Cable geometry and the calculation of current-carrying capacity

The main purpose of this article is to express the calculation of current-carrying capacity in simple formulas. The allowable current for underground cables is usually limited by the maximum permissible temperature of the insulation. The temperature rise is of course a function of the ability of the cable system to dissipate the heat generated. The chief difficulty in the calculation of current-carrying capacity is the determination of the thermal resistances of the path through which the heat must flow. The main part of this paper deals with the errors in the standard formulas for calculating the thermal resistance and geometric properties between the conductors and the sheath. A graphical method of correcting the errors is obtained in terms of what is called the “geometric factor,” the results are tabulated for 2, 3 and 4-conductor cables throughout the range of practical sizes and an empirical formula is given. The check between the results of the graphical correction method and the published experimental data on this subject is very satisfactory, and emphasizes the errors in the standard formulas. The thermal resistance between the sheath and the duct is mentioned briefly, and an approximate method of finding the resistance between the duct and the region at base temperature is outlined. The previous work is then combined into a simple formula giving the allowable current for n-conductor cables, there being any number of similar cables in the duct bank. The formula is also enlarged to cover the case of cables in the metric and square inch systems, and cables buried directly in the ground. The method of including the effect of induced sheath currents in single-conductor cables and of dielectric losses is shown. Finally, the procedure to use in case the cables in the duct bank are not all of the same type is outlined. In Appendix A the geometric factor for three-conductor cables under three-phase voltage is discussed, Russell's formula for this geometric factor being compared with the experimental determinations and an empirical formula for it is given. A formula is also given for the calculation of dielectric losses in three-conductor cables. The geometric factors for three-conductor cables in all other connections (i. e., the geometric factor for one conductor against the other two and sheath, or between any two conductors, etc.) are then derived in terms of the two geometric factors already obtained. In Appendix B are given examples of the calculation of current carrying capacity under various conditions, and of dielectric loss. In Appendix C an example is given which shows the error introduced by using an approximate formula for the calculation of the thermal resistivity of the insulation of a three-conductor cable based upon experimental measurements, the case taken up being a table in the Research on the Heating of Buried Cables.