Augmented Bolza-Based Optimal Control Approach for Frequency Regulation and Power Tracking in Islanded Microgrids

The variability of renewable energy sources (RESs) and load demand variations may lead to power alternations in converter control actions, potentially compromising stability and reliability and posing operational security risks, particularly in islanded microgrids. To address these challenges, this research introduces an innovative optimal control approach structured around a reformulated version of the Bolza problem. A variational control methodology is employed to ensure regularity, with boundary conditions derived to optimize power tracking and frequency control at nodes. Additionally, a solution dimension reduction technique leveraging the augmented Bolza problem is proposed to efficiently approximate the optimal control solution. The effectiveness of the proposed control methodology is validated through MATLAB/Simulink simulations by comparing the novel augmented Bolza-based control approach with conventional methods from the literature, namely Model Predictive Control (MPC) and Pontryagin's Minimum Principle (PMP). A real-time hardware-in-the-loop experimental test is conducted to validate the superiority of the proposed methodology.