| Summary: | This paper presents a comprehensive three-dimensional (3D) finite-element (FE) study of skin and proximity losses in a five-segment, helically twisted underground power cable. Unlike conventional two-dimensional (2D) analyses—which assume parallel conductors and consequently overestimate eddy current losses—our 3D approach accurately captures the effects of varying lay lengths (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula>). Simulations are performed from 0 Hz (DC) to 50 Hz, showing that while the per-unit-length DC resistance remains unaffected by twisting, the AC resistance can increase significantly depending on the pitch. At 50 Hz, the ratio of AC to DC resistance (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mi>AC</mi></msub></semantics></math></inline-formula>/<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mi>DC</mi></msub></semantics></math></inline-formula>) ranges from about 1.32 for very tight twists (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><mo>=</mo><mn>0.1</mn><mspace width="0.166667em"></mspace><mi mathvariant="normal">m</mi></mrow></semantics></math></inline-formula>) to nearly 1.72 for gentle pitches (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><mo>=</mo><mn>5.0</mn><mspace width="0.166667em"></mspace><mi mathvariant="normal">m</mi></mrow></semantics></math></inline-formula>). Further analysis reveals that short lay lengths enhance magnetic field coupling, improving current distribution and partially mitigating losses. To quantify these findings, an exponential-saturation model is proposed to describe <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mi>AC</mi></msub></semantics></math></inline-formula>/<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mi>DC</mi></msub></semantics></math></inline-formula> as a function of lay length, achieving excellent agreement (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>R</mi><mn>2</mn></msup><mo>≈</mo><mn>0.996</mn></mrow></semantics></math></inline-formula>) with the 3D FE data. These results underscore the importance of considering full 3D geometry in cable design, offering a practical tool for optimizing both mechanical reliability and electromagnetic performance in high-voltage underground applications.
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