Detection of false data injection attacks in smart grid based on a new dimensionality-reduction method

•A new dimensionality-reduction method is proposed to find an orthonormal basis to maximize the discrimination of the secure and attacked data classes.•A sequential optimization algorithm (SOA) on finding the dimension-reduced orthonormal basis is developed.•Numerical results based on the real load data of NYISO show the robustness of the proposed method. The false data injection attack is emerging as a dangerous cyber-attack for smart grid since it can bypass traditional bad data detection mechanisms and cause erroneous estimation on system states. To accurately detect such a devastating attack, we propose a statistical FDI attacks detection approach based on a new dimensionality-reduction method and a Gaussian mixture model. The proposed method consists of two phases: a dimensionality-reduction process in phase I and a semi-supervised learning process based on the Gaussian mixture model in phase II. To increase the discrimination between the normal data and bad data, a new orthonormal basis with a reduced dimension is constructed by exploiting minimum classification error performance index for the labeled dataset. Based on the reduced basis, the coordinates of the data under the newly obtained basis are checked using a Gaussian mixture model and a semi-supervised learning algorithm. If the outputs of the Gaussian mixture model exceed the pre-determined threshold, then FDI attacks can be distinguished from the normal pattern. The proposed method is tested on the IEEE 14-bus system using real load data from New York independent system operator considering attacks on various state variables, which demonstrates that the proposed method has about 1.5%~5% of accuracy improvement compared to some other detection methods. The generality of the proposed method is also demonstrated on different load patterns and larger systems such as IEEE 30-bus and IEEE 118-bus systems. [Display omitted]