Scalable and Robust State Estimation From Abundant But Untrusted Data

Power system state estimation is an important problem in grid operation that has a long tradition of research since 1960s. Due to the nonconvexity of the problem, existing approaches based on local search methods are susceptible to spurious local minima, which could endanger the reliability of the system. In general, even in the absence of noise, it is challenging to provide a practical condition under which one can uniquely identify the global solution due to its NP-hardness. In this study, we propose a linear basis of representation that succinctly captures the topology of the network and enables an efficient two-stage estimation method in case the amount of measured data is not too low. Based on this framework, we propose an identifiability condition that numerically depicts the boundary where one can warrant efficient recovery of the unique global minimum. Furthermore, we develop a robustness metric called "mutual incoherence," which underpins theoretical analysis of global recovery condition and statistical error bounds in the presence of both dense noise and bad data. The method demonstrates superior performance over existing methods in terms of both estimation accuracy and bad data robustness in an array of benchmark systems. Above all, it is scalable to large systems with more than 13,000 buses and can achieve accurate estimation within a minute.