Feed-Forward Disturbance-Compensated Grid-Forming Frequency Control Using Offline Model Predictive Control for Islanded Microgrids

In low-inertia islanded microgrids, frequency stability is critically challenged by unpredictable power imbalances arising from renewable intermittency and load fluctuations. Droop- and virtual synchronous machine (VSM)-based grid-forming (GFM) controls inherently leave a steady-state frequency deviation, since the deviation itself serves as the power-sharing signal of primary control. This paper proposes a feed-forward disturbance-compensated GFM frequency control, in which a robust disturbance observer (DOB) estimates the aggregated supply–demand imbalance from the measured frequency deviation, and an offline model predictive frequency controller (MPFC) injects the compensating power into the active power reference, restoring the nominal frequency proactively without modifying the virtual inertia or damping of the underlying VSM. The design model embeds the diesel governor dynamics so that the observer estimates only the residual imbalance, structurally avoiding conflicts with the existing diesel controls, and an observability analysis justifies the reduced fourth-order design model. Both gains are obtained from Lyapunov-based linear matrix inequality optimization under polytopic parameter uncertainties and are computed entirely offline, so that the real-time computation reduces to a few matrix–vector products at a 1 ms control period. Simulations on a 300 kVA islanded microgrid show that, against five baseline controllers including VSM with secondary frequency restoration, the proposed method achieves disturbance-estimation convergence within about 0.3 s, reduces the frequency-nadir depth by up to 72% and the RoCoF by 32% for supply-side disturbances.