## 4 Results and Discussion
### Transient Electromagnetic-Thermal Behavior of HTS Coils under the L-I-L Fault  
In this section, the worst short circuit fault in the generator output terminal is studied: a sudden three-phase short circuit fault at the no-load operation. When a short circuit fault occurs at a time when  
Figure 7: Perpendicular magnetic flux density magnitude distribution of the area containing the HTS tapes. the electromotive force of the phase-A is passing through zero, the maximum fault current occurs in phase A [16], which is the worst scenario for the A1 HTS coil studied in this paper. When the fault happens, the generator short circuit fault protection system will act to cut off the fault current to remove the fault. Therefore, it is only necessary to pay attention to whether the short circuit fault will cause permanent harm to the superconducting coil within a short period of time after the fault occurs. The short circuit fault occurs at t = 0.04 s of the simulation and the circuit breaker can clear the fault in 0.08 s [17], which means that longer simulation is unnecessary. Figure 9 depicts the variations in the total current, the critical current (CC), the superconducting layer current (SLC) and the copper layer current (CLC) of turn 42 and turn 43 of the A1 coil before and after the occurrence of the worst short circuit fault. The scale of the \(x\)-axis has been changed to make it easier for the reader to observe the waveform at 0.04-0.06 s. Figure 10 depicts the variations in the ohmic loss values and temperature values of turn 42 and turn 43 after the occurrence of the worst short circuit fault. Turn 42 and turn 43 are chosen because the former has the lowest critical current and the most obvious temperature rise in each turn of the coil, while the latter has the highest critical current. As will be shown below, although the total current is the same for both them, during a short circuit fault, due to their different magnetic field environments, their critical current values are different. This difference in the critical current values at the beginning results in their different subsequent copper layer shunting and temperature rise phenomena in each HTS tape. It can be clearly found that the total current increases rapidly after the occurrence of the short circuit fault. The critical current of turn 42 is much lower than that of turn 43 because of the different magnetic field environments on their surfaces. When the total current first exceeds the CC of turn 42 (0.0428 s), the excess current flows through the copper layer, producing the ohmic loss and raising the temperature. However, turn 43 is still in the superconducting state. As the short circuit current increases further, the total current exceeds the CC of turn 43 (0.0436 s); due to its high critical current, the copper layer current of turn 43 is less than turn 42's, resulting in less ohmic loss and a lower temperature rise. Figure 8: Normalized current density distribution of the HTS tapes. Figure 10: Waveforms of the ohmic loss values and the temperature values of turn 42 and turn 43 after the occurrence of the worst short circuit fault. Figure 9: Waveforms of the total current, the critical current (CC), the superconducting layer current (SLC) and the copper layer current (CLC) of turn 42 and turn 43 before and after the occurrence of the worst short circuit fault. For turn 43, due to the non-periodic current component in the short circuit transient process, a peak value (0.0471 s) appears in the first half-cycle after the short circuit fault happens. With this component gradually decaying to zero, the waveform will eventually stabilize into a steady state. Since there is not much of a temperature rise for turn 43 after the first and also the highest peak current (0.0471 s), the subsequent smaller current peaks (for example, the 0.0671 s moment) also cannot induce much of a temperature rise in turn 43.