In the paper the authors proposes a Second-Order Super-Twisting Integral Sliding Mode Control for a Grid-connected Double-Stage AC-DC/DC-AC Power Converter (DSACPC) of a renewable electrical energy system. The DSACPC consists of a Permanent Magnet Synchronous Generator (PMSG) directly connected to the renewable electric source, a generator-side controlled rectifier and a grid-side inverter. The proposed control strategy applied both to two stages is able to maximize the extracted energy from the renewable source, while to regulate the DC-link voltage and to achieve unity power factor and low distortion currents. The employed control strategy can regulate both the reactive and active power given to the utility grid independently and consents to the system to be enclosed in a smart-grid thanks to its performance. In fact the system giving the desired active power to the grid can be used also as a reactive power compensator in grid balanced conditions or as a system of current harmonic rejection in the case of unbalanced conditions of the grid. For the formulation of the control a sliding-Mode Observer is designed. Simulations and experimental results prove the high efficiency and high performance of the full proposed control system.