### CORRECTION OF THE IEC FORMULA FOR THE EDDY-CURRENT LOSS FACTOR: THE CASE OF SINGLE-CORE CABLES IN TREFOIL FORMATION WITH METALLIC SCREENS BONDED AND EARTHED AT ONE END

Marko Šućurović, Dardan Klimenta, Dragan Tasić

DOI Number
https://doi.org/10.2298/FUEE2402391S
First page
391
Last page
408

#### Abstract

The purpose of this paper is to propose and apply the correct formula for the eddy-current loss factor for the case of three single-core cables in trefoil formation with metallic screens and armourings bonded and earthed at one end. This metallic screen bonding design is contrasted to the design where metallic screens and armourings are bonded and earthed at both ends, that is, the eddy-current loss factor is contrasted to the circulating-current loss factor. Ampacity calculations are carried out for 12 different underground lines with power cables of the type Cu/XLPE/CTS/PVC/AWA/PVC 1/C 19/33 kV (BS 6622), assuming that the 33 kV cables are installed directly in the soil without drying out. The ampacity is calculated analytically in accordance with IEC 60287-1-1 and IEC 60287-2-1, and numerically in accordance with IEC TR 62095. The numerical calculations are carried out to verify the accuracy of the proposed formula using the finite element method (FEM) in COMSOL 4.3. A validation of the proposed formula is conducted based on the manufacturer's technical data for the considered cables. The calculated ampacity values determined the incompleteness of the current IEC formula for the eddy-current loss factor, and verified the accuracy of the proposed one.

#### Keywords

ampacity, circulating-current loss factor, eddy-current loss factor, finite element method (FEM), metallic screen bonding design, power cable

PDF

#### References

Electric cables – Calculation of the current rating – Part 1-1: Current rating equations (100% load factor) and calculation of losses – General. IEC 60287-1-1:2023 CMV, Ed. 3.0, 2023.

P. G. Heyda, G. E. Kitchie and J. E. Taylor, "Computation of eddy-current losses in cable sheaths and busbar enclosures", Proc. Inst. Electr. Eng., vol. 120, no. 4, pp. 447-452, April 1973.

R. L. Jackson, "Eddy-current losses in unbounded tubes", Proc. Inst. Electr. Eng., vol. 122, no. 5, pp. 551–557, May 1975.

E. Kuffel and J. Poltz, "AC losses in crossbonded and bonded at both ends high voltage cables", IEEE Trans. Power Appar. Syst., vol. PAS-100, no. 1, pp. 369–374, January 1981.

J. S. Barrett and G. J. Anders, "Circulating current and hysteresis losses in screens, sheaths and armour of electric power cables – mathematical models and comparison with IEC Standard 287", IEE Proc. – Sci. Meas. Technol., vol. 144, no. 3, pp. 101–110, May 1997.

O. E. Gouda and A. E. E. Farag, "Factors affecting the sheath losses in single-core underground power cables with two-points bonding method", Int. J. Electr. Comput. Eng., vol. 2, no. 1, pp. 7–16, February 2012.

G. J. Anders. Rating of Electric Power Cables: Ampacity Computations for Transmission, Distribution, and Industrial Applications. New York: McGraw-Hill Professional and IEEE Press, 1997.

M. Santos and M. A. Calafat, "Dynamic simulation of induced voltages in high voltage cable sheaths: Steady state approach", Int. J. Electr. Power Energy Syst., vol. 105, pp. 1–16, February 2019.

S. M. Noufal and G. J. Anders, "Sheath losses correction factor for cross-bonded cable systems with unknown minor section lengths: Analytical expressions", IET Gener. Transm. Distrib., vol. 15, no. 5, pp. 849–859, March 2021.

M. N. Abed, O. A. Suhry and M. A. Ibrahim, "Simulation of sheath voltage, losses and loss factor of high voltage underground cable using MATLAB/Simulink", Int. J. Power Electron. Drive Syst., vol. 13, no. 1, pp. 220–215, March 2022.

M. Rasoulpoor, M. Mirzaie and S. M. Mirimani, "Electrical and thermal analysis of single conductor power cable considering the lead sheath effect based on finite element method", Iran. J. Electr. Electron. Eng., vol. 12, no. 1, pp. 73–81, March 2016.

A. Ariyasinghe, C. Warnakulasuriya, S. Kumara and M. Fernando, "Optimizing medium voltage underground distribution network with minimized sheath and armor losses", In Proceedings of the 14th Conference on Industrial and Information Systems (ICIIS). Kandy, Sri Lanka: IEEE, 2019, pp. 119–124.

