## 6 Conclusions  
This study compares two-dimensional (2D) and three-dimensional (3D) finite element (FE) models in analyzing skin and proximity effects in segmented power cables with parallel conductors. Evaluating single-, three-, and five-segment configurations across frequencies of 0, 50, 150, and 250 Hz, the research demonstrates that 2D models offer comparable accuracy to 3D models with significantly reduced computational resources. The key findings of this study are as follows:  
* **Accuracy of 2D Models**: Two-dimensional FE models achieved \(\text{R}_{\text{AC}}/\text{R}_{\text{DC}}\) ratios within 2% of 3D models, with errors below 0.6% at 50 Hz. This validates their effectiveness in capturing electromagnetic behavior in parallel conductor conditions;
* **Computational Efficiency**: Two-dimensional models require substantially less processing time and memory, making two-dimensional models ideal for large-scale and iterative studies;
* **Impact of Segmentation**: Increasing segments from one to five slightly reduced the \(\text{R}_{\text{AC}}/\text{R}_{\text{DC}}\) ratio, indicating mitigation of skin and proximity effects. However, the modest reduction suggests that additional strategies are needed to counteract skin effects at higher frequencies; \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Segment** & **Benchmark** & **2D Models** & **3D Models** \\ \hline
1-Segment & 1.86 & 1.85 & 1.86 \\
3-Segment & 1.76 & 1.76 & 1.76 \\
5-Segment & 1.73 & 1.74 & 1.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Validation of \(\text{R}_{\text{AC}}/\text{R}_{\text{DC}}\) ratios against [12]. * **Frequency Dependence**: The R\({}_{\rm AC}\)/R\({}_{\rm DC}\) ratio increases with frequency, highlighting the need for design optimizations to manage skin effects in high-frequency applications. Segmentation provides partial mitigation but is insufficient alone;
* **Mesh Design Considerations**: Appropriate mesh density in 2D models is crucial for low discretization errors. While 3D models can achieve similar accuracy with fine meshes, their higher computational costs make 2D models more practical for many applications. Despite these promising results, the study has limitations. Simulations focused only on the conductive core, assuming infinitely long cables with parallel flux lines and fully compressed hexagonal conductor arrangements. Additionally, materials were treated as homogeneous with fixed resistivity, ignoring potential variations from manufacturing processes or temperature changes. Future research should incorporate additional cable components, explore finite-length effects and helical twisting, investigate non-parallel conductor arrangements. These advancements will enhance the robustness and applicability of FE models for diverse power cable designs. In conclusion, 2D FE models are highly efficient and sufficiently accurate alternatives to 3D models for analysing skin and proximity effects in segmented cables with parallel conductors. The 2D and 3D FE simulations result in the same skin and proximity losses when all conductor strings are in parallel with each other. Future work will extend these models to include twisted or transposed conductors and advanced insulation layers, as well as material and temperature variations, to further investigate the skin and proximity effects in power cables. Integrating materials with \(\mu_{r}\) greater than unit can potentially help in distributing flux lines more uniformly, which may result in lower skin and proximity losses. Conceptualization, S.A.; methodology, S.A. and S.H.K. ; simulation, S.A.; validation, S.A. and S.H.K. ; formal analysis, K.T.V.G. ; writing--original draft preparation, S.A.; writing--review and editing, S.H.K. and K.T.V.G. ; supervision, S.H.K. and K.T.V.G. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The data presented in this study are available in this article.