Increased renewable energy penetration into conventional power plants results in significant frequency regulation (FR) problems, particularly at island power systems. To overcome FR problems, an energy storage system plays an important role. Therefore, a battery energy storage system (BESS) is proposed to provide primary frequency control (PFC) for San Cristobal Island hybrid wind diesel power system (WDPS) in this paper. The aim of this paper is to highlight the improvements achieved using BESS and estimate the optimal size of that BESS for San Cristobal WDPS. Therefore, a permanent magnet synchronous generator (PMSG) based variable speed wind turbine (VSWT) with synthetic (droop) control is used, which enables VSWT to release inertia during contingencies. A novel controller tuning methodology, named student psychology-based algorithm (SPBA), is used to optimally tune the BESS with hybrid WDPS and to estimate BESS size. In addition, several configurations set such as BESS with VSWT and/or diesel power plant (DPP) or both, are presented in this paper to highlight the optimal tuning effects. Moreover, the BESS based WDPS is tested under various real-world scenarios such as loss of wind generator, steadily increase wind speed ( Delta V-w approximate to 0.81 ms(-1)), variable wind speed, variable load demand ( Pload ) and simultaneously change in V-w and P-load. Finally, hybrid BESS based WDPS is tested in a real time environment (OPAL-RT) which validates its performance. Results show the significant reduction in frequency deviation, optimal sizing of BESS and optimal tuning of the whole WDPS.