Denoising and detrending of measured oscillatory signal in power system

Size: px

Start display at page:

Download "Denoising and detrending of measured oscillatory signal in power system"

Magdalene Fletcher
6 years ago
Views:

1 Dechag YANG 1, Christia REHTANZ 1, Yog LI 1, Qiaji LIU 2, Kay GÖRNER 1 Techische Uiversity of Dortmud (1), ABB (Chia) Limited (2) Deoisig ad detredig of measured oscillatory sigal i power system Abstract. This paper presets a ovel method for deoisig ad detredig of oscillatory sigal measured from wide area measuremet system (WAMS) usig empirical mode decompositio (EMD) ad time-frequecy aalysis. First of all, the measured sigal is decomposed ito a set of itrisic mode fuctios (IMFs) by EMD. Next, the IMFs are divided ito three parts based o their time ad frequecy distributios. The, the oise ad higher frequecy compoets, tred compoets ad meaigful oscillatio modes are idetified respectively. The proposed method are validated by the actual measured sigal from WAProtector ad the estimated tred is cofirmed by comparig with the slidig liear tred estimated method ad other oliear tred estimated methods. Streszczeie. W artykule zaprezetowao ową metodę usuwaia szumu z sygału okresowego w systemach WAMS. W pierwszej kolejości przeprowadza się dekompozycję sygału a fukcje, które astępie dzieloe są a trzy części w zależości od rozkładu czasowoczęstotliwościowego. (Usuwaie szumu i tredu w zmierzoym sygale okresowym systemu WAMS) Keywords: empirical mode decompositio; itrisic mode fuctios; sigal eergy; frequecy distributio estimated tred Słowa kluczowe: szum, tred, WAMS. Itroductio I recet years, Wide Area Measuremet System (WAMS) based Phasor Measuremet Uits (PMUs) has bee built, which provides favorable opportuity to moitor ad aalyze dyamic features of iter-coected power system ear o real time [1,2]. Nevertheless, the iformatio, which cotais useful data ad captured by WAMS, are polluted by kids of oise. It requires outstadig techiques to extract ad estimate the oscillatio modes ad parameters of iterests. Deoisig ad detredig of oscillatory sigal is importat for several reasos. First, the meaigful oscillatio modes are polluted by all kids of oise. Therefore, deoisig is the first step before applicatio of modal idetificatio methods. Secodly, time-varyig treds cotai useful iformatio o the slow ad fast evolutio of system dyamics. Detredig ca trace the slow dyamic variatios i the sigal that relate with the load diversificatio, topological chagig ad cotrollig actios. Further, deoisig ad detredig maybe helpful to isolate ad idetify evets or localized variatios i time that caot be isolated by traditioal statioary models. Formerly, o-statioary time-series models based o both parametric ad oparametric methods have bee utilized with varied success for feature extractio ad modal idetificatio of time-varyig systems. Waveletbased methods have show to be effective i oliear sigal. However the effectiveess depeds o the proper choice of a basis wavelet fuctio, because the choice of the wavelet filters determies the tred model. It is ecessary to have prior kowledge of the sigal. I fact, it is impossible to kow the feature of measured sigal i advace sice power system is a typical time-varyig dyamic system. It limits the applicatio of wavelet i aalysis of the oliear ad o-statioary sigal [3]. Aimig at the shortcomigs of wavelet decompositio, a data-drive techique, empirical mode decompositio (EMD) has show the merit of producig basis fuctios from the sigal itself. EMD has attracted icreasig attetio to tred estimatio based o its self-adaptive ad local ability [4,5]. Paper [4] described the basic priciples, decompositio features ad results aalysis of EMD. As for the tred of oliear sigal, it is cosidered as the residue of the traditioal EMD. For a sigle tred, the EMD expressed good performace whe it was used to aalyze the log term load data ad the tred estimate was give by the residue compoets of the EMD. However, as for the complicated sigal, it is obviously that the residue has less meaig with the actual tred accordig to the defiitio of the EMD processig. Paper [6] applied a iterative algorithm to idetify the tred i PMU data to study electromechaical mode based o the EMD by choosig the accurate high ad low frequecy. Traditioal EMD techique is preseted to idetify the tred ad to deoise from measured power system oscillatios sigal. At the begiig, the importace of tred idetificatio is listed. The performaces of proposed method are compared with the wavelet shrikage techique. However, it does ot give a reasoable ad covicig defiitio about the tred ad oise compoet [5,7]. From above aalysis, the mai problems i uderlyig compoets estimatio are summarized as follows: (1) there is o cosistet defiitio about tred. There are may special defiitios i differet applicatio area. Moreover, the tred relates with the time scale. (2) Most of the metioed methods aalyzed just based o the time domai ad eglected the distributio i frequecy domai ad relatioships betwee differet oscillatio modes. (3) as we kow, there is o paper to aaly the IMFs both from time ad frequecy domai. Aimig at these problems, a ovel method of deosig ad detredig of measured oscillatory sigal form WAMS is preseted i this paper. First of all, measured iformatio is decomposed ito a set of IMFs by EMD. Next, the IMFs are classified ito three parts accordig to the eergy relatioships amog IMFs ad their correspodig distributios i frequecy domai. The, the flow chart of proposed method is itroduced ad the validity ad feasibility of the proposed method are evaluated by the actual measured sigal from WAProtector. Empirical Mode Decompostio (EMD) The EMD is a iterative process which decomposes a time depedet sigal x( ito its ow IMFs. The algorithm diagram of the EMD ca be see i Fig.1 [4]. Fig.1 shows two iteratios i the process of EMD. The iteral iteratio loop is siftig, which is used to extract the IMFs while the exteral loop is the mai iteratios, which is used to defie the umbers of IMFs ad to ed the processig of decompositio. PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN , R. 88 NR 3b/

