Multivariate Gaussian-Based False Data Detection Against Cyber-Attacks

Abstract

Modern distribution power system has become a typical cyber-physical system (CPS), where reliable automation control process is heavily depending on the accurate measurement data. However, the cyber-attacks on CPS may manipulate the measurement data and mislead the control system to make incorrect operational decisions. Two types of cyber-attacks (e.g., transient cyber-attacks and steady cyber-attacks) as well as their attack templates are modeled in this paper. To effectively and accurately detect these false data injections, a multivariate Gaussian based anomaly detection method is proposed. The correlation features of comprehensive measurement data captured by micro-phasor measurement units ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> PMU) are developed to train multivariate Gaussian models for the anomaly detection of transient and steady cyber-attacks, respectively. A <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -means clustering method is introduced to reduce the number of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> PMUs and select the placement of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> PMUs. Numerical simulations on the IEEE 34 bus system show that the proposed method can effectively detect the false data injections on measurement sensors of distribution systems.