Transmission lines are the backbone of electric power transmission, and accurate control of their operating parameters is crucial for grid safety, stability, and disaster prevention. Under complex service conditions, conductors are subjected to coupled mechanical, meteorological, and geological loads. Conductor sag-a key parameter reflecting the mechanical state of transmission lines-is highly susceptible to abnormal variations beyond design safety margins due to typhoon-induced galloping, ice accumulation from heavy snow, and tower displacement caused by subsidence in goaf areas. Exceeding critical sag thresholds may lead to ground discharge (due to insufficient clearance), tower collapse (from excessive structural stress), or conductor breakage (especially over large rivers or valleys), jeopardizing grid transmission efficiency and infrastructure safety. Therefore, developing a new sag monitoring system based on advanced technology is essential for timely condition assessment and enhanced grid emergency response. This system detects gradual changes in the mechanical state of conductors during disaster evolution, providing accurate data support for pre-disaster early warning, in-disaster decision-making, and post-disaster reconstruction, ultimately improving the disaster resilience and operational reliability of transmission lines in complex environments.

Based on laser point cloud data of transmission lines, this study designs methods for conductor tracing, missing data reconstruction, and sag calculation using a 3D point cloud k-dimensional tree (kd-tree) and simulated annealing (SA)-optimized penalized least squares B-spline smoothing. The workflow consists of three main steps: (1) Conductor tracing, in which a kd-tree index is built for the acquired point cloud to enable neighborhood searches and target conductor extraction; (2) Missing data reconstruction, in which the integrity of the extracted conductor point cloud is evaluated, and missing segments are reconstructed via SA-optimized penalized least squares B-spline fitting; (3) Sag calculation, in which the maximum sag is computed from the processed point cloud to obtain accurate sag values.

The effectiveness of the method was validated through six sets of transmission line point cloud experiments of varying scales, including data structure performance comparison, conductor tracing tests, data reconstruction experiments, sag calculation trials, and sag measurements under multiple operating conditions. The results demonstrate the following: (1) High efficiency for large-scale point clouds-tracing time for 10 million points was 45.30 s, and for 1 million points, it was 6.74 s; (2) High accuracy and robustness-successful conductor tracing and data reconstruction were achieved for a 712 m span with a 23.84% missing data rate (sag error less than 0.63%), and a root mean square (RMS) fitting error of 9.62 mm was obtained for a 320 m span with a 10.56% missing data rate; (3) Voxel downsampling of the point cloud reduced data density, slightly compromising measurement accuracy but significantly decreasing computational load and improving efficiency, thereby supporting deployment on portable platforms.

This study proposes a sag measurement method for overhead transmission lines based on laser point cloud data. The method employs a kd-tree for spatial indexing and point cloud reconstruction, enables conductor tracing through neighborhood search, and uses SA-optimized penalized least squares B-spline fitting for shape reconstruction and recovery of missing conductor points. It addresses two major challenges: computational inefficiency due to large-scale point cloud data, and sag calculation errors caused by incomplete conductor point clouds. The study also establishes sag calculation formulas tailored to point cloud data, providing a valuable reference for future overhead transmission line inspections and a reliable monitoring tool for grid risk warning and analysis.

In recent years, with the rapid development of the economy, the demand for electricity and the scale of the global power grid have rapidly expanded. As an important channel for power transmission, the safe and stable operation of transmission lines is of vital importance. The sag of power conductors is a crucial parameter that can affect the working state of transmission lines. Therefore, achieving effective monitoring and adjustment of the sag of power conductors in transmission lines has become an important task in power line inspection. Effective monitoring of sag provides an important guarantee for the healthy operation of a transmission network.

This paper proposes an experimental platform for collecting the point cloud data of overhead transmission lines with an unmanned aerial vehicle (UAV) LiDAR as the main body. A software and hardware system applied to the sag measurement of power conductor point clouds is designed. A method for tracing the transmission conductors and completing the missing point clouds based on three-dimensional point clouds is proposed. By taking advantage of the high precision of laser point clouds, an accurate measurement of the conductor sag is realized. The specific process steps are as follows: 1) the UAV point cloud collection platform is used to collect the point cloud data of the overhead transmission line, and the point cloud data of the transmission line in the target section are obtained. 2) Kd-tree spatial reconstruction is carried out on the obtained point clouds of the overhead transmission line to accelerate the positioning speed of the target points and the searching speed of the neighboring points. 3) On this basis, conductor tracing is carried out on the reconstructed point clouds of the transmission line, and the target conductor is extracted from them. 4) The integrity of the collected point clouds of the power conductor is checked. If there are missing data, the cubic spline interpolation method is used to perform spatial shape fitting on the conductor point clouds. Then, according to the fitting results, data completion processing is carried out on the missing data part to obtain the complete conductor point clouds. 5) Finally, for the obtained complete conductor point cloud data, the sag of the target section of the conductor is calculated according to the sag calculation model and the final measurement result is obtained.

This paper conducts measurement experiments on a typical section of the JL3/G1A-630/45 overhead transmission line of the Hanzhong–Zhengzhou line to verify the performance of the proposed sag measurement system. Verified by the measurement experiments, this measurement system can effectively and accurately measure the sag of power conductors and exhibits good robustness and high efficiency. It can accurately complete the task of measuring the conductor sag even when there are missing conductor data. In addition, this sag measurement system is a noncontact measurement, which has the advantages of convenience and safety. It provides a novel means for sag monitoring of high-voltage overhead transmission lines and can provide certain technical references for subsequent work, such as the inspection of the transmission network of the power system.