## 1 Introduction  
Twisted and stranded conductors are ubiquitous in high-voltage and extra-high-voltage (EHV) underground power cables. By helically arranging conductor segments or sub-bundles, cable manufacturers can improve mechanical robustness and mitigate certain electromagnetic imbalances [1, 2]. While these benefits are well recognized, the electromagnetic implications of twisting--particularly on skin and proximity losses--are also significant. Under alternating-current (AC) conditions, twisting modifies both the skin and proximity effects [3, 4], which, in turn, affect the AC resistance and power dissipation of the cable. Several studies on twisted conductors provide important background for the present work. For example, ref. [5] investigated the influence of inner skin- and proximity effects on conduction in Litz wires using three-dimensional finite-element (3D-FE) simulations, highlighting the critical role of twisting in current redistribution. Ref. [6] further analyzed loss mechanisms in multistranded twisted wires via 3D-FE simulations, demonstrating that twisting not only affects the strand-level eddy currents but also introduces additional bundle-level losses. In high-speed permanent magnet machines, ref. [7] showed that transposition of insulated strands can reduce bundle proximity losses, emphasizing the sensitivity of loss mechanisms to the twisting configuration. Complementary analytical approaches have also been developed, ref. [8] formulated a complete analytical model to capture the effects of twisting on Litz-wire losses, while [9] provided a 3D finite-element simulation of Litz wires with multilevel bundle structures that captures the complexity of the twisting operations. Finally, ref. [10] exploited helicoid symmetry to reduce the dimensionality of eddy-current problems in power cables, offering further insights into the impact of twisting on conductor performance. While DC resistance (\(R_{\text{DC}}\)) grows with length, AC resistance (\(R_{\text{AC}}\)) also includes frequency-dependent skin and proximity effects [11; 12]. In multi-segment cables, twisting reorients segments along \(z\), altering how eddy currents form near segment boundaries. Consequently, \(R_{\text{AC}}\) is not solely a function of length but also the electromagnetic coupling among segments. Thus, shorter lay lengths can yield different \(R_{\text{AC}}/R_{\text{DC}}\) values than more gently twisted cables. Unlike previous two-dimensional (2D) analyses that approximate sub-conductors as parallel elements [13; 14], the present study employs a comprehensive 3D FE approach that explicitly accounts for the helical geometry. This paper focuses on a five-segment underground cable design, where each segment is treated as a solid bundle of hexagonally packed copper strands. Fourteen distinct 3D models are constructed, each one completing exactly one full 360\({}^{\circ}\) rotation around the cable's central axis with a different _lay length_\(\lambda\) (0.1 m to 5.0 m). Simulations performed from 0 Hz (DC) to 50 Hz reveal that while the per-unit-length DC resistance remains constant with twisting, the AC resistance changes significantly with varying lay length. Specifically, at 50 Hz, the ratio \(R_{\text{AC}}/R_{\text{DC}}\) ranges from about 1.32 for very tight twists (lay length \(\lambda=0.1\) m) to nearly 1.72 for gentle twists (\(\lambda=5.0\) m). An exponential-saturation model is proposed to describe this trend, yielding excellent agreement (\(R^{2}\approx 0.996\)) with the 3D FE data. These findings underscore the importance of accurately capturing 3D twisting effects not only for loss prediction but also for optimizing both mechanical and electromagnetic performance in high-voltage underground cable designs. The paper also discusses mesh design, numerical errors, and a general method to incorporate effective conductor length changes due to twisting.