On the application of wavelet transform for symmetrical components computations in the presence of stationary and non-stationary power quality disturbances

Symmetrical components method allows systematic analysis of unbalanced three-phase systems. This method represents the backbone for many applications in an electric power system (EPS) such as fault analysis, power system protection, power and energy measurements. Moreover, with the increased penetration of plug-in hybrid electric vehicles (PHEVs), studying and evaluating the distribution system unbalance considering power quality disturbance pronounced by fleet of these vehicles, becomes a necessity. In time-invariant polluted environment, the measurements of the symmetrical components for the fundamental and harmonic components could be performed using Fourier basics. However Fourier-based techniques are unsuitable in the presence of any time-variant power quality disturbance which is typically the case when considering PHEVs and other nonlinear industrial process such as computer numerical control (CNC) machines. In this paper, time-frequency expressions for the symmetrical components are developed using different wavelet transforms: Discrete Wavelet Transform (DWT), Wavelet Packet Transform (WPT) and Stationary Wavelet Transform (SWT). The paper also includes a comparative study of the results obtained when applying the developed approach using different wavelet basis functions, such as Daubechies, Coiflets and Symlets into three case studies (two synthetic and one real) including unbalanced three-phase system under different operating conditions while considering different kind of disturbances. The results are analyzed and conclusions are presented. The outcomes of this study lay the ground for further studies in unbalanced distribution system with high penetration of PHEVs, two-way protection devices for smart grid and power quality evaluation.

Research highlights
► Symmetrical components are re-defined using different wavelet transforms and basic functions.
► Instead of applying the ‘a’ operator, a time shift ‘m’ is used advancing or delaying the samples to obtain the sequence components.
► The results indicate that using DWT with db43 or sym20 can provide acceptable results.
► The outcome lays the ground for more realistic analysis of unbalanced distribution system power flow.