## 8 Results of the Parametric Analyses Carried Out with the Proposed Tool
### Impact of the Cable's Active Power
This is because the AC losses in the superconductor, which significantly contributed to the total losses and the corresponding operating costs, did not vary linearly with the power or current flowing in  
Figure 9: Total losses along the cable length, calculated assuming a constant transfer of power during the year equal to \(P_{max}\). The cases considered had \(V_{rms}=220\) kV, \(cos\varphi=0.9\), and \(L_{line}=50\) km. the tapes but followed the functions in Equations (31) and (33), which are also dependent on the temperature and critical current. By summing the costs incurred throughout the year in the different time intervals (i.e., integrating the profiles in Figure 10 over time), the operating costs shown in Figure 8 were reproduced and thus justified. Furthermore, Figure 9 also explains the rising trend of the capital costs of the cooling stations with the power shown in Figure 7, given that these must be sized proportionally to the growing losses they must manage and therefore require greater investment costs. The main economic indexes discussed thus far are directly dependent on their corresponding optimized cable structures. Therefore, it is of interest to show the main characteristics of the computed geometries. Figure 11 displays the dimensions of some selected coaxial layers within the cable, as determined by the optimization process under the same conditions as the other figures shown in this section. The blue-purple bars represent the radii of the selected layers, and the values of these bars refer to the left axis of the figure. Specifically, the optimized radius of the former \(R_{f}\) increased with the power, ranging from 1 cm to 2.5 cm. The inner and outer radii of the annular gap are also shown. From their difference, the optimized thickness of the annular gap \(t_{an}\) can be deduced, which increased from 1 cm to 2.4 cm and thus increased the power. Additionally, the trend of the external radius of the cryostat, representing the total radial size of the cable, is illustrated. This dimension ranged from 10.7 cm for the 1 GW case to 12.6 cm for the 3 GW and 3.5 GW cases. Thus, the cable encumbrance remained quite limited despite the high power and voltage levels involved. The small variation in the cryostat's outer radius among the different cases explains the trend of \(Q_{cryo}\) in Figure 9; as shown in Equation (37) it depends on \(R_{cryo_{ext}}\) (as well as \(R_{cryo_{int}}\)) and the nitrogen temperature in the annulus, which could only vary by a few degrees Kelvin between the different cases. Then, Figure 11 also shows the optimized thicknesses of the concentric insulation layers, depicted as red-yellow bars, whose values refer to the right axis of the figure. The inner insulating layers were thicker than the outermost ones, which directly followed from Equations (11) and (12), because these layers must sustain the same \(V_{rms}\) level as the others while having lower inner radii. For the same reason, as \(P_{max}\) increased, the thickness of these layers decreased, a trend previously observed for medium-voltage coaxial cables [35; 36]. Figure 10: Time-varying operating costs per kilometer of cable during a year. The cases considered had \(V_{rms}=220\) kV, \(cos\varphi=0.9\), \(L_{line}=50\) km, and \(P_{max}\) equal to 1.5 GW or 2 GW. It is also interesting to examine the optimized number of HTS tapes wound in parallel around each layer as \(P_{max}\) varied, as shown in Figure 6.0 Up to the 2 GW case, each phase consisted of a single layer, but starting from the 2.5 GW case, the innermost phase required two layers to meet the constraints. The difference of one unit notable in some cases between the two parallel layers of phase 1 was due to the numerical approximation of the _round_ function in Equation (17) and the slightly larger circumference of layer 2 compared with layer 1, as layer 2 was wound around layer 1. Overall, the number of tapes per phase increased with the power.