Island operation of distributed generation sources is encountered when there is a balance of generation and load power in local grid in the moment of disconnection from the main grid. Absolutely reliable protection methods in such case are only remote operation system based communication methods which are non-economical. This dissertation deals with probability quantification for the occurrence of such unwanted island operation, with emphasis on a particular type of power plant - a photovoltaic power plant consisting of multiple inverter units connected to the medium voltage power grid. This particular type of power plant has several characteristics which make it different from other classic types of energy sources, for which reasons also the approach to the research of island operation of this type of power plants has to differ from classical approach. First topic of research is the analysis of the structure of a typical photovoltaic power plant consisting of multiple inverter units connected to the medium voltage power grid. Theoretical contributions of all power plant elements to the total active and reactive power are determined. P-Q diagram of all possible operation points of the power plant, at the point of connection to the grid, is determined, then a comparison of calculated values with the actual measurements carried out on the case study power plant is performed, followed by analysis and correction of the model. Following that, the methodology is proposed for calculating the probability of island operation. For the probability calculation the following data is used: predetermined P-Q diagram of the power plant, network configuration data, statistical operating parameters of the grid and of the consumers, and the probability density curves for photovoltaic power plant generation power and load power of the local grid consumers, modeled with triangular probability distribution proposed from literature analysis and available data from measurements in the distribution system operator grid. The method is applicable to the most commonly used passive methods of island protection, for which the non-detection zone was then analyzed. The probability calculation for the applied protection functions was performed on the case study power plant and the local grid, on the basis of which conclusions were drawn.