Purpose – Analytical determination of harmonic components of current in electric circuits containing semiconductor converters with the use of a small parameter method (SPM) in frequency domain. The paper aims to discuss these issues. Design/methodology/approach – A SPM realized in frequency domain was used in the analytical analysis of electric circuits with semiconductor converters. An automated method of formation of orthogonal harmonic components of electrical values on the basis of discrete convolution algorithm was used to provide the possibility of realization of calculation in frequency domain. A nonlinear characteristic of a semiconductor converter was presented by the method of numerical approximation. A numerical structured simulation method was applied to determination of the reference values of current in the analyzed circuit. Laws of theoretical electrical engineering were used for formation of the equations of voltage balance in the circuit with a nonlinear element. Findings – It is shown that application of a SPM with its realization in frequency domain enables significant simplification of the process of the analysis of electric circuits with semiconductor converters in an analytical form and facilitation of calculation automation. Analytical and numerical calculation of a circuit with a diode under active-inductive load demonstrated efficiency and sufficient accuracy of the proposed method. It is shown that increase of the order of approximating polynomial and of the number of the analyzed harmonics provides the improvement of the accuracy of numerical calculations. Practical implications – The results of the work can be used in calculation of electrotechnical devices containing semiconductor appliances and electric devices with nonlinear characteristics. Moreover, the obtained results enable studying the processes of compensation of current higher harmonics in electric networks with a nonlinear load containing semiconductor converters. Originality/value – For the first time it was proposed to apply a SPM with its realization in frequency domain to the analysis of nonlinear electric circuits. The significance of the paper consists in the fact that the offered method makes it possible to carry out both circuit analytical and numerical analysis with the possibility of its automation.

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Both a classical instantaneous power method and a method based on equations of instantaneous power orthogonal components balance have been used to analyze power processes in electric circuits with semiconductor elements. Automated method of forming instantaneous power harmonic components was used to obtain analytical expressions and numerical values of instantaneous power components of analyzed electric circuits. A coefficient for estimation of a semiconductor converter nonlinearity degree has been offered.

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)