Inspired by induction machines working principles, this paper presents the idea of phase-locked-loop-less (PLL-less) operation of grid-connected voltage source converters (VSCs) under new concept of inducverter. The proposed controller eliminates the need for a dedicated synchronization process and the related PLL, and therefore it offers a simpler and more reliable control strategy compared to the conventional methods. In addition, it represents an improved performance, as it provides real and true auto-start and auto-synchronization with a grid without the need for grid voltage information. A current damping/synchronization unit enables grid auto-synchronization by using local current information and can track grid voltage frequency, angle, and amplitude variations while feeding constant amount of power, which is of high-interest in frequency varying grids and also in the case of grid voltage angle jump. Another advantage of the inducverter is that it introduces virtual inertia to the grid to regulate frequency, which enhances frequency dynamics of smart grids. Beside the current synchronization unit, the proposed strategy has a single-loop controller core with control over both power and current, which is implemented in a hybrid dq and abc frame using a virtual adaptive lead or lag impedance. The controller also offers stable and high-performance synchronization and operation under unbalanced and/or distorted grid conditions. The work beside synchronous current converters gives a bird's eye view to research in the new area of PLL-less and virtual inertia-based operation of VSCs and fulfill a unified set of controllers for the smart grid integration. Simulation, hardware-in-loop, and experimental results are presented to validate effectiveness of the controller.