Mathematical Modeling of Heating Systems Considering Distributed Energy Generation
DOI:
https://doi.org/10.25729/esr.2025.01.0003Keywords:
Bi-level programming, method of undetermined Lagrange multipliers, distributed energy generation, centralized-distributed heating systemAbstract
The analysis of scientific and methodological studies has revealed a substantial interest in the issues related to the development of centralized-distributed heating systems. In this context, the need arises to devise new approaches to managing the operation and expansion of these systems, as well as to revising the available methods of their design and mathematical modeling. The global experience shows that the integration of distributed generation facilities into district heating systems enhances their reliability, safety, and energy efficiency. This is due to their increasing controllability, improvement in environmental characteristics, as well as the possibility for operation of distributed generators both autonomously under emergencies and within a single network. The paper presents the key technological heating diagrams implementing distributed generation. A two-level hierarchy of building a centralized-distributed heating system is proposed. The study on optimal distribution of loads between centralized sources and a peak boiler house, along with the corresponding flow distribution in the networks, relies on the method of undetermined Lagrange multipliers. This method facilitates calculating the costs of heat production and transportation through the networks. Heat flow is controlled through the implementation of intelligent control systems. Such systems allow for prompt response to changes in demand for heat and, accordingly, adequate adaptation of centralized and distributed sources to the altered conditions of their operation. Thus, we achieve both the optimization of heat transfer agent costs and the minimization of the risks associated with overloads during emergencies.
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