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This paper proposes a robust control scheme for the grid-connected single-phase converter of small permanent-magnet synchronous generator (PMSG) wind turbines under distorted grid voltages. The single-phase grid current is controlled to be sinusoidal by eliminating the high-order harmonic components. For this, the fundamental and high-order harmonic components of the grid voltage and current are extracted by the composite observer without a delay. Then, a phase-lock loop (PLL) scheme is employed for the fundamental component of the grid voltage to detect the phase angle of the grid voltage for the grid current controller. The multi-PR (proportional-resonant) controllers are used to regulate the grid current. In the system, the boost converter controls the DC-link voltage and the grid converter controls the generator output power. The validity of the proposed scheme is verified by the simulation and experimental results.