Mathematical models for analyzing the functioning of electricity storing systems

<p style="text-align: center;"><strong>The annotation</strong></p><p>&nbsp;&nbsp;&nbsp;&nbsp; &ldquo;Mathematical models for analyzing the functioning of electricity storing systems,&rdquo; the VKR&rsquo;s title, is done in the field of considerable interest for both applied mathematics and practical applications of storing systems.</p><p>A rapid development of clean technologies for generating electricity and&nbsp; attempts to bring into step a variable electricity demand of numerous electrical grid customers during day, evening, and night hours with the volumes of electricity currently produced by traditional source of energy make the problem of storing electricity one of the key problems in the energy sector in every country.</p><p>This VKR offers an overview of the current and prospective electricity storage technologies, including such types of storing systems as pumped hydroelectric energy storages, compressed air energy storages, flywheels, capacitors and super capacitors, superconducting magnetic energy storages, thermal energy storages, different chemical batteries and others.</p><p>The choice of an optimal storage technology in the framework of a particular electrical grid much depends on a number of factors such as the amount of energy to be stored, the time for which this stored energy is required, environmental restrictions, and the cost of storing. A set of known mathematical models describing the functioning of electricity storage systems, including a model of hybrid power systems, a model of pumped hydroelectric energy storages, and a model of compressed air energy storages are presented in the VKR, along with a description of current trends in developing electricity storing systems in the 21th century. Also, a mathematical model of a electricity storage system that allows one to formalize a specific task of interaction of all elements of the regional electricity network as a several person game is presented there.</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <u>The purpose</u> of the VKR was to analyze the current status quo in the field of the mathematical modeling of storing systems, and the following <u>tasks</u> were set:</p><p>a) to study the existing principles of the electricity storage systems,</p><p>b) to provide a classification of the existing methods,</p><p>c) to survey the existing mathematical models of the energy storage,</p><p>d) to develop a particular mathematical model of an electricity storage system.</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The theoretical significance of the work is associated with an analysis of basic mathematical models describing electricity storing systems, provided in the VKR, whereas the practical significance of the work is associated with the demonstration of a possibility to use a particular mathematical model for storing electricity in a description of the interaction of the producers and consumers of electricity in a regional electrical grid in the form of a several-person game on polyhedral sets of the player strategies.</p><p>&nbsp;</p><p><strong>Key words:</strong></p><p>Renewable energy sources</p><p>Energy storage systems</p><p>Batteries</p><p>Electricity markets</p><p>Power grid</p><p>Mathematical model</p>