In general, severe load imbalances in small AC micro-grid systems can degrade their operational performance and their maintenance. This is because the unbalanced load in the micro-grid affects the energy flow and the voltage regulation functions of each phase. In order to solve the voltage imbalance problem, several algorithms for the 3-phase 4-leg CVCF inverter have been proposed, but the control algorithms are not enough to operate the 4-leg CVCF inverter in a stable manner. Therefore, this paper proposes a single-phase voltage and power control algorithm for the 3-phase 4-leg CVCF inverter based on a dq control in order to improve the voltage imbalance problem caused by a severely unbalanced load, where the single phase voltage control algorithm is composed of an αβ-dq and a dq-αβ transformer, a voltage and a current controller, and an off-set controller and a PWM, and the single-phase power control algorithm is also composed of an αβ-dq and a dq-αβ transformer, an active/reactive power and a current controller, and an off-set controller and a PWM. Additionally, this paper performs modeling of the single-phase voltage and the power controller for a 4-leg CVCF inverter using the Matlab/Simulink S/W. From the simulation results, it is confirmed that the transient stability of the proposed single voltage control algorithm can be improved compared to the conventional control algorithm, and voltage control can also be maintained in a stable manner under extremely unbalanced conditions. Further, it is confirmed that 3-phase currents of the proposed single-phase power control algorithm are controlled in a stable manner under extremely unbalanced conditions.