## 4 Results and Discussion  
### AC Loss of HTS Coils under the Rated Operation  
The induced AC loss on HTS armatures will directly affect the efficiency of the generator and thereby increase the cost of cooling. Hence, accurately and quickly estimating the AC loss of the HTS generator is urgent and beneficial. The T-A formulation model has offered a convenient tool to solve this problem. In this section, the AC loss of HTS coils in the generator during the rated operation will be calculated and discussed.  
The calculated AC loss values of several representative turns, which are placed at different locations in the HTS coil, are summarized in Table 2. It can be seen that different turns of the coil have significantly different AC loss values. The calculated current waveform of the A1 coil in one cycle at the rated condition is shown in Figure 6, and four typical time moments, A, B, C and D, are chosen to show the calculation results.  
\begin{table}
\begin{tabular}{c c} \hline
**Turn Number** & **AC Loss (W)** \\ \hline
1 & 0.31 \\
21 & 0.60 \\
42 & 1.94 \\
43 & 0.11 \\
63 & 0.14 \\
84 & 0.55 \\ \hline \end{tabular}
\end{table}
Table 2: AC loss values of several representative turns.  
Figure 5: The manufactured generator stator.  
Figure 6: Current waveform of the studied A1 coil in one cycle.  
The critical current of the HTS tapes is mainly influenced by the magnetic field perpendicular to the tape surface. Figure 7 shows the perpendicular magnetic flux density magnitude distributions of the area around the HTS tapes. First, due to the lower coil being closer to the rotor than the upper coil, its surface magnetic field is significantly larger than that of the upper coil. The turn in the lower coil has a greater AC loss value than the corresponding turn with the same distance to the stator iron teeth in the upper coil (e.g., turn 42 and turn 84). In addition, the perpendicular magnetic field in region A1+ is much greater than that in the A1\(-\) region. Although the average perpendicular magnetic field of turn 42 in the A1\(-\) region is less than turn 21, the average perpendicular magnetic field of turn 42 in the A1\(+\) region is much greater than turn 21, which makes the AC loss of turn 42 greater than turn 21.  
Figure 8 shows the normalized current density distribution of the HTS tapes. The normalized current density distribution is similar to the perpendicular magnetic field distribution. The critical current degradation is more severe in each turn of the lower coil due to the greater perpendicular magnetic field, so the current penetration into the interior of the HTS tapes is more severe, making the AC loss greater than the upper coil. Turn 42 in the lower coil suffers the maximum surface perpendicular magnetic field and has the minimum critical current because it is nearest to the iron teeth, which attracts the flux lines. Its current penetration is also the most severe and it has the greatest AC loss value.  
The generator has three phases and is symmetrical. Since the current and magnetic field of each coil have three phases and are symmetrical, with only the phase angle being different, the AC loss is the same for all six coils. The calculated total AC loss of the 6 HTS coils is 229.38 W. Considering that the cooling penalty is about 10 [28], the loss ratio is about 5.29%.