A numerical method for exploring an electric circuit when changing the parameters of an unlimited number of elements
Nikolay Savelov, Andrey Alekhin · Известия высших учебных заведений Электромеханика · 2025
A new efficient numerical method for studying the operating modes of an electric circuit at different values of the ele-ment parameters is proposed. It ensures the calculation of the circuit currents and voltages with minimal computational costs after changing the parameter of the next element. The method is efficient when changing the parameters of both several and all elements of the circuit. It is based on a new modification of the Gauss elimination method for solving systems of linear algebraic equations. The ratio of the number of multiplication or division operations required to calcu-late new values of the currents of each branch corresponding to the new value of the changed parameter of the next element to the number of these new values of the currents for a sufficiently large number of changes in the parameter of each element is close to two. The method is characterized by a small error. Since the computational costs of analyz-ing the circuit after the next change in the parameter of some element are small, there is no need to determine the cur-rents corresponding to the intermediate values of the element parameters based on approximation. Instead, it becomes possible to quickly directly calculate the currents. Software has been developed in C++, which calculates the values of all or user-selected currents after each change in the parameter of the next element. The program creates three-dimensional graphs corresponding to the change in the parameters of two elements. It also allows you to obtain a group of three-dimensional graphs corresponding to the change in the parameters of three elements, which gives some infor-mation about the corresponding four-dimensional space. The results of numerical experiments confirming the effec-tiveness of the proposed method are given. An automated mode for forming the initial system of equations and chang-ing systems based on Kirchhoff's laws for electrical circuits is used. To reduce computational costs, the sparseness of the corresponding matrices is taken into account.