Mathematical Model of a Local Grid with Small Modular Reactor NPPs
Authors: Saukh S. , Borysenko А. 
Published: June 2022

The technical and economic processes of the Local Grid, regional electricity system comprising small modular reactor nuclear power plants, renewable electricity generators, and electricity storage systems are investigated. Smart grid technologies are used in the management of such a system. In relation to the electricity system, the Local Grid acts as a consumer or producer of electricity depending on the price situation in the wholesale market and its own ability to balance the volume of electricity generation-consumption.
The Local Grid market is considered to be perfect, otherwise the wholesale electricity market is characterized by imperfect competition. The mathematical model of the Local Grid is offered. The presented model adequately reproduces the characteristics of the interaction between the local market and the wholesale market. The mathematical model is generated in the form of the commitment problem for small modular reactors and electricity storage systems. The model reflects the technological limitations for the loading modes of small modular reactors and units of the energy storage system, which operate in the modes of direct and reverse energy conversion. In particular, the model reflects the shunting modes and start-shutdown modes of small modular reactors and charge-discharge modes of energy storage system units, which together determine flexibility of the operation modes for the entire power system. The commitment problem of small modular reactors of a nuclear power plant, units of the electricity storage system, and transmission lines connecting the Local Grid with the power system is a mixed integer programming problem with an objective function of minimized system costs.
Cluster integer functions are used to reduce the dimensionality of the problems of mathematical modeling the loading modes of the Local Grid in the descriptions for the sets of the same type small modular reactors, as well as the same type energy storage units. The Local Grid model reproduces the modes of its disconnection from the system operator's network to increase nuclear safety in the event of a natural disaster or hostilities. The results of computational experiments on modeling the commitment modes of the local electrical grid are presented.
The experiments used standard data on the volume of electricity consumption and its production from renewable energy sources. The results of the computational experiment confirm the adequacy of the suggested mathematical model for the Local Grid. The presented model is suitable for the use both independently – to analyze Local Grid functioning - and in combination with the models of electric power industry - to determine the impact of the Local Grids on the electricity system.
The article is developed based on the results of the research carried out under target program “Support of State-Priority Research and Scientific and Technical (Experimental) Solutions of the Department of Physical and Technical Problems of Energy of the NAS of Ukraine for 2022 – 2023” with program expenditure classification code 6541230 (applied research).