A graph and diffusion theory-based approach for localization and recovery of false data injection attacks in power systems

False Data Injection Attacks (FDIAs) pose a serious threat to power systems by interfering with state estimation and jeopardizing their safety and reliability. Detecting and recovering from FDIAs is thus critical for maintaining power system integrity. The increasing integration of renewable energy sources and the extensive use of power electronic devices introduce significant randomness in both power generation and loads, leading to significant power fluctuations and dynamic changes in power flows. These variations challenge the accuracy of existing FDIA detection and recovery methods. To address these challenges, an innovative data recovery framework is proposed, comprising two key stages: the FDIA localization stage and the FDIA data recovery stage. In the first stage, a Line Message Passing Neural Network (LMPNN) based FDIA localization model is employed to precisely identify the attacked data and generate a mask input for the recovery stage. In the data recovery stage, an FDIA data recovery model, named Denoising Diffusion Graph Models (DDGM), is designed to recover data with minimal error while conforming to the physical laws of the grid. Both models utilize node graph and line graph representations to depict measurements on buses and branches. By leveraging an optimized graph neural network, and inviting a loop-structured framework that combines a denoising diffusion model with a graph neural network these models effectively extract data features and inherent dynamic properties, enabling superior localization of FDIAs both in node and edge spaces and ensuring accurate recovery of compromised data even in the presence of high uncertainty and significant power fluctuations. By incorporating physical laws through a customized loss function embedding Kirchhoff's circuit laws into the training process of DDGM, the model ensures the recovered data to be physically consistent with power system dynamics. Experimental validations on IEEE 39-bus and 118-bus test systems, under conditions of high fluctuations in generation and loads, demonstrate that the proposed models outperform existing methods, achieving significant improvements inaccuracy and robustness.