Detection and Localization of False Data Injection Attacks in Smart Grid Based on Joint Maximum a Posteriori-Maximum Likelihood

State estimation plays a central role in ensuring the secure operation of the smart grid. However, deliberately designed false data injection attacks (FDIAs) can pass by conventional detections to manipulate the process of state estimation by injecting malicious data into measurements. Ultimately, FDIAs make the result of state estimation deviate from secure value and affect the security and stable operation of the power system. In this paper, we consider the different distribution characteristics between normal measurements and false measurements and build a Gaussian mixture model (GMM). Particularly, we focus on achieving joint detection and localization of FDIAs. To tackle these challenges, a model-based algorithm named Joint Maximum a Posteriori - Maximum Likelihood (JMAP-ML) is proposed to estimate the individual parameters of GMM and achieve joint detection and localization of FDIAs with high accuracy. Different testing scenarios in the IEEE-14-bus and IEEE-30-bus power systems are simulated to show the performance of the proposed algorithm on parameters estimation, FDIAs detection and localization. Numerical examples demonstrate the proposed algorithm achieves satisfactory results in detecting and localizing FDIAs compared to the other algorithms.