Voltage sensing in a three phase grid connected inverter is expensive and introduces vulnerability in the presence of faulty components. To cater and mitigate for this problem, here, a sensorless current control strategy is implemented that consists of two basic elements. First, a passivity-based current controller is derived using the assumption of known grid voltage. Next, a dual second-order generalized integrator (DSOGI) structure is utilized to extract the positive sequence grid voltage from the passivity-based current controller outputs using simple algebraic manipulations based on the basic circuit equations. These positive sequence estimated grid voltages are utilized in the passivity based current controller to achieve the necessary required control action. The proposed methodology has been verified on a reduced scale laboratory prototype was built and experimental validation of the proposed control come estimation technique was verified.