Measurement based method for online characterization of generator dynamic behaviour in systems with renewable generation

Transcription

1 Papadopoulos, Panagots. and Papadopoulos, Theoflos A. and Chrysochos, Andreas I. and Mlanovć, Jovca V. (8) Measurement based method for onlne characterzaton of generator dynamc behavour n systems wth renewable generaton. IEEE Transactons on Power Systems. ISS , Ths verson s avalable at Strathprnts s desgned to allow users to access the research output of the Unversty of Strathclyde. Unless otherwse explctly stated on the manuscrpt, Copyrght and Moral Rghts for the papers on ths ste are retaned by the ndvdual authors and/or other copyrght owners. Please check the manuscrpt for detals of any other lcences that may have been appled. You may not engage n further dstrbuton of the materal for any proftmakng actvtes or any commercal gan. You may freely dstrbute both the url ( and the content of ths paper for research or prvate study, educatonal, or not-for-proft purposes wthout pror permsson or charge. Any correspondence concernng ths servce should be sent to the Strathprnts admnstrator: strathprnts@strath.ac.uk The Strathprnts nsttutonal repostory ( s a dgtal archve of Unversty of Strathclyde research outputs. It has been developed to dssemnate open access research outputs, expose data about those outputs, and enable the management and persstent access to Strathclyde's ntellectual output.

2 Ths artcle has been accepted for publcaton n a future ssue of ths journal, but has not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TPWRS , IEEE > REPLACE THIS LIE WITH YOUR PAPER IDETIFICATIO UMBER (DOUBLE-CLICK HERE TO EDIT) < Measurement based method for onlne characterzaton of generator dynamc behavour n systems wth renewable generaton Panagots. Papadopoulos, Member, IEEE, Theoflos A. Papadopoulos, Senor Member, IEEE, Andreas I. Chrysochos, Member, IEEE, Jovca V. Mlanovć, Fellow, IEEE Abstract Ths paper ntroduces a two-step methodology for onlne dentfcaton of the partcpaton of generators n power system oscllatory modes, based on measured responses. The domnant modes n generator measured responses are ntally dentfed usng a mode dentfcaton technque and then ntroduced, n the next step, as nput nto a clusterng algorthm. Crtcal groups of generators that exhbt poorly or negatvely damped oscllatons are dentfed, n order to enable correctve control actons and stablze the system. The uncertantes assocated wth the operaton of modern power systems wth Renewable Energy Sources (RES) are nvestgated as well as the mpact of the dynamc behavor of power electronc nterfaced RES. Index Terms clusterng, onlne dynamc securty assessment, renewable generaton, uncertantes, unsupervsed machne learnng. D I. ITRODUCTIO URIG the past years there has been a substantal ncrease n the nstallaton of Renewable Energy Sources (RES), manly drven by clmate change and varous socal, economc and techncal reasons. RES are ntermttent n nature whch s one of the man reasons for the change n power system operatng condtons, power flows and topology. Ths coupled wth the fact that they exhbt dfferent dynamc behavour than conventonal generators leads to both spatal and temporal varaton n power system dynamcs and consequently operaton under hgh uncertanty. Apart from the Ths work was supported by the EPSRC project ACCEPT under EPSRC- Inda collaboraton scheme (grant number: EP/K3673/). The work of A. I. Chrysochos was conducted n the framework of the act Support of Post-Doc Researchers under the Operatonal Program Human Resources Development, Educaton and Lfelong Learnng 4-, whch s mplemented by the State Scholarshps Foundaton and co-fnanced by the European Socal Fund and the Hellenc Republc. P.. Papadopoulos and J. V. Mlanovć are wth the School of Electrcal and Electronc Engneerng, The Unversty of Manchester, Manchester, M6 QD, U.K. (e-mal: mlanovc@manchester.ac.uk, panagots.papadopoulos@manchester.ac.uk). T. A. Papadopoulos s wth the Power Systems Laboratory, Dept. of Electrcal & Computer Engneerng, Democrtus Unversty of Thrace, Xanth, Greece, GR 67, (e-mal: thpapad@ee.duth.gr). A. I. Chrysochos s wth Cablel Hellenc Cables S.A., Vohalco Group, GR, Sousak