LSTM-Enhanced Model Predictive Virtual Inertia Control for Frequency Stability in Low-Inertia Islanded Microgrids

Frequency instability caused by reduced system inertia in inverter-dominated islanded microgrids represents a critical challenge in renewable-integrated power systems. Conventional fixed-parameter controllers exhibit limited adaptability to uncertain and time-varying low-inertia conditions. This paper proposes an LSTM–MPC + VIC framework that embeds a Long Short-Term Memory (LSTM) surrogate predictor directly within a Model Predictive Control (MPC) optimisation loop, coordinated with a Virtual Inertia Controller (VIC) for immediate transient support. The LSTM provides data-driven frequency predictions without requiring precise analytical system modelling, while the VIC supplies reactive inertial damping within the same control cycle. The proposed controller is evaluated against Proportional–Integral–Derivative (PID), PSO-optimised PID, and standard MPC baselines on a 50 Hz islanded microgrid. Results demonstrate the lowest maximum frequency deviation of 0.009748 Hz, fastest settling time of 36.34 s, and minimum integral absolute error of 0.12283 Hz·s among all controllers. A Lyapunov-based Input-to-State Stability (ISS) analysis, incorporating the load disturbance term via Young’s inequality, confirms an ISS ultimate bound of 0.057866 Hz and an effective decay rate of 1.2952 s−1. Robustness is further validated through multi-scenario testing, parametric sensitivity analysis, component ablation, and computational feasibility assessment, confirming suitability for real-time deployment in low-inertia microgrid systems.