Braess paradox and double-loop optimization method to enhance power grid resilience

Multiple physical failures and severe power disruptions occur in power grid under extreme operation conditions. In this paper, we study power grid resilience and derive quick recovery methods through adjusting the operating modes of available components and reconfiguring the remaining network. The largest amount of power that is available to the loads after reorganizing the remaining undamaged components in the post-disaster stage is identified as an important resilience indicator. An interior point method is firstly used to find the largest amount of power supply (LPS) of fixed topology. The post-disaster network should contain as many available components as possible in order to give the best topological connection. However, disconnecting some undamaged components proactively can further increase the LPS. This phenomenon can be interpreted as the Breass paradox and is effectively a combinatorial network reconfiguration. A double-loop optimization strategy is proposed to achieve the LPS available to the post-disaster network, where the interior point method serves the inner optimization loop and the outer optimization loop generates an optimal topology using a genetic algorithm. Simulation results verify the efficacy of the proposed method in achieving a quick power recovery in extreme events. Our work provides useful advice to power grid operators on how to effectively coordinate available resources after extreme events occur.