A graph theory and coalitional game theory-based pre-positioning of movable energy resources for enhanced distribution system resilience

This article proposes an approach based on graph theory and coalitional game theory for pre-positioning of movable energy resources (MERs) to improve the resilience of the electric power supply. By utilizing the weather forecasting and monitoring data, the proposed approach determines staggering locations of MERs in order to ensure the quickest possible response following an extreme event. The proposed approach starts by generating multiple line outage scenarios based on fragility curves of distribution lines, where the fuzzy k-means method is used to create a set of reduced line outage scenarios. The distribution network is modeled as a graph and distribution network reconfiguration is performed for each reduced line outage scenario. The expected load curtailment (ELC) corresponding to each location is calculated using the amount of curtailed load and probability of each reduced scenario. The optimal route to reach each location and its distance is determined using Dijkstra's shortest path algorithm. The MER deployment cost function associated to each location is determined based on the ELC and the optimal distance. The MER deployment cost functions are used to determine candidate locations for MER pre-positioning. Finally, the Shapley value, a solution concept of coalitional game theory, is used to determine the sizes of MERs at each candidate location. The proposed approach for pre-positioning of MERs is validated through case studies performed on a 33-node and a modified IEEE 123-node distribution test systems.