Frequency Restoration in Islanded Multi-Source Microgrids via Approximate Optimal Dispatch: Oracle-QP Policy Imitation by a DNN with a Fast Analytical Safety Filter

This preprint presents a hybrid control architecture for frequency restoration in an islanded low-inertia multi-source microgrid comprising two photovoltaic units, two diesel generators, and a battery energy storage system. An Oracle Quadratic Program, referred to as Oracle-QP, generates reference dispatch actions while accounting for power bounds, actuator ramp-rate limits, battery state-of-charge constraints, power balance, and a soft one-step frequency-protection condition. A deep neural network is trained through supervised imitation learning to approximate the Oracle dispatch policy with low-cost online inference. Before application to the microgrid, each nominal DNN action is processed by a fast analytical safety filter. The filter clips commands to their admissible actuator bounds, redistributes the power mismatch within the available operating margins, and applies a conservative one-step frequency guard that accounts for actuator lag and ramp limits. An optional QP-based safety projection is also implemented in the project, but the numerical results reported in this preprint use the fast analytical safety filter. The training dataset was generated from 30 randomized Oracle episodes, with 1001 samples per episode. The proposed controller was evaluated on 100 separately seeded disturbance episodes using frequency nadir, RMS frequency deviation, maximum rate of change of frequency, power-mismatch RMSE, final battery state of charge, and controller runtime. The learned policy with the fast analytical safety filter closely follows the Oracle-QP behaviour across the evaluated scenarios. The mean computation time per control step was reduced from 1.085 milliseconds for the Oracle-QP controller to 0.218 milliseconds for the learned policy, corresponding to an approximately five-fold reduction in online computation time. The results demonstrate a practical combination of optimization-based reference dispatch, imitation learning, and explicit online constraint handling for frequency restoration in islanded multi-source microgrids. Publication status: Independent research preprint, Version 1.0.