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Power Line Autonomous Inspection (PLAI) plays a crucial role in the construction of smart grids due to its great advantages of low cost, high efficiency, and safe operation. PLAI is completed by accurately detecting the electrical components and defects in the aerial images captured by Unmanned Aerial Vehicles (UAVs). However, the visible quality of aerial images is inevitably degraded by adverse weather like haze, rain, or snow, which are found to drastically decrease the detection accuracy in our research. To circumvent this problem, we propose a new task of Power Line Aerial Image Restoration under Adverse Weather (PLAIR-AW), which aims to recover clean and high-quality images from degraded images with bad weather thus improving detection performance for PLAI. In this context, we are the first to release numerous corresponding datasets, namely, HazeCPLID, HazeTTPLA, HazeInsPLAD for power line aerial image dehazing, RainCPLID, RainTTPLA, RainInsPLAD for power line aerial image deraining, SnowCPLID, SnowInsPLAD for power line aerial image desnowing, which are synthesized upon the public power line aerial image datasets of CPLID, TTPLA, InsPLAD following the mathematical models. Meanwhile, we select numerous state-of-the-art methods from image restoration community as the baseline methods for PLAIR-AW. At last, we conduct large-scale empirical experiments to evaluate the performance of baseline methods on the proposed datasets. The proposed datasets and trained models are available at https://github.com/ntuhubin/PLAIR-AW.