Single-circuit equivalent of a double-circuit line with parallel operation of circuits

Analysis of modes in circuits with two-chain lines sometimes requires reducing them to an equivalent single-chain line. The solution to this problem for a single-line circuit is known, and there are corresponding expressions for determining the coefficients of an equivalent 4-pole in terms of the coefficients of the original 4 -poles. However, in some cases, there is a need to analyze modes in a 3-phase formulation, where there may be schemes with parallel 3-phase circuits. In this case, the problem arises of reducing parallel independent 3-phase lines to a 3-phase equivalent. For this purpose, the modal method for determining matrix phase coefficients is used. A special approach is required when converting a 6-phase line (two circuits on the same support) to a 3-phase circuit, when it is necessary to consider the mutual influence of the circuits. This research aims to provide a solution to the problem of reducing a 6-phase line to a 3-phase equivalent in parallel operation of circuits. Calculations based on the proposed algorithm for the 3-phase equivalent of a 500 kV 6-phase line with a length of 500 km are presented. The results satisfy the fundamental property of the n-th order multipole coefficients.