Дослідження динаміки процесу спотворення синусоїдальної напруги вищими гармоніками

Анотація

Study of the Dynamics of the Distortion process of the Sinusoidal Voltage from Higher Harmonics

A. M. Gladkij

Introduction. Increasing number of modern computer-integrated technologies leads increasing  the share of consumers with nonlinear loads, which cause distortion of sinusoidal voltage from  higher harmonics. This adversely affects other equipment, by cause of the overheating and damage, disruptions of device synchronization, data network failures, and other negative effects. These factors necessitate the development of new methods for research, analysis and minimization of nonlinear voltage distortion.

The purpose of the work - research of distortions of the form of the sinusoidal voltage from higher harmonics, definition of numerical characteristics of distortions and possibilities of their minimization.   

Methods. The study of the dynamics of distortions of the waveform of a sinusoidal voltage of higher harmonics was performed by numerical simulation of the instantaneous voltage u(t) using the automated system in the form:

  u(t)=sin(wt+j₁)+K_nsin[n(wt+j₁)+j_n],

where t -  time, w - frequency, j_n - initial phase, n = 2, 3, ..., - number, N - quantity, K_n=U_n/U₁ - coefficient of harmonic, U₁, U_n  - amplitude harmonics.

Evaluation of the distortion of the voltage waveform was carried out with deviation from the sine wave reference points – the peak value of the voltage U and phase of the amplitude values of the voltage φ

Results. The simulation and analysis of distortions of the sinusoidal voltage from  second and third highest harmonics were carried out. Dependence of the bending voltage from phase received and рhase of the bending voltage from initial phase of the second and third harmonics, аnd evaluations of the distortions caused by these harmonics were done. The formulas are given for estimating the extreme deviations of the amplitude: U_mаx=1+K_n; phase: j_m=аrссоs(nК_n); the initial phase harmonics j_n, in which the phase deviation φ is equal to zero: j₂=±p/2 і j₃=0, j₃=±p, and the equation for j_n і φ, in which the deflection amplitude is zero.

Discussion. Obtained estimates of distortions of sinusoidal voltage from higher harmonics can be used to determine permissible levels of nonlinear distortions, calculation of amplitude measurement errors, frequency and phase difference from higher harmonics, methods development for minimization of distortions, etc.