2 The oliear ad o-statioary sigal ca be decompositio ito a set of IMFs based o the EMD. The decomposed results ca be expressed as follows: (1) x( c ( r( j1 c j ( is the IMFs; is the umber of IMFs; r( meas the residue of the sigal. Fig. 1 The flow chart of EMD Time-frequecy aalysis of IMFs I this sectio, a ovel method to determie the oscillatory meaigful modes cotaied i the measured data is proposed based o the time-frequecy aalysis. As for the time domai, it is clear that the meaigful compoets have higher eergy tha the higher frequecy compoets or oises. Further more, Huag has poited that although the results of EMD caot be proved orthogoal i theory, the practical decompositio result usually is ear orthogoal. Therefore, the eergy of the origial sigal is equals to the sum of IMFs eergies ad residue s eergy. I paper [8], the author proposed a method to calculate the eergy of sigal. The basic priciples of this method are itroduced i this part. For a specified sigal (, the eergy criterio is described as follows: t (2) E 2 2 ( dt 0 t 1 E 0 is the eergy of origial sigal; t 1 is the start time; t 2 is the start time. The discretized form of (2) ca be expressed as: N 2 (3) E0 i1 After the EMD, the origial sigal ( is decomposed as several IMFs ad oe residue. The, (4) Esum Er Eimf j i1 E sum is the total eergy of IMFs ad residue; E r is the eergy of the residue; E imf(i) is the eergy of the i th IMF. (5) E E 0 100% E 0 is the eergy decompositio error. Actually is ca be used to idicate the orthogoality of EMD, if equals to zero, it meas the IMFs are fully orthogoal. (6) i 100% Eimf i1 E imf (i) is the eergy coefficiet of IMFi. This parameter is used to describe the eergy relatios amog IMFs. Obviously, the eergies of IMFs which stads for the meaigful oscillatio modes are higher. Accordig to the theory i paper [9,10], the mea values of IMFs cotias help iformatio i determig the oise ad iterestig oscillatio mode. By decompositio, the umber of extrema decreases whe goig from oe residual to the ext, thus guarateeig that the complete decompositio is achieved i a fiite umber of steps. However, differet siftig stop criterios will affect the umbers of IMFs ad their correspodig mea values. Here, the mea values are proposed as a supplemetal criterio to calculate the umber of IMFs which cotai the pletiful oscillatory iformatio. A key property of the EMD is its ability to act as a filter. Actually, the processig of EMD ca be cosidered as the separatio of differet frequecy compoets. First, the Higher Frequecy Compoets (HFCs) or oises are extracted ad they are deoted as the fore IMFs. The, the meaigful compoets which are polluted by oise i origial sigal are idetified ad they are saved as the middle IMFs. Next, the Artificial Compoets (ACs) or Ultra Low Frequecy Compoets (ULFCs) are left. Ad the last extracted fuctio is usually mootoe, or has oe extrema. It is called as the residue. For the frequecy domai, it has bee obviously proved that the rage of the low frequecy is 0.1Hz-2.5Hz. Therefore, the frequecies of IMFs which located fully or partially i metioed rage ca be cosidered as the physically meaigful compoets. Accordig to above desicripitio ad the priciples of EMD, the decompositio results of complex measured data ca be rewritte as the geeral form [5]: (7) x( j1 c ( r( j p c ( i i1 NoiseHFCs r c ( k k p1 Physically meaigful compoets c ( r( l lr1 ACsULFCs c i ( is the HFC or oise ad p is correspodig umber; c k ( is the IMF cotais the meaigful compoets ad r-p is the umber; c l ( is the AC or ULFC ad -r is the correspodig umber. r( is the residue. By deoisig the HFC or oise ad by detredig the ULFC or AC as well as redidue, the uderlyig pheomea of iterest ca be selected as the oscillatory modes. Fig.2 The sketch diagram of proposed method Proposed method From above aalysis, there are three criterios imposed o the decomposed results of EMD. The eergy ad mea value are the evaluatio idexes i time domai while the 136 PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN , R. 88 NR 3b/2012

