Integration of Failure Detector in Bias Filter for Estimation of False Data Injection Cyberattacks

Abstract

In order to enable many of the required smart grid functionalities, distribution systems are becoming increasingly dependent on state estimators. Many cyber-attacks attempt false data injection (FDI) attacks on such state estimators. The majority of the existing literature deal with FDIs in distribution systems state estimation either by the analysis of the residual vector elements, or by the analysis of historical data. In this work, we adopt an alternative approach for the detection of FDIs in distribution system state estimation, wherein FDIs are modelled as measurement biases and a bias filter is employed for FDI detection. Additionally, in order to enable the detection of time-variable FDIs, a failure detector is integrated in the recursive formulation of the bias filter, which is based on the Kalman filter. The developed approach is accordingly capable of identifying time-varying FDIs, which can evade many of the existing FDI detection methods. Simulation case studies are performed on the IEEE 13-node and 123-node feeders with different FDIs and the performance of the proposed approach is analyzed. INDEX TERMS Distribution system online monitoring, false data injection, Kalman filter, state estimation NOMENCLATURE Acronyms CBF Constant bias filter DS Distribution system FDI False data injection KF Kalman filter mFDBF Modified failure-detector in bias filter PDF Probability distribution function rBDD Residual-based bad data detector SCADA Supervisory control and data acquisition SE State estimation WLS Weighted least squares Indices a, b, c Three phases (superscript) i, j, s DS node index (subscript) k Discrete time index (subscript) T Matrix transpose (superscript) Sets φ Set of nodes with power measurement ψ Set of nodes with voltage measurement Variables , Voltage magnitude and angle at node i phase p , Active and reactive power at node i phase p b Bias vector z Measurement vector x State vector ̂ State estimates at time k r Residual vector ω Measurement noise Functions and matrices h(x) Measurement function Hk Measurement function Jacobian G Estimation gain matrix R, Q Measurements and states covariance matrix