架空输电线路是电力系统应对自然灾害冲击的承灾载体, 导线弧垂是影响输电线路运行状态的重要参数, 有效监控导线弧垂是防范电力系统灾害的重要手段。该文首先针对输电线路激光点云数据, 基于三维点云k维树最近邻搜索和模拟退火策略的惩罚最小二乘B样条平滑逼近拟合方法, 提出了导线寻踪、缺失数据补全和弧垂计算等方法, 测量了导线弧垂; 然后, 进行了数据结构对比和补全试验, 在对10.56%数据缺失率导线的数据补全试验中, 补全后数据与原真实数据的均方根误差为9.62 mm, 在对712 m档距23.84%数据缺失率导线的弧垂测量试验中, 测量误差小于0.63%。验证了该文所提方法能够准确测量导线弧垂, 且具有鲁棒性好、体量小和速度快等优点, 便于现场作业中在便携式平台上部署。该文研究结果可为电力系统的风险预测、监测和预警研判提供技术支持。

Objective: 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. Methods: 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. Results: 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. Conclusions: 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.