DATA COMPRESSION OF POWER SYSTEM DATA FOR NETWORK OPERATION AND CONTROL USING WAVELET TRANSFORMS

Transcription

1 DATA COMPRESSION OF POWER SYSTEM DATA FOR NETWORK OPERATION AND CONTROL USING WAVELET TRANSFORMS Tim B. LITTLER The Quee's Uiversity of Belfast - Uited Kigdom t.littler@qub.ac.uk ABSTRACT Wavelet trasforms itroduce ew classes of basis fuctios for time-frequecy sigal aalysis ad have iheret properties that are particularly useful for the compressio of aalogue poit o wave trasiet ad disturbace power system sigals. This paper examies the compressio properties of the discrete wavelet ad evaluates the trasform usig actual power system data. The results preseted i the paper idicate that compressio ratios up to : with acceptable distortio are achievable. The paper discusses the applicatio of wavelet compressio for rapid iformatio access ad exchage i etwork operatio ad cotrol. INTRODUCTION Power systems are frequetly affected by faults, which give rise to trasiets ad disturbaces o the power etwork. Trasiet ad disturbace faults ad evets, moitored by digital fault recordig istrumetatio or protectio relays (with fault recordig), are geerally stored as composite aalogue ad digital time-tagged fault records. The records are typically trasferred over commuicatios liks to a utility cotrol cetre for fault reportig, aalysis ad archival. The records provide useful iformatio for fault aalysis, assessmet ad adjustmet of protectio, plat coditio moitorig, ad maiteace. The prospect of gaiig access to composite data for etwork operatio ad cotrol provides obvious beefits for etwork maagemet provided that rapid ad efficiet iformatio exchage is guarateed. The mai limitatio of remotely accessig poit o wave data is the time required to trasfer the volume of data that costitutes a fault icidet. Fault records ca be large (> Kbytes per record) ad the commuicatios lik ca preset a bottleeck if it is limited by badwidth or peripheral modem speed. The problem is compouded if system moitorig ivolves a large umber of uits. Thus compressio of the data coupled with high-speed commuicatio liks is essetial to icrease badwidth ad reduce commuicatios trasfer time. Wavelet trasforms provide a versatile ad adaptive method of implemetig efficiet data compressio for aalogue data with iheret provisio for fast ad icremetal retrieval of data usig multiresolutio compactio of large data sets. A data compressio scheme usig wavelet trasforms ivolves sigal pre-processig by wavelet aalysis to alter the statistical bias of the data to improve compressibility. A compressio scheme usig a filter or trasform to aalyse (or pre-process) the raw sigal data prior to loss-less compressio is geerally kow as trasform compressio. A trasform scheme for compressio ad codig has evolved from applicatios i speech ad image codig [, 2]. Data compressio algorithms cotaied i MP3, MPEG, ad JPEG formats for music, video, ad still image compressio, respectively, each rely o acceptable lossy trasform preprocessig to extract the iformatio cotet from each data stream, prior to loss-less compressio by a symbolic codig algorithm. I a trasform compressio scheme, the aalysig trasform extracts the iformatio cotet of the sigal to yield a trasform vector with coefficiet amplitudes determied by sigal expasio across the trasform domai. The vector is scalar quatised, to assig more bits to higher amplitude trasform coefficiets ad fewer bits to lower amplitudes. A quatisatio scheme may be as simple as roudig or trucatig floatig-poit values to fixed-poit itegers. The quatised coefficiets are symbolically compressed usig loss-less etropy or a dictioary based codig scheme, such as arithmetic codig. Whe symbolically coded the output sequece is geerally shorter tha the origial sigal, cotaiig oly the iformatio which best matched the aalysig trasform, Figure. The basis of trasform compressio is thus that sparse trasform coefficiets are themselves more easily compressed, rather tha the origial sigal samples. S() Trasform Filter (T) Quatizer (Q) Etropy Coder (E) Figure : A scheme for data compressio usig trasform pre-processig y() I this paper, the expasio properties of the discrete wavelet trasform are briefly cosidered. A data compressio scheme usig wavelet trasforms is itroduced, with results obtaied from the applicatio of the scheme to sampled power system data. WAVELET TRANSFORMS A wavelet trasform expads a sigal i terms of the chose basis wavelet usig the traslatio (shift i time) ad dilatio (compressio i time) of the wavelet. If the basis wavelet is chose correctly, the wavelet trasform will provide a expasio that is localised i time ad frequecy yieldig QUB_Littler_B Sessio 3 Paper No

2 wavelet coefficiets at differet scales, [3]. The wavelet expasio cotrasts with the Fourier trasform where the aalysig basis fuctio is a fixed trigoometric polyomial ad the expasio of the sigal is ormally restricted to frequecy localisatio with a loss of time referece (although this limitatio ca be miimised usig a widow). The dual time-frequecy localisatio property at differet scales gives the wavelet trasform much greater compact support for the aalysis of sigals with short term trasiet compoets ad also meas that more eergetic wavelet coefficiets are localised ad therefore sparse, i the trasform domai, thus providig a basis for data compressio. Wavelet aalysis is based o the decompositio of a sigal accordig to scale, rather tha frequecy, usig basis fuctios with adaptable scalig properties. This method of aalysis is geerally referred to as multiresolutio aalysis. A rage of basis fuctios has bee mathematically derived for the purpose of multiresolutio aalysis. The multiresolutio aalysis of a sigal usig the discrete wavelet trasform (DWT) yields approximatio ad detail coefficiets from the origial sigal by covolutio of the sigal with low-pass filter coefficiets, represeted by h(), ad high-pass filter coefficiets, represeted by g(), derived from a chose aalysig basis wavelet at differet scales, Figure 2, [4]. The choice of aalysig wavelet determies the degree of timefrequecy localisatio ad correspodig eergy of the wavelet coefficiets. The aalysig wavelet is used i a DWT filter cofiguratio as the basis fuctio to expad the sigal to yield a cotiguous vector of approximatio ad detail wavelet coefficiets at differet scales. The expasio of a sigal, S(), by the aalysig wavelet, represeted by ϕ(), i a DWT filter cofiguratio is based o iterative traslatio (represeted by j) ad dilatio (represeted by k) of the sigal parameterised as S j,k. covolutio with h() ad g() i a DWT filter cofiguratio such that approximatio (S j,k ) ad detail (D j,k ) coefficiets are created by: S j k = h 2kS j+,, (2) D j k = g 2kS j+,, (3) The coefficiets are decimated after iteratio of expressio (2) ad (3) thereby dow-samplig the previous sequece to elimiate redudat iformatio, [4, 5]. The aalysis is referred to as decompositio ad the expressios show that the calculatio of the coefficiets proceeds hierarchically. A quadrature mirror filter (QMF) is used to implemet the DWT filter cofiguratio such that the clusters of output coefficiets are cocateated to produce the wavelet coefficiet vector, Figure 3. S() FIR LP 2: FIR HP 2: FIR LP 2: FIR HP 2: FIR LP2 2: FIR HP2 2: S(j,k) = {sss} 2 D(j-3,k) = {dss} 3 D(j-2,k) = {ds, ds} 4 D(j-,k) = {d, d, d2,d3} Figure 3: A QMF cofiguratio with low ad high pass elemets.2 Amplitude Time (ms) Figure 2: A aalysig wavelet used as a expadig basis fuctio The QMF bak creates a series of decompositio levels at differet scales with the output coefficiets cocateated at each level. The multiresolutio expasio of a sigal creates sparse coefficiets thus capturig the iformatio i a sigal usig a small umber of eergetic coefficiets, Figure 4. The maximum umber of scaled levels of S() is defied by l = log 2 N where N is the sigal legth. If a orthoormal aalysig wavelet is used for sigal expasio, the sigal may be directly recostructed from the coefficiets usig the same QMF bak ad filter coefficiets by iterpolatig each level as determied by the expressio: If it is assumed that the discrete sigal already represets a approximatio at a scale j =, the startig poit for the DWT is the primitive fuctio: = S ( f ϕ k) () ( ), k k The aalysis proceeds by expadig S,k through discrete S + = 2 h 2 S + 2 g 2 D j, k k j, k j, (4) Z Z WAVELET COMPRESSION A data compressio scheme usig the DWT to pre-process QUB_Littler_B Sessio 3 Paper No

