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Numerical calculatin and circuit interpretation of transients in electric circuits

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Category: Power supply technologies

Last Updated on 29 July 2014

Published on 17 October 2013

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Authors:

S.M. Tikhovod, Cand. Sci. (Tech.), Associate Professor, Zaporozhye National Technical University, Senior Lecturer of the Department of Theoretical and General Electric Engineering, Zaporozhye, Ukraine.

N.A. Kostin, Dr. Sci. (Tech.), Professor, Dniepropetrovsk National University of Railway Transport, Professor the Department of Electrical Engineering and Electromechanics, Dniepropetrovsk, Ukraine.

Abstract:

Purpose. To develop the universal software Colo-IDU in order to increase the speed of calculation of transients in complex electric circuits.

Methodology. We have used the polynomial ap-proximation of the solution time function and mathematic apparatus of matrix algebra. Integro-differential dynamical equations of electric processes have been formulated in matrix form with the help of polynomial notion of solution function, derivative and integral of solution function in the series of the discrete marks of calculation.

Results. The calculations of transients in the modeled circuit have demonstrated that calculation of a transient by means of the offered method takes four times less processing time than Gear’s multistep calculation but the accuracy is the same. The comparison of the numerical calculation with the precise calculation obtained analytically confirms adequacy of the proposed method and the software developed on its base.

Originality. We have modified the numerical com-putation of the integro-differential equations which is known as BDF (back derivation formulas) and developed the circuit model of numerical calculation of tran-sient in electric circuits on its base. The circuit model allows us to switch from electric circuit, where the processes are described by means of integro-differential equations, to the equivalent circuit with the current displayed as vectors. The vectors images contain coefficients of polynomial approximation of current depending on time. We have shown that Kirchhoff’s rules are valid for the images of current and result into algebraic equations.

Practical value. The developed method provides the possibility to use the entire circuit theory machinery for the images of current. Based on this the universal software package Colo-IDU for the transient analysis in the complex electric circuits has been designed. 

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