Design of Multi-Level Mathematical Model for Radial Supply Networks in Power Systems

Abstract

Today, the rapid advancement in technology and the expansion and development of human needs for sustainable technologies have placed greater emphasis on electrical energy. Consequently, enhancing reliability in electrical systems within the power industry has become highly significant. The objective of this research is to present a mathematical model to calculate and improve reliability, taking into account economic constraints in the power distribution network. This research is practical in terms of its objectives and outcomes, and it is operational in nature, based on operations research. It employs mathematical modeling and Python software, using data from the period between 2019 to 2023. Utilizing expert opinions and the Analytical Hierarchy Process (AHP) method, the findings indicate that parameters such as disconnectors, high and low voltage busbars, power transformers ranging from 20 kV to 400 V, communication cables, capacitors, generators, and UPS systems are crucial in assessing the reliability of this network. Accordingly, a suitable mathematical model has been developed considering the objective and constraints associated with each parameter. The designed model was then implemented in Python software to obtain the reliability at each stage based on the software's output. To verify the performance of the calculated power system, it was also implemented and analyzed in ETAP software, which is specialized for electrical systems. Given that increasing reliability also raises costs, and these two objectives are contradictory, this study aims to increase reliability and reduce costs in each of the power lines under study. Throughout all these stages, cost constraints will be considered based on the cost list for electrical installations, buildings, and equipment, determining the optimal state that maximizes reliability in each power line while minimizing costs imposed on the system. Using expert opinions and decision-making techniques, the findings indicate that parameters such as circuit breakers, high and low voltage busbars, 20 kV to 400 V power transformers, communication cables, capacitors, generators, and UPS are of greater importance in calculating the reliability of this network. The results show that after 50 iterations and simulations, the ultra-emergency line has a higher importance and ranking in reliability among the four output feeders. In all stages, the reliability of all lines has been calculated considering economic constraints. Considering the comprehensiveness of this study, the results can serve as a suitable basis for implementing research and operational projects in extensive radial networks in the power industry. Before execution, all stages of simulation, implementation, and reliability calculation of the lines can be computed and compared.