The application of mathematical simulation for solution of linear algebraic and ordinary differential equations in electrical engineering

Abstract

The application of mathematical simulation for the solution of linear algebraic and ordinary differential equations regarding to complex electrical circuits, systems of automatic control and regulation is discussed in the paper. MatLab software package of mathematical simulation and one of its built-in environments - Simulink were chosen to be used in the experiment. MatLab is the most commonly used application in engineering practice in comparison with the other similar programs and it has proved to be reliable for technical calculations. The calculation methods of complex electrical circuits by the solution of linear algebraic and differential equation systems were developed and tested. The equations of electric equilibrium were written for each element of an electric circuit on the basis of Ohm’s and Kirchhoff’s laws. The example of the calculation of branches currents and nodal potentials of electric circuit by the matrix method in MatLab was presented. The approximated polynomial function was calculated and its graph was plotted applying the developed technique. Thus, the coincidence with the original data was proved. The calculation of differential equations of successively connected inductive and resistive elements of electric circuit was made in Simulink environment. Finally, the dependences of voltage and current on time were found using the direct Laplace transformation. The graphs were plotted due to the application of the oscilloscope built into the program. It has been concluded that the application of mathematical simulation for engineering calculations in order to solve the problems of automatic control and power engineering is the most suitable and universal technique.