**Table 3.** SC Parameters.


**Table 4.** Specifications of 33 kV SC.


In the following part, systematic iterative simulations have been performed, which include (i) 3-Phase-to-ground faults at two di fferent fault locations, (ii) a Phase-to-Phase-to-ground fault and (iii) a Phase-to-ground fault. In all cases the faults initiate at *t* = 5.06 s and last for 120 ms. To obtain a high-fidelity insight of the transient phenomena of SCs, a sampling frequency of *f* = 2 MHz has been used (accounting for simulations and records).

## *3.1. Fault Analysis of the SCs*

Initially, a 3-Phase-to-ground fault with fault resistance *Rf* = 0.01 Ω was triggered at 50% of the HTS cable's length at *t* = 5.06 s, and it was cleared after 120 ms. Figure 7 shows the stages of the quenching process, Figure 8a illustrates the fault current signatures contributed by the wind farm and the SG at Bus 11, while Figure 8b presents the corresponding voltage signatures. The resulting fault current distribution among the di fferent layers of the three phases is shown in Figure 8c–h. At the superconducting state (stage 1) and the flux flow state, which is a moderately resistive state, the current flows through the HTS layers, presenting high peaks due to the low resistance of the superconductor when the fault occurs. However, as the fault current exceeds the critical value *IC* in the flux flow mode (stage 2), the temperature rises continuously and the value of the resistance of the superconductor increases rapidly to very high values, reaching the normal state (stage 3). Therefore, as it can be seen from Figure 8d,f,h, the main current has been diverted to the copper stabilizer layers, indicating that the normal state has been reached, while the HTS layers conduct approximately zero current. Figures 9 and 10 illustrate the changes in the resistance values and the temperature rise, respectively. Initially, the temperature is 70 K for the three phases and the equivalent resistance of the superconductor is approximately zero. Once the temperature exceeds 92 K, which is the critical value, at *t* = 5.064 s, the HTS tapes enter the normal state and their resistance starts to increase rapidly. For stage 2, the equivalent resistance of the superconductor is calculated based on Equation (16). The current distribution starts to change, and the fault current is diverted to the stabilizer layers. Subsequently, in the normal state (stage 3) the equivalent resistivity is equal to the maximum resistivity of the copper stabilizer layer obtained by Equation (17). Therefore, the proposed design has achieved the current sharing between the HTS and stabilizer layers, aiming to improve the performance of the cable and self-protecting it from being destroyed.

**Figure 7.** Stages of quenching process for phase A, B, and C for 3-Phase-to-ground solid fault at 50% of cable's length.

As discussed earlier, the installation of the SCs impacts the magnitude of fault currents. Indeed, from the fault current waveforms plotted in Figure 8, at the time of the fault event at *t* = 5.06 s, the highest first current peak is approximately 15 kA. As the value of the layers' resistance increases immediately, the magnitude of the fault currents decreases. Specifically, at *t* = 5.064 s, when the values of resistances and the temperature reach high values, the fault current starts flowing through the stabilizer layers, presenting peaks of approximately 5.5 kA. During the current elimination within the first fault cycle, some peaks are presented at the 3-Phase fault voltages. Moreover, it is noticeable that after *t* = 5.069 s and before the fault clearance at *t* = 5.18 s, the magnitude of fault currents at Bus 11 are limited and the phase voltages show higher magnitudes compared to steady state. This is interpreted based on the large equivalent resistance inserted by the SCs. Hence, it is evident that SCs provide

effective limitation of fault currents in systems containing SGs and converter-interfaced generators. Such fault current limiting capability seems to be an interesting feature in regards towards protecting networks with varying short-circuit levels. Furthermore, the high voltage magnitudes during transient conditions raises new challenges for the voltage-assisted protection schemes. Normally, during the fault events, the voltage magnitude is anticipated to be reduced. However, in this case, when the fault occurs at *t* = 5.06 s, the 3-Phase voltages decrease for few milliseconds, but when the equivalent resistance of the superconductor increases, the fault current decreases, while the 3-Phase voltages present high peaks. The introduction of high equivalent resistance leads to voltage spikes across the superconductor. The faults at the SCs can be considered as high impedance faults in nature, jeopardizing the operation of the existing protection schemes.

