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This paper proposes a control strategy to reduce the voltage imbalances by injection of a proper negative-sequence current into the microgrid. This task can be done by each inverter connected to the microgrid in a shared way. The current compensation reference is obtained through a negative-sequence voltage control loop, avoiding the load current measurement. The detection of the negative-sequence voltage, at the converter connection point, is performed by a double second order generalized integrator, properly tuned for this purpose. Besides, a current limiter is used to limit the current compensation and avoid the converter overload. This strategy neither requires any hardware modification of the converter nor additional sensors. This new control strategy is simulated in Matlab/Simulink and experimental results are presented to prove its effectiveness.