IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 1, JANUARY 2007 27 A Novel MDL-based Compression Method for Power Quality Applications Moisés V. Ribeiro, Member, IEEE, Seop Hyeong Park, Member, IEEE, João Marcos T. Romano, Senior Member, IEEE, and Sanjit K. Mitra, Life Fellow, IEEE Abstract—This paper introduces a novel source coding method for voltage and current signals, called fundamental, harmonic and transient coding method (FHTCM), which is a generalization of the enhanced disturbance compression method (EDCM). The pro- posed method makes use of notch filtering–warped discrete Fourier transform (NF–WDFT) technique for estimating the parameters (amplitude, frequency, and phase) of the fundamental and har- monic components acquired from power lines so that only the tran- sient components are compressed with wavelet transform (WT) coding technique. For the WT-based compression of transient com- ponents, we formulate a minimum description length (MDL) cri- terion, taking into account the selection of wavelet bases in a dic- tionary, wavelet decomposition structure, and quantization. Com- putational simulations have verified that the proposed method out- performs the EDCM as well as the traditional WT-based compres- sion techniques. Index Terms—Data compression, fundamental and harmonics, minimum description length, notch filtering, parameter quanti- zation, power quality, warped discrete Fourier transform (DFT), wavelet transforms (WTs). I. INTRODUCTION R ECENT advances in the signal processing field have stim- ulated a great deal of interest in the use of digital signal processing techniques for the monitoring and analysis of events in power systems. This has led to the development of feasible and efficient signal processing techniques for the estimation of harmonic parameters; the detection, compression, and classifi- cation of events; and the localization of sources of power-quality (PQ) problems. The compression of PQ events has necessitated the develop- ment of efficient and low-complexity algorithms. Let us con- Manuscript received December 1, 2004; revised February 3, 2006. This work was supported in part by CAPES under Grant BEX2418/03-7, in part by CNPq under Grants 552371/01-7 and 150064/2005-5, and in part by FAPESP under Grant 01/08513-0, all from Brazil. Paper no. TPWRD-00571-2004. Moisés V. Ribeiro was with the Department of Electrical and Computer En- gineering, University of California, Santa Barbara, CA 93106 USA. He is now with the Department of Electrical Circuit, Federal University of Juiz de Fora, Juiz de Fora, MG 36 036 330, Brazil (e-mail: mribeiro@ieee.org). S. H. Park is with the Department of Electronic Engineering, Hallym Univer- sity, Chuncheon, Gangwon-do, 200-702, Korea (e-mail: spark@hallym.ac.kr). João Marcos T. Romano is with the Department of Communications, School of Electrical and Computer Engineering, University of Campinas, Campinas, SP 13 081 970, Brazil (e-mail: romano@decom.fee.unicamp.br). S. K. Mitra is with the Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106 USA (e-mail: mitra@ece. ucsb.edu). Color versions of Figs. 4, 6, 8, 10, 12, and 14 are available online at http:// ieeexplore.org. Digital Object Identifier 10.1109/TPWRD.2006.887091 sider, for example, the installation of 1000 pieces of monitoring equipment in a distribution system. If the analog-to-digital con- verter (ADC) uses 16-bit word length and a sampling rate of 15 360 Hz for the acquisition of power line signals, then the band- width required for the transmission of all monitored signals to a processing center is as high as 234 375 Mbits/s. To get around this bandwidth requirement, it is necessary to compress the PQ events [1]. The wavelet transform (WT) is suitable for the compression of wideband signals like PQ events since WT has good local- ization in both time and frequency domains [2]. It has also been shown that various wavelet thresholding schemes have near-op- timal denoising properties [3]. For these reasons, a variety of compression techniques based on WT or wavelet packet trans- form (WPT) [4] have been successfully applied so far to PQ events compression [5]–[18]. For an effective reduction of the redundancy in events, we need to select the best basis representation. In [19]–[24], this topic has been addressed by considering a statistical model for the distribution of wavelet coefficients and by using the min- imum description length (MDL) criterion introduced by Ris- sanen [25], [26]. Hamid and Kawasaki [5] have applied Saito’s MDL crite- rion [19] to disturbance event compression to select the optimal bases of WT and keep intact the best number of wavelet coeffi- cients. However, the MDL used in [5] does not take into account quantization in its formulation [19]. Yu et al. [22] and Chang et al. [23] used the MDL crite- rion taking into account the quantization for the compression of image signals. However, both methods are not suitable for the compression of events because the image statistical models are not practical to represent the events in power line signals. Hsieh et al. proposed a WT-based approach with a sinusoidal reference signal subtraction [7]. However, their approach did not provide the detailed method for generating the reference sinu- soidal signal. Riberio et al. advanced EDCM which makes use of the Kalman filter for the estimation of the fundamental sinusoidal component and then separate it from the events [12], [13]. In the EDCM, the deterministic sinusoidal component and the residual signal are compressed by the parameter quanti- zation and WT-based compression techniques, respectively. Simulation results [13] have verified that it outperforms other well-known WT-based event compression methods. However, there is room for improvement in the performance of EDCM. First, the fundamental component is not the only de- terministic component included in the power signal. The har- 0885-8977/$20.00 © 2006 IEEE