In recent years, there have been some natural and human-made disasters and severe social clashes in globally important energy regions, which has had a negative impact on the environment in general and on the development of the energy market in particular. Therefore, the development of the modern energy industry is aimed at the broad involvement of renewable energy sources (RES) in the energy balance of the world’s advanced countries. At the EU level, particular attention is given to increasing the proportion of RES in total energy consumption to 12% with the installed capacity of solar photovoltaic (PV) systems up to 3 GW. The purpose of our study is to propose a mathematical model of the electricity generation processes in renewable solar and wind energy systems by methods of the theory of impulsive, random processes as well as recommendations for the development of RES based on the analysis of the trends in consumption and production of energy resources, their supply-demand proportion, and a model for the development of the energy market. Our findings show that the proposed model will allow to optimize the structure and create adaptive energy systems of RES. © 2019, Econjournals. All rights reserved.