A Wavelet-Based Data Compression Technique for Smart Grid

212 IEEE TRANSACTIONS ON SMART GRID, VOL. 2, NO. 1, MARCH 2011

A Wavelet-Based Data CompressionTechnique for Smart Grid

Jiaxin Ning, Member, IEEE, Jianhui Wang, Member, IEEE, Wenzhong Gao, Member, IEEE, andCong Liu, Member, IEEE

Abstract—This paper proposes a wavelet-based data compres-sion approach for the smart grid (SG). In particular, wavelet trans-form (WT)-based multiresolution analysis (MRA), as well as itsproperties, are studied for its data compression and denoising ca-pabilities for power system signals in SG. Selection of the Order2 Daubechies wavelet and scale 5 as the best wavelet function andthe optimal decomposition scale, respectively, for disturbance sig-nals is demonstrated according to the criterion of the maximumwavelet energy of wavelet coefficients (WCs). To justify the pro-posed method, phasor data are simulated under disturbance cir-cumstances in the IEEE New England 39-bus system. The resultsindicate that WT-based MRA can not only compress disturbancesignals but also depress the sinusoidal and white noise contained inthe signals.

Index Terms—Data compression, disturbance analysis, wavelettransform.

I. INTRODUCTION

T HE AGING electric power infrastructure is confrontingincreasing obstacles to accommodate complex customer

demands and emerging technologies. Higher-level usages ofrenewable energy sources (RESs), flexible alternating currenttransmission systems (FACTSs), and plug-in hybrid electricvehicles (PHEVs) call for intelligent, real-time, and robustoperation, protection, and control of the power grid. In thiscontext, the smart grid (SG) is proposed to change the overallpattern of power grid operation and management in favor ofobtaining economic efficiencies, robust control, and environ-mental benefits. It is desirable that the overall performanceof bulk power systems is essentially augmented by SG tech-nologies in a dynamic, adaptive, and optimal manner withgreater reliability and stability and more flexible compatibilitywith existing and future technologies. The concept of SG is toestablish the seamless communication throughout each levelof the power grid in order to reinforce the transparency andmobility of power grid information and, therefore, to be able

Manuscript received October 05, 2010; accepted October 27, 2010. Date ofpublication December 10, 2010; date of current version February 18, 2011.Paper no. TSG-00151-2010.J. Ning is with EnerNex Corporation, Knoxville, TN, USA (e-mail:

[email protected]).J. Wang and C. Liu are with Argonne National Laboratory, Argonne, IL, USA

(e-mail: [email protected]; [email protected]).W. Gao is with Department of Electrical and Computer Engineering, Univer-

sity of Denver, Denver, CO, USA (e-mail: [email protected]).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/TSG.2010.2091291

to coordinate system operation and management throughout alllevels of the power grid.Recent studies focus on the technical transition from the con-

ventional power grid to the SG. In other words, many studieshave been carried out to observe how grid performance can beimproved in a communication-guaranteed and intelligence-en-abled environment. Concerning the transmission level(s) of thepower grid, the operation and control of huge amounts of RESpenetration [1], [2], wide-area protection and control [3], [4],and the regulation of energy storage systems (ESSs) [5] drawsignificant research interest in the context of SG. In [6] and [7],the functionalities and applications of the smart transmissionsystems are synthesized and anticipated.Apart from the concerns above, this paper focuses on the

issue of data congestion in SG, given that the overwhelmingflows of data may lead to dramatic deterioration in the effec-tiveness and efficiency of communication in the SG. In the fu-ture SG, the data reflecting system statuses across all levels ofthe grid may be generated by smart metering systems, super-visory control and data acquisition (SCADA) systems, wide-area monitoring systems (WAMSs), and other monitoring de-vices. The huge amounts of data need to circulate and be storedamong control centers, utilities, and customers in a near real-time manner. In examining the case of WAMSs, for example, in2004, the Tennessee Valley Authority (TVA) launched a projectcalled Phasor Data Concentrator (PDC) [8], [9], an effort in col-lecting electrical information of the grid from phasor measure-ment units (PMUs), which are the major measuring devices inWAMSs. Currently, 120 PMUs are deployed in the Eastern In-terconnection. These PMUs transmit themeasurements 30 timesper second to the PDC in TVA and the measurement archivalrate reaches 150 million times per hour. The storage utiliza-tion rate reaches 36 gigabytes per day. Moreover, because thisPDC project aims to coordinate the independent system opera-tors (ISOs) and utilities in the Eastern Interconnection, data con-gestion will also be confronted in the communication system ofWAMSs, when such a large number of measurement data arecirculating among ISOs and utilities. The overall data size inthe future SG is expected to be fairly large as a result of the fullimplementation of SG techniques in the next few years.Therefore, the use of data compression techniques will be de-

sirable to help mitigate the burden of the communication sys-tems and the storage utilization. In addition to data compres-sion, the valuable information contained in the data should beconserved to the greatest extent possible so as to accurately re-flect the system statuses. The basic requirements for data com-pression can be generalized as follows.

