Unbalanced conditions are widely present in the power systems and microgrids. Inverters are essential to convert DC current into AC current. These power converters, to work properly, have to be controlled, even under these unbalanced conditions. In this paper a new control strategy is proposed for three single-phase inverters connected to a RL load under unbalanced conditions. The proposed strategy takes the classical strategy and add constants to the Park transform. Thus, it is possible to control the currents to obtain proper waveforms for the currents. The proposed technique is proved using simulations and obtaining experimental results implementing experimental setups.