Representation of Transient Processes on a Hyperplane Using Examples from Electrical Engineering

Abstract

Vector representation of transient processes on a plane with two coordinate systems makes it possible to visualize all the parameters of transient oscillations, namely, amplitude, frequency, phase, and attenuation. On a complex plane with two coordinate systems, the origin of the vector is determined by the damping factor and the cyclic frequency and is set on the scale of axes of the complex frequency plane, while the length and the phase of the vector are set on the scale of complex amplitude. Such a representation significantly improves visualization of processes and, consequently, increases the informativeness of the research. The use of the hypervector representation of transients is illustrated by various examples. When analyzing the functioning of an automatic excitation controller (AEC) in certification tests, the vector representation of transient processes clearly demonstrates the effect of the AEC and allows one to quantitatively control the effect of channel stabilization on oscillation modes. The vector representation of the dominant oscillations in various implementations of the circuits reveals the most extreme situations for which it is necessary to test the AEC tuning for a specific station. Investigation of the vectors of the voltage-frequency oscillation measured at different points of the system makes it possible to localize the source of low-frequency oscillations.