1949-3053/$26.00 © 2010 IEEE

NING et al.: A WAVELET-BASED DATA COMPRESSION TECHNIQUE FOR SMART GRID 213

• Power system data can be compressed at the sendingterminals so as to inject amounts of data that have beencompressed as much as possible into the communicationsystems.

• The compression should keep the valuable informationcontained in the data.

• The compressed data can be near-perfectly reconstructedfor analysis when received at receiving terminals.

This paper proposes a wavelet-based approach [10] for datacompression [11], [12] in the SG context. By a process of mul-tiresolution analysis (MRA), wavelet transform (WT) can or-thogonally decompose a time series into scaling coefficients(SCs) and wavelet coefficients (WCs), in which the trivial datapoints can be deleted such that the overall size of the data canbe compressed. And the nature ofWT satisfies a near-perfect re-construction of the time series via an inverse MRA. Moreover,with the rapid development of computing techniques, the algo-rithm of MRA can be implemented for online applications [13],[14]. Thus, it is feasible to embed awavelet-based data compres-sion algorithm into themonitoring devices, in which the data canbe compressed before it is sent out in order to mitigate the datacongestion. In addition, WT is capable of depressing the sinu-soidal and “white” noise in the data. This property could benefitthe preprocessing of the data in the measuring devices.To justify the proposed approach, this paper utilizes a set of

simulated PMU data to discuss the advantages of WT on datacompression. The simulated PMU data are obtained from simu-lations in the Power System Simulator for Engineering (PSS/E).In PSS/E, the dynamic frequency and voltage signals are sim-ulated during system disturbances in the IEEE New England39-bus system. The disturbances include generation loss andload change, which are major concerns for WAMSs in the inter-connected systems. Nevertheless, without loss of generality, theproposed approach is capable of compressing any type of gridsignal into the format of a time series. As a byproduct of datacompression, the denoising property of WT is also discussed toshow the immunity of the proposed approach to the various datanoise.The paper is organized as follows: in Section II, WT-based

MRA and its properties are briefly introduced; in Section III,the selections of wavelet function and decomposition scale fordisturbance signals are conducted for data compression and de-noising; in Section IV, a numerical simulation is carried out tojustify the effectiveness of WT-based MRA on data compres-sion and denoising; the conclusion is presented in Section V.

II. WT-BASED MULTIRESOLUTION ANALYSIS

WT-based MRA is illustrated in Fig. 1, where (a) shows theprocedure for decomposing a signal, and (b) shows the proce-dure for reconstructing a signal. and are the low-pass filterand high-pass filter, respectively. The filters are constructed bya scaling function and a wavelet function , satisfying. In Fig. 2, the waveforms and frequency responses of the

Order 2 Daubechies (db2) scaling function and wavelet func-tion are shown as an example. The MRA generates SCs or “Ap-proximation” and WCs or “Detail” . SCs represent the

Fig. 1. Procedure of WT-based MRA. (a) Decomposition. (b) Reconstruction.

Fig. 2. Order 2 Daubechies scaling and wavelet functions and their spectrum.(a) Scaling function of db2. (b) Wavelet function of db2. (c) Low-pass filter ofdb2 (for decomposition). (d) High-pass filter of db2 (for decomposition).

low-frequency components, and WCs represent the high-fre-quency components. By transforming a signal, the features ofthe signal can be extracted from SCs and WCs. To disturbancesignals in power systems, WCs are more important because thetransient features of the signals are mostly represented by thehigh-frequency components [15].Property 1—Nonredundant Transform: WT-based MRA is

theoretically a type of nonredundant transform. As indicated bythe “ ” shown in Fig. 1(a), a two times downsampling rate isadopted to each scale to ensure the equivalence in the numberof sampling points before and after the decomposition.Assuming and contain sampling points at lowest

scale , the sampling points at any scale can be written as

(1)

Therefore, the number of sampling points before and after thedecomposition (with an absolute symmetric wavelet function)satisfies

(2)


If the wavelet function is not absolutely symmetric, as in, forexample, Daubechies wavelet family (i.e., its near-symmetricproperty), the relationship in (2) can be expressed as

(3)

