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In this article, an optimal virtual flux predictive direct power control (VF-PDPC) is proposed for three-phase grid connected voltage source inverter (VSI) operating under unbalanced and distorted grid supply voltage. The concept of virtual flux and extension pq theory is introduced in the conventional PDPC, where the former enhances its resilience toward distorted supply voltage while the latter enhances its resilience toward unbalanced supply voltage. The inherent advantages of the conventional PDPC scheme, such as simple implementation, fast dynamic responses, and no demand of modulators are retained. Getting rid of the complicated positive and negative sequence extraction of grid components, power compensation, or any tuning work, the proposed optimal VF-PDPC achieves excellent power tracking capability, and sinusoidal grid currents with low harmonics under various grid voltage conditions. Simulation results are presented to verify the effectiveness of the proposed control scheme when compared to the conventional PDPC, conventional VF-PDPC, and optimal PDPC. [ABSTRACT FROM AUTHOR]

Highlights: [•] A secondary control architecture for a low-voltage AC microgrid is proposed. [•] This secondary layer relies on a primary layer analyzed in a previous article. [•] Each inverter feeds the reactive power demand of its associated loads. [•] A centralized controller transmits compensating values for voltage and frequency. [•] A model predictive controller is applied for frequency restoration. [ABSTRACT FROM AUTHOR]

Highlights: [•] A control layer for a low-voltage AC microgrid with distributed storage is proposed. [•] The inverters interact with the microgrid through RL impedance. [•] Decoupled droop control techniques are proposed and analyzed. [•] The dynamic response can be adjusted without modifying the droop coefficients. [•] The resulting primary control layer can be easily actuated for power dispatching. [ABSTRACT FROM AUTHOR]