Supply Resilience Constrained Scheduling of MEGs for Distribution System Restoration: A Stochastic Model and FW-PH Algorithm

Mobile emergency generators (MEGs) are critical resources for distribution system restoration after disaster- induced outages. However, insufficient fuel storage can cause MEGs to cease operation, leading to secondary interruptions of restored services. To enhance supply resilience, we include fuel tank (FT) dispatch as part of the MEG-aid restoration strategy. An integrated sequential service restoration model is developed to optimize the spatiotemporal travel behavior of MEGs and FTs, restoration paths, and load pickup sequences in the distribution network. To account for uncertain distribution line faults and traffic congestion, a stochastic programming approach is used. The proposed method optimally prepositions MEGs and routes them to target locations to restore critical loads by gradually forming microgrids. Moreover, the FTs in the transportation network are scheduled to ensure adequate fuel for the uninterrupted and reliable operation of MEGs. The presence of both uncertainty and discreteness presents computational challenges to the stochastic mixed-integer programming model. Thus, a distributed algorithm that combines the progressive hedging and Frank-Wolfe methods is applied to enhance computational efficiency while ensuring global convergence. Simulation results showed the effectiveness of the proposed method in improving the reliability of restoration schemes and computational efficiency.