Property 2—Threshold Denoising: A threshold can be ap-plied to depress low-value amplitudes in details, most of whichare caused by high-frequency noise. The reconstruction of ap-proximation and details after thresholding can return a cleanersignal with little distortion.Several wavelet-based thresholding methods [16], [17] have

been developed. The selection of thresholdingmethods deservesparticular consideration in the future for SG applications. In thispaper, universal thresholding is chosen to process disturbancesignals because of its computational simplicity and efficiency.Universal thresholding is calculated by

(4)

where stands for noise variance at scale .The threshold can be applied onto WCs by (5) as follows:

(5)

After thresholding, the amplitude of WCs beneath thethreshold is set to be zero. In this way, the noise is largelydepressed because the small amplitudes in WCs usually reflectthe major energy of noise [16].Property 3—Data Compression: After applying (5) to WCs,

the low-value amplitudes in WCs are depressed to 0. Becauseonly nonzero points are our interest of analysis, the signal canbe compressed by eliminating all zero points in WCs and thencan be sent to the receiving end, where the signal can be recon-structed as shown in Fig. 1(b).The question for WT-basedMRA is whether or not the mean-

ingful information of power system signals can be retained andmaintained after the denoising and compression steps. In thereminder of the paper, a numerical experiment is carried outto check the performance of WT-based MRA to disturbancesignals.

III. SELECTION OF WAVELET AND DECOMPOSITION SCALE

Before WT-based MRT is applied for data compression, thebest wavelet function and the optimal decomposition scale needto be carefully selected. Wavelet energy is the index to reflectthe energy concentration of WCs on certain scales. The largerthe wavelet energy, the more the information is preserved afterthe decomposition. In this paper, wavelet energy is chosen as thecriterion to determine the best wavelet function and the optimaldecomposition scale for disturbance signals [15]. The definitionof total wavelet energy is given by

(6)

Fig. 3. Diagram of IEEE New England 39-bus system.

and wavelet energy in each scale is given by

(7)

where subscript stands for the scale, and the maximum numberof scale is ; subscript stands for the point in WCs; and isthe length of WCs at scale .The candidates of wavelet functions consist of Daubechies

wavelet family and Symlets wavelet family .stands for the order of the wavelet function. In this paper,

db2–db10 and sym2–sym10 are chosen as wavelet candidates.These wavelets have been chosen because they have shown ex-cellent performance in analyzing dynamic signals with discon-tinuity and abrupt change [18], [19]. The wavelet correspondingto the highest total wavelet energy in (6) is chosen as the bestwavelet function, and the scale corresponding to the highestwavelet energy in (7) is chosen as the optimal decompositionscale.The testing disturbance signals are also generated in the IEEE

New England 39-bus system (Fig. 3). Three types of distur-bances are adopted in this paper: generation loss, load drop,and load surge. Generation loss is generated at Buses 33 and34, respectively; while load drop and load surge are generatedat Buses 16 and 20, respectively. During the simulation, fre-quency and voltage are recorded at Bus 19. The results are listedin Tables I and II. In Table I, the elements highlighted in yellowindicate the highest wavelet energy of a specific signal corre-sponding to a certain wavelet function. It can be seen that mostof the highest wavelet energy levels of the different signals pointto db2 and sym2. Because both wavelets return the same totalwavelet energy to all signals, either one can be chosen as thebest wavelet for disturbance signals. In this paper, db2 is de-termined to be the wavelet function for MRA. In Table II, thesignals are decomposed by db2 into 6 scales, and it is evidentthat the wavelet energy at scale 5 is the highest for most of thedisturbances. Thus, scale 5 is determined as the optimal decom-position scale for MRA in this paper.


TABLE IRESULTS OF SELECTION OF WAVELET FUNCTION

DB Daubechies wavelet function; SYM Symlets wavelet function

TABLE IIRESULTS OF SCALE SELECTION

frequency; v voltage.GL generation loss; LD load drop; LS load surge

IV. NUMERICAL EXPERIMENTIn this section, the disturbance signals, simulated in PSS/E,

are used as system dynamic signals to test the proposed method.The IEEE New England 39-bus system is adopted as the testsystem, in which the simulation time step is 0.004167 s (1/4cycle), and the simulation time is 2 s (equivalent to 482 samplepoints). The simulation focuses on the first 2 s after disturbancesoccur, during which the automated system control devices (gov-ernor or power system stabilizer) have not responded to the dis-turbances. The topology of the system is shown in Fig. 3, where“G” stands for generators, “ ” stands for loads, and numbers1–39 are bus numberings.Without loss of generality, the loss of Generation 4 (denoted

as GL4) at Bus 33 is used to test the property of WT-basedMRA. The measuring location is supposed to be deployed atBus 19; and the measurements include frequency and voltage.