Kornthas, Kornthos, Greece, (e-mal: achrysochos@fulgor.vonet.gr). drect mpact caused by RES, the dsplacement of synchronous generaton and consequent nerta reducton s also affectng sgnfcantly the power system dynamc behavour. These changes mght lead to system operaton closer to the stablty lmt and hence more prone to nstablty and ultmately blackouts. In ths context, close to real-tme dentfcaton of the dynamc behavor of power systems and mpedng nstablty that enables the applcaton of correctve control actons becomes ncreasngly attractve. Moreover, the wde avalablty of measured data from Phasor Measurement Unts (PMUs) coupled wth the advances n data analytcs and machne learnng provde an array of tools that can be effectvely used for such purposes. Varous data mnng technques, Decson Trees (DTs) []- [3], Ensemble Decson Trees (EDTs) [4], [5], Support Vector Machne (SVM) [6] and Artfcal eural etworks (As) [7] have been used n onlne dynamc securty assessment. Most commonly, the predcton focuses on bnary classfcaton,.e. whether the system wll reman transently stable or not. There have been also some approaches [5], [8] for groupng of unstable generators after the fault s cleared. Whle ths nformaton s valuable for assstng correctve control actons, such as controlled slandng, these approaches focus manly on aperodc (frst swng) nstablty. They do not provde any nformaton regardng the oscllatory behavor of generators n case they are frst swng stable (ncludng potental oscllatory nstablty), whch s wthn the scope of the proposed method n ths paper. The concept of slow coherency s about dentfyng generator groups that tend to swng together and can therefore represent oscllatory behavor of generators [9]. Measurementbased methods have also been developed to dentfy generator coherent groups [], []. However, nformaton from ths type of methods focus on dentfyng coherent groups of generators that tend to swng together but do not drectly provde nformaton on the dampng of oscllatons after a specfc dsturbance, whch s very mportant when further correctve control acton needs to be taken. In [], classfcaton trees are used to predct well or poorly damped oscllatons usng power flow data, however, these trees need to be traned before ther applcaton n an onlne manner. In [3], a method for the onlne clusterng of the oscllatory (c) 8 IEEE. 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3 Ths artcle has been accepted for publcaton n a future ssue of ths journal, but has not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TPWRS , IEEE > REPLACE THIS LIE WITH YOUR PAPER IDETIFICATIO UMBER (DOUBLE-CLICK HERE TO EDIT) < behavour based on features extracted from Recurrence Quantfcaton Analyss (RQA) s presented. The extracted features from RQA do not provde a drect physcal meanng on the oscllatory behavour of the generators though, especally when dstngushng between poorly and negatvely damped oscllatons. Furthermore, dfferent methods based on the dentfcaton of parameters of oscllatory modes drectly from tme doman (TD) responses have been used n the past. They nclude Prony method [4], the Egenvalue Realzaton Algorthm (ERA) [5] and the Matrx Pencl (MP) method [6]. Alternatvely, there are also methods that derve the domnant modes usng frequency doman (FD) responses [7] or a combnaton of the above as n the recently proposed hybrd FD/TD approach [8]. Such methods extract the domnant modes of measured responses wth relatvely hgh accuracy but do not provde any nformaton on the partcpaton of ndvdual generators n these oscllatory modes. Ths paper proposes, an ntegrated onlne method based on PMU measurements for the dentfcaton of generator oscllatory behavor n case of frst swng stable response of the system. The proposed method enables the applcaton of more effectve correctve control by provdng addtonal actonable nformaton for system operators consderng the partcpaton of ndvdual generators n poorly or negatvely damped oscllatory modes followng a dsturbance. Addtonally, t deals wth practcal applcaton aspects when appled to a large number of cases for varyng operatng condtons mposed by RES ntermttent behavour. The dstnct contrbutons of the proposed method are: ) Mode dentfcaton s appled to TD responses of ndvdual generators to dentfy both stable and unstable modes contrary to a sngle pont of measurement usually used n the lterature [4]-[8]. ) Two post-processng technques are ncorporated,.e. surplus mode flterng and sldng wndow, to deal wth challenges ntroduced by usng a fxed model order and slowly growng oscllatory modes, respectvely. 