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IEC TR 62095:2003

Electric cables - Calculations for current ratings - Finite element method

Edition date: 2003-06-13
In Force
Available languages: English, French
Summary: 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.

Dans les calculs de capacité de transport des câbles, les aspects les plus importants sont la détermination de la température de l'âme du câble lorsqu'il est soumis à une charge donnée ou, inversement, l'évaluation de l'intensité du courant admissible pour une température d'âme donnée. Il faut donc déterminer la chaleur produite à l'intérieur du câble et sa dissipation à l'extérieur, pour un matériau d'âme et un courant de charge donné. La capacité du milieu environnant le câble à dissiper la chaleur est un élément de toute première importance pour ces calculs; elle est susceptible de varier largement en raison de différents facteurs tels que la composition et le taux d'humidité du sol ou la température ambiante et les conditions de vent. Les modes de transfert de chaleur du câble vers son environnement sont multiples. Pour les liaisons souterraines, le transfert de chaleur à partir de l'âme, l'isolation, les écrans et autres parties métalliques, se fait par conduction. Les modalités de dissipation de la chaleur sont quantifiables grâce à l'équation de transmission de la chaleur décrite à l'Annexe A (équation A.1). Les calculs de capacité de transport des câbles de puissance demandent la résolution des équations de transmission de la chaleur, qui constituent une relation fonctionnelle entre l'intensité du courant écoulé par le câble et la température à l'intérieur du câble et dans son environnement. La résolution analytique de ces équations se heurte souvent à la difficulté du calcul de la distribution des températures dans le sol entourant le câble. Une résolution satisfaisante est possible analytiquement lorsque le câble est assimilé à une source à section nulle placée dans un milieu homogène et infini. Cette hypothèse n'étant pas vérifiée dans les configurations d'installation réelles, une hypothèse alternative est souvent soulevée, à savoir celle de l'isothermie de la surface du sol. En pratique, la profondeur de pose est de l'ordre d'une dizaine de fois le diamètre des câbles, et, dans la plage habituelle de températures atteintes par les câbles, l'hypothèse de l'isothermie de la surface du sol est acceptable. Pour les cas où cette hypothèse n'est pas réalisée, notamment pour les câbles à fort diamètre ou les câbles enterrés à faible profondeur, il est nécessaire d'appliquer des coefficients correctifs ou d'utiliser les méthodes de calcul numérique. Lorsque la surface du sol est supposée isotherme, les équations de conduction de la chaleur en régime permanent peuvent être résolues en admettant que le câble est posé dans un milieu homogène semi-infini. Les méthodes de résolution des équations de conduction de la chaleur sont décrites dans la CEI 60287 (régime permanent) et la CEI 60853 (régime cyclique), et permettent de résoudre la plupart des problèmes posés dans la pratique. Lorsque ces méthodes sont inapplicables, les équations de conduction de la chaleur peuvent être résolues par des approches numériques. Parmi ces approches, la méthode des éléments finis présentée dans ce document, se prête particulièrement bien à l'analyse des câbles souterrains.
ICS: 29.060.20-Cables
CTN: TC 20 - 1214

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