Fig. 4. Frequency and voltage responses at Bus 19 to GL4.

In Fig. 4, the frequency and voltage at Bus 19 during GL4 at0.5 s of simulation time are illustrated. At the moment a distur-bance occurs, both frequency and voltage experience an abruptdrop in their values; and then, both variables start low-frequencyoscillation because of the transient response of the system.The WT-based MRA to the frequency and voltage are shown

in Figs. 5 and 6, respectively. The Order 2 Daubechies waveletis chosen as the wavelet function, and scale 5 is selected as themaximum decomposition scale. From Figs. 5(a) and 6(a), it canbe seen that both frequency and voltage have abrupt change inthe waveforms at 0.5 s due to the disturbance. Figs. 5(b) and 6(b)are the SCs of frequency and voltage signals which approximateenvelops of the signals and, thus, represent the low-frequencyfeatures of the signals. Note that the absolute amplitude of SCsonly reflects the distribution of signal’s energy at scale 5 afterthe transform and have no direct relationship with its amplitudein time domain. In practice, the signal needs to be reconstructed


Fig. 5. WT-basedMRA to frequency. (a) Frequency signal. (b) Approximationat scale 5. (c) Detail at scale 5. (d) Detail at scale 4. (e) Detail at scale 3. (f) Detailat scale 2. (g) Detail at scale 1.

Fig. 6. WT-based MRA to voltage. (a) Voltage signal. (b) Approximation atscale 5. (c) Detail at scale 5. (d) Detail at scale 4. (e) Detail at scale 3. (f) Detailat scale 2. (g) Detail at scale 1.

to utilize its actual amplitude in time domain. In Figs. 5(c)–(g)and 6(c)–(g), the WCs of frequency and voltage signals are dis-played. The WCs reflect the high-frequency features of the sig-nals at each scale because the nonzero points of WCs are onlylocalized around 0.5 s. At different scales, the WCs exhibit dif-ferent values because of the filter property that varies acrossscales. In the previous section, scale 5 has been proven to be theoptimal decomposition scale for disturbance signals. Therefore,in Figs. 5(c) and 6(c), one can see that a distinguishable ampli-tude in accurately indicates the occurrence of the disturbanceat 0.5 s. At other scales (see in Figs. 5(d)–(g) and 6(d)–(g)), al-though the large amplitudes of WCs appear around the distur-bance moment, the accuracy is incomparable to scale 5. It seemsthat, in Figs. 5(g) and 6(g), can also indicate the occurrenceof the disturbance. However, a finer observation of revealsthat it is less precise than and the amplitude of at 0.5 s isless noticeable than as well. This feature of can be usedfor signal recognition and other quantitative analysis.In Table III, the lengths (standing for one-dimensional data

size) of frequency signals and the lengths of SCs and WCsare listed, respectively. Table III shows that there are 10 moresampling points after the decomposition. Although Daubechies-based WT is not a perfect nonredundant transform because ofits near-symmetric property as explained by (3), the redundant

TABLE IIICOMPARISON OF DATA LENGTHS BEFORE AND AFTER WT

Fig. 7. The testing frequency signals. (a) The original signal. (b) The signalmixed with 60-Hz periodic noise with the amplitude of 0.1. (c) The signal mixedwith the white noise with the amplitude of 0.05.

Fig. 8. Denoising to the frequency signal mixed with the periodical noise.(a) The original signal. (b) The signal mixed with the periodical noise. (c) WCsof the original signal. (d) WCs of the polluted signal.

points are trivial when compared with the total length of thesignal (10 points versus 482 points).Denoising is often introduced into signal processing to coun-

teract the pollution of noise to the signal. In power systems,the noise is usually sorted into two types: periodical noise andwhite noise. In this paper, the 60 Hz periodical noise and thewhite noise are mixed with the frequency signal to justify thedenoising of WT-based MRA. In Fig. 7, the frequency signalshown in Fig. 4 and its polluted mixtures with 60-Hz periodicnoise with the amplitude of 0.1 and the white noise with the am-plitude of 0.05 are plotted.The polluted signals are decomposed by a db2 wavelet into

5 scales. Universal thresholding are applied to the WCs by (5).In Figs. 8 and 9, the WCs at scale 5 are exhibited for both theoriginal signal and the polluted signal after the denoising. Com-paring the amplitude of (c) and (d) in Figs. 8 and 9, it can be


Fig. 9. Denoising to the frequency signal mixed with the white noise. (a) Theoriginal signal. (b) The signal mixed with the white noise. (c) WCs of the orig-inal signal. (d) WCs of the polluted signal.

