I. Introduction
Owing to the latest improvement of power distribution systems with renewable energy sources, the control of grid-connected voltage-source inverter (VSI) systems has been studied by many researchers in recent years [1], [2]. In such systems, a coupling filter (L or LCL) is required between the VSI and grid so as to alleviate the harmonics of the grid current. In recent years, the use of an LCL filter is considered by many researchers because of its prominent features like the operation ability at lower switching frequencies, the ability to provide better harmonic attenuation, and the ability to offer lower ripple in the grid current. However, such filter suffers from three disadvantages: 1) the risk of unstable operation because of two extra poles; 2) the requirement of LCL resonance damping; and 3) the increased complexity of the control algorithm. Therefore, the control methods developed for an LCL-filter-based system should not only cope with these disadvantages, but also should achieve a set of objectives, such as sinusoidal grid current with considerably small total harmonic distortion (THD), fast transient response, high robustness against parameters variation, implementation simplicity, and achieving zero steady-state error in the grid current.