3) The generators are clustered nto groups n the second step of the method, based on the partcpaton of ndvdual generators n poorly or negatvely damped oscllatory modes whch s an addtonal feature compared to exstng mode dentfcaton methods [4]-[8]. 4) Un-supervsed machne learnng s used to derve the generator groups wthout the need of generatng smulated scenaros for tranng. 5) Monte Carlo (MC) smulatons can be performed offlne to nvestgate the probablstc oscllatory behavour of ndvdual generators takng nto consderaton uncertantes of modern power systems (ncludng RES). II. PROPOSED METHODOLOGY Once a contngency s dentfed as frst swng stable, the proposed two-step method s appled to dentfy possble groups of generators that exhbt poorly or negatvely damped oscllatons, as shown n Fg.. Therefore, the proposed method can be seen as complementary to the method presented n [5] as t frst addresses aperodc nstablty and then the proposed method n ths paper, oscllatory nstablty. The frst step of the proposed methodology nvolves the applcaton of MP on the rotor angle responses of each generator obtaned from avalable measurng nfrastructure or PMU measurements. Ths s n order to dentfy the domnant modes contaned n the oscllatory responses of each generator [9]. It should be noted that n ths paper, smulatons are used as a substtute for measurements to nvestgate the performance of the proposed method under a very large number of cases. Addtonally, a surplus mode flterng approach s appled as part of the frst step, to ensure consstency durng the clusterng procedure n the second step as well as to automate the procedure when dealng wth a large number of case studes under dfferent operatng condtons. The second step nvolves the applcaton of a clusterng method, namely the k-medods algorthm [], to cluster generators n relevant groups,.e., exhbtng well or poorly/negatvely damped modes usng the least damped extracted modes dentfed n the prevous step as clusterng features. Therefore, the partcpaton of ndvdual generators n poorly or negatvely damped modes can be derved n ths manner. Ths s an added feature to measurement-based mode dentfcaton technques and thus detaled nformaton can be provded to system operators when desgnng and actvatng correctve control actons. In addton, a sldng wndow approach can be appled, f needed, to capture slowly growng oscllatons that mght appear at a later tme (outsde of the selected ntal tme wndow). Fnally, by applyng the proposed procedure to MC dynamc smulatons performed offlne, the probablstc oscllatory behavour of ndvdual generators s nvestgated. The proposed method offers a systematc approach regardng onlne dentfcaton of poorly/negatvely damped oscllatory modes and the partcpaton of ndvdual generators n them as well as wth practcal aspects that arse from the applcaton of mode dentfcaton technques on a very large number of dverse cases for dfferent operatng condtons. It should also be noted that the dfferent dynamc behavour of power electronc nterfaced unts, ncludng the effect of ther uncertan behavour causng a wder varaton n operatng condtons, as well as the consequent nerta reducton, are part of the motvaton for the development of the proposed method. The aforementoned RES behavour justfes the need for such onlne methods and s therefore consdered n ths paper as explaned n the followng Sectons. The method s generalzed n the sense that any mode dentfcaton and clusterng method can be used as part of the proposed two-step procedure. The rest of ths secton descrbes each step n detal. A. Mode Identfcaton The power system rngdown response y(t) followng a perturbaton can be approxmated by a sum of damped snusods (modes) []. s ˆ( ) =+ t y t Ae cos( ωt ϕ) = where = ±j are the system egenvalues and = f,, () (c) 8 IEEE. Personal use s permtted, but republcaton/redstrbuton requres IEEE permsson. See for more nformaton.

