@article{JING2026, 
author = {Xiaochuan JING and Peng LI and Haichao DU and Yuxin WANG and Qingwei MENG},
title = {A method for measuring the sag of conductors based on the point cloud of overhead transmission lines},
year = {2026},
journal = {Journal of Tsinghua University (Science and Technology)},
volume = {66},
number = {7},
pages = {1307-1319},
keywords = {point cloud completion, laser point cloud, nearest neighbor search, conductor sag},
url = {https://www.sciopen.com/article/10.16511/j.cnki.qhdxxb.2026.26.001},
doi = {10.16511/j.cnki.qhdxxb.2026.26.001},
abstract = {ObjectiveTransmission 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.MethodsBased 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.ResultsThe 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.ConclusionsThis 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.}
}