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This paper presents a robust control scheme for a static synchronous compensator (STATCOM) coupled with a battery energy storage system (BESS) for improving the dynamic oscillations damping and the transmission power quality in electric power systems. The presented STATCOM/BESS controls both reactive and active power injection/absorption to/from the power system. It is investigated the performance of a supplementary damping controller (SDC) added to the reactive power control scheme. The SDC is designed by a robust control technique structured in the form of linear matrix inequalities (LMIs). The main objectives, from the application viewpoint, are the improvements of the damping of oscillations in tie-lines (precisely, voltage and active power flow oscillations which are related to the presence of inter-area oscillations mode), and also, the minimization of their peak values during transients. The tests were realized in a two-area four-machine power system, and the results show the proposed control scheme presents a good performance for several different operating points.