A control strategy for a three-phase grid connected inverter with LCL filter based on Lyapunov energy function during unbalanced grid conditions is presented in this paper. To reduce complexity and number of variables the control strategy is accomplished in a stationary two phase reference frame. Dual second-order generalized integrator structure (DSOGI) is utilized to extract the positive and negative sequence components of voltages and currents for unbalanced operation. A virtual resistor based active damping methodology based on indirect capacitor current feedback is employed to nullify the resonance oscillations due to the third order (LCL) filter. By using Lyapunov energy function based control, a direct grid current control architecture is achieved at the desired power factor.