A research report on the phase-domain trajectories of fault recording and their mathematical models

Abstract

In currently known theories and algorithms of fault recording analysis and application, there is little literature where fault feature parameters are mined deeply from electrical physical quantities themselves. In this report the calculation method of the phase angles of the reference point and sample points is obtained, which ensures the correspondence of the time-domain waveform of digital fault recording with its phase-domain trajectory. The relationship between the initial phase angle of a sinusoid and the position of its trajectory, the characteristics of the trajectories of three-phase short-circuit currents containing dc components and the mathematical models of these trajectories are analyzed. Taking a rectangular wave current and a triangle wave current as example, the characteristics of the trajectories of non-sinusoidal and periodical waveforms containing harmonics are analyzed as well as their mathematical models. The research results show that the relationship between the initial phase angle of a sinusoid and the position of its circular trajectory is definite; the dc components have no impact on the positions of the trajectories of the short-circuit currents, but on their sizes and shapes; the harmonics have an impact on the shapes of the trajectories, and their positions are decided by the initial phase angles of the ac fundamental components in the waveforms. Subsequent study of the algorithm of fault recording analysis will be spread based on the contents in this report.