3 frequecy distributio is the criterio i frequecy domai. The flow chart of the proposed method used for detredig ad deoisig is show i Fig.2. Actual applicatio to measured data from WAProtector Geerally, it is difficult to get the real-time operatio data from trasmissio level because of the cosideratio of busiess beefit ad competitio. Therefore, the measured iformatio from distributio side is helpful to aalyze the oscillatio dyamic ad tred. Here, the WAProtector system [11] is used for presetatio of realtime measured data obtaied from WAMS, real-time calculated values ad archived data. The locatios of PMUs i UCTE (Uio for the Coordiatio of Trasmissio of Electricity) are istalled as Fig.3. GPS From Fig.4, it is clear that the measured sigal has typical oliear ad ostatioary characteristics. It is heavily polluted by all kids of oises, icludig the small burrs ad ear Gauss white oises. The, the proposed sigal is employed to deoise ad detred. Firstly, EMD is used to decompose measured sigal ito a set of IMFs ad oe residue. The decomposed results is show i Fig.5. From the decomposed results i Fig.5, it is clear that there are 11 IMFs ad oe residue. This residue is mootoe ad it just stads for the simple directio of the origial sigal. Obviously, it is ot reasoable whe the residue is oly cosidered as the tred of the sigal. Moreover, the tred i measured sigal has direct relatios with the time scale. I Fig.4, we ca see that the tred is icreasig from 23:58 to 24:00 while it is decreasig from 24:00 to 00:01. There is a abrupt desced ear 24:00 ad a obvious protuberace ear 00:01 respectively. From the time domai aalysis, the eergy coefficiet of every IMFs are calculated based o (2-6). The results are show i Fig.8 Data Ceter Fig.3 Simplified geographical scheme of studied system From 23:58:00, Feb, 23, 2011 to 00:20:00, Feb, 24, 2011, there was a obvious dyamic oscillatio durig this period. The frequecy sigal i Dortmud is show i Fig.4. Fig.6 The eergy coefficiet of IMFs The last IMF cotais the most eergy ad the value is ear 50% of total eergies of IMFs. Next, the eergy of IMF6 is ear 33%. Furthermore, IMF9 ad IMF10 also have obvious eergies. The eergies of other IMFs are small. I order to explore the features of IMFs more clearly, the mea values of IMFs are calculated ad the results are show i Fig.7. Fig.4. The frequecy sigal i Dortmud durig recorded time Fig.7 The computed meas of IMFs Fig.5 Decompositio results of measured sigal It ca be see from Fig. 7 that: (1) the mea value of IMF is becomig bigger ad bigger with the further decompositio; (2) the mea values of IMF1-IMF4 is smaller comparig with other IMFs; (3) IMF5 ca be cosidered as the kot or kee of the calculated values. Accordig to the priciples of EMD, each IMF ca be cosidered as oe AM-FM sigal ad has special frequecy distributio i frequecy domai. Here, Fast Fourier Trasform (FFT) is utilized to aalyze the frequecy distributio of every IMF. The calculated frequecy spectrums of origial sigal ad IMFs are show i Fig.8. The logarithmic form is employed i order to display the results more clear i the low frequecy area. PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN , R. 88 NR 3b/

Fig.8. Frequecy distributios of IMFs I Fig.8, we ca see that the frequecy distributios of all the IMFs ca be divided ito three parts: 1-10Hz, 0.1-1Hz

Therefore, they are cosidered as the higher frequecy compoets or oises. The frequecies of IMF8-IMF11 are i the rage of 0.003-0.1Hz.

