Impedance source inverters (Z-source and Quazi-Z-source (QZS)) are the promising converter topologies in the future generation because of the buck, boost and buck-boost modes of operation. In this paper, three phase voltage sensorless grid connected QZS inverter is proposed to inject Maximum Direct Power. The new system uses the Virtual Flux Oriented Control (VFOC) algorithm for current control and virtual Flux (VF) estimation method for grid voltage. The complete Virtual Flux direct Power control (VFOC-DPC) exemplify the performance and operation of the proposed system compared to the conventional DPC algorithm is presented. Proposed strategy is also investigated under predistorted and unbalance grid conditions. VFOC-DPC provides numerous benefits mainly providing balanced sinusoidal line currents when the supply voltage is unbalanced. Simulation results are presented under unbalanced and pre-existing harmonic content in the grid voltage to verify the VF estimation of grid voltage. Tracking of active- reactive power is accurately done with current control loops providing good steady state and transient response to step change in reference.