In the present study, a predictive battery energy storage system (BESS) for application in geographical non-interconnected islands with high renewable energy penetration is proposed, capable of performing load levelling. The system under consideration is composed of diesel and heavy oil generators, a photovoltaic farm, and a small wind turbine. The proposed solution integrates machine learning (ML) methods for the forecasting of load and intermittent solar and wind power productions, alongside a custom scheduling algorithm, which calculates the necessary BESS setpoints that accomplish the desired levelling effect. An important feature of the scheduling algorithm is that the charge and discharge energy amounts of each day are by design equal and independent of the forecasts' accuracy. This aspect enables economic investigations to identify the appropriate BESS capacity for the particular system, also taking into account the battery's capacity degradation. The overall system is modelled and simulated utilizing the open-source languages Python and Modelica. Simulations presented a 9.8% peak-to-mean ratio (PMR) reduction of the thermal plant's load. Furthermore, economic investigations estimated a marginal BESS cost of 287.1 euro/kWh revealing the financial viability of the proposed integrated system, in at least the case of geographical islands.