8, the frequecies of IMF5, IMF6 ad IMF7 are located i the same frequecy as the rage of low frequecy oscillatio. All of them are take as the meaigful compoets i the oliear ad oatatioary sigal.

4 Fig.8. Frequecy distributios of IMFs I Fig.8, we ca see that the frequecy distributios of all the IMFs ca be divided ito three parts: 1-10Hz, 0.1-1Hz ad Hz. The frequecies of IMF1-IMF4 are all i the high frequecy rage. They are the same as the higher frequecy distributio of origial sigal. Therefore, they are cosidered as the higher frequecy compoets or oises. The frequecies of IMF8-IMF11 are i the rage of Hz. They are cosidered as the lower frequecy compoets i the origial sigal. Actually, the frequecy rage of low frequecy oscillatio is 0.1-1Hz. From Fig.8, the frequecies of IMF5, IMF6 ad IMF7 are located i the same frequecy as the rage of low frequecy oscillatio. All of them are take as the meaigful compoets i the oliear ad oatatioary sigal. Detredig ad deoisig idetificatio Detredig ad deoisig processes ca be implemeted based o the time ad frequecy domai. Accordig to (7), the aalyzed sigal ca be rewritte as: x( 4 i 1 IMF ( i 7 k5 IMF ( k 11 l8 IMF ( r( The, the oises or HFCs ad the extracted oscillatory modes are show i Fig 9. (a) l origial waveform best. The tred is idetified by subtractig the detred sigal from the origial waveform. It ca be observed that the detred.m is just suitable for the liear sigal. It could omit some major tred features i oliear ad ostatioary origial waveform. I order to deal with the oliear sigal, we proposed a slidig detred method. First of all, the sigal is broke ito several segmets ad the liear treds for each segmet are calculated. The the averagig meas of these treds are located ad smoothed by slidig widow. The smoothed lie is cosidered as the tred of whole sigal. I fact, the size of widow should be adjusted accordig to the features ad time scales of origial. Here, the size of widow is set as 500 (the legth of time spa is 10s) ad the estimated tred is show i Fig.10. Wavelet shrikage ca be selectively used to approximate the origial sigal to ay order of accuracy ad leads to a fier recostructio of system motio. For the selected sigal, a decompositio level of 10 is chose for the wavelet shrikage approach ad the db4 is chose as the specific wavelet. The 8th level recostructio of sigal is also show i Fig.10. Accordig to the theory proposed by A.R. Messia i paper [7], the local meas of the first siftig step of IMF1 (or the time average of the first siftig step of IMF1 ad first siftig step of IMF2) also is approximated as the tred of the origial sigal. However, the selected sigal is heavily polluted by the oises, it is ot correct if we extract the local meas of the first siftig step as the tred. From the eergy ad frequecy distributio aalysis, IMF1 to IMF4 are all extracted as the oises or HFCs. Hereby, the left sigal compoets is reset as the ew sigal. The the calculated time average of local meas both the first siftig step of IMF1(the IMF5 of origial sigal)ad the first siftig step of IMF2 (the IMF6 of origial sigal) is approximately thought as the tred ad the results is also show i Fig.10. From the aalysis i both time ad frequecy domai, IMF8, IMF9, IMF10 ad IMF11 are divided ito the tred part. Therefore, the estimated tred is extracted ad show i Fig.10 based o the proposed techique. (b) Fig.10.Comparisos of estimated treds Fig.9 Idetificatio results by proposed method. (a) oise or HFCs; (b) meaigful oscillatio modes I order to evaluate the performaces of the proposed method i estimatig the tred, the treds idetified by slidig detred fuctio, wavelet decompositio ad local mea method are compared. I paper [12] the fuctio of detred.m is described. This method is used to idetify a straight lie, which ca fit the Accordig to the treds estimatio, the mai coclusios are summarized as follows: (1) All the metioed methods ca be used to extract the tred from oliear ad ostatioary sigal. (2) The performaces of slidig detred method depeds o the size of widow. It is ecessary to have pletiful kowledge about the sigal i advace. (3) Local Mea method ca be used to extract the treds. However, the performace is easily affected by the oise. It ca be used to aalyze the measured sigal from the simulatio model. (4) Both the wavelet shrikage ad the proposed method have the good performaces i determie the tred. The wavelet shrikage relates with the wavelet fuctio ad the decompositio level while the proposed method is based o the eergy of the sigal which is more reasoable to explore the dyamic features of sigal. It is 138 PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN , R. 88 NR 3b/2012

