Determining the factors affecting the characteristics of photovoltaic modules in the conditions of Krasnoyarsk Krai

The paper determines the factors affecting the characteristics of photovoltaic modules in the conditions of Krasnoyarsk Krai. During the work the dependences of the energy of solar radiation in the territory of the Krasnoyarsk Krai on the height of the sun above the horizon, as well as the spectral composition of solar radiation on the same parameters were identified. The results obtained will help determine the rational modes of a photovoltaic power station and the need to use light filters in certain areas of the region.

Krasnoyarsk State Agrarian University is conducting research to improve the technical characteristics of photovoltaic power stations, studying the areas of their effective application in agriculture, as well as substantiating the areas of application in terms of economic efficiency.
A number of studies [1-5, 8, 13, 14, 17-19] revealed that the increase in energy generated by a photovoltaic power station on a cloudy and sunny day depends largely on a number of factors, one of which is the spectral composition of solar radiation irradiating the photovoltaic (PV) module.
According to the studies described by N.N. Kalitin in the book "The Rays of the Sun" [15], the intensity and spectral composition of radiation depend on the temperature of the heated radiating body. The spectral composition of radiation is related to temperature by the following regularity: the higher the body temperature is, the shorter the waves are which it emits and the greater the radiation intensity is. There is a definite relationship between the spectral distribution of the energy radiated by a blackbody and its temperature [15].
The intensity of radiation incident on a horizontal surface also depends on its angle of incidence and is described by the following dependence: if the sun rays fall at an angle of 30°, then radiation per unit area will be half as much as when they normally fall; at solar altitude angle of 10° it amounts six times less, and at a height of 5° -twelve times [15].
A sun ray traversing the Earth's atmosphere, depending on the height of the sun above the horizon, passes through a greater or lesser mass of the atmosphere associated with the path length of the ray. Solar radiant energy, passing through the Earth's atmosphere, changes both quantitatively and qualitatively. This is due to a not completely transparent atmosphere. Some of the solar radiant energy is scattered along the way, some is absorbed [6,7,15]. Figure 1 shows the spectral composition of solar radiation for the visible part of the spectrum from the altitude 90° to 0.5°. At a solar altitude angle of 90°, all five components, which together give white color, are in almost the same amount. As the sun approaches the horizon, the short-wave part weakens more than the longwave part. With a solar altitude angle of 10°, half of all radiation is red rays, a quarter yellow and the last quarter three other colors. With the position of the sun at the horizon, there are practically no violet and blue rays, only red, yellow, and green remain, with the overwhelming majority being red [15].
To determine the height of the sun above the horizon, the time of day was calculated when the sun was at its highest point relative to the city of Krasnoyarsk as a reference point for further calculations of the solar altitude in the regional centers of the Krasnoyarsk Krai.
The calculations were conducted using the calculator for calculating the azimuth and altitude of the sun [16], with the presented calculation algorithm. In the calculator, select the city of interest (Krasnoyarsk), then select the day and month (for calculating the average monthly time, the 1 st , 10 th , 20 th and 30 th of the month were taken), next select the time at which the sun is at its maximum height (at the zenith).
The next step is to calculate the average monthly time of day the sun is at its zenith. Knowing the average monthly time of the day the sun was at the reference point (the city of Krasnoyarsk), the solar altitude in the regional centers of the Krasnoyarsk Krai will be calculated using the same methodology as the calculation of the time of day. As in the case of the calculator for calculating the sunrise and sunset times, the calculator allows one to set the coordinates and time zone manually. In the calculations, a negative height above the horizon can be obtained, which corresponds to the dark time of the day -the sun is "below" the horizon (in the northern regions of the Krasnoyarsk Krai).
Paul Schlyter, the developer of the calculator (Stockholm, Sweden), claims that the error in the calculations does not exceed one arc minute for dates in the range 1900 -2100 [16].
For clarity and further data processing, the method of constructing models of curves and surfaces is applied using interpolation in the Matlab Application, CurveFittingToolbox [8 -14].
After processing the vectors of data on the solar altitude in the regional centers of the Krasnoyarsk Krai for months, a graphic image is obtained.
In order to obtain data on the dependences of the distribution of solar energy on the solar altitude angle in the territory of the Krasnoyarsk Krai in selected coordinates (regardless of regional centers), a graphic image must be converted to three-dimensional surfaces, which will provide an opportunity to analyze and evaluate the dependences of the distribution of solar energy on the solar altitude in coordinates independently of regional centers (reference vector points) (figure 2).   Several studies have demonstrated that the increase in the energy generated by a photovoltaic power station on a cloudy and sunny day largely depends on the spectral composition of the light irradiating AGRITECH-III-2020 IOP Conf. Series: Earth and Environmental Science 548 (2020) 032036 IOP Publishing doi:10.1088/1755-1315/548/3/032036 5 the PV module. During the work the dependences of the energy of solar radiation in the territory of the Krasnoyarsk Krai on the height of the sun above the horizon, as well as the spectral composition of solar radiation on the same parameters were identified. The results obtained will help determine the rational modes of a photovoltaic power station and the need to use light filters in certain areas of the region.