Defense hardening of electricity-hydrogen networks for extreme weather: A risk limitation approach with endogenous uncertainties

Defense hardening can effectively enhance the resilience of distribution networks against extreme weather events. Currently, most existing hardening strategies focus on reducing load-shedding. However, for electricity-hydrogen distribution networks (EHDNs), controlling hydrogen leakage risk is crucial to preventing severe incidents, such as explosions. This paper proposes an optimal hardening strategy for EHDNs against extreme weather, aiming to minimize load shedding while limiting the leakage risk of hydrogen pipelines. Specifically, improved endogenous uncertainty models are developed to characterize failure probabilities, enhancing the representation of failure correlations under the combined influence of both disaster intensity and hardening. Then, to derive the optimal hardening strategy, the failure models are integrated into a two-stage distributionally robust optimization incorporating a hydrogen leakage chance constraint (HLCC) with endogenous uncertainties. To efficiently handle the HLCC under endogenous discrete uncertainties, a second-order cone transformation is introduced. Moreover, to address the intractable inverse of the second-order moment under the proposed endogenous uncertainties, lifted variables are adopted to refine the main-cross moments. These reformulate the hardening problem as a two-stage mixed-integer second-order-cone programming problem, which is finally solved by the column-and-constraint generation algorithm. Case studies demonstrate the effectiveness of the proposed method.