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A line frequency transformer is usually employed in grid-connected power converters, from both renewable and traditional energy sources, in order to suppress the DC current component and the ground leakage current. Solutions employing a high frequency transformer or employing no transformer at all have recently been investigated in order to reduce size, weight and cost. As a consequence, unless a suitable remedy is adopted, a DC current component exceeding the limits enforced by international standards may be injected into the grid. This paper proposes a simple and cheap solution to reduce the DC current component injected into the grid in the case of a full-bridge, single-phase, transformerless converter. The proposed strategy is intrinsically insensitive to offset measurement errors and can be utilized as a robust and dynamic offset compensator for the current transducer. The simulation results have confirmed the theoretical behavior of the proposed solution, while the experimental ones, performed for different values of output power and for different current control architectures, have shown its effectiveness.