A model for the thermal behaviour of an offshore cable installed in a J-tube

With the expansion of offshore wind farms and oil platforms, industrials are concerned about J-tubes and the thermal limiting point imposed to submarine cables installed inside. Nowadays, current rating of such cables is not covered by the scope of IEC 60287 [1, 2] and a de-rating coefficient of 0.88 is generally used to avoid overheating of cables, defined by ERA in 1988 [3]. Furthermore, load cycles and weather conditions create unsteady thermal behaviour inside the offshore cable.
Currently only a few works deal with this situation by using time consuming finite elements calculation, in steady state and transient [4, 5, 6]. Other works uses simple models based on 1D energy balance, reliable only in steady state, which return conductors temperature exclusively [7, 8, 9].
In this paper, we introduce a model based on Lumped Element Method, which is convenient to simulate an energy cable in different environment, especially here in a J-tube. This method relies on electrical-thermal analogy by representing heat flux through thermal conductances, allowing us to have access to 2D temperature field in the cable and J-tube using thermal nodes. In a first step, we validate this model by comparison with previous work in steady state, for a 132Kv SL-type XLPE insulated cable [9]. Then, we extend this work to transient by adding thermal capacitances to each node, and we study the cable thermal behaviour depending on weather conditions (sun, wind, ambient temperature). In addition, based on IEC 60853 standards [10], we study the effect of load cycles on the offshore cable, which are very present in offshore windfarm due to the fluctuation in the energy production (wind variability). A comparison is made with thermal measurements through a thermocouple in the cable installed in a J-tube on an offshore platform.

References
[1] IEC. IEC 60287 1-1 : Calcul du courant admissible - Equations de l’intensité du courant admissible (facteur de charge 100 %) et calcul des pertes – Généralités. 2014.
[2] IEC. IEC 60287-2-1 : Calcul du courant admissible - Calcul de la résistance thermique. 2015.
[3] M Coates. Rating cables in J-tube. Technical report, 1988.
[4] J. Pilgrim, S. Catmull, R. Chippendale, R. Tyreman, and P. Lewin. Offshore Wind Farm Export Cable Current Rating Optimisation. EWEA Offshore Wind, Conference, 2013.
[5] Richard Chippendale, Priank Cangy, and James Pilgrim. Thermal Rating of J tubes using Finite Element Analysis Techniques. Jicable 2015, (1):4–9, 2015.
[6] Lei You, Jian Wang, Gang Liu, Hui Ma, and Ming Zheng. Thermal Rating of Offshore Wind Farm Cables Installed in Ventilated J-Tubes. Energies, 11(3):545, 2018.
[7] Hartlein and Black. Ampacity of electric power cables in vertical protective risers. IEEE Transactions on Power Apparatus and Systems, PAS-102(6):1678–1686, 1983.
[8] George J. Anders. Rating of cables on riser poles. Jicable, pages 602–607, 1995.
[9] R. D. Chippendale, J. A. Pilgrim, K. F. Goddard, and P. Cangy. Analytical thermal rating method for cables installed in J-Tubes. IEEE Transactions on Power Delivery, 32(4):1721–1729, 2017.
[10] IEC. IEC 60853-2 : Calculation of the cyclic and emergency current rating of cables – Part 2: Cyclic rating of cables greater than 18/30 (36) kV and emergency ratings for cables of all voltages. 2008.