Decentralized method for nonconvex robust static state estimation of integrated electricity-gas systems

State estimation (SE) is the foundation for situational awareness and energy management of integrated electricity-gas systems (IEGSs). However, centralized SE can be inappropriate due to the heavy communication burden and privacy concerns of different entities. In this paper, a novel decentralized methodology is proposed for robust static SE of IEGSs with nonconvex property. The centralized robust SE is first formulated to minimize the weighted squares of all measurement residuals along with an L1-norm term representing sparse bad measurements while fulfilling all zero-injection constraints and coupling constraints. The non-smooth and nondifferentiable pipeline gas flow equation is modeled as nonlinear complementary constraints and relaxed by the FischerBurmeister function for greatly improving convergence performance. Then the centralized formulation is decomposed into a decentralized formulation by proper network partitioning. The boundary injections are augmented into local variable vectors, resulting in a separatable objective function and a group of linear consensus constraints. In view of the non-convex nature of the formulation, a distributed algorithm, called the augmented Lagrangian alternating direction inexact Newton algorithm, is utilized to solve the model in a fully decentralized manner without central coordination. Numerical studies on three typical IEGSs validate the accuracy, robustness, convergence performance, and computational efficiency of the proposed decentralized robust SE method with promising results.