Cooperative Adaptive PID-Like Voltage Regulation in Inverter-Based Islanded Microgrids Under Unknown Uncertainties

As modern distributed generators (DGs) always involve heterogeneous and unknown disturbances, a lack of accurate knowledge about the entire microgrid (MG) dynamics arises. Hence, an appropriate secondary control strategy is helpful to improve the voltage regulation process in an uncertain and unknown environment. To this aim, in this article, we suggest a novel distributed adaptive proportional-integral-derivative (PID)-like controller able to counteract unknown uncertainties arising from external disturbances and parameter mismatches, as well as unavoidable deviations induced by primary droop control while recovering the desired voltage reference value. By leveraging Lyapunov theory, an adaptive mechanism is provided to adjust control parameters for dealing with different operating conditions. The stability of the entire MG, analytically derived by also exploiting the Barbalat lemma, proves that all DGs within the electrical grid track the reference signal despite the presence of unknown uncertainties, with bounded adaptive control gains in steady-state phases. A detailed simulation analysis confirms the theoretical derivation and the effectiveness of the proposed controller in ensuring the voltage restoration in different troublesome scenarios, where both reference/loads variations and plug-and-play phenomena occur.