In the theoretical part of the thesis – in the second and third chapters – the principle of operation is described, and the basic equations are of the system components (photovoltaic source, batteries, transformer, PI controller, boost DC-DC converter and single-phase bridge inverter), with clarification of the concept of unipolar and bipolar PWM modulation. Simulation models of system components in Simulink are also described. The choice of parameters is shown, as well as the associated block dialog boxes. The fourth chapter includes a simulation analysis and comments on the obtained results, starting from a simpler system configuration to a more complex one, in order to better understand the impact of individual components and changes in the associated parameters on the behavior of the system. The simplest configuration consists of batteries, an inverter, and a load. This configuration was used for the adjustment of the parameters of the load voltage PI controller and for the determination of the minimum number of batteries required for the linear operating range of the inverter. This configuration was then upgraded with an inductive filter, the inductance of which was determined by trial and error with the goal of reducing the THD of the load voltage to less than 5%, both in the case of unipolar and bipolar PWM modulation. The considered system was further upgraded with an ideal transformer, in order to raise the output voltage level of the inverter. The final configuration of the island PV system consists of a PV source, a boost DC-DC converter, batteries, an inverter, an inductive filter, a transformer, and a load. After determining the settings of the reactive components of the boost DC-DC converter and adjusting the parameters of the PI controller of the PV source voltage, the impact of changes in solar irradiation and temperature of the PV source and load power on the system power balance (i.e., on battery charging and discharging) was analyzed, with a fixed PV voltage. Finally, the impact of the batteries’ SOC on the system’s operation was analyzed.