IEC TR 62095:2003

FOREWORD
1 Introduction
  1.1 General
  1.2 Field of application
  1.3 Information obtained from the finite element method
  1.4 Alternative methods
2 Overview of the finite element method
3 Practical considerations when applying the finite element
  method for cable rating calculations
  3.1 Selection of the region to be discretised
  3.2 Element sizes
  3.3 Boundary conditions
  3.4 Representation of cable losses
  3.5 Selection of a time step
4 Examples of application of the finite element method for
  cable rating calculations
  4.1 Example 1
  4.2 Example 2
  4.3 Example 3
Annex A - Development of equations
  A.1 Heat transfer equations
  A.2 Approximating polynomials
  A.3 Finite element equations
  A.4 Examples
Bibliography

The most important tasks in cable current rating calculations are the determination of the conductor temperature for a given current loading or, conversely, the determination of the tolerable load current for a given conductor temperature. In order to perform these tasks the heat generated within the cable and the rate of its dissipation away from the conductor, for a given conductor material and given load, must be calculated. The ability of the surrounding medium to dissipate heat plays a very important role in these determinations and varies widely because of factors such as soil composition, moisture content, ambient temperature and wind conditions. The heat is transferred through the cable and its surroundings in several ways. For underground installations the heat is transferred by conduction from the conductor, insulation, screens and other metallic parts. It is possible to quantify the heat transfer processes in terms of the appropriate heat transfer equation as shown in Annex A (equation A.1). Current rating calculations for power cables require a solution of the heat transfer equations which define a functional relationship between the conductor current and the temperature within the cable and its surroundings. The challenge in solving these equations analytically often stems from the difficulty of computing the temperature distribution in the soil surrounding the cable. An analytical solution can be obtained when a cable is represented as a line source placed in an infinite homogenous surrounding medium. Since this is not a practical assumption for cable installations, another assumption is often used; namely, that the earth surface is an isotherm. In practical cases, the depth of burial of the cables is in the order of ten times their external diameter, and for the usual temperature range reached by such cables, the assumption of an isothermal earth surface is a reasonable one. In cases where this hypothesis does not hold; namely, for large cable diameters and cables located close to the ground surface, a correction to the solution has to be used or numerical methods should be applied. With the isothermal surface boundary, the steady-state heat conduction equations can be solved assuming that the cable is located in a uniform semi-infinite medium. Methods of solving the heat conduction equations are described in IEC 60287 (steady-state conditions) and IEC 60853 (cyclic conditions), for most practical applications. When these methods cannot be applied, the heat conduction equations can be solved using numerical approaches. One such approach, particularly suitable for the analysis of underground cables, is the finite element method presented in this document.