Dynamic Line Rating allows for better utilisation of overhead electrical infrastructure by dynamically determining the current carrying capacity in real-time. It is implemented by combining measurements of the environmental effects with a known model of the conductors. These models can be automatically generated from surveys collected using LiDAR on aircraft. But this approach is expensive and requires conductors to be clear of nearby objects and well easily separable from each other; restricting the application of this technology from use in urban environments. To facilitate the automated reconstruction of conductors in these challenging environments a new method using a structured search anchored to utility poles is proposed. Two core concepts to recover conductors are developed, sag-compensation, to remove the non-linear sag from the conductors before clustering, and a 3D to 2D projection, to increase conductor point density and simplify the clustering phase. These concepts are an improvement over the previous state of the art, which have first classified individual conductor points before per- forming conductor recovery. It is this novelty which allows the performance previously only achieved on high tension lines in sparse environments, to now be possible in the more dense and cluttered urban setting. Rather than require surveys to be conducted using costly aerial platforms, the proposed method is designed to work with the limitations of data collected from road- bound vehicles. A low-cost LiDAR based system for surveying infrastructure is presented alongside the conductor recovery method. With this approach, overhead electrical infrastructure in urban environments can be more accurately and rapidly surveyed like their high tension counterparts at a fraction of the cost, lowering the barrier to deployment and resources to maintain dynamically rated infrastructure.