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Mathematical modelling and investigation of skin and proximity effects in supertension power cables

Ahmadi, S. (2024). Mathematical modelling and investigation of skin and proximity effects in supertension power cables. (Unpublished Doctoral thesis, City St George’s, University of London)

Abstract

The increasing demand for energy-efficient and low-carbon electricity transmission has accelerated the deployment of underground and submarine power cables, where conductor losses directly reduce system efficiency and increase operating temperatures and emissions. Traditional analytical models, based predominantly on two-dimensional (2D) cross-sectional analysis, are unable to capture the complex electromagnetic interactions introduced by conductor segmentation, inter-strand insulation, and helicoidal twisting. This thesis addresses this limitation by developing and validating a comprehensive finite element modelling (FEM) framework that advances from conventional 2D simulations to fully three-dimensional (3D) geometries, enabling accurate quantification and minimisation of skin and proximity effects in high-voltage (HV) cable systems.

The research is structured around three core objectives. First, a high-fidelity 2D solver is established, benchmarked against existing literature and capable of predicting AC-to-DC resistance ratios (Rac/Rdc) with high accuracy. Segmenting a 2,711 mm² copper conductor into five sectors reduced Rac/Rdc from 1.84 to 1.74 at 50 Hz, though further subdivision yielded diminishing returns. A significant breakthrough emerged with the inclusion of a 75–100 μm dielectric layer between strands, which decoupled magnetic flux lines and nearly eliminated non-uniform current density, causing Rac/Rdc to collapse towards unity.

Building on this, a novel cable architecture is developed comprising a single segment of round conductor strands, each enveloped in a 100 μm insulating layer. This design achieved Rac/Rdc = 1.02 at 50 Hz—just 2% above its DC resistance—while maintaining the same copper cross-section as the five-segment reference. The practical impact is substantial: under a 1 kA load, this design reduces losses by approximately 4.6 kW per km, translating to savings of 40 MWh and £4,000–£6,000 annually per kilometre, along with an 8–12 tonne reduction in CO₂ emissions. These results demonstrate that inter-strand insulation breaks the conventional trade-off between conductor size and AC efficiency.

Last but not least, a 3D FEM solver is deployed on high-performance computing resources. It reproduces 2D results for parallel conductors and is then applied to twisted five-segment cables with varying lay lengths. The simulations reveal an exponential-saturation relationship between twist and AC losses, offering predictive capability for balancing mechanical flexibility with electrical performance—something impossible with 2D analysis alone.

This thesis contributes: (i) a validated FEM framework linking segmentation, insulation, and twist geometry; (ii) empirical evidence that modest insulation can nearly eliminate AC losses; and (iii) a practical, energy- and cost-efficient cable design. These innovations offer a new benchmark in electromagnetic modelling and immediate applications for low-loss, low-carbon HV transmission.

Publication Type: Thesis (Doctoral)
Subjects: T Technology > T Technology (General)
T Technology > TK Electrical engineering. Electronics Nuclear engineering
Departments: School of Science & Technology > Engineering
School of Science & Technology > School of Science & Technology Doctoral Theses
Doctoral Theses
[thumbnail of Ahmadi thesis 2024 PDF-A.pdf] Text - Accepted Version
This document is not freely accessible until 30 June 2028 due to copyright restrictions.

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