Advanced Calculation of the Catenary Length in the Spans of Overhead Lines
*Alen Hatibovic
Last modified:
20170611
Abstract
Advanced Calculation of the Catenary Length in the Spans of Overhead Lines
Alen Hatibovic
Optimum Solar Kft.
Baja, Hungary
hatibovic.alen@gmail.com
Key Words: Overhead Lines, Catenary, Conductor Curve, Inclined Span, Level Span
Taking into the consideration the sag of overhead lines (OHL), the conductor within the span is always longer than the span itself. This way the conductor length calculation has an importance when constructing overhead lines.
Literatures for OHL design generally give a solution for the conductor length calculation in level spans, but very rarely in inclined ones. Furthermore, the available length formulas are defined for determining the conductor length in a full span, i.e. for frequent conventional tasks, but not for rare unconventional tasks; for instance, the conductor length calculation in an arbitrary part of the span, either a level or inclined one. These are the reasons for deriving the algorithm for calculation of the conductor length, which ensures adequate calculation in each case, i.e. in level and inclined spans as well, and also in a full span and in its part. Such a complex task can be effectively solved by an appropriate application of the integral calculus. Since the conductor curve is sometimes considered as a catenary but sometimes as a parabola, two different calculations for the conductor length are necessary. This article shows the mentioned calculation in the case when the conductor curve in a span is considered as a catenary. Then the necessary data are the following:
h1 – height of the left–hand side support point
h2 – height of the right–hand side support point
S – span length
c – parameter of the catenary
x1 – start point of part of a span [x1, x2]
x2 – end point of part of a span [x1, x2].
The new formula, which is derived for the conductor length calculation in the part of inclined span, is a universal one for the calculations based on the catenary model, since it can be directly used for deriving the final formulas for length calculations in a full inclined span, but also in a level span (full or part), taking into account the following self–evident facts:
• Full span is a special case of the span–part, when the start and end points of the latter are the x–coordinates of the two support points in a given span.
• Level span is a special case of an inclined span, when the support points are on the same elevation.
Considering the fact that currently there is no publication which deals widely with the calculation of the conductor length in a span, and also there is no publication which gives the length formulas for all characteristic cases or, if there is, it gives only approximate ones; this article shows the derivations of the following formulas, covering both very frequent and very rare tasks in practice:
• Formula for the catenary length in part of an inclined span
• Formula for the catenary length in a full inclined span
• Formula for the catenary length in part of a level span
• Formula for the catenary length in a full level span.


