Analysis of electric circuits with semiconductor converters with the use of a small parameter method in frequency domain

Abstract

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.

Development of the analitical method for nonlinear circuits analysis with the use of the admittance and resistance orthogonal components

“…The calculation of nonlinear electric circuits is known to be the basis of the analysis of various electric engineering devices [1][2][3][4][5][6], as nonlinearity is inherent in practically all electrical engineering devices without exception [7][8][9][10][11][12][13][14]. The calculation of nonlinear electric circuits comes to the solution of the direct (currents are determined by the known parameters of the circuit) and the inverse (the circuit parameters are determined by the known values of current and voltage) problems of electrical engineering [15,16].…”

“…">Literature review and problem statementThe calculation of nonlinear electric circuits is known to come to the calculation of nonlinear equations describing the physical phenomena in electric circuits [1, 4, 8-10, 12, 13, 15, 17]. The literature review revealed that the method of small parameter is a well-known representative of the classical methods for the solution of such equations [10,13,15]. The use of this method is restricted by the following drawbacks: the complication of mathematical and calculation dependences with each consecutive approximation and 4 проаналізовано аналітичні вирази для складових миттєвої провідності та опору.…”

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

“…Today, the task of studying the processes occurring in circuits with semiconductor converters, which are the elements of a clearly pronounced nonlinearity, remains relevant. 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].…”

Innovative technique for evaluating electric power distortion in cable transmission line

“…The effect of inactive power components on network mode parameters is considered in work [10]. To quantify this effect, quadratic norms of the electric power components are used [11]. A similar technique for the selection of electrical power alternative indicators was proposed in work [12].…”