MATHEMATICAL MODEL OF A MULTIWIRE TRANSMISSION LINE WITH MINIMAL DISSIPATIVE AND DISPERSIVE EFFECTS

Abstract

In this paper, we consider the problem of calculating the regime in a long multiwire line by a
numerical method and the justification of the method for minimizing parasitic oscillations in the numerical
solution of telegraph equations. A mathematical model of a multiwire electric line with distributed parameters with losses is given. Relations are obtained for the calculation of currents and voltages in the phase
coordinate system. The justification of the numerical method for calculating the regime in such a line is given, taking into account the mutual influence of the phases and the load of the line. For this, the method of the
first differential approximation was used. A difference modified calculated scheme for telegraph equations in
a diagonal form is constructed using Riemann invariants, with dissipative and dispersion terms in these relations. This expression is called the first differential approximation and determines the order of approximation of the dissipative and dispersion terms and the qualitative properties of the constructed difference
scheme. Minimizing this expression will minimize the effects of dissipation and dispersion. The conditions for
minimizing the dissipative and dispersion terms in the calculated numerical scheme and minimizing the error
in the numerical solution are obtained. The results of the calculation of the wave process in the phase of an
air multiwire line with a voltage of 110 kV are presented. Two weight parameters were introduced into the
calculation program in such a way as to take into account the limiting states of the calculated schemedispersion and dissipation effects. For values that correspond to the condition for minimizing the dispersion
effect, the input pulse propagates along the line without distortion, the damping is caused by the presence in
the line of non-zero longitudinal resistance and the transverse active conductivity of the line. If the calculations are performed with non-optimal values of the weight parameters, non-physical distortions appear at
the wave front. The obtained results confirm the possibility of minimizing the dissipative and disperse effects
of the numerical solution when using the proposed mathematical model of a multiwire line and the calculation scheme