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This paper proposes a control strategy for the autonomous (islanded) operation of a four-wire, electronically-coupled distributed generation (DG) unit which can feed a highly unbalanced load, e.g., due to the presence of single-phase loads. In the grid-connected mode, the power-electronic interface of the DG unit enables the exchange of real and reactive power with the distribution network, based on the conventional -frame current control strategy. The current control scheme is disabled subsequent to the detection of an islanding event, and the proposed controller is activated. The proposed control strategy utilizes: i) an internal oscillator to maintain the island frequency and ii) a feedback control system to regulate the island voltage. The proposed control strategy provides a set of balanced three-phase voltages for the load, despite the load imbalance and parameters uncertainties. The proposed control strategy also guarantees robust stability, fast dynamic response to disturbances, and zero steady-state error. A stability analysis is also carried out to determine the robust stability margin of the closed-loop islanded system. Effectiveness of the proposed control strategy is evaluated based on time-domain simulation studies in the PSCAD/EMTDC software environment and verified based on laboratory experiments.