The paper is focused on numerical modeling of multi-strand cable lines placed in free air. Modeling is carried out within the framework of the so-called multi-physics approach using commercial software. The paper describes in detail the steps undertaken to develop realistic, reliable numerical models of power engineering cables, taking into account their geometries and heat exchange conditions. The results might be of interest to the designers of multi-strand cable systems.

Skin and proximity effects have a considerable impact on current distribution in multi-strand cable lines. Under unfavorable heat exchange conditions some strands may be subject to excessive overheating, what may lead to serious malfunctions or even fires of the installation. The paper proposes a new criterion for a quick choice of spatial configurations, for which the effect might be minimized. A comprehensive analysis of literature cases is provided, including the recommendations of the U.S. National Code and the Canadian standard.

Designing high-voltage underground transmission lines poses complex challenges in heat management, trench optimization, and determining cable ampacity. This article introduces an innovative proposal that focuses on adjusting the dimensions of the thermal backfill as a primary strategy to enhance ampacity compared to the traditional approach of increasing the cross-sectional area of the cable core. The methodology employs a particle swarm optimization (PSO) technique with adaptive penalization, restart strategies, and parameter self-adaptation implemented in MATLAB. The objective of this approach is to provide more efficient solutions than traditional MATLAB PSO, demonstrating improved convergence and more accurate results with a success probability of 66.1\%. Although traditional PSO is 81\% faster, the proposed PSO stands out for its precision. Additionally, the incorporation of thermal backfill results in an 18.45\% increase in cable ampacity. Variations in the thermal resistivity of the soil, backfill, and ambient temperature are highlighted as sensitive factors affecting ampacity and backfill dimensions. This method is presented as a crucial tool in the early stages of the project and underground installation in operation with maximum ampacity, contributing to the continuous improvement of energy efficiency.