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

TL;DR

This paper introduces a novel two-stage submodular optimization framework for dynamic thermal rating placement and operation scheduling to mitigate cascading failure risks in power systems, with proven submodularity and improved solution guarantees.

Contribution

It proposes the first submodular model for joint DTR placement and operation scheduling, enabling efficient risk mitigation with better approximation guarantees.

Findings

Submodularity of the total objective function is proven.

The proposed algorithm outperforms previous methods in approximation quality.

Case studies validate the effectiveness of the approach.

Abstract

Cascading failure causes a major risk to society currently. To effectively mitigate the risk, dynamic thermal rating (DTR) technique can be applied as a cost-effective strategy to exploit potential transmission capability. From the perspectives of service life and Braess paradox, it is important and challenging to jointly optimize the DTR placement and 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 only based on traditional models. 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 algorithms is verified by case results.