Two-stage stochastic programming model and solution strategy for proactive planning and reactive operations of resilient power systems under disruptions

This paper proposes a two-stage stochastic optimization model for proactive planning and reactive operation of resilient power systems under transmission line disruptions. The model, formulated using Generalized Disjunctive Programming (GDP), minimizes total cost, including investment, operation, and resilience penalties, while ensuring load satisfaction under uncertainty. First-stage decisions include line hardening, line addition, and installation of distributed generators or batteries, whereas second-stage decisions include line switching and generator re-dispatch. To improve computational efficiency, two solution strategies are proposed: (i) critical line identification, which focuses on lines whose failures cause major operational issues, and (ii) a scenario reduction-based decomposition algorithm, which gradually adds disruption scenarios instead of solving all at once. Case studies of systems with different scales show that the proposed decomposition algorithm performs more efficiently than Big-M and Hull reformulations. The positive Value of the Stochastic Solution (VSS) further demonstrates that considering disruption scenarios leads to more resilient and cost-effective planning solutions.