MATHEMATICAL MODEL OF SOLAR RADIATION INCIDENT ON AN ARBITRARILY ORIENTED SURFACE FOR ANY REGION IN RUSSIA

Abstract

The paper deals with an original model of solar radiation incident on an arbitrarily oriented surface. This model has been designed to predict the main characteristics of solar radiation for any geographical point in Russia. The model is based on the isotropic model developed by Liu and Jordan and enables the researches to determine the values of solar radiation incident on an arbitrarily oriented surface at any given time period with the sampling interval of one second. The model implies the use of numerical values of the atmospheric transparency index and the surface albedo obtained from the NASA SSE (Surface meteorology and Solar Energy) database as initial data to ensure precise modeling of the incident solar radiation values including those for regions with no systematic actinometric observations. The paper presents the results of modeling the average daily values of solar radiation for ten Russian settlements located in the region between latitude of 43–62oN and longitude of 50–158oE. In order to verify the adequacy of the model, the results of instrumental terrestrial actinometric measurements are taken from meteorological stations included in the World Meteorological Organization network. The verification results show that the average relative model error for the considered meteorological stations does not exceed 11.7% for total solar radiation and 24.5% for scattered radiation. The authors developed the histograms of modeling errors in comparison with data from the World Radiation Data Center and NASA SSE. The analysis of the histograms revealed no systematic errors in the model since the errors were distributed uniformly and symmetrically with respect to the zero level. The paper compares the results of modeling the diurnal variation of solar radiation for 4 typical months of the year in Yekaterinburg with data from the World Radiation Data Center published in the periodic bulletin “Solar Radiation and Radiation Balance Data (The World Network)”. The developed model is implemented as a separate subsystem in MatLab/Simulink to enable its integration into the general model of the energy complex of an arbitrary configuration. The model can be used for studies concerned with the design, development and improvement of the energy systems including solar energy installations.