The influence of a constant speed wind turbine in an electrical network during torque impact can lead to various problems. The disturbances affect active power quality, reactive power and r.m.s. phase to phase voltage. In this paper, we propose an original system and control to solve firstly the problems due to the variation of DC-voltage source and secondly the brutal impact of active and reactive powers. The principle of the proposed wind energy system with STATCOM supercapacitor energy storage is to limit the rapid variation of active power and give the required reactive power compensation to the induction machine during the torque change. The supercapacitor is directly coupled to the common DC-link of the whole bidirectional DC-AC converter. The control strategy of the STATCOM uses a Linear Matrix Inequalities (LMIs) approach to regulate the currents injected or absorbed by the inverter. The same strategy is used to control the variable DC supercapacitor voltage. The simulation results of the STATCOM using a state-feedback with integral controller for i(d), i(q) currents of the converter and a simple proportional (K-p) controller cascaded to d axis current loop for DC voltage source are presented and discussed. Finally, implementation in real time is performed and the first experimental results are presented to validate the proposed control. (C) 2015 Elsevier Ltd. All rights reserved.