2.2.1. Equivalent Circuit

Each phase of the cable consists of (i) several HTS tapes connected in parallel, in order to cope with the large operating current, and (ii) two copper-stabilizer layers connected in parallel with the HTS layer. The rest of the cable layers shown in Figure 2 have been neglected for simplicity reasons as the increase of the temperature mainly affects the resistance of the HTS and the copper stabilizer layer. The number of the tapes and the layers have been selected after taking into consideration the value of the designed critical current *IC*, while the geometric characteristics of the tapes have been determined

based on the maximum quenching voltage [38]. In particular, the rated current *Irated* during the steady state operation has been considered equal to 80% of the critical current *IC* [39]. Therefore, the number of tapes can be calculated by the following equation,

$$I\_{\rm rated} = 0.8 \cdot I\_{\rm C\\_initial\\_per\\_stage\text{ }\mathcal{H}} \tag{4}$$

where *IC*\_*initial*\_*per*\_*tape*, corresponds to the initial value of the critical current for each YBCO tape, and has been estimated based on validated manufacturers' data presented in [8], where *n* is the number of tapes.

The equivalent impedance of each phase is dependent on the current distribution among the HTS and the copper layers. Figure 4. shows the equivalent circuit of the three phase triaxial SCs. The resistance of the HTS layers is introduced as a variable resistance which represents the quench phenomenon with an initial value of approximately zero. The PI section model has also been used, in order to implement the self- and mutual-inductances and the capacitance of the cable. The resistance of the copper stabilizer has been modelled as a variable resistor. Once the current increases to higher than the critical value *IC*, the HTS tapes resistance starts to increase and the current flows in both the superconducting and the copper layers. During this process, heat is generated in the tape resulting in a dramatic temperature rise. Once the temperature exceeds *TC* , the cable reaches the normal state mode and the current flows through the copper layer.

**Figure 4.** Equivalent electrical circuit of the modeled cable.
