An analytical method for calculation of passive filter parameters with the assuring of the set factor of the voltage supply total harmonic distortion

Abstract

An analytical method for calculation and choice of passive filter parameters by the analytical expressions of the nonlinear load current harmonic components with the assuring of the set value of the factor of the supply network voltage total harmonic distortion is offered. It is proposed to obtain the current expressions with the use of the small parameter method realized in the frequency domain. The analytical calculation is performed with the use of the automated method for generation of the electrical values components on the basis of the discrete convolution method. The operability of the proposed method is demonstrated by the example of an electricity supply network section with a nonlinear load and a linear reactor. Streszczenie. W artykule opisano analityczną metodę obliczania i doboru parametrów filtra pasywnego z wykorzystaniem wyrażeń analitycznych opisujących nieliniowe składowe harmoniczne przy zapewnieniu zadanej wartości współczynnika całkowitego zniekształcenia harmonicznych napięcia sieci zasilającej. Proponowane jest uzyskanie wyrażeń za pomocą metody małego parametru zrealizowanej w dziedzinie częstotliwości. Obliczenia analityczne przeprowadza się za pomocą zautomatyzowanej metody otrzymywania wartości wielkości elektrycznych w oparciu o metodę splotu dyskretnego. Możliwości proponowanej metody wykazano na przykładzie części sieci zasilającej z obciążeniem nieliniowym i reaktorem liniowym. (Analityczna metoda obliczania parametrów filtra pasywnego przy zadanym współczynniku całkowitego zniekształcenia harmonicznych napięcia zasilania)

Improvement of the method for analysis of nonlinear electrotechnical systems based on the small parameter method

“…Presented research shows the possibility of implementation of the SPM in frequency domain with its practical use, specifically: the presented method enables qualitative analysis of indicators of operation of nonlinear load and the current spectrum, which is a good basis for the development of the method for selection of the tools for active and passive filtering that was already partially presented in paper [21].…”

“…In contrast to numerical methods, analytical methods have a significant advantage. They allow us to conduct a qualitative analysis and give an adequate evaluation to the processes in the NEC and estimate the influence of all factors in the course of operation of a system, their contribution and importance [1,3,5,9,10,21].…”

“…Based on the analysis of the literary sources, to solve such problems, researchers often choose the small parameter method (SPM) [3,5,9,10,21], which belongs to the perturbation methods, as the most efficient, universal, and simple to implement. SPM is one of the most effective tools of modern applied mathematics, which is widely used in mechanics, physics, and other sciences that operate with differential equations.…”

“…These are nonlinear circuits of power systems [9,10], nonlinear circuits of power active filters [11], control systems, which are based on the p-q theory [12] and cross-vector [13] theories of instantaneous power. The main issues that are tackled by researchers in the analysis of such systems include: determining the patterns and an increase in effectiveness of energy conversion [11][12][13][14][16][17][18], determining the nature of occurrence of reactive power [12,15,20], and development of effective methods for calculation of currents of researched circuits [21].…”

“…It should also be noted that the relevant problem today is selection of tools [19] of active and passive filtration [22,23]. But the correct choice of the tools for passive filtration requires the analysis of indicators of operation of a connected nonlinear load, which is possible using the analytical methods of calculation of electrical circuits [21].…”