**Figure 8.** Fault current and voltage signatures for 3-Phase-to-ground solid fault at 50% of cable's length.: (**a**) phase currents at Bus 11, (**b**) phase voltages at Bus 11, (**c**) current in HTS layer of phase A, (**d**) current in copper layer of phase A, (**e**) current in HTS layer of phase B, (**f)** current in copper layer of phase B, (**g**) current in HTS layer of phase C, (**h**) current in copper layer of phase C.

**Figure 9.** Equivalent resistance for phases A, B, and C for 3-Phase-to-ground solid fault at 50% of cable's length.

Additionally, the fault currents, the voltage signatures, and the current distribution characteristics for a Phase-A-to-ground and a Phase-A-B-to-ground faults at the 50% of the HTS cable's length with *Rf* = 0.01 Ω are reported in Figure 11 and Figure 12, respectively. The faulted phases of the proposed SCs have been found to behave in a similar way as in the previous case of the 3-Phase-to-ground fault. The characteristics of the superconductor resistance have the same trend as those presented in Figure 9 for the faulted phases. However, the equivalent resistance of the HTS layers of non-faulted phases remains at 0 Ω, as they do not quench and operate at superconducting state. Regarding the temperature rise for the faulted phases, it can be described based on Figure 10, while for the non-faulted phases the operating temperature remains constant at 70 K prior to and during the fault. For the non-faulted phases, the fault current flows only through the HTS layer. Therefore, the specific design target of the current limitation can be verified for different fault types with approximately zero fault resistance. Once the value of the fault current density exceeds the critical value *JC*(*T*) (Equation (11)) within the first fault cycle, the resistivity of the HTS layer increases based (refer to Equation (15)) and the fault current diverts to the copper stabilizer layer. The feasibility of the parallel stabilizer layer can been confirmed for 3-Phase-to-ground, Phase-A-to-ground and Phase-A-B-to-ground faults by observing the current distribution characteristics in Figure 8, Figure 11, and Figure 12 respectively. As the quenching process evolves, the temperature of the SCs increases, reaching values higher than the critical *TC*; during the normal resistive mode, the value of the SCs equivalent resistance is only determined by the value of the stabilizer layer given by Equation (17). The further increase in temperature results in an increase in the resistivity of the copper stabilizer layer (Equation (17)) which leads to further reduction in fault current. The accuracy of the fault current limiting capability is verified by Figure 8 for a 3-Phase-to-ground fault, where the first peak of the fault current at *t* = 5.06 s is approximately 15 kA; however, within the first cycle, and before the fault clearance at *t* = 5.18 s, the peak of the fault current is reduced to 1.8 kA. The same behaviour is observed for a Phase-A-to-ground and Phase-A-B-to-ground fault, as depicted by Figure 11 and Figure 12, respectively. The first peak of the fault current flowing through HTS layer, has values of 15 kA for the faulted phases, while the resulted fault current flowing through the stabilizer layer has been limited to approximately 1.7 kA.

**Figure 10.** Temperature for phases A, B, and C for 3-Phase-to-ground fault at 50% of cable's length.

**Figure 11.** Fault current signatures for Phase-A-to-ground solid fault at 50% of cable's length: (**a**) phase currents at Bus 11, (**b**) phase voltages at Bus 11, (**c**) current in HTS layer of phase A, (**d**) current in copper layer of phase A, (**e**) current in HTS layer of phase B, (**f**) current in copper layer of phase B, (**g**) current in HTS layer of phase C, (**h**) current in copper layer of phase C.

**Figure 12.** Fault current signatures for Phase-A-to-ground Phase-A-B-to-ground solid fault at 50% of cable's length: (**a**) phase currents at Bus 11, (**b**) phase voltages at Bus 11, (**c**) current in HTS layer of phase A, (**d**) current in copper layer of phase A, (**e**) current in HTS layer of phase B, (**f**) current in copper layer of phase B, (**g**) current in HTS layer of phase C, (**h**) current in copper layer of phase C.
