Mathematical model for the substantiation of the rational structure of the electrical circuit of stations with solar generation

Abstract

Purpose. The purpose of this study is to develop a generalized mathematical model for substantiating the rational electrical configuration of photovoltaic power plants, that provides a comprehensive framework for selecting the optimal system configuration by simultaneously considering technical, economic, operational, and power system operating factors. Methodology. The research is based on the application of systems analysis, mathematical modeling, graph theory, multi-objective nonlinear optimization, and structural analysis of electric power systems. The objective function is formulated using an integrated rationality criterion that combines capital and operating costs, power losses, reliability indicators, power quality indices, and operating constraints. Pareto-based multi-objective optimization is employed to determine rational photovoltaic system configurations under multiple conflicting criteria. Findings. A generalized mathematical model for selecting the rational electrical configuration of photovoltaic power plants has been developed. The proposed approach provides a formal representation of alternative system topologies within a unified multi-objective nonlinear optimization framework. An integrated rationality criterion, a system of constraints, and an optimization variable vector accounting for equipment characteristics, electrical network topology, and internal grid parameters have been established. The developed model provides a scientific basis for numerical simulations, digital twin development, techno-economic comparison of alternative configurations, and further advancement of methodologies for selecting rational photovoltaic plant structures. Originality. The originality of the study lies in the development of a generalized mathematical model that integrates graph-based representation of photovoltaic plant topology with multi-objective nonlinear optimization through an integrated rationality criterion. Unlike existing approaches, the proposed model simultaneously considers electrical topology, operating conditions, power losses, reliability indices, power quality, life-cycle cost, and technical constraints within a unified mathematical formulation. Practical value. The proposed model can be applied to the design, modernization, and techno-economic assessment of photovoltaic power plants. It may serve as the basis for decision-support systems and intelligent optimization tools and can be integrated into simulation software to automate the selection of rational electrical configurations. Its application is expected to improve the efficiency, reliability, and technical justification of engineering decisions during the early stages of photovoltaic power plant design.