Hourly wind speed and light intensity at one day

This paper investigates the resilience of secondary frequency consensus control in distributed renewable energy microgrids (REMs) subjected to False Data Injection Attacks (FDIA). First, an explicit analytical expression for the FDIA tolerance boundary is derived using Lyapunov stability analysis, clearly quantifying the maximum attack intensity that REMs can withstand while maintaining frequency stability. Unlike existing qualitative analyses, this rigorous quantification provides operators with precise criteria for proactive vulnerability assessment. Second, based on the derived boundary, an integrated resilience framework is proposed, combining FDIA detection with adaptive compensation into a cohesive closed-loop control strategy. Third, to address instability and slow convergence issues inherent in conventional Q-learning methods within nonlinear REM, this paper innovatively applies a Double Replay Q-learning approach for adaptive frequency restoration following severe FDIA scenarios. By integrating double Q-tables and prioritized experience replay mechanisms, the proposed algorithm significantly accelerates frequency recovery and enhances robustness. Numerical simulations demonstrate that the proposed integrated framework and improved Q-learning method achieve faster recovery, higher stability, and superior resilience compared to existing approaches.