Mathematical design of nonlinear electric

Authors

  • P. Rozhkov O.M. Beketov National University of Urban Economy in Kharkiv
  • S. Rozhkova Kharkiv National Automobile and Highway University

Keywords:

a nonlinear electric circle, differential equation, initial conditions, the method of fitting, ferromagnetic core

Abstract

It is proposed to use the method of attachment for the calculation of current in a sequential nonlinear electric circuit of an alternating current. At the first stage, the analytical solution of the second-order non-uniform linear differential equation is considered, taking into account the initial conditions for a sequential electric circuit, which consists of active resistance, inductance and capacitance. The right-hand side of the equation is represented by the harmonic function of the electromotive force with initial phase shift. As a result of the solution of the differential equation by means of the Laplace transform, was obtained analytic functions of the charge, current, and second derivative charge on time for real, multiple and complex roots of the characteristic equation. The use of the method of attachment allows us to conduct mathematical modeling of processes in an electric circuit with a nonlinear characteristic of any of its elements. In the second stage, the case of using a reel with ferromagnetic core as a nonlinear element of the electric circuit is considered, and the active resistance and capacitance are linear elements. The ferromagnetic core significantly influences the inductance of the circle and makes it dependent on the current flowing in the circle. Output data for the magnetization curve characterizing the dependence of the magnetic properties of the core material on the current are presented as a set of experimental points. To obtain an analytic dependence, a cubic spline-interpolation of experimental data was performed. For the analysis of the dependence of the shape and value of the current on the type of ferromagnet as a core, steel 3411 and steel 1512 are considered. For the analysis of the influence of the active resistance on the form and the value of the current in the circle, calculations were made for two values of the active resistance, which differ tenfold. The obtained graphs of time-dependent currents for different core ferromagnets and the same values of active resistance have the same form, but the magnitudes of currents after the end of the transition process differ sometimes in two times. The greatest influence on the shape and magnitude of the current is the value of the resistance. The shape of the current with increasing resistance begins to approach harmonious. This is due to a decrease in the current and a decrease in the variation of the inductance of the circle.

References

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Published

2019-10-03

How to Cite

Rozhkov, P., & Rozhkova, S. (2019). Mathematical design of nonlinear electric. Lighting Engineering & Power Engineering, 3(53), 82–86. Retrieved from https://lepe.kname.edu.ua/index.php/lepe/article/view/398