5 obvious that the proposed method presets a powerful choice to separate the tred ad oscillatio mode uder the oise polluted circumstace. Coclusios As the first step of dealig with the measured sigal from WAMS, detredig ad deoisig have sigificat importace i extractig the meaigful iformatio ad oscillatory modes. I this paper, a ovel detredig ad deoisig method which cosiders the features of sigal both i time ad frequecy domai is proposed. Sigal eergy algorithm is proposed to calcualte the eergy of each IMF i time domai, while the FFT is used to aalyze the frequecy distributio. The complex oliear ad ostaioary sigal is divided ito three parts based o proposed techique. The proposed method are validated by the actual measured sigal from WAProtector ad the estimated tred is cofirmed by comparig with the slidig liear tred estimated method ad other oliear tred estimated methods. REFERENCES [1] Kamwa I, Belad J, Trudel G, et al. Wide-area moitorig ad cotrol at Hydro-Quebec: Past, preset ad future. Proceedigs of IEEE Power Egieerig Society Geeral Meetig, Motreal, Caada, [2] A.G. Phadke, R.M. de Moraes, The Wide World of Wide-Area Measuremet, IEEE Power ad Eergy Magazie, 6(2008), No.5, [3] Toa R, Beqlilou C, Espua A, et al. Dyamic data recociliatio based o wavelet tred aalysis, Idustrial & Egieerig Chemistry Research, 44(2005), No. 12, [4] Huag N. E, She Z, Log S. R. The empirical mode decompositio ad Hilbert spectrum for oliear ad ostatioary time series aalysis. Proceedigs of the Royal Society of Lodo, 454(1998), [5] Messia A.R, Vittal V, Heydt G. T et al. Nostatioary Approaches to Tred Idetificatio ad Deoisig of Measured Power System Oscillatios IEEE Tras. Power systems, 24 (2009),No. 4, [6] Zhou N, Trudowski D, Pierre J. W. et al.a Algorithm for Removig Treds from Power-System Oscillatio Data. Proceedigs of IEEE power Egieerig Society Geeral Meetig, [7] Messia A R. Iter-area oscillatios i power systems a oliear ad o-statioary perspective. Berli, Spriger Press, [8] Mu G, Shi K, A J, et al.sigal eergy method based o EMD ad its applicatio to research of low frequecy oscillatio. Proceedigs of the CSEE, 28(2008), No.19, (i chiese) [9] Fladri P, Rillig G, Goçalvés P. Empirical mode decompositio as a filter bak. IEEE Sigal Process. Lett, 11(2004), No.2, [10] Fladri P, Goçalvés P, Rillig G. Detredig ad deosig with empirical mode decompositios. Proceedigs of the Europea Sigal Processig Coferece (EUSIPCO '04), Aalborg,Demark,2004. [11] Babik Tadeja, Gabrijel Uros, Mahkovec Boja,et al. Wide Area Measuremet System i Actio IEEE Lausae Power Tech, Lausae, Switzerlad [12] Matlab User's Guide, versio , The MathWorks, Ic., Ja Authors: M.-Sc.Dechag Yag.Istitute of Power Systems ad Power Ecoomics, Emil-Figge-Str. 70, Dortmud, Germay. yag.dechag.cau@gmail.com; Prof. Dr.-Ig. Christia Rehtaz.Istitute of Power Systems ad Power Ecoomics, Emil-Figge-Str. 70, Dortmud, Germay. Christia.Rehtaz@tu-dortmud.de The Correspodece address ad the are: Dechag Yag, Raum 2.16 Gebäude BCI-G2. 2. Etage Emil-Figge-Straße 70 Dortmud 44227, Germay Phoe: yag.dechag.cau@gmail.com PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN , R. 88 NR 3b/

A THRESHOLD DENOISING METHOD BASED ON EMD

Joural of Theoretical ad Applied Iformatio Techology 1 th Jauary 13. Vol. 47 No.1-13 JATIT & LLS. All rights reserved. ISSN: 199-864 www.jatit.org E-ISSN: 1817-319 A THRESHOLD DENOISING METHOD BASED ON