A scalable stochastic scheme for identifying critical substations considering the epistemic uncertainty of contingency in power systems

This paper proposes a scalable stochastic tri-level defender-attacker-defender (DAD) optimization model for large-scale power systems, aiming to identify critical substations for protection against extreme events such as floods and cyber-attacks. Given that the system planner may not know the exact number of components in contingency, stochastic optimization is utilized to handle this epistemic uncertainty. Unlike conventional stochastic DAD model that only consider the uncertainty of direct line disconnection, the proposed model focuses on the uncertainty on the number of damaged substations in context of cascading failures that initiated from substations to their associated lines. The degree of epistemic uncertainty on the number of damaged substations is classified as 3 types, which can be used to reduce the size of the proposed model. Due to the contingency screening for power systems being a high order NK problem, solving this tri-level model is of high computation complexity. Therefore, a network-flow-embedded (NFE) two-stage robust column and constraints generation algorithm is devised. The network flow model is used to approximate the DC optimal power flow in bottom level of the proposed model, eliminating the bi-linear terms introduced by line flow constraints. Tight upper bounds of the corresponding dual variables are derived based on the dual formulation of the network flow model. Numerical results based on the IEEE RTS 24-bus and 118-bus systems validate the effectiveness of the proposed model and demonstrate the greatly improved computational performance of the NFE C&CG algorithm-