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This article presents a novel approach to the study of practicable ratios of overvoltage's in abnormal modes of transmission lines extra high voltage. An approach takes into account influence of asymmetry, which is caused by phase difference of overhead lines parameters. The method relies upon improved mathematical model of transposed transmission line, which permits comprehensive research of origin process anomalous overvoltage's with real ratio of symmetrization. Researches of the following schemes of conductor transposition were made: line without transposition, not complete cycle of transposition, complete cycle of transposition and ideal transposed line. For the account real transposition in developed model was used equivalent matrix of line scheme which caused cascade connection of fourterminal networks. To research the conditions of abnormal overvoltage initiations were sated up equivalent circuits relative to switching ' off phase of two accidents of open-phase modes: single-phase auto reclose and phase interruption. The functions of abnormal overvoltage's were obtained on length and compensation ratio of overhead line, which were constructed for various transposition schemes. Critical values of line length for evolution abnormal overvoltage's were determined. [ABSTRACT FROM AUTHOR]