## 5 Results and Discussion
### AC Condition (50 Hz)  
At 50 Hz, skin and proximity effects concentrate current near segment boundaries; moreover, the twisting modifies how segments interact over the cable length. Table 5 compiles the extracted total power loss in Watts, the total \(R_{\rm AC}\) in Ohms, and the per-meter \(R_{\rm AC\_2D}\) for each of the 14 models. The final column lists \(R_{\rm AC\_2D}/R_{\rm DC\_2D}\).  
A key observation is that all models have \(R_{\rm AC\_2D}/R_{\rm DC\_2D}=R_{\rm AC}/R_{\rm DC}>1.0\), as theoretically expected (\(R_{\rm AC}\) can never be below \(R_{\rm DC}\)). Notably, shorter lay lengths (\(\lambda=0.1,\ 0.2,\ 0.4\) m) produce smaller \(R_{\rm AC}/R_{\rm DC}\) (around 1.32-1.55), while longer lay lengths approach \(\approx 1.70\)-1.72.  
These differences are attributed to how the magnetic fields from each segment interact along the twisted path. In the gently twisted scenario (large \(\lambda\)), each segment remains offset over a longer distance, enhancing local eddy currents near boundaries [11; 12]; thus, \(R_{\rm AC\_2D}\) is relatively higher. In a tightly twisted scenario, the segment alignment changes more rapidly, distributing the current distortion differently and leading to a somewhat lower \(R_{\rm AC\_2D}\).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \(\lambda\) & \(P_{\rm loss}\) & \(R_{\rm DC}\) & \(I_{\rm twist}\) & \(R_{\rm DC\_2D}\) & \(R_{\rm DC\_2D}\)-cal & \(R_{\rm DC\_2D}\) \\ (m) & (mW) & (\(\mu\Omega\)) & (m) & (\(\frac{\mu\Omega}{\rm m}\)) & (\(\frac{\mu\Omega}{\rm m}\)) & \(\frac{\mu\Omega}{\rm m}\)) & \(\frac{\mu\Omega}{\rm R_{DC\_2D}}\)-cal \\ \hline
0.1 & 0.1709 & 1.709 & 0.2688 & 6.36 & 6.36 & 1.00 \\
0.2 & 0.1892 & 1.892 & 0.2975 & 6.36 & 6.36 & 1.00 \\
0.4 & 0.2922 & 2.922 & 0.4594 & 6.36 & 6.36 & 1.00 \\
0.6 & 0.4127 & 4.127 & 0.6490 & 6.36 & 6.36 & 1.00 \\
1.4 & 0.9230 & 9.230 & 1.4513 & 6.36 & 6.36 & 1.00 \\
2.0 & 1.3117 & 13.117 & 2.0625 & 6.36 & 6.36 & 1.00 \\
2.2 & 1.4416 & 14.416 & 2.2668 & 6.36 & 6.36 & 1.00 \\
2.6 & 1.7017 & 17.017 & 2.6758 & 6.36 & 6.36 & 1.00 \\
3.0 & 1.9621 & 19.621 & 3.0852 & 6.36 & 6.36 & 1.00 \\
3.4 & 2.2226 & 22.226 & 3.4948 & 6.36 & 6.36 & 1.00 \\
3.6 & 2.3529 & 23.529 & 3.6997 & 6.36 & 6.36 & 1.00 \\
3.8 & 2.4832 & 24.832 & 3.9046 & 6.36 & 6.36 & 1.00 \\
4.0 & 2.6135 & 26.135 & 4.1096 & 6.36 & 6.36 & 1.00 \\
5.0 & 3.2654 & 32.654 & 5.1346 & 6.36 & 6.36 & 1.00 \\ \hline \end{tabular}
\end{table}
Table 4: Power-loss calculations at 0 Hz (DC).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \(\lambda\) & \(P_{\rm loss}\) & \(R_{\rm AC}\) & \(I_{\rm twist}\) & \(R_{\rm AC\_2D}\) & \(R_{\rm DC\_2D}\) & \(R_{\rm DC\_2D}\) \\ (m) & (mW) & (\(\mu\Omega\)) & (m) & (\(\frac{\mu\Omega}{\rm m}\)) & (\(\frac{\mu\Omega}{\rm m}\)) & \(\frac{\mu\Omega}{\rmIn the present model, each segment is considered a single solid region with no internal transposition as the individual conductor strings are not electrically insulated within segments, and it is only the five segments that are insulated by a relatively thin layer of air. The twisting primarily repositions entire segments around the \(z\)-axis passing through the cable's center. In an individually insulated conductor scenario, the net effect can significantly alter electromagnetic coupling between conductors as well as segments, thereby impacting how current distributes at steady state.