Accurate Analytical Formula for Calculating Armour Losses in Three-Core Power Cables

Core Concepts

This paper presents an accurate analytical formula for calculating armour losses in three-core power cables, which can be used to improve the efficiency and cost-effectiveness of cable design.

Abstract

The paper starts by introducing the magnetic field generated by three twisted filamentary conductors carrying balanced three-phase currents. It then transforms the N-wire armour into an equivalent tube representation to simplify the analysis.
The authors derive an analytical formula for the armour losses by solving Maxwell's equations for the twisted three cores surrounded by the equivalent tube armour. The formula is validated against 3D Finite Element Analysis (FEA) simulations, showing excellent accuracy with a maximum deviation of 2.4% for fully armoured cables.
The key highlights of the paper are:

Derivation of an accurate analytical formula for armour losses in three-core power cables
Transformation of the N-wire armour into an equivalent tube representation to simplify the analysis
Validation of the formula against 3D FEA simulations, demonstrating high accuracy
The formula can be directly implemented in the IEC 60287 framework for total loss calculations and cable rating
The authors note that the proposed model is easy to use and can be implemented in a spreadsheet or programming language, enabling better design of submarine three-core cables.

Stats

The paper provides the following key data:

Core helix radius (ap): 52.25 mm
Mean radius of armour layer (R): 115.6 mm
Armour wire radius (r): 2.5 mm
Armour wire conductivity (σ): 5.3763 MS/m
Armour wire relative permeability (μr): 150-j50, 600-j350
Pitch of armour wires (pa): -100 m, -4 m, -2.4 m
Pitch of cores (pc): 1.2 m, 4 m, 2.4 m
Number of armour wires (N): 25 to 135
Electrical angular frequency (ω): 314.16 rad/s
Core current (Ic): 1000 A

Quotes

"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."
"The proposed armour loss formulation (40) is compared with results from FEA in COMSOL Multiphysics 5.6. The COMSOL model used herein is a modified version of the COMSOL Cable Tutorial Series' short twisted-periodicity model [21]."

Key Insights Distilled From

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

by Marius Hatlo... at arxiv.org 04-11-2024

https://arxiv.org/pdf/2404.06998.pdf

Deeper Inquiries

How can the proposed analytical formula be extended to account for other cable components, such as the conductor and screen losses, to provide a comprehensive loss calculation model

The proposed analytical formula for armor losses in three-core power cables can be extended to account for other cable components by incorporating additional loss mechanisms into the model. To provide a comprehensive loss calculation model, the formula can be modified to include conductor losses and screen losses.
Conductor losses typically arise from the resistance of the conductors as current flows through them. This can be accounted for by introducing terms in the formula that consider the resistance of the conductors, the current magnitude, and the frequency of operation. By including conductor losses, the overall power dissipation in the cable can be more accurately estimated.
Screen losses, on the other hand, are related to the shielding properties of the cable's screen or sheath. These losses can be influenced by factors such as the material of the screen, its thickness, and the frequency of the electromagnetic fields. By incorporating screen losses into the analytical formula, a more holistic approach to calculating losses in three-core power cables can be achieved.
By integrating conductor and screen losses into the analytical formula alongside armor losses, a comprehensive model for calculating total losses in three-core power cables can be developed. This enhanced model would provide a more accurate representation of the total power dissipation in the cable, taking into account all relevant loss mechanisms.

What are the potential limitations or assumptions of the equivalent tube representation, and how could they be further improved or relaxed

The equivalent tube representation used in the analytical model for armor losses in three-core power cables has certain limitations and assumptions that could be further improved or relaxed for a more accurate representation of the cable system.
One potential limitation is the assumption of a constant field inside the armor tube, which may not hold true in all scenarios, especially for complex cable designs or high-frequency operations. To improve this aspect, a more detailed analysis of the field distribution within the armor tube could be conducted, considering variations in the field strength and direction.
Another limitation is the simplification of the tube thickness compared to the armor radius, which may not be valid for all cable configurations. Relaxing this assumption and considering more realistic geometries could enhance the accuracy of the model. Additionally, the truncation of the linear system in the derivation of the effective permeability could introduce errors, and a more comprehensive approach to solving this system could lead to more precise results.
To improve the model, these limitations could be addressed by conducting further numerical simulations, refining the assumptions made, and validating the model against more complex cable designs and operating conditions. By iteratively refining the model based on experimental data and advanced simulations, the accuracy and applicability of the equivalent tube representation can be enhanced.

How could the insights from this work on three-core power cables be applied to analyze losses in other types of cable configurations, such as single-core or multi-core cables

The insights gained from the analysis of losses in three-core power cables can be applied to analyze losses in other types of cable configurations, such as single-core or multi-core cables, by adapting the analytical framework and considerations to suit the specific characteristics of these cables.
For single-core cables, the analytical model can be modified to focus on the unique aspects of a single conductor, considering factors like skin effect, proximity effect, and dielectric losses. By adjusting the parameters and equations in the model, the losses in single-core cables can be accurately estimated based on the specific design and operating conditions.
In the case of multi-core cables, the analytical model can be expanded to account for interactions between multiple cores, including mutual inductance, coupling losses, and interference effects. By incorporating these additional factors into the model, a more comprehensive analysis of losses in multi-core cables can be achieved, providing insights into the overall power dissipation in such cable configurations.
By leveraging the foundational principles and methodologies developed for three-core power cables, the analysis of losses in other cable configurations can benefit from a structured approach that considers the unique characteristics and complexities of each cable type. This cross-application of insights can lead to a more unified and versatile framework for analyzing losses in various cable configurations.