This paper proposes a installation of a static synchronous compensator (Statcom) used battery energy storage system (BESS) for compensting the reactive power of the micro-grid in Gapa island. At present, the micro-grid in Gapa island has two squirrel cage induction generator (SCIG), and it consums a lot of the reactive power. To reduce the capacity of the Statcom, a SCIG is replaced by a permanent magnet synchronous generator (PMSG). The simulation will be carried out in two cases: (i) real system with two SCIGs; (ii) modified system with one SCIG, one PMSG and the Statcom. With the statcom, the reactive power is compensated and the grid voltage is stable. The simulation results will valuate the effectiveness of the proposed control method.