## 8 Results of the Parametric Analyses Carried Out with the Proposed Tool
### Impact of the Cable's Active Power
However, there was a decrease in the passage between the 2 GW and 2.5 GW cases, as dividing the HTS tapes of phase 1 into two layers required winding them into smaller circumferences, which in turn also reduced the circumferences of the inner and outer layers (from which a slight reduction in the values of \(R_{f}\) and \(R_{xy\theta_{ext}}\) followed for the 2.5 GW case compared with the 2 GW case). As the circumferences of the outermost HTS layers reduced, the number of tapes composing them had to decrease. Figure 6.1 Radial dimension of the former, the annular gap, and the cryostat (left side) and the thicknesses of the 3 insulating layers of the cable (red side). The cases considered had \(V_{rms}=220\) kV, \(cos\varphi=0.9\), and \(L_{line}=50\) km. Figure 6.2 Number of HTS tapes per layer, varying the maximum active power transferred. The cases considered had \(V_{rms}=220\) kV, \(cos\varphi=0.9\), and \(L_{line}=50\) km. Figure 13 presents the optimized system variable \(\sqrt{2}\left|\frac{I_{tap_{i,1}}}{I_{c}\left(T_{HTS_{max}},\ \left|B\right|_{i,1},\ \theta_{i,1}\right)}\right.\) for the three phases as red-yellow bars, with values displayed on the right axis. For all powers and phases, this parameter fell within the range specified in Table 5, indicated by the red dashed horizontal lines. The corresponding \(I_{c\gamma_{Ti}}\) values for the same phases are also displayed in Figure 13 as blue-purple bars whose values refers to the left axis. As expected, OSCaR suggested using lower-quality tapes for the outermost phases, which had larger circumferences and therefore required more HTS tapes, preventing their excessive underloading. This proportionality seemed to reverse for phase 1 from the 2 GW case onward. However, this might be explained by the fact that the total number of tapes in phase 1 increased significantly when reaching \(P_{max}=2.5\) GW, requiring two parallel layers, as shown in Figure 6.3 In fact, while the current increased by 25% between 2 GW and 2.5 GW, the number of tapes almost doubled, with a consequent impact on the optimized \(I_{c\gamma_{Ti}}\) and \(\sqrt{2}\left|\frac{I_{tap_{i,1}}}{I_{c}\left(T_{HTS_{max}},\ \left|B\right|_{i,1},\ \theta_{i,1}\right)}\right.\) When approaching the highest power level, the critical current proposed for all phases seemed to be uniform with the values closer to the upper limits, trying to maintain the ratio with the operating current being relatively low. It is worth noting how for the 1 GW case, the solver did not meet the constraint for the minimum \(I_{c\gamma_{Ti}}\) for phase 3, whose limits are reported in Table 5 and indicated by blue dashed horizontal lines. This could be due to an incorrect combination of user-defined parameters and constraints proposed by the authors in Section 7, leading to the selection of particularly poor-performing HTS tapes for this outer phase. Nonetheless, this is the only constraint not respected in all of the parametric analyses shown. By combining the values from Figures 12 and 13, it can be concluded that the solver suggests using better-performing tapes in the phases where they are needed in lower quantities. However, understanding how the capital cost of the tapes shown in Figure 7 is divided between the various phases is not straightforward. This allocation depends on factors such as the radii of the HTS phases, their winding angles, and the quantitative discounting process. To provide readers with a range of total HTS tape lengths required for a 50 km line, these varied from 7000 km for the 1 GW case to 12,000 km for the 3.5 GW case. These quantities likely exceed the current production capabilities of most manufacturers but offer an insight into the scale of investment needed for the future application of superconducting cable technology. Finally, Figure 14 shows the optimized values for the LN2 mass flow rate \(m_{LN2}\) for the various cases analyzed. The flow rate increased with the power, staying within the user-defined limits (indicated by dashed horizontal lines).