Evaluating Resilience of Electricity Distribution Networks via a Modification of Generalized Benders Decomposition Method

This article presents a computational framework to evaluate the resilience of electricity distribution networks (DNs) to a class of cyber-physical failures. In our model, we consider an attacker who targets multiple DN components to maximize the loss of the DN operator. We consider two types of operator responses: i) coordinated emergency response and ii) uncoordinated autonomous disconnects, which may lead to cascading failures. To evaluate resilience under response i), we consider a bilevel mixed-integer second-order cone program. This problem is computationally challenging to solve due to mixed-integer variables in the inner problem and nonconvex constraints. Our solution approach exploits the properties of power flows on radial DNs operating in a postattack contingency state to refine the classical generalized Benders decomposition method. Specifically, we suggest a modification of the right-hand side of the generalized Benders cut to be a value determined by the sum of values of a subset of inner dual cost coefficients. We show how the size of this subset can be selected to achieve a reasonable tradeoff between solution accuracy and computational effort. Furthermore, we evaluate DN resilience under response ii) by sequentially computing autonomous component disconnects due to operating bound violations resulting from the initial attack and the potential cascading failures. Our approach is useful for estimating the gain in resilience under response i), relative to ii).