Detection of false data injection attacks against state estimation in smart grids based on a mixture Gaussian distribution learning method

One of the most addressed attacks in power networks is false data injection (FDI) which affects monitoring, fault detection, and state estimation integrity by tampering measurement data. To detect such devastating attack, the authors propose a statistical anomaly detection approach based on Gaussian mixture model, while some appropriate machine learning approaches are evaluated for detecting FDI. It should be noted that a finite mixture model is a convex combination of some probability density functions and combining the properties of several probability functions, making the mixture models capable of approximating any arbitrary distribution. Simulations results confirm superior performance of the proposed method over conventional bad data detection (BDD) tests and other learning approaches that studied in this article. It should be noted that using data which change significantly over a day can be highly clustered, and therefore, detected much easier compared with small changes in the loads. So without loss of generality, in the simulations it is assumed that the power demand follows a uniform distribution in a small range. However, the detector can be trained regularly based on the updated load profile