Time-domain waveforms and phase-domain trajectories of fault recording and mathematical models of phase-domain trajectories

Abstract

Abstract In order to form the phase-domain trajectories of fault recording and their mathematical models to construct a theoretical basis to mine fault feature parameters deeply, after analyzing the status of existing fault recording analysis and its application, its time-domain waveforms and phase-domain trajectories are plotted by the function of a polar coordinate system in matlab. The mapping relationship between the time-domain waveforms of sinusoids and their phase-domain trajectories is proposed, and the relationship between the initial phase angle of a sinusoid and the position of its trajectory is analyzed, as well as the characteristics and mathematical model of the trajectories of short-circuit currents containing dc components and non-sinusoidal periodical currents containing harmonics. The 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 and harmonics in short-circuit currents have different impacts on their trajectories. The dc components have no impact on the positions of the trajectories of the short-circuit currents, but on their sizes and shapes; while the harmonics have an impact on the shapes of the trajectories and their positions are decided by the initial phase angles of the waveforms. Subsequent study of the algorithm of fault recording analysis will be spread based on the contents in this paper.