<p>The limited battery capacity of unmanned aerial vehicles (UAVs) poses a significant challenge for long-distance and uninterrupted power transmission line (PTL) inspections. To address this issue, we propose a tethered UAV (TUAV)-assisted wireless charging framework, enabling the inspection UAV to operate continuously without requiring battery replacements or frequent returns to charging stations. This approach significantly enhances inspection efficiency and operational endurance. To ensure that the inspecting UAV completes its task with minimal system-wide energy consumption, we formulate an optimization problem that jointly considers the UAV’s inspection trajectory, available battery capacity, and the TUAV’s transmission power. Given the non-convexity and NP-hard nature of the problem, we employ a problem decomposition strategy to improve tractability. Specifically, we first determine the optimal sequence of power tower visits to minimize the UAV’s energy consumption due to trajectory length, which is transformed into a Traveling Salesman Problem formulation. Then, we jointly optimize the UAV’s available battery capacity and the TUAV’s transmission power to further minimize the TUAV’s energy consumption. To solve this problem efficiently, we introduce a path discretization approach, converting the continuous-time optimization into a discrete path problem. The remaining non-convex elements are addressed using the successive convex approximation technique, ensuring computational efficiency and convergence. Numerical results validate the superiority of the proposed solution, demonstrating approximately 40% energy savings compared to existing algorithms while achieving significantly faster convergence. These advantages highlight the efficiency and practicality of our approach, making it a promising and sustainable solution for UAV-assisted PTL inspections.</p>