## 8 Results of the Parametric Analyses Carried Out with the Proposed Tool
### Impact of the Cable's Active Power  
In this analysis, a 50 km long cable was connected to a load with a \(cos\varphi\) equal to 0.9 at a voltage level of 220 kV. OSCaR was run while varying the peak active power from 1 GW to 3.5 GW in increments of 0.5 GW, computing the optimal set of system variables \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Unit** & **Value** & **Reference** \\ \hline \(\%_{max}\)\({}_{phases}\) & \% & 0.8 & \\ \(\%_{max}\)\({}_{layers}\) & \% & 0.1 & \\ \(I_{c}\)\(77\)\(K_{max}\) & A & 275.0 & \\ \(I_{c}\)\(77\)\(K_{min}\) & A & 150.0 & \\ \(\Delta P_{LN2}\)\(max\) & bar & 12 & [38] \\ \(\Delta T_{LN2}\)\(max\) & K & 10 & [38] \\ \(T_{0}\) & K & 68 & [38] \\ \(P_{0}\) & bar & 15 & [38] \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Values of the parameters referring to electrical and fluid dynamic constraints. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Unit** & **Value** & **Reference** \\ \hline \(f\) & Hz & 50 & \\ \(\eta_{p}\) & & 0.7 & [41] \\ \(\eta_{cry}\) & & 0.1 & [40] \\ \(\rho_{LN2}\) & kg/m\({}^{3}\) & 893.0 & [40] \\ \(c\rho_{LN2}\) & J/kg\(\cdot\)K & 2662.0 & [40] \\ \(\mu_{LN2}\) & μPa\(\cdot\)s & 25.08 & [40] \\ \(\rho_{Cu}\) & kg/m\({}^{3}\) & 8850.0 & \\ \(q_{cl}\) & W/kA per current & 45.0 & [20] \\ \(q_{del}\) & lead & 0.05 & [20] \\ \(T_{amb}\) & K & 293.1 & \\ \(Rinstall\) & m & 0.5 & \\ \(h_{y}\) & hours & 8760 & \\ \(yr\) & years & 40 & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Values of the other parameters which were not previously mentioned. and the corresponding cost indexes and cable configuration for each case. \(P_{max}\) refers to the maximum power delivered by the cable during its yearly operation. The power trend profile in Figure 4 (blue curve) was thus scaled based on the value of \(P_{max}\). Compared with the medium voltage lines discussed in [35; 36], longer line lengths were investigated here, as the authors considered that HVAC cables might be more suitable for these extended distances. Figure 6 shows the total costs per kilometer of the line (expressed in EUR M/km) for the various cases, distinguishing between the overall capital and operating costs. As expected, the costs increased with the power, although not linearly. Compared with the 1 GW value, the costs per kilometer, and therefore the costs of the entire line, increased by 21% when the power was doubled and by 60% when it was tripled. When neglecting the practical challenges of managing extremely high-power lines and sizing their ancillary devices, the economic benefit of having more powerful individual lines rather than multiple less-powerful cables in parallel is evident. Overall, the estimated cost of the proposed HTS lines varied from EUR 5.3 M/km for the 1 GW scenario to EUR 9.2 M/km for the 3.5 GW case. Readers should consider these results as qualitative, given that they were derived from several approximations and user-defined parameters available or hypothesized by the authors in Section 7. Furthermore, it can be seen that the ratio between the capital and operating costs was strongly unbalanced toward the first values. In fact, the sum of the operating costs over the entire estimated lifespan of the cable (\(yr=40\) years) contributed only between 15% and 16.4% of the total costs. Then, Figure 7 expands the different contributions to the capital costs shown in Figure 6. The main capital costs, in order of their contribution to the total costs, were related to the purchase of the superconducting tapes, the cabling of the various materials together, the civil engineering work to install the cable, the cooling stations, the costs of the accessory components (categorized as other costs), and the cost of the cryostat. The remaining cost terms were minor if not negligible, such as the costs for terminations, which have been divided in Figure 7 by the entire cable length and therefore yielded minimal results. Figure 6: Total cost per kilometer of a cable, varying the maximum active power transferred.