Distributionally robust service restoration for integrated electricity-heating systems considering secondary strikes of subsequent random events

The multi-energy system has become a pivotal technology for achieving zero‑carbon transition. To address the extreme events with increasing frequency, this paper proposes a novel service restoration (SR) strategy for the integrated electricity-heating system to effectively restore critical loads after such events. The novel SR strategy encompasses defensive microgrid reconfiguration, mobile emergency generators allocation, and reserve commitment. Besides, the virtual energy storage of the heating system is utilized as an emergency resource in the SR process. By modeling the uncertain failures with a combination of ambiguity sets and support sets, the proposed SR strategy can effectively manage secondary strikes from subsequent random events. A distributionally robust optimization (DRO) model is then presented to identify the worst-case probability distribution of these uncertainties, enabling robust restoration decisions. To solve the DRO model efficiently, this paper proposes a solution method that employs logical constraint relaxation to tackle the non-convex challenges posed by discrete decision variables. Additionally, an improved column and constraint generation algorithm is developed. Case studies on modified 6-bus and 6-node systems, as well as IEEE 33-bus and 32-node systems, demonstrate the effectiveness of the proposed model and solution methodology.