D. Chatzipetros and J. A. Pilgrim, "Impact of proximity effects on sheath losses in trefoil cable arrangements", IEEE Trans. Power Deliv., vol. 35, no. 2, pp. 455–463, April 2020.

J. C. del-Pino-López and P. Cruz-Romero, "Use of 3D-FEM tools to improve loss allocation in three-core armored cables", Energies, vol. 14, no. 9, p. 2434, April 2021.

P. Zamani, A. Foomezhi and S. G. Nohooji, "A review of medium voltage single-core cable armouring, induced currents and losses" Energy Power Eng., vol. 13, no. 7, pp. 272–292, July 2021.

B. Perović, D. Klimenta, D. Tasić, N. Raičević, M. Milovanović, M. Tomović and J. Vukašinović, "Increasing the ampacity of underground cable lines by optimising the thermal environment and design parameters for cable crossings", IET Gener. Transm. Distrib., vol. 16, no. 11, pp. 2309–2318, June 2022.

T. Szczegielniak, P. Jabłoński and D. Kusiak, "Analytical approach to current rating of three-phase power cable with round conductors", Energies, vol. 16, no. 4, p. 1821, February 2023.

G. Aubert, J.-F. Jacquinot and D. Sakellariou, "Eddy current effects in plain and hollow cylinders spinning inside homogeneous magnetic fields: Application to magnetic resonance", J. Chem. Phys., vol. 137, p. 154201, October 2012.

Standard MV power cables – BS6622/BS7835 single core armoured 33 kV XLPE stranded copper conductor. Feb. 17, 2024. Available at: https://www.cablejoints.co.uk/upload/33kV_Single_Core__XLPE_AWA_Stranded_Copper_Conductor_HV_Cable.pdf.

Standard MV power cables – BS6622/BS7835 single core armoured 33 kV XLPE stranded copper conductor. Dec. 31, 2023. Available at: https://www.powerandcables.com/wp-content/uploads/2017/03/33kV-MV-Cables-BS6622-BS7835-Single-Core-XLPE-AWA-Stranded-Copper-Conductors.pdf.

Electric cables – Calculation of the current rating – Part 2-1: Thermal resistance – Calculation of the thermal resistance. IEC 60287-2-1:2023 CMV, Ed. 3.0, 2023.

Electric cables – Calculations for current ratings – Finite element method. IEC TR 62095:2003, Ed. 1.0, 2003.

Heat transfer module user’s guide. COMSOL Inc., Version 4.3, 2012.

Application note 3.1 – Cable sheaths – Overvoltage protection. Dec. 31, 2023. Available at: https://library.e.abb.com/public/42ff93fa18234d5982dad9bfc38482b7/ABB_AppNotes_3.1_Cable%20sheaths%20overvoltage%20protection%201HC0138880%20EN%20AA.pdf?x-sign=GeI5dghuY/Ig/vL9TLJsm1/UdXVxiljfhZeY1f3k+41SzISTBP+ntPkLSoppBhPH.

Electric cables – Armoured cables with thermosetting insulation for rated voltages from 3.8/6.6 kV to 19/33 kV – Requirements and test methods. BS 6622:2007, Ed. 4.0, 2007.

Conductors of insulated cables. IEC 60228:2023 CMV, Ed. 4.0, 2023.

Electric cables – Calculation of the current rating – Part 3-1: Operating conditions – Site reference conditions. IEC 60287-3-1:2017 RLV, Ed. 2.0, 2017.

L. Heinhold. Power Cables and Their Application-Part 1. Berlin: Siemens Aktiengesellschaft, 1990.

M. Stojanović, J. Klimenta, M. Panić, D. Klimenta, D. Tasić, M. Milovanović and B. Perović, "Thermal aging management of underground power cables in electricity distribution networks: a FEM-based Arrhenius analysis of the hot spot effect", Electr. Eng., vol. 105, pp. 647–662, 2023.

D. Klimenta, B. Perović, J. Klimenta, M. Jevtić, M. Milovanović and I. Krstić, "Controlling the thermal environment of underground cable lines using the pavement surface radiation properties", IET Gener. Transm. Distrib., vol. 12, no. 12, pp. 2968–2976, May 2018.

### Refbacks

• There are currently no refbacks.

ISSN: 0353-3670 (Print)

ISSN: 2217-5997 (Online)

COBISS.SR-ID 12826626