Wavelet Packet Transform-Based Power Quality Indices for Balanced and Unbalanced Three-Phase Systems Under Stationary or Nonstationary Operating Conditions

Three-phase power-quality indices (PQIs) can be used to quantify and hence evaluate the quality of the Electric Power System (EPS) waveforms. The recommended PQIs are defined based on the fast Fourier transform (FFT) which can only provide accurate results in case of stationary waveforms, however in case of nonstationary waveforms even under sinusoidal operating conditions, the FFT produces large errors due to spectral leakage phenomenon. Moreover, FFT is incapable of providing any time-related information which is a required property when dealing with time-evolving waveforms since it can provide only an amplitude-frequency spectrum. Since wavelet packet transform (WPT), which is a generalization of the wavelet transform, can represent EPS waveforms in a time-frequency domain, it is used in this study to define and formulate three-phase PQIs. In order to handle the unbalanced three-phase case, the concept of equivalent voltage and current is used to calculate those indices. The results of four numerical examples considering stationary and nonstationary, balanced and unbalanced three-phase systems in sinusoidal and nonsinusoidal situations indicate that the new WPT-based PQIs are closer to the true values. In addition, phase and overall crest factors are redefined in the time-frequency domain using WPT while a new crest factor is introduced in this paper. The redefined crest factors and the new crest factor help identifying and quantifying the waveform impact based on the time-frequency information obtained from the WPT. New crest factor can only be determined via WPT, which proves the powerful of this method and its suitability to define three-phase PQIs in nonstationary operating conditions.