This paper aims to show an optimum sizing procedure of autonomous PV/wind hybrid energy system with battery storage and a break-even analysis of this system and extension of transmission line. We use net present value (NPV) method for the comparison of autonomous hybrid energy system and extension of transmission line cases. The case study is completed for the satisfaction of the electricity consumption of global system for mobile communication base station (GSM) at Izmir Institute of Technology Campus Area, Urla, Izmir, Turkey. First, we optimize the PV/wind energy system using response surface methodology (RSM) which is a collection of statistical and mathematical methods relying on optimization of response surface with design parameters. As a result of RSM, the optimum PV area, wind turbine rotor swept area, and battery capacity are obtained as 3.95m2, 29.4m2, 31.92kWh, respectively. These results led to $37,033.9 hybrid energy system cost. Second, break-even analysis is done to be able to decide the optimum distance where the hybrid energy system is more economical than the extension of the transmission line. The result shows that, if the distance between national electricity network and the GSM base station location where the hybrid energy system is assumed to be installed is at a distance more than 4817m, the installation of hybrid energy system is more economical than the electricity network.