Mathematical Model of Electrical Line with Transposition of Phase Circuits

The purpose of this paper is to elaborate the mathematical model and the method of calculation of the permanent regime in the line with many conductors with transposed phases. The mathematical model is based on the telegraph equations and takes into account the fact that the electric lines are lines with distributed parameters. As a subject of the study it is selected the 110 kV overhead power line with two compact circuits with the conductors placed horizontally and circularly transposed. The initial and boundary conditions are formulated for the case of two-circuit electric line and the adjustment of the phase angle of the voltages at the line input. In the transposition the values of the conductor parameters change by leap, which complicates the process of calculating the operating mode. The developed model and elaborated software include all these features. Based on the developed model, calculations of the operating mode of the two-circuit electric circuit and of the self-compensated line were performed. Numerical solutions have been obtained regarding the evolution of active and reactive power in the phases of the line in its various sections under regulation and non-regulation of the phase shift angle for the cases without and with the transposition of the phase conductors. The applicability of the model for studying power transfer processes in multi-conductor power lines has been demonstrated. There were obtained the numerical solutions useful for estimating the degree of mutual influence of phases on the ability to transfer power to load under the transposition of conductors