IEC TR 62095-2003 pdf – Electric cables – Calculations for current ratings – Finite element method

IEC TR 62095-2003 pdf – Electric cables – Calculations for current ratings – Finite element method.
1 Introduction 1.1 General 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 classical cable rating calculations, the heat conduction equation is solved under several simplifying assumptions [1 ] 2 . This limits the field of the applicability of the analytical methods. The limitations of the classical methods will be apparent from a few examples. In the analytical methods described in IEC 60287 [2], IEC 60853-1 [3] and IEC 60853-2 [4], the case of a group of cables is dealt with on the basis of the restricted application of superposition. To apply this principle, it must be assumed that the presence of another cable, even if it is not loaded, does not disturb the heat flux path from the first cable, nor the generation of heat within it. This allows separate computations to be performed for each cable with the final temperature rise being an algebraic sum of the temperature rises due to cable itself and the rise caused by the other cables. Such a procedure is reasonably correct when the cables are separated from each other. When this is not the case, for example for cables in touching formation, the temperature rise caused by simultaneous operation of all cables should be considered. A direct solution of the heat conduction equation employing the finite element method offers such a possibility. Numerical methods also permit more accurate modelling of the region’s boundaries for example, a convective boundary at the earth surface, constant heat flux circular boundaries for heat or water pipes in the vicinity of the cables, or an isothermal boundary at the water level at the bottom of a trench. Thus, when an isothermal boundary cannot be assumed, for example, for cables installed in shallow troughs or directly buried not far from the ground surface, the finite element method provides a suitable tool for the thermal analysis.