3 Split Level (s) the data was developed as part of the research recorded i this paper. A compressio scheme was established usig loss-less codig of the trasform coefficiets. DWT trasform. The distortio of the recostructed sigals were assessed by evaluatig the sigal to oise ratio (SNR), ad (ormalised) percetage root mea square (RMS) measures of sigal distortio (PRD): - SNR( db) = Log 2 ( S( ) ) (5) 2 ( S( ) S' ( ) ) The PRD was determied by takig the iverse of equatio (5) ad expressig the result as a percetage. The recostructio, S () was compared with the origial sigal, S(), i each case APPLICATION AND RESULTS Frequecy[Time] Figure 4: Wavelet coefficiets geerated at differet scales A threshold T was applied to further improve coefficiet compressibility by selectig eergetic coefficiets above the threshold ad settig to zero those below, Figure 5. A detailed descriptio of this method of compressio is cotaied i [, 4]. The compressio ratio was defied by the parameter C r = N / K e where K e is the umber of absolute eergetic coefficiets retaied at a specific scale, i.e. K e T, ad N the total umber of sigal samples. A pricipal applicatio for the proposed scheme has bee the efficiet compressio of poit o wave data i order that the data might be used i cojuctio with additioal Remote Termial Uit (RTU) data from Supervisory Cotrol ad Data Acquisitio (SCADA) systems to provide greater iformatio for etwork operatio decisios ad ear real-time cotrol actios. Although RTU systems provide local measuremets of aalogue voltage ad curret, amog other substatio parameters, i geeral the measuremets are ormally restricted to RMS or istataeous values from regular pollig of acquisitio uits, [7]. I the evet of a fault or maloperatio, however, the ability to visualise a sequece of time-tagged evets, from pre-fault through to post-fault, across a wide umber of aalogue ad digital circuits meas that a protectio or cotrol egieer is capable of providig a iformed respose to a icidet usig the additioal iformatio derived from fault records. Thus the target applicatio for the proposed wavelet-based compressio scheme is the acquisitio platform, (DFR, DPR, or ative RTU uits), used to sample local poit o wave data. The essece of the proposed scheme is therefore that if the data ca be effectively compressed without excessive loss of feature itegrity, ad rapidly trasferred across a commuicatio lik i a acceptable time frame, it may be used to remove ucertaity i etwork ad cotrol decisio processes. Figure 5: Coefficiet selectio usig a threshold The quatised coefficiet vectors produced by each trasform were compressed usig the forward Lempel-Ziv-Welch (LZW) algorithm. The LZW algorithm is widely used for loss-less compressio of differet types of data, icludig image ad text, [6]. The compressed sigals were subsequetly decompressed usig the iverse LZW algorithm, ad the sigals recostructed from the coefficiet vectors usig the iverse Two applicatios of the proposed scheme are preseted i the followig case studies. The first applicatio describes the proposed scheme usig a voltage sigal derived from a distributio level cable fault. The secod applicatio uses a complete fault record from a trasmissio level coductorclashig icidet. 33 kv Distributio Level Cable Fault I particular applicatios a reduced SNR (or PRD) may be tolerable if the data is urgetly eeded to determie the active state of a moitorig ode i the etwork. The sigal used i this example provides a istace where reduced SNR is perhaps tolerable. The sigal ad was obtaied from a 33 kv QUB_Littler_B Sessio 3 Paper No

