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This paper introduces an improved current control strategy for a grid-connected inverter system operating under distorted grid voltage conditions. Although existing current controllers for grid-connected inverters have proportional integral gains with suitable bandwidth, low-order harmonic components can be generated by distorted grid voltages. The proposed improved current controller is established in a synchronous reference frame that rotates at harmonic frequency. The input signals for the harmonic current controller should contain only the specific harmonic components requiring suppression. Therefore, the proposed current controller uses a harmonic extractor to distinguish current signals from fundamental and specific harmonic components. The harmonic extractor retains only the relevant harmonic components for individual current controllers with high harmonic signal ratios. This paper introduces two different strategies to extract specific harmonic components for the current controller. The proposed control strategy does not require any additional hardware filter circuits and can be implemented easily by designing a suitable digital filter. When using the proposed method, grid current quality is significantly improved compared to conventional methods that do not include harmonic extractors. The effectiveness of the proposed method is verified through simulations and practical experiments.