Resilient Cyber-Physical Energy Systems Using Prior Information Based on Gaussian Process

The power grid infrastructure is a large-scale, heterogeneous, and complex cyber-physical system, which forms the lifeline of modern societies. The trend of tight coupling of physics, communication, and computation in cyber-physical energy systems (CPESs) is evident by the inclusion of numerous measurement sensors. This contributes to enhancing the monitoring and control functionalities of CPESs. At the same time, the occurrence of adverse effects constitutes a vital dimension of CPES operation. Increasing the resilience of critical energy systems is of key importance for safeguarding the national economy and security. This article considers the problem of optimal estimation with sensing measurements subject to arbitrary corruption resulting from adverse effects. Such signals can cause false situation awareness and/or trigger a sequence of cascading effects leading to an ultimate system failure. We formulate the problem as a constrained optimization with additional prior information posed as a set inclusion constraint on the measurement vector. It is shown that if the prior set satisfies certain conditions, the resulting recovery error bound is improved. The approach demonstrates enhancement of the CPES resiliency by using the Gaussian process as the basis of a prior generative probabilistic regression model using historical data. The validation of the resiliency mechanism using prior information is performed using the New York Independent System Operator grid data, demonstrating 100% successful state recovery for up to 60% of CPES sensor failures.