Extreme weather events, such as hurricanes and ice storms, pose a top threat to power distribution systems as their frequency and severity increase over time. Recent severe power outages caused by extreme weather events, such as Hurricane Harvey and Hurricane Irma, have highlighted the importance and urgency to enhance the resilience of electric power distribution systems. The goal of enhancing the resilience of distribution systems against extreme weather events can be fulfilled through upgrading and operating measures. This work focuses on investigating the impacts of upgrading measures and preventive operational measures on distribution system resilience. The objective of this dissertation is to develop a multi-timescale optimization framework to provide some actionable resilience-enhancing strategies for utility companies to harden/upgrade power distribution systems in the long-term and do proactive preparation management in the short-term.

In the long-term resilience-oriented design (ROD) of distribution system, the main challenges are i) modeling the spatio-temporal correlation among ROD decisions and uncertainties, ii) capturing the entire failure-recovery-cost process, and iii) solving the resultant large-scale mixed-integer stochastic problem efficiently. To deal with these challenges, we propose a hybrid stochastic process with a deterministic casual structure to model the spatio-temporal correlations of uncertainties. A new two-stage stochastic mixed-integer linear program (MILP) is formulated to capture the impacts of ROD decisions and uncertainties on system responses to extreme weather events. The objective is to minimize the ROD investment cost in the first stage and the expected costs of loss of load, DG operation, and damage repairs in the second stage. A dual decomposition (DD) algorithm with branch-and-bound is developed to solve the proposed model with binary variables in both stages. Case studies on the IEEE 123-bus test feeder have shown the proposed approach can improve the system resilience at minimum costs.

For an upcoming extreme weather event, we develop a pre-event proactive energy management and preparation strategy such that flexible resources can be prepared in advance. In order to explicitly materialize the trade-off between the pre-event resource allocation cost and the damage loss risk associated with an event, the strategy is modeled a two-stage stochastic mixed-integer linear programming (SMILP) and Conditional Value at-Risk (CVaR). The progressive algorithm is used to solve the proposed model and obtain the optimal proactive energy management and preparation strategy. Numerical studies on the modified IEEE 123-bus test feeder show the effectiveness of the proposed approach to improve the system resilience at different risk levels.