Application of the ruling span concept for overhead lines in mountainous terrain

The ruling span method is used by line engineers to calculate the approximate tension in a multi-span dead-ended line section. Providing satisfactory results for level spans, it may, however, result in an error of over 30% if it is used to calculate tensions in significantly long and steep spans e.g., in mountainous terrain. Following the ruling span concept in general, this paper presents equations to calculate tensions for inclined single spans or multi-span line sections based on calculation of conductor length in three-dimensional space. These equations include the equivalent parameters such as equivalent inclined span, equivalent slope, equivalent load, equivalent effective tension-all needed to take into account the effect on tension of the changing geometry and length of conductors in significantly inclined spans. The numerical examples show the effect of span inclination on conductor tension calculated using these equations. A simple and accurate equation (without hyperbolic functions) is derived to calculate conductor length in an inclined span. This paper also addresses calculation of sags in nonlevel spans. The presented method integrates the practicality of the ruling span concept with the accuracy of the three-dimensional vector method for analysis of inclined spans. This method is most efficient for overhead lines in mountainous terrain.