Multi-Stage Coordinated Restoration of Integrated Gas-Electricity Distribution System with Nonanticipativity: A Bi-Level Frequency Calibration-Based Distributionally Robust Approach

Frequent natural disaster promotes the critical importance of coordinating the restoration of integrated gas and electricity distribution systems (IGEDSs). A bi-level frequency calibration framework of IGEDS is proposed in this paper to ensure frequency stability, where a multi-stage optimal restoration problem with a dynamic discretized frequency reserve model is solved in the upper level, and time-domain simulation is conducted to check frequency stability and frequency reserve utilization of distributed generators (DGs)/wind turbines (WTs) in the lower level. Specifically, the multi-stage optimal restoration problem optimizes the total operation cost during the restoration process utilizing repair crew dispatch, line pack of gas pipeline, gas storage, power-to-gas (P2G), and frequency reserve of DGs and WTs, while considering both nonanticipativity constraints of outage uncertainty and distributionally robust constraints of energy uncertainty. Moreover, an improved decomposition and nested progressive hedging (ID&NPH) algorithm is presented to solve the proposed model. Numerical analysis indicates that the proposed model could effectively improve the load restoration of IGEDS under extreme disasters.