MODIFICATION OF NUMERAL CALCULATION OF TRANSIENTS IN ELECTRIC CIRCUITS ON BASIS OF TCHEBYSHEV’S POLYNOMIALS
DOI:
https://doi.org/10.15588/1607-6761-2019-4-2Keywords:
transient, numeral methods, scheme model, polynomial approximationAbstract
Purpose. Modification of the numerical calculation method of transients in linear electric circuits, as well as the development of a schematic model of the method, leading to ease the calculation and to increase the speed of calculation on a computer..
Methodology. Polynomials approximation of functions, numeral methods of solution of integro-differential equations, matrix methods, computer programming and methods of electric circuits theory are used.
Findings The improved method of transient calculation is worked out as the modification of the known one. It allows to reduce the computer modeling time of dynamic electric processes in linear electric circuits. The example of the application of the proposed method is shown. Based on the developed method, the computer program was compiled for calculating the transient in the model circuit. This example showed the reduction in CPU time of 45% compared with the use of known methods
Originality. The approximation of the functions of currents with time by series in the Chebyshev orthogonal polynomials is used. Chebyshev polynomials possess the property of the approximation error uniformity of functions in the entire range of the argument, which distinguishes them from a number of other orthogonal functions. It is proposed to use a polynomial approximation not of the solution functions themselves, but of its derivative. This significantly reduces the approximation error of both the solution function and the derivative of the solution, which appears in the calculation method.. It is shown how, in the proposed method, integro-differential equations of state are transformed into linear algebraic equations. The schematic model of the proposed numerical calculation method is developed. The schematic model allows you to move from an electrical circuit in which processes are described by integro-differential equations to an equivalent circuit with images of currents. Images of true currents in the equivalent circuit are interpreted as direct currents. It is shown that the Kirchhoff laws are valid for current images in the equivalent circuit, which leads to the calculation of a system of algebraic equations. Such a circuit model creates convenience for an engineer performing transient calculations.
Practical value. The developed method opens up the possibility of using the entire diverse apparatus of the theory of electric circuits for working with current images. Based on this, a universal software package is developed for calculating transients in electrical circuits of arbitrary
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