This article deals with the determination of the main operating parameters of a photovoltaic solar module. In laboratory tests, the study of the dependence of current, voltage and power on time and density of solar radiation, as well as monitoring of environmental parameters: temperature and humidity of the outside air. Analysis of the test results shows that a photoelectric module with an installed capacity of 800 W and a total battery capacity of 800 Ah provides the electric power industry with a daily consumption of 2.0 ... 2.2 kWh. The discharge time of the battery varies from 11.7 to 3.5 hours when the average electric load of the consumer changes from 300 to 1000 watts.

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In this paper, we comprehensively consider the problems that depend on the parameter. The necessary and sufficient conditions for the existence of a unique solution of equations and systems of equations that depend on the parameter are investigated. Finding solutions to equations and systems of equations that depend on parameters is one of the most difficult areas of elementary mathematics. To solve them, you need to find ways that require special logical thinking, which must satisfy some additional conditions, for example, to determine a single solution, a solution in a set of all possible values of unknowns, cases when all the solutions of one system are solutions of another, and so on. One of these cases is the use of invariant properties. The article uses various examples of using invariant properties of transformations to consider methods and techniques for solving equations and systems of equations that depend on a single parameter. As a result, due to the presence of invariant properties of transformations, we see that the desired solution is found quickly and easily.

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