Resilient control of AC microgrids via MSOGI-FLL and virtual complex impedance

This paper presents a novel and resilient control strategy for isolated AC microgrids based on a Multiple Second-Order Generalized Integrator with Frequency-Locked Loop architecture and a complex virtual impedance design. The proposed method addresses key challenges associated with power sharing accuracy, harmonic distortion, and system robustness in the presence of nonlinear loads, frequency variation, and complex inverter-to-load impedance characteristics. The main innovation lies in the integration of multi-harmonic Multiple Second-Order Generalized Integrator with Frequency-Locked Loop signal decomposition with adaptive complex virtual impedance and coordinated droop-based control, providing improved harmonic suppression, precise power sharing, and enhanced transient stability compared to existing approaches. A novel signal conditioning scheme based on Multiple Second-Order Generalized Integrator with Frequency-Locked Loop is employed to extract fundamental and selected harmonic components of inverter currents while rejecting DC offsets. The extracted signals are used to synthesize an adaptive virtual complex impedance that enhances droop-based power sharing under coupled resistive-inductive line conditions. To accurately assess system dynamics, a linear time-periodic model is developed for the Multiple Second-Order Generalized Integrator with Frequency-Locked Loop, enabling the derivation of harmonic transfer functions and stability margins. The control strategy is further augmented by a coordinated Battery Management System, ensuring energy balance and flexibility in transient scenarios. Simulation results involving three parallel single-phase inverters confirm the proposed method's ability to achieve accurate active and reactive power sharing, minimize circulating currents, and maintain robust performance under distorted and unbalanced operating conditions. The effectiveness of the proposed control is validated through detailed comparisons with conventional droop methods.