The paper presents the method for calculating the capacity of an autonomous solar power plant and its components. This method allows considering a load variation during the day as well as specifying the required capacity of the battery and excluding an unjustified overestimation of the power plant component capacities along with the increase in efficiency of the autonomous solar power plant. Formula for determining the required battery capacity of an autonomous solar power plant could be easily generalized for any number of changes in the load schedule steps. Virtual instruments (calculators) for calculating the capacity of an autonomous solar power plant and its components have been developed on the basis of this method in LabVIEW environment. These calculators may have a rather high visibility, ease of use and low memory requirements along with less computing time spent on calculations. The first calculator may allow recalculating capacities of loads on the power plant main supply bus as well as determining the energy consumption of loads per day. The second calculator may be used for determining the required capacity and number of batteries as well as the capacity of the charger, inverters, main supply bus and solar modules along with the solar power plant efficiency.

At present, discrete wavelet transform (Mallat algorithm) is used for signal decomposition and reconstruction. Discrete wavelets are asymmetrical, not smooth functions and do not allow decomposition of signals with a multiplicity of less than two, which limits the number of decomposition levels. Continuous wavelet transform has a number of positive properties (symmetry, smoothness of the basis function) which are necessary for signal analysis and synthesis. The paper proposes algorithms for calculating direct and inverse continuous wavelet transforms in the frequency domain, which allows decomposing, reconstructing and filtering the image with high speed and accuracy. It is established that application of fast Fourier transform reduces the conversion time by four orders of magnitude in compared to direct numerical integration. The results of applying algorithms to the images obtained with an optical microscope are presented. Orthogonal symmetric and anti-symmetric wavelets with rectangular amplitude frequency response are also presented. It is shown that these firstly designed wavelets allow one to reconstruct the signal even faster than the algorithms created using fast Fourier transform. Continuous wavelet transform has been found to allow multiscale analysis of signals with a multiplicity of less than two. In addition, the construction of orthogonal wavelets in the frequency domain with the maximum possible number of zero moments allows one to analyze the finer (high-frequency) structure of the signal, as well as to suppress its slowly changing components, which makes it possible to concentrate energy in a few significant coefficients, which is a prerequisite for compression. INDEX TERMS algorithms, image filtering, signal analysis, wavelet transforms

In the Mallat algorithm, calculations are performed in the time domain. To speed up the signal conversion at each level, the wavelet coefficients are sequentially halved. This paper presents an algorithm for increasing the speed of multiscale signal analysis using fast Fourier transform. In this algorithm, calculations are performed in the frequency domain, which is why the authors call this algorithm multiscale analysis in the frequency domain. For each level of decomposition, the wavelet coefficients are determined from the signal and can be calculated in parallel, which reduces the conversion time. In addition, the zoom factor can be less than two. The Mallat algorithm uses non-symmetric wavelets, and to increase the accuracy of the reconstruction, large-order wavelets are obtained, which increases the transformation time. On the contrary, in our algorithm, depending on the sample length, the wavelets are symmetric and the time of the inverse wavelet transform can be faster by 6–7 orders of magnitude compared to the direct numerical calculation of the convolution. At the same time, the quality of analysis and the accuracy of signal reconstruction increase because the wavelet transform is strictly orthogonal.

The Laws of Ohm (1826) and Kirchhoff's laws (1847) are the basis for the theory of electric circuits. Using them when calculating electrical circuits, we need to create and solve a system of equations for circuit currents and nodal voltages. Kirchhoff's Theorem (1847) on finding currents of branches does not require the compilation and solution of this system of equations. Belov G. A. and Zakharov V. G. (2003) re-proved the Kirchhoff's Theorem (1847) and supplemented it with eight rules for calculating electric circuits. With the help of these rules, the currents of branches and nodal voltages are formed from a loop or nodal determinant and an electric circuit. At the same time, duplicate operations occur in the process of forming expressions of currents and voltages according to these rules. In this paper, we prove the theorems of the Fast Kirchhoff method about a complete and truncated tree, about a unique branch and loop, about common branches and loops, as well as the formulas of the Fast Kirchhoff method for generating currents of branches and nodal voltages.In the Fast Kirchhoff method, when calculating an electric circuit, there are no duplicate operations when generating currents of branches and node voltages, and this reduces the calculation time.

The simulation of transient processes in the complex load node with powerful induction motors at the moment of power loss is carried out. For the modeling the method of synthetic schemes (Dommel's algorithm) was used. Calculations are carried out within the dynamic model of motors in phase coordinates. The results of simulation and analysis modes of the load node with two induction motors connected to the electric buses of 10 kV and fed through a step-down transformer with 16 MVA capacity are presented. The applied model of power transformer consists of inductively coupled branches. The features of single and joint run-out of motors with different torque of mechanical loads are analyzed. Estimates of the parameters and time intervals at which the run-out of the motors is close to synchronous are obtained, the features of energy recuperation and the interaction of the motors in the load node are analyzed.