TABLE IVLENGTH OF THE COMPRESSED SIGNAL

Fig. 10. Denoising results for the signal polluted by the periodical noise.(a) The original signal. (b) The polluted signal. (c) The reconstructed signalafter denoising.

seen that the thresholding does not affect the property of WCs.The value of WC at 0.5 s remains the same and accurately indi-cates the occurrence moment of the disturbance. This result isimportant because WCs contain most of the high-frequency in-formation, which helps us recognize the dynamic feature of thesignal.After denoising, the nonzero points in WCs from scale 1

through scale 5 can be extracted so as to compress the lengthof the original WCs. The lengths of the compressed WCs arelisted in Table IV, which shows that the lengths of the com-pressed WCs are reduced by around 1/5.4 times in comparisonwith the original WCs. Figs. 10 and 11 show the reconstructedsignals after the denoising and compression. One can see thatthe signals are recovered although there is slight distortion. Thesignal-to-noise (SNR) ratio, criterion for denoising, before and

Fig. 11. Denoising results for the signal polluted by the white noise. (a) Theoriginal signal. (b) The polluted signal. (c) The reconstructed signal after de-noising.

TABLE VSNR RATIO AND RMS ERROR BEFORE AND AFTER DENOISING

the periodical noise; the white noise.

after the denoising and compression is listed in Table V, as wellas the root-mean-square (rms) error, criterion for signal distor-tion, between the original signal and the reconstructed signal.Table V shows that the SNR is improved up to two times com-pared to the ratio before denoising. In addition, the rms erroris improved by about 10 times. WT-based MRA provides ex-cellent performance in terms of depressing noise, as well as re-ducing signal distortion.

V. CONCLUSIONThis paper proposes a WT-based MRA to perform data com-

pression in the smart grid context. The proposed approach is ca-pable of effectively compressing the size of disturbance signalsas well as depressing sinusoidal and white noise in the signals.The Order 2 Daubechies wavelet and scale 5, respectively, asthe best wavelet function and the optimal decomposition scalefor disturbance signals has been selected according to the cri-terion of the maximum wavelet energy of wavelet coefficients.A numerical simulation is conducted to exhibit the propertiesof WT-based MRA for data compression and denoising. Theanalysis for the results shows the effectiveness of WT-basedMRA on data compression and denoising for disturbance sig-nals. Without loss of generality, the proposed method can beimplemented in smart grid to mitigate data congestion and im-prove data transmission and quality.

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Jiaxin Ning (S’08–M’10) received the B.S. and M.S. degrees in electrical en-gineering from Chongqing University, China, in 2004 and 2007, respectively,and the Ph.D. degree in electrical engineering from Tennessee TechnologicalUniversity, Cookeville, in 2010.He is currently a Senior Consultant on electric power research, engineering,

and consulting at EnerNex Corporation, Knoxville, TN. His scope of workcovers modeling and simulation of renewable energy sources, power systemoperation and control, and power quality analysis.

Jianhui Wang (M’07) received the B.S. degree in management science and en-gineering and M.S. degree in technical economics and management from NorthChina Electric Power University, China, in 2001 and 2004, respectively, andthe Ph.D. degree in electrical engineering from Illinois Institute of Technology,Chicago, in 2007.He is currently an Assistant Computational Engineer with the Decision and

Information Sciences division at Argonne National Laboratory, Argonne, IL.Dr. Wang is the Chair of the IEEE Power & Energy Society (PES) power

system operation methods subcommittee and Cochair of an IEEE task force onintegration of wind and solar power into power system operations. He is aneditor of the IEEE TRANSACTIONS ON SMART GRID.

Wenzhong Gao (S’00–M’02–SM’03) received the M.S. and Ph.D. degrees inelectrical and computer engineering specializing in electric power engineeringfrom Georgia Institute of Technology, Atlanta, in 1999 and 2002, respectively.His current teaching and research interests include renewable energy and dis-

tributed generation, smart grid, power-system protection, power-electronics ap-plications in power systems, power-systemmodeling and simulation, and hybridelectric propulsion systems.

Cong Liu (S’08–M’10) received the B.S. and M.S. degrees in electrical engi-neering from Xi’an Jiaotong University, China, in 2003 and 2006, respectively,and the Ph.D. degree from Illinois Institute of Technology, Chicago, in 2010.Currently, he is a Postdoctoral Appointee in the Decision and Information

Sciences Division, Argonne National Laboratory, Argonne, IL. His research in-terests include power systems and natural gas systems analysis, optimization,and operation.

A Wavelet-Based Data Compression Technique for Smart Grid

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