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Computation of the current rating in underground installations with multiple cables

F.M. Echavarren, L. Rouco, E. Navarro, J.P. Fernández, A. González

This paper presents an approximation to compute the current rating in underground installations with multiple cables. The model considers the temperature distribution along the whole installation, using continuous conductive heat transfer models. The temperature distribution is obtained as the superposition of the partial temperature distributions obtained for the different heat sources of the installation. The convection and radiation heat transfer models are computed using empirical approximations and adapted to conductive heat transfer equivalent models, using equivalent thermal conductivities. The methodology usually used to compute the current rating in underground installations is based on a discrete thermal model of the different layers of the cables (conductor, insulation, jacket, etc). This technique is the base of IEEE and IEC standards on current rating computation of cable systems, and consists of consider each layer of each cable as a thermal resistance. Hence the different layers between the conductor and the ambient are considered as a series thermal resistances circuit. This series circuit is passed through by the heat flow associated with the active power losses of the cable. Heat flow through a thermal resistance raises the temperature gradient between the two sides of the thermal resistance. The sum of the temperature gradients determines the total temperature difference between the ambient and the conductor. The accuracy of this methodology depends on the computation of the different thermal resistances between the conductor and the ambient. The thermal resistances computation is based on shape factors. The use of shape factors assumes some simplifications, such as consider the boundaries between the different cable layers as isothermal surfaces. In addition, the thermal resistances model makes difficult to evaluate the influence in the temperature of a conductor of the current through other cables. In consequence, the current rating computation may be imprecise. The methodology presented in this paper has some advantages with respect to the thermal-electrical analogy method, such as more accuracy in mutual heat influence between different cables or the hot spot localization ability. To illustrate the performance of the method, the current rating of an actual underground 132 kV installation is computed. Using these current rating results and both sheath currents and insulation losses, a finite elements model of the installation is built. Then, the temperature distribution obtained with continuous conductive heat temperatures distributions is contrasted against a finite elements model of the installation.

Keywords: Cable System, Current Rating, Conductive Heat Transfer, Finite Elements Model, Poisson’sequation

CIGRE Session 2008. Paris (France). 24-29 August 2008

Published: August 2008.

    Research topics:
  • *Steady-state: load flows, analysis of power system constraints, optimal load flows, voltage control ancilliary service,short-circuits, protections in transmission and ditribution networks
  • *Energy systems: Heat transfer, Fluid dynamics, Thermoelectricity, Hydraulic and thermal machines, Energy efficiency and savings


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