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This paper reports a new control strategy to improve sharing of unbalanced currents in islanded LV microgrids. This technique provides fast and effective sharing of positive-, negative- and zero-sequence currents, and is the first example of zero-sequence current sharing in the literature. The controllers are designed in the stationary frame. The control structure consists of four loops: (1) the current controller; (2) the voltage controller; (3) the droop controller and the (4) negative and zero sequence current controllers. The output current is considered unknown for the controller and is added to the control system as a disturbance. The proposed controller features a high gain in fundamental and harmonic frequencies, hence a good voltage quality is obtained in the presence of unbalanced and nonlinear loads. To this aim, a proportional-resonant (PR) controller is adopted as the current controller. By using a multi-resonant controller as current controller, a unified control structure is obtained which is suitable for both grid-connected and islanded modes. The voltage controller is designed using a resonant controller so that the voltage can have low VUF and THD in the presence of unbalanced and nonlinear loads. Furthermore, in this paper, the droop method is applied to the control structure to share real and reactive powers. Simulation studies show that the conventional droop method cannot share the oscillatory part of the output power that is due to the presence of unbalanced loads in the microgrid. This paper relies on using zero and negative sequence virtual impedance controller to share the oscillatory part of output power. By using zero-sequence virtual impedance controller (ZSVIC) and negative-sequence virtual impedance controller (NSVIC), the zero and negative sequence currents in the microgrid are controlled and shared effectively. By compensating zero- and negative-sequence currents locally, the flow of these currents in the microgrid is minimized, and the overall power quality of the islanded LV microgrid is improved. [ABSTRACT FROM AUTHOR]