IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 24, NO. 4, OCTOBER 2009 2099 Fuzzy-Wavelet-Based Electric Power Quality Assessment of Distribution Systems Under Stationary and Nonstationary Disturbances Walid G. Morsi, Student Member, IEEE, and M. E. El-Hawary, Fellow, IEEE Abstract—Evaluating the electric power quality (EPQ) becomes very important task due to the widespread use of nonlinear loads, Distributed Energy Resources (DERs) and the economic impact of poor EPQ. In a deregulated environment, having different power quality indices (PQIs) with different values has no significance unless they are combined into single value that could represent them. In this paper, a new fuzzy-wavelet packet transform based PQI is introduced that amalgamates the recommended PQIs after being redefined in the time-frequency domain using wavelet packet transform for compatibility purposes with nonstationary disturbances. In order to handle the uncertainties associated with the electric power system operations, Fuzzy systems are used in this paper. In order to study the effect of wavelet filter length and the choice of the best wavelet basis function, the new fuzzy devel- oped modules along with the reformulated PQIs are used in three case studies considering electric arc furnace load supplied from stationary low distorted voltage, stationary high distorted voltage and nonstationary distorted voltage (voltage dip) in addition to a real case study considering variable speed drive. Index Terms—Fuzzy logic system, nonstationary, power factor, power quality (PQ), wavelet packet transform (WPT). I. INTRODUCTION I N the last decade, the power distribution system has been subjected to major changes due to integrating more renew- able energy sources with the electric grid along with nonlinear loads such as electric arc furnaces (EAFs), variable frequency drives (VFDs), etc. on one hand and the greater sensitivity of customers’ equipments to any disturbance that could be due to fault or voltage and current variations on the other hand. As a consequence the need for evaluating the electric power quality has arisen for the purpose of accurately quantifying the power quality disturbance, estimating the associated economic impacts on the electric power system (EPS) operation and deciding a cost-effective power-quality (PQ) mitigation technique. Studies [1]–[8] provide surveys on PQ conducted in different countries around the world. Manuscript received May 16, 2008; revised January 16, 2009. Current version published September 23, 2009. This work was supported by the Izaak Walton Killam Memorial predoctoral scholarship. Paper no. TPWRD-00328-2008. W. Morsi is with the Department of Electrical and Computer Engineering at the University of New Brunswick, Fredericton, NB E3B 5AE, Canada (e-mail: wmorsi@unb.ca). M. E. El-Hawary is with the Department of Electrical and Computer Engineering, Dalhousie University, Halifax, NS B3J 2X4, Canada (e-mail: elhawary@dal.ca). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRD.2009.2027514 In order to achieve those objectives, different techniques have been proposed in the literature for defining power quality in- dices (PQI) that could be used for evaluating the electric PQ in this new environment. Heydt [9] and [10] has credited to dis- cuss the pitfalls of the recommended PQ indices contained in [11] while in [12] the windowed Fourier transform (WFT) was used for quantifying the electric PQ by reformulating the rec- ommended PQI in the WFT domain. Unfortunately the main disadvantage with the WFT is a trade-off has to be made be- tween the length of the window and the frequency resolution in the spectrum and therefore increasing the time resolution comes at the expense of the frequency resolution and vice versa leading to losing frequency or time information when considering non- stationary disturbances [13]. Kandil et al. [14] developed modified versions of the rec- ommended PQIs using the discrete wavelet transform (DWT). Using such transform, the time and frequency information could be preserved especially while considering time-evolving voltage and current waveforms. They compared their approach with the fast Fourier transform (FFT) based on PQI but only for sta- tionary case studies. The main limitation with the DWT is the in- accessibility of some frequency sub-bands since it can’t provide uniform frequency spectrum because only one configuration of the decompositions exists. The result is that the frequency scale is dyadic and therefore many frequency sub-bands are merged together especially for high frequencies. The wavelet packet transform (WPT) is considered a gen- eralization of the wavelet transform. Many configurations for waveform decomposition can be achieved via WPT algorithm and therefore uniform frequency scales can be realized while the DWT can be considered as a special case of the WPT. Barros and Diego [15] proved the effectiveness of using the WPT for the measurements of harmonic groups for voltage and current root mean square values. It was shown in [15] that the WPT can provide better results than the IEC method presented in [16] and therefore WPT could be the most suitable time-frequency trans- form for PQI measurements especially under nonstationary op- erating conditions. The PQIs that could be used for evaluating the electric PQ are the displacement power factor, transmission efficiency power factor, oscillation power factor, voltage and current total har- monic distortion (or total demand distortion) as presented in [11] and [17]–[19]. For different operating conditions, different values for these PQIs can be obtained leading to ambiguity in ranking or determining quantitatively or qualitatively the elec- tric PQ without having a single index that could represent these indices. As a first step toward this objective, the authors in [20] 0885-8977/$26.00 © 2009 IEEE