Optimization Problems of Green Energetics

Abstract

Introduction. The widespread introduction of "green energy", which is based on renewable energy sources (RES), is recognized as the main direction on which the efforts of the world community should be concentrated in the fight against global warming. The complex network structure of the modern global economy requires a deep scientific substantiation of measures for such a transformation of the energy sector and forecasting their long-term consequences, which, in the face of growing uncertainty associated with the emergence of a large number of new systemic risks, is not an easy task. The decarbonization of the energy sector through greater use of renewable energy is thus a complex minimax optimal control problem and requires the creation of appropriate mathematical models for its solution. The article proposes a mathematical model for determining the dynamics of changes in the share of green energy (SGE) in the overall energy balance, which minimizes the growth rate of greenhouse gases (GG) in the atmosphere and maintains a given standard of living for the population. The purpose of the article is to investigate, using mathematical modeling, how a change in the SGE affects the level of decarbonization and the quality of life of the population, to determine the optimal levels of the SGE, at which the level of GG is minimized and energy production and production functions of some sectors of the economy are maximized. Results. A mathematical model has been developed to determine the conditions under which the growth rate of GG concentration in the atmosphere is minimized and a given standard of living of the population is maintained. The model combines in a single structure similarly described sectors of the economy, each of which is considered in terms of productivity levels, the number of jobs and structural disturbances (six-sector Lorentz model with varying coefficients depending on the level of GG. The model allows us to explore how changes in GG levels and the relationship between various sectors of the economy affect the risks of sustainable development and the quality of life of the population. The conditions for the occurrence of turbulent modes of operation are determined, which lead to an increase in the total number of structural disturbances and a decrease in the total level of productivity. Conclusions. The obtained results show that there is a critical level, starting from which the further growth of SGE in the overall energy balance leads to a reduction in the total volume of products created by the energy sector, which negatively affects the quality of life of the population. The development of this work will be aimed at identifying effective trajectories for the transformation of the energy sector in order to minimize GG emissions and structural disturbances and maximize the levels of production functions of economic sectors. A multicriteria optimal control problem will be investigated, which would allow solving practical problems of energy transformation under conditions of increased uncertainty and risks. Keywords: mathematical modeling, green energy, risk management.