The growing dependence of modern-day societies on electricity increases the importance of effective monitoring and maintenance of power lines. Endowing UAVs with the appropriate sensors for inspecting power lines, the costs and risks associated with the traditional foot patrol and helicopter-based inspections can be reduced. However, this implies the development of algorithms to make the inspection process reliable and autonomous. Visual methods are usually applied to locate the power lines and their components, but poor light conditions or a background rich in edges may compromise their results. To overcome those limitations, we propose to address the problem of power line detection and modeling based on LiDAR. A novel approach to the power line detection was developed, the PL ² DM - Power Line LiDAR-based Detection and Modeling. It is based in a scan-by-scan adaptive neighbor minimalist comparison for all the points in a point cloud. The power line final model is obtained by matching and grouping several line segments, using their collinearity properties. Horizontally, the power lines are modeled as a straight line, and vertically as a catenary curve. The algorithm was validated with a real dataset, showing promising results both in terms of outputs and processing time, adding real-time object-based perception capabilities for other layers of processing.