Jeju Island, which is the largest island in Korea, has an electric system which has special characteristics where a portion of the required electricity is being provided from the mainland through HVDC lines controlled by the frequency mode. Also, owing to its abundant wind resources, it is favorable for the installation of large scale wind farms with some already being operating and many under construction. Furthermore, the island which has been selected for the Smart Grid test bed will involve generation and power system infrastructure utilizing various renewable sources being tested at the site. Owing to the increase in the load demand and increase in the stability of the island system, the second HVDC line is under construction. This paper deals with the analysis of the 2013 power system of Jeju Island with the inclusion of the wind farms and multiple HVDC to examine the stability of the island system. Several contingency cases are being simulated to form an optimal operational strategy for the operation of the two HVDC lines.