Analytical Formula for Calculations of Armour Losses in Three-Core Power Cables

TL;DR

This paper derives an analytical, first-principles formula for armour losses in armoured three-core cables by representing the twist-armour as an anisotropic, non-conducting tube and solving Maxwell's equations for the combined twisted-core excitation. The armour response is captured through an effective permeability tensor, determined from longitudinal and transverse external-field analyses, and a thin-shell approximation yields a closed-form expression for the internal armour field and losses, culminating in an IEC 60287 compatible loss factor $\lambda_2$. Validation against 3D FEA (COMSOL) shows excellent agreement, with maximum deviations around 2.4–3.2% across tested configurations, and the exact solution converging even closer (≈1.7%). The result provides a practical, implementable tool for accurate armour-loss calculations that underpin complete loss budgets and cables ratings, including groundwork for integration into CIGRE Technical Brochure 908.

Abstract

Over the past decade, significant progress has been made in the field of loss and rating calculations for armoured three-core cables. This development was prompted by an industry realization that the applicable international standards often overestimate losses, leading to unnecessarily bulky and more expensive cables. Starting with first-principles, this paper presents an accurate analytical formula for armour losses in three-core cables. The formula has undergone rigorous validation against 3D Finite Element Analysis (FEA) and demonstrate excellent accuracy. In the specific cases examined, the largest deviation from FEA results in terms of armour loss is approximately 2.4 percent for fully armoured cables. Although this study specifically focuses on armour losses, it establishes the groundwork for precise loss calculations in armoured three-core cables, including the conductor and screen losses. And the work presented here formed the basis for the complete loss calculations presented in the CIGRE Technical Brochure 908.

Figures (5)

• Figure 1:
• Figure 2:
• Figure 3: The modified COMSOL model based on comsoltutorial, with three twisted edge current enclosed in a ring of twisted armour wires.
• Figure 4: Armour losses for different combinations of core and armour wire pitches and relative permeabilities, computed by (\ref{['eq:loss']}) as functions of number of armour wires.
• Figure 5: Effective relative permeability of the armour layer in the $\varphi'$-direction as a function of relative wire spacing $d_a'/2R$. The solid lines are generated from \ref{['eq:muvarphi']}, whilst the dashed lines are obtained after truncating the linear system of \ref{['TransverseCoefficientAm']} to 17 unknowns and 17 equations.