State Estimation for Smart Grid Under Hybrid Cyberattacks: Analysis of Attack Stealthiness and Estimator Stability

This article investigates state estimation in a smart grid subject to hybrid denial-of-service (DoS) and false data injection (FDI) attacks. The contributions are threefold. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Estimator design:</i> An approximate optimal state estimator (AOSE) is designed by merging the exponentially growing Gaussian-mixture into a single Gaussian density. The resulting AOSE balances estimation accuracy and online computational burden, making it implementable for real-world applications. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Stealthiness analysis of attacks:</i> Unobservable hybrid DoS and FDI attacks can be exactly detected in some cases. It is proved that the unobservable hybrid attacks are stealthy for a stable smart grid. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Stability of AOSE:</i> It is proved that, despite accumulated approximation errors, the AOSE for a smart grid under the stealthy hybrid attacks is stable with a mild initial condition. Finally, some simulations on a three-generator six-bus system validate the performance and stability of the AOSE.