HTS racetrack coil using the charge time constant. The charging time constant, \(\tau\), can be defined as the time interval between B\({}_{1}\) and B\({}_{2}\) in Figure 7, where B\({}_{1}\) is the magnetic field density at the moment when the power supply current is fully charged, and B\({}_{2}\) is the sum of B\({}_{1}\) and B, which is 0.63 between B\({}_{1}\) and a fully charged level. In Figure 7, the charging time constant (\(\tau\)) is 89.34 s. The \(R_{C}\) value of the coil calculated from the charging time constant is 145 \(\mu\Omega\). Here, \(L\) and \(\tau\) are the coil inductance and the time constant, respectively. Figure 8 shows the measured results of the magnetic field distribution in the NI HTS field coil measured at an excitation current of 100 A. For this measurement, a field mapper with a three-axis motor for sensor movements was used. Considering the charging delay phenomenon of the NI HTS field coil, the magnetic field distribution measurement was performed after 800 s. As indicated in the graph, the central magnetic field generated from the NI HTS field coil at an excitation current of 100 A is 25 mT, and the magnetic field density increases toward the coil winding part. \[l_{max}=\sqrt{\pi^{2}/k\Omega\sqrt{EI/\rho S}}\]0 Measured magnetic field distribution of the fabricated NI HTS field coil. \[l_{max}=\sqrt{\pi^{2}/k\Omega\sqrt{EI/\rho S}}\]1 (**a**) Pictures of the fabricated NI HTS field coil, and (**b**) test set-up. \[l_{max}=\sqrt{\pi^{2}/k\Omega\sqrt{EI/\rho S}}\]2 Charging test result of the fabricated NI HTS field coil. Based on the aforementioned design process, an NI HTS FSM with a 12-tooth stator was initially chosen. Table 2 presents the design parameters of the NI HTS FSM. A liquid nitrogen cryostat, a vacuum-layered cryostat with a pair of current leads, a liquid nitrogen inlet, a liquid nitrogen outlet, and leading-in tubes, were designed. In order to account for the radiation heat loss, multi-layer insulation (MLI) in the vacuum layer was considered. According to Equations (7)-(9), the total heat loss for each cryostat was calculated and found to be approximately 15 W when three layers of MLI were inserted into the vacuum space. Figure 9 shows the designed LN\({}_{2}\) cryostat. \begin{table}
\begin{tabular}{c c} \hline
**Item** & **Value** \\ \hline
2G HTS wire & 2G HTS wire manufactured by AMSC \\ Wire width & 12 mm \\ Winding structure & Racetrack and single pancake \\ Length of the straight coil part & 600 mm \\ Inner radius of the coil end part & 65 mm \\ Total winding turns & 40 \\ Insulation type & No-insulation \\ Inductance & 1.3 mH \\ Operating temperature & 77 K \\ Nominal operating current & 100 A \\ \hline \end{tabular}
\end{table} 
Table 1: Key Parameters of the NI HTS Field Coil. \begin{table}
\begin{tabular}{c c} \hline
**Item** & **Value** \\ \hline Maximum output power & 36 kW \\ Phases & 3 \\ Rotating speed & 1000 rpm \\ Stator inner diameter & 563 mm \\ Air-gap distance & 3 mm \\ Rotor inner diameter & 175 mm \\ Active stack length & 600 mm \\ No. of stator slots & 12 \\ No. of rotor poles & 10 \\ Stator tooth arc & 7.5\({}^{\circ}\) \\ Slot arc & 8.25\({}^{\circ}\) \\ Winding turns per armature coil & 12 \\ No. of field coils for flux regulation & 12 \\ Winding turns per field coil for flux regulation & 20 \\ \hline \end{tabular}
\end{table} 
Table 2: Key Design Parameters of the FSM. Figure 9: Liquid nitrogen (LN\({}_{2}\)) cryostat for the NI HTS field coil.