4 cable fault recorded by a DFR istalled at the supply itake poit (32 kv) of the distributio substatio. The 2-bit sigal was sampled at 48 Hz. The fault was later established as damage to a cable caused by cotractor s mechaical equipmet. Voltage (kv) Time (ms) Figure 6: Cable fault sigal from a 33 kv distributio feeder The sigal i Figure 6 shows a voltage dip from 33 kv to 7.8 kv with fault clearace by the local protectio withi ms. The sigal icludes small iceptio trasiets at the begiig ad ed of the fault voltage. The sigal was compressed by a DWT, usig a Symmlet -poit aalysig basis fuctio (with 4 levels of decompositio), ad five applied threshold values, (C r = 2:, 4:, :, 2:). The sigal was recostructed i each case from the remaiig coefficiets ad the recostructios plotted i ascedig order i Figure 7. A SNR measure was computed i each case ad marked beside each sigal. I this example, the particular area of iterest was the depth ad duratio of the voltage dip. The depth idicates the severity of the fault ad the duratio reveals how quickly the protectio maaged to clear the fault. 5 Cr = 2: SNR = db Cr = 4: SNR = db Cr = : SNR = db Cr = 2: SNR = 5.4 db Time (ms) Figure 7: Recostructios of Figure 6 with differet compressio ratios Both parameters are key idicators of utility power quality ad the accurate measuremet of each dip is importat to esure that the protectio does ot sustai its operatio for ay loger tha is absolutely required such that sesitive loads (semicoductor ad process fabricatio plats, for example) ca ride-through the dip ad ot be affected. If a dip has bee accurately recorded ad quatified, the utility protectio policy ca adjust the protectio settigs to reduce the duratio of subsequet dips. The recostructio sigals i Figure 7 show that the sigal character ad localised trasiet structures were preserved by the DWT dow to the threshold for C r = : with a calculated SNR = 25.4 db (PRD = 5.3%). The pre-fault voltage for the recostructio (C r = :) was measured as 32.9 kv ad the fault voltage as 7.2 kv. At C r = 2:, the sigal was sigificatly distorted ad would geerally be usuitable for measuremet purposes. 4kV Coductor Clashig Icidet The fault record i Figure 8 was derived from a coductorclashig icidet o a 4 kv trasmissio lie. The 2-bit sigals were sampled at 24 Hz for 23 ms duratio. The voltage ad curret chaels each had 496 iteger-word samples ad the file size was bytes. Although displayed, the digital protectio circuit chaels were ot icluded i the tests. I a complete compressio scheme the digital chaels ad record text iformatio would be separately compressed by a loss-less method (such as LZW) ad stored with the compressed aalogue chaels. The record was aalysed by the DWT usig a Daubechies-2 aalysig basis fuctio ad the wavelet coefficiets quatised ad compressed by the LZW algorithm. The compressed record was ecoded by a simulated modemcodig algorithm (Shao-Fao ecoder) ad trasmitted over a simulated public switched telephoe lie (PSTN) lie usig a XMODEM K protocol at 92 baud. The simulated PSTN lie efficiecy was set to.75 ad baud rate assumed to be equivalet to umber of bits per secod, with bits/byte asychroous data trasmissio (8 data bits + 2 start ad stop frame bits). The compressed record was recostructed at the receivig ed by the iverse LZW ad DWT algorithms. As a test of the performace of wavelet pre-processig, each sigal from the record was directly compressed usig the LZW algorithm (with o pre-processig). The origial (ucompressed) ad direct LZW compressed records were also trasferred over the same lie for compariso. The compressed file size for each aalogue chael was determied from direct applicatio of the loss-less LZW algorithm ad (lossy) DWT + LZW compressed records, Table. The PRD figures i Table represet the distortio itroduced by the lossy pre-processig of the DWT algorithm ad quatisatio process. QUB_Littler_B Sessio 3 Paper No

