Sag Calculations for Transmission Lines

A survey of sag monitoring methods for power grid transmission lines

“…One of the earliest works on numerical methods for sag-tension calculation was by Dwight in 1926 [47], where the hyperbolic cosine function in the sag-tension formula was expanded into a Taylor series and approximations were then made by taking the first few terms of the series in the calculation. Both levelled supports and inclined supports were studied in [47]. The changes in temperature corresponding to changes in deflection and loading were also considered in the sag calculation by calculating the expansion of the span length due to a temperature increase.…”

“…One of the earliest works on numerical methods for sag‐tension calculation was by Dwight in 1926 [47], where the hyperbolic cosine function in the sag‐tension formula was expanded into a Taylor series and approximations were then made by taking the first few terms of the series in the calculation. Both levelled supports and inclined supports were studied in [47].…”

“…In [66], a hybrid numerical method was proposed for composite conductors based on a modification to the numerical method to accurately calculate the sag for composite conductors that have a bilinear relationship between sag and temperature instead of the linear relationship for single‐material conductors. The main algorithm still followed the numerical method as in [47] ‐ [58] but it used the stress–strain curves of composite conductors to determine the initial load distribution between the components of the conductor for higher accuracy. Specifically, it calculated the sag as a function of the length and slack as $$$$\begin{equation} S=\sqrt {\frac{3D(l-D)}{8}}, \end{equation}$$$$and then updated the length of the overhead line in the span l as a function of the thermal expansion and mechanical elongation using the stress–strain curves, where D is the slack.…”

Uprating of transmission lines by means of HTLS conductors for a sustainable growth: Challenges, opportunities, and research needs

“…50ºC-70ºC [84]. The RSM has been widely applied to determine the tensions and sags on overhead power lines [85]. It assumes the same temperature for all spans and that once tensioned, conductors tend to slide along the suspension insulators, thus equalizing tension differences, so the horizontal tension component is identical in each suspension span, because the longitudinal swing of suspension insulators.…”

“…In [88] a method to determine the tension and sag for level or non-level multiple span tension sections is presented, which allows evaluating the conditions in which the conductor temperature changes along the section. Finally, a method based on the formulation in [16] is presented in [85], which considers different conductor types in the same tensioning section, while allowing to deal with different temperatures on each individual level or non-level spans, which can be equal or unequal.…”