Derivation of Equations for Conductor and Sag Curves of an Overhead Line Based on a Given Catenary Constant

Abstract

When the spans of an overhead line are large (for instance over 400 metres) the conductor curve cannot be considered as a parabola, since in that case the difference in comparison to the catenary cannot be neglected. At such times the exact calculation has to be applied, i.e. the conductor curve has to be considered as a catenary (hyperbolic cosine). The catenary based calculation does not have limitations, it can be used for small and large spans as well, but in comparison to the parabola method it is significantly more complicated. This article shows the way of derivation of new equations for the conductor and sag curves based on a known catenary constant, which refers to the chosen conductor type, span length, tension and temperature of the overhead line. The shown formulas ensure exact computing of the conductor height and sag at any point of the span, avoiding errors generated by the approximation of the catenary by a parabola.