5 The results i Table idicate that wavelet pre-processig sigificatly reduces chael size, with compressio of sigals to < % of origial size, compared to direct LZW compressio of each sigal. The improvemet was attributed to the property of aalysig basis wavelet to capture the iformatio cotet of a sigal ad retai feature itegrity. x3 Vr x3 Vy x3 Vb x2 Ir x2 Iy- x2 Ib- x8 I Mesh #2 at Trasmissio Circuit,2:46: Sat 4 Mar 995 (63) Aalogue over o chael 2 'Iy ' FPFM FPFM T/R FMFP L.S. FMFP H.S FIRST I/T FPSM FPSM T/R FPSM COMP SPARE SECOND I/T FEEDER END M/C4 PROT SGT4 T/R Figure 8: Fault record from coductor clashig icidet This wavelet pre-processig accouts for the similar size, 8%, of each compressed chael. The distortio icurred by each chael was miimal with PRD figures <%. As aticipated, the PRD figures show that the chaels with highest distortio were those with lower dyamic rage ad reduced sigal-to-quatisatio oise ratio (SQNR), chaels Ib ad I. Chael LZW DWT + LZW PRD Ir 3% 7.5%.7% Iy 3.7% 7.6%.3% Ib 29.8% 8.6% 7.9% I 26% 8.5% 8% Vr 59% 8.8% 4.8% Vy 48.2% 8.8% 2.8% V 6.9% 8.7% 3.7% I 39.9% 9% 7.7% Table : Compressed file size ad PRD distortio The resultat size of the LZW ad DWT + LZW compressed files was bytes ad 556 bytes, respectively. The trasfer time (i secods) for the origial, LZW ad DWT + LZW records was measured ad tabulated, Table 2. The figures i Table 2 reflect the data trasfer times oly, igorig the modem coect ad discoect sequece times. The trasfer times show that the DWT + LZW record was trasferred across the PSTN lie approximately 2 times faster tha the origial record. The sigificat reductio i commuicatios time meas that the proposed method has potetial for real-time applicatios i protectio telemetry ad cotrol, fault recordig, ad differetial protective relayig schemes. Origial LZW WPT + LZW 45.5 s 8.5 s 3.8 s Table 2: Trasfer time at 92 baud for a typical SCADA RTU modem CONCLUSION This paper has examied the aalysis properties of the discrete wavelet trasform as a method of pre-processig to improve the compressibility of a sigal. The basis of the scheme described i the paper is that a loss-less compressio algorithm ca more effectively reduce the size of a sigal by ecodig the wavelet coefficiets rather tha the origial sigal samples. The wavelet trasform provide beeficial aalysis properties for sigals that cotai trasiets ad localised short-term evets. Additioal research is required to establish wavelet basis fuctios that best represet idividual trasiet ad short-duratio features ad provide a optimum basis for data compressio. The results recorded i the paper idicate that compressio ratios up to : with acceptable measurable ad visible distortio are achievable. Although it is coceded that the wavelet pre-processig is a lossy step, the results obtaied i this research cofirm that i certai istaces miimal distortio of a sigal may be acceptable if rapid access to poit o wave sigals is provided. The purpose of usig the proposed method is to reduce the data commuicatios burde across existig serial ad modem based commuicatios systems to improve the level of iformatio that is accessible for protectio ad cotrol decisio makig. This paper forms part of o-goig research ito data compressio schemes for power system data. REFERENCES [] Mallat S.G., A Theory for Multiresolutio Sigal Decompositio: The Wavelet Represetatio, IEEE Tras. o Patt. Aalysis ad Machie Itell., Vol., No.7, July 989. [2] Meyer Y., Wavelets: Algorithms ad Applicatios, SIAM Publicatio, Philadelphia, 993, pp. 3-3 ad -5. [3] Daubechies I., The Wavelet Trasform: Time Frequecy Localizatio ad Sigal Aalysis, IEEE Tras. o Ifo. Theory, Vol. 36, No. 5, Sep. 99. [4] Strag. G., Nguye T.Q., Wavelets ad Filter Baks, Wellesley-Cambridge Press, 996. [5] Daubechies I., Orthoormal Bases of Compactly Supported Wavelets, Comm. o Pure ad Appl. Math., Vol. XLI, 988, pp [6] Ziv J., Lempel A., A Uiversal Algorithm for Sequetial Data Compressio, IEEE Tras. o Ifo. Theory, Vol. IT-23, No. 3, May 977. [7] Shepherd B., Tobias J.C., Cochet-Muchy A., Experiece o the Serial Iterfacig of Protectio QUB_Littler_B Sessio 3 Paper No

6 Relays to Telecotrol Systems., Proc. 6th IEE Iteratioal Coferece o Developmets i Power System Protectio, Publicatio No. 434, pp , 997. QUB_Littler_B Sessio 3 Paper No