Robust Line Hardening Strategies for Improving the Resilience of Distribution Systems With Variable Renewable Resources

Line hardening refers to strengthening certain distribution lines that will not be subject to outages during extreme conditions. Line hardening provides a resilient solution in the case of major faults in a radial or meshed distribution system. We propose a robust optimal line hardening method coupled with multiple provisional microgrids to improve the distribution system resilience against worst N-k contingencies. In this case, provisional microgrids, which are interconnected by hardened liens, do not have the islanding capability and depend on the supply provided by one or more electrically connected microgrids for islanding purposes. A trilevel optimal model is considered with the objectives of minimizing the costs of line hardening and the operation of multiple islanded provisional microgrids, which could include the cost of load shedding in each provisional microgrid considering the worst N-k contingencies. Specifically, a two-stage robust optimization model is formulated and Benders decomposition (BD) algorithm coupled with iterative relaxation procedure (IRP) is developed to enable the tractable computation. In our work, the master problem determines line hardening strategies and the subproblem discovers the impact of the worst N-k contingencies corresponding to the optimal operation of reformed provisional microgrids. The second-stage which includes the max-min subproblem is solved efficiently using linearization techniques, duality theory, and IRP. Our numerical results for the IEEE distribution test systems validate the effectiveness of the proposed model and reveal that distributed generation is critical in increasing the resilience of distribution systems corresponding to the worst N-k contingencies in provisional microgrids.