Post-contingency coordinated corrective control of electricity–gas interconnected systems based on adaptive orthogonal collocation

In multi-area electricity–gas interconnected systems, a disturbance in one system may trigger cascading failures between the coupling systems without efficient online coordination to alleviate overloads in power lines or over-limit pressure in pipelines. This paper focuses on post-contingency coordinated corrective control, formulated as a decentralized security-constrained optimal energy flow (D-SCOEF) problem to minimize the total control cost. The heterogeneous energy flow is modeled by integrating steady-state power flow with partial-differential-equation (PDE)-based transient gas flow. To enhance computational efficiency, a space–time orthogonal collocation (OC) method is employed to approximate the PDE-based transient gas flow. Recognizing the critical influence of the number of OC points on numerical accuracy, an adaptive OC (AOC) method is proposed. Furthermore, a decentralized solving framework leveraging the auxiliary problem principle (APP) is introduced. By incorporating the iterative process of the AOC method into the APP-based D-SCOEF coordination, this framework not only ensures computational efficiency but also safeguards the data privacy of independent system operators. Case studies on a single pipeline segment validate the proposed AOC method’s computational efficiency and accuracy compared to existing approaches. Benchmark systems, including the IEEE 118-bus electricity network and 20-node gas systems, further demonstrate the solving framework’s performance and the effectiveness of the derived control strategies.