Use of Spectral Transforms for Analysis of Power Consumption of Local Object

The paper is devoted to the use and comparative analysis of discrete spectral transforms of Fourier, Hartley, Wilenkin-Crestenson and transform at the oriented basis (OB). These methods are considered for analysis of discrete time dependence of electrical energy consumption in local objects like MicroGrid. The prediction of electrical power consumption in such object is quite actual task. One of the ways to solve it is use of spectral and wavelet analysis methods. The non-stationary character of power consumption time dependence curve needs to fulfill preliminary stage of smoothing. This is why wavelet analysis could be effectively used here – as a result of its use we obtain smoothed and compressed version of initial signal (so called “trend”). And the core of wavelet is defined by the type of basic function. These could be, in particular, basic functions of spectral transforms. This is why it was decided to compare different spectral methods – Fourier, Hartley, Wilenkin-Krestenson, and spectral transform at oriented basis. Comparison of spectral methods was carried out according to the following criteria: number of computational operations, simplicity and accuracy of calculations. The amplitude-frequency and phase-frequency spectra of the investigated signal for different spectral methods are considered. The process of finding the spectrum for the above methods was considered for the interval from 0 to 26. The interval was chosen based on demands of the transform at oriented basis where it’s necessary to provide the lengths of initial discrete function dividable to 3 (N=33=27). For the rest methods the interval could be changes accordingly. Thus it gives more objective assessment of the use of spectral methods for the analysis of power consumption of a local object. During the analysis of different spectral methods it was taken into account that Fourier and Wilenkin-Crestenson transforms operate with complex values of the spectra, while Hartley and OB-transforms deal with the real numbers. At the same time, Wilenkin-Crestenson and OB-transforms operate with the number presented in m-ary counting system. It should be noted that the transition to the m-ary system makes it possible to significantly simplify the calculation process at the interval of determination for the Wilenkin-Crestenson method. The Hartley transform differs from the Fourier transform because it operates only with real values, that leads to significant decreasing of the values of basic function and therefore simplifies and accelerates the calculation of the spectrum. It was shown that, in contrast to the Fourier transform, the transform at the oriented basis is asymmetrical, that is, for direct conversion, the angle of inclination of the transformation axis is possible. Comparisons of the considered methods were made on the basis of the values of the required amount of memory for the operation and storage of the program for the calculation of the spectra, as well as the time of performing mathematical operations for the calculation of the spectra of the daily power consumption function. In this way, the transform at the oriented basis is most effective for simplifying and speeding up the calculations. Given that the analysis of fractional power consumption is advisable to perform at a sampling interval of less than one hour, the advantage of this method becomes indisputable, thus showing that the method at the oriented basis is the most appropriate among the considered ones, because with a certain set of parameters allows to accelerate significantly spectrum for analyzing the power consumption signal.