Problems of the Regional Energetics (Dec 2014)
REACTIVE POWER IN THE LONG ELECTRICAL LINES
Abstract
This paper presents a numerical method for the calculation of electric circuits with distributed parameters with losses that may vary over time. It is proposed to use the energy integral in order to estimate the accuracy of numerical solutions. The elaborated numerical scheme, named Albatross, is conservative with minimal dissipation and dispersion. These properties lead to the fact that the computational error does not accumulate, that gives the possibility to realize the transparent calculations of non stationary solutions without loss of accuracy at large time intervals corresponding to 300…500 electromagnetic wave runs along the line length right up to steady-state regime. The results of calculations for non-homogeneous circuits with distributed parameters are presented graphically. These results can be used as a model to develop new approximate methods for numerical solution of electrotechnical problems. The solutions of these problems have been obtained by means of operator method, complex amplitude method, Fourier method as well as by numerical method Albatross. The results of calculations for various modes in the half-wave transmission line are represented. The comparison between the physical and mathematical experiments in analyzing of different regimes in half-wave electrical transmission line is represented. The comparison of accuracy of the solutions obtained by proposed method, by Finite Difference Time Domain (FDTD) method and by Godunov’s scheme for telegraph equations is carried out. It is illustrated, that FDTD method has some limited application for solving the telegraph equations in spite of the fact that it is of second order of accuracy.
