Resilient Load Frequency Control for Gas–Electricity Coupling Systems Against Gas Pressure False Data Injection Attacks

The coupling of power and natural gas infrastructures introduces gas-side constraints and cyberattack risks into load frequency control (LFC). This paper proposes an auxiliary Kalman filter (AKF)-based tube-based MPC (TMPC) framework for gas–electricity coupling systems under gas pressure false data injection attacks (FDIAs). A pressure-dependent gas turbine (GT) power limit is incorporated into the frequency control constraint, and an auxiliary pressure model is identified from attack-free data as a virtual pressure sensor. Residuals, normalized innovation squared statistics (NIS), and cumulative sum (CUSUM) statistics are used for attack detection, while compromised pressure measurements are reconstructed using the AKF estimates. Simulations on a two-area power system coupled with an 11-node gas network show that under attack-free operations, the integral absolute error (IAE) values of TMPC, conventional MPC, and PI control are 0.7040, 1.9626, and 2.9834 Hz·s, respectively. Thus, TMPC reduces the accumulated frequency deviation by approximately 64% and 76%, compared with conventional MPC and PI control, respectively. Under FDIAs, the IAE decreases from 1.1645 to 0.7039 Hz·s after AKF-based pressure reconstruction, corresponding to an approximately 40% reduction. Meanwhile, the mean absolute error (MAE) of gas pressure reconstruction decreases from 0.1714 to 0.0157 bar, corresponding to an approximately 91% reduction in pressure reconstruction error. Compared with the denoising autoencoder (DAE) and graph signal recovery approaches, the proposed method achieves the highest detection rate of 98.39%, effectively limiting FDIA propagation to GT constraints and frequency regulation.