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 DGs/ 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 distributed generators (DGs)/ wind turbines (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.