The evaluation of fractal dimension and transfer function of the clouds
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Abstract
In the presented paper data on installed capacity of renewable energy in Ukraine is given. The application of Heisenberg's uncertainty principle leads to the necessity of implementation of two-channel control on the basic interval to ensure maximum efficiency of the solar power stations. When implementing the solar power plants control it is necessary to evaluate the physical parameters of the environment, such as: humidity and temperature; presence of clouds, the direction and speed of their movement, the complexity of the surface of clouds and their density. In the presented paper on the example of cumulus clouds two of the set of physical parameters that characterize the state of the cloud cover are evaluated. The case when the linear velocity of the clouds is much greater than the velocity of the sun, which is defined by its angular displacement, is investigated. On some interval the position of the sun is remain fixed while the clouds and their projections are moving. When the cloud passes over the solar power station part of the solar panels generates more energy and part of the panels generates less. This indicates the possibility of using the concept of fractal dimension. The formula for fractal dimension calculation is given. It is shown that the values of the fractal dimension of the projection of the cloud cover area on the solar power station section depend on two factors. First, the total average value of the solar radiation intensity that passes between the clouds. Secondly, the selected value of the difference between the radiation intensity before and after the cloud. In order to determine whether the solar panel cell is shaded with the presence of haze the S curve is used. It allows determining the cell's state depending on the solar radiation intensity. If the value of the solar radiation intensity is less than a certain threshold, the cell is considered shaded. Otherwise it is considered not shaded. The formulas for determining the image and the original of cloud transfer function are given. Since solar panels consist of separate cells it is expedient to provide the calculations for discrete values. It is shown that in order to determine the virtual cloud density the two-dimensional discrete Vilenkin-Krestenson transformation with a finite argument can be used. Comparing to discrete Fourier transformation it operates with a significantly smaller number of values of the basic functions. The formulas for direct and reverse Vilenkin-Krestenson transformation are given. Matrix form for basic functions is represented. If the information about direction of the cloud motion is not significant it is advisable to use a symmetric transformation on finite intervals. Basic functions for symmetric transformation on finite intervals are presented. Knowing the transfer function of the cloud and fractal dimension of the projection of the cloud cover area on the solar power station section allows finding the sections with self-similar properties.
Ref. 11, fig. 2.
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