Two-Stage Submodular Optimization of Dynamic Thermal Rating for Risk Mitigation Considering Placement and Operation Schedule

Cascading failure causes a major risk to society currently. And dynamic thermal rating (DTR) technique is a cost-effective approach to mitigate the risk by exploiting potential transmission capability. From the perspectives of service life and Braess paradox, it is important and challenging to jointly optimize the DTR placement and its operation schedule for changing system state, which is a two-stage combinatorial problem with only discrete variables, suffering from no approximation guarantee and dimension curse in traditional solving algorithms. Thus, the present work proposes a novel two-stage submodular optimization (TSSO) of DTR for risk mitigation considering placement and operation schedule. Specifically, it optimizes DTR placement with proper redundancy in first stage, and then determines the corresponding DTR operation for each system state in second stage. Under the condition of the Markov and submodular features in sub-function of risk mitigation, the submodularity of total objective function of TSSO can be proven for the first time. Based on this, a state-of-the-art efficient solving algorithm is developed that can provide a better approximation guarantee than previous studies by coordinating the separate curvature and error form. The performance of the proposed optimization model is verified by case results.