Scientific and Technical Journal


ISSN Print 2221-3937
ISSN Online 2221-3805
The article is devoted to theoretical and mutual influences in the accounting system of two coupled transmission lines of electric energy having a common wire. The aim is to conclude the analytical expressions describing the change complexes instantaneous values ​​of currents and voltages in related lines depending on the distance.
Under the related lines are understood line with distributed parameters, together with galvanic, capacitive and magnetic coupling.
To achieve this goal in the primary parameters of the conventional single line introduced additional parameters characterizing the specific (per unit length) mutual inductance lines, specific capacitance between the conductors and the resistivity of the insulation between them.
Taking into account the additional primary input parameters based on Kirchhoff's laws for instantaneous values ​​of currents and voltages a system of differential equations.
For AC sinusoidal mode composed of equations is transformed into a system of ordinary differential equations for the complex amplitude of currents and voltages at any point lines. This system is solved for the two cases, the initial conditions: in certain complexes of currents and voltages at the start and end lines. These two combinations of initial conditions are classical in theoretical electrical engineering and allow us to determine the current and voltage as a function of time at any point connected lines.
Work is of practical interest due to several circumstances. First, modern cable line transmission of electricity, operating in a sinusoidal signal is a prototype developed mathematical model of the system of coupled lines. At small distances between the conductors, given the concentration of the magnetic field inside the system and greater length of such lines, the mutual influence on each other conductors become so important that they no longer possible to ignore.
Secondly, in the case of unbalanced load, with the help of the developed mathematical model can account for the effect of higher current and voltage harmonics on adjacent conductors link.
Third, when a pulse mode caused by load switching, developed a mathematical model to calculate the transitional regime in coupled transmission lines using the spectral method or a numerical modification - a method of periodization temporal characteristics.
In a further refinement of the proposed approach is promising to consider the case of three-phase electric power transmission line to ground.
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26 May 2020

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