Systematic methodology for calculating transient processes in linear electric circuits by the classical method

Abstract

Purpose. Traditionally, transient calculations by classical method were performed only in linear electrical circuits containing no more than two reactive elements. If the number of reactive elements was three, the problem became significantly more complicated, and with a larger number, the problem could not be solved at all. A systematic methodology for calculating the transient process by the classical method in linear electrical circuits containing several reactive elements is proposed.

Methodology. Methods of integrating ordinary differential equations, matrix methods, computer programming, theory of electrical circuits.

Findings. The paper proposes a systematic method for calculating the transient process in linear electrical circuits containing more than two reactive elements using the classical method. This is achieved by dividing all variables into groups: derivatives of state variables, state variables, and dependent variables. Each group of variables constitutes a separate vector. By matrix transformations, The differential-algebraic equations of state are converted into normal form by matrix transformations. This made it possible to find the roots of differential equations. The constants of integration were also found by matrix transformations.

Originality. In existing textbooks, the classical method of calculating transients in linear electrical circuits is limited to considering circuits containing no more than two independent reactive elements, because with a larger number of reactive elements, the problem becomes dramatically more complicated. This work removes this limitation.

Practical value. A computer program has been developed to calculate the transient process in a linear electrical circuit containing three independent reactive elements. The program can be modified to simulate more complex circuits with more reactive elements. Analytical methods for calculating transients can be used to estimate the error of calculations using approximate methods, such as numerical methods. Analytical methods allow obtaining an exact solution in analytical form, which is described by mathematical expressions. The obtained mathematical expressions of the solution results allow better perform their research.