Mathematical approximation of the production of a photovoltaic system

The production data of solar systems are well described by their density and distribution function. However, the mathematical description of this empirical curve is not known in closed form. So as to define the distributions, they should be approximated with special distributions. As the incident solar irradiation to the surface of photovoltaic modules can be approached with Beta-distribution, the daily average production, total daily production and the daily maximum values can be reached with that distribution as well. However, to define the parameters of a special mathematical distribution, significant resources are required. A great number of calculation software for engineers can assist the empirical density function to be adjusted by special distributions so that the parameters are displayed as the result of the calculation. Awareness of these parameters can help determine the empirical curve approximation, and the goodness of approximation can be measured with pre-defined error indicators. In this study the electricity production of photovoltaic systems, placed in different parts of Hungary, was examined from different aspects. The approximation of empirical density- and distribution functions, received from the defined aspects, with Beta-distribution has proven to have appropriate accuracy, since the error indicators in most cases were found to have a very low value.