4 Ths artcle has been accepted for publcaton n a future ssue of ths journal, but has not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TPWRS , IEEE > REPLACE THIS LIE WITH YOUR PAPER IDETIFICATIO UMBER (DOUBLE-CLICK HERE TO EDIT) < 3 A, are the angular frequency, dampng, ampltude and phase angle of the -th mode, respectvely. The dscrete-tme representaton of () can be wrtten as (), gven that the record conssts of w equally t-spaced samples. Fg.. Schematc of the applcaton of the proposed method. where: Sldng Wndow [ ] ˆ = n y n Bz = λ = t () z e (3) Thus, the sgnal s descrbed by a fnte summaton of p mode pars (B, z ), where B s the resdue of the correspondng dscrete-tme pole z. The problem s to mnmze the error between the real y[n] and the estmated ŷn [ ] responses, by calculatng accordngly the mode pars of () as shown n (4). Damped PMU measurements w n= Matrx Pencl Surplus Mode Flterng K-medods ( [ ] ˆ [ ]) st step: Mode Identfcaton nd step: Clusterng mn J= yn yn (4) For ths purpose, the MP method s adopted, whch uses sngular value decomposton (SVD) [6] to estmate the system modes, by flterng out nose or any addtonal components. The MP algorthm s summarzed as follows [6]: ) Buld Hankel matrces H and H wth entres the samples of the rngdown response y[n] of the system. ) Perform SVD of H, defned n (5), and estmate the system order by retanng the largest sngular values. Poorly/negatvely damped Further correctve actons = T H PSQ (5) 3) Buld vectors V and V by deletng the last and the frst row of the untary vector V, respectvely, whose elements correspond to most sgnfcant values of S. Calculate matrces Y and Y by: Y = VV T (6a) Y = VV T (6b) 4) Poles z are the generalzed egenvalues resultng from: Y Y I= (7) λ Snce the system modes are dentfed by means of (3) usng the calculated z, (8) can be solved n the least squares sense to estmate the assocated resdues B. z z L z B [ ] [ ] z z L z B = y M M O M M M w w w z z L z B y[ w ] To evaluate the accuracy of the dentfed modes the R coeffcent, defned n (9), s adopted, where y s the mean of y[n]. Ths R examnes the qualty of the reconstructed sgnal to the orgnal response ft. R = n= w w ( yn [ ] yn ˆ [ ]) n= [ ] yn y B. Surplus Mode Flterng Based on Energy The applcaton of the MP to measured responses wll result n the dentfcaton of the domnant modes contaned n the rngdown as well as nto a number of artfcal surplus modes, due to nose, etc. These modes are typcally characterzed by low energy and mght sometmes exhbt low or even negatve dampng []. Snce the least damped mode of each generator s selected as an nput parameter to the clusterng algorthm, t s very mportant to exclude/separate the surplus modes from the domnant ones to reduce the number of possble false alarms. For ths purpose, the normalzed energy of each mode (E,n ) s calculated accordng to () and (). Modes wth less than % normalzed energy (emprcally chosen n ths case) are consdered artfcal and dscarded from the procedure. j ( real( )) j= y (8) (9) + E = w Bz () E n, = E = E () It should be noted that more advanced mode dentfcaton technques automatcally determnng the requred order could systematcally solve ths ssue, thus addtonal flterng mght not be essental. However, such methods could ncrease sgnfcantly the computatonal burden by ntroducng addtonal computatons, e.g. by teratve loops [8]. C. Unsupervsed Machne Learnng Snce the domnant modes of the response of each generator are obtaned followng the proposed mode dentfcaton (c) 8 IEEE. Personal use s permtted, but republcaton/redstrbuton requres IEEE permsson. See for more nformaton.

5 Ths artcle has been accepted for publcaton n a future ssue of ths journal, but has not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TPWRS , IEEE > REPLACE THIS LIE WITH YOUR PAPER IDETIFICATIO UMBER (DOUBLE-CLICK HERE TO EDIT) < 4 procedure, the least damped mode (ncludng negatvely damped modes) s selected as the nput feature for the clusterng algorthm. The clusterng algorthm s appled for the least damped mode obtaned for the ntal tme wndow T w as well as for any consecutve sldng wndows as explaned above. K-medods s used for two man reasons. Frst, the target of the proposed algorthm s to dstngush between generators exhbtng poorly/negatvely damped and well damped oscllatory behavor. The number of clusters s therefore constant (k = ), thus k-means and k-medods wth predefned number of clusters can be consdered as a good choce. A larger number of clusters (e.g., 3, 4 etc.), however, could be defned by a system operator, as a part of the proposed methodology, f more detaled nformaton on the generator groupngs was desrable. Addtonally, the k-medods algorthm offers the advantage over k-means that the cluster centrod s not the mean value of the cluster objects but one of the actual objects of the cluster. Ths means that the cluster centrod corresponds to the actual least damped mode assocated wth one of the generators belongng to each cluster and therefore has a physcal meanng. The k-medods algorthm s very smlar to k-means and ams at clusterng the objects of a dataset (generators n ths case) nto k groups based on a number of features (the frequency and dampng rato of the least damped mode n the examned problem). Therefore, a number of G observatons correspondng to the total number of generators n the system occur, each characterzed by two features. Therefore, a xg matrx wth nformaton obtaned from the mode dentfcaton step s used as nput to the clusterng algorthm. K-medods s a parttonng technque that uses one representatve object n each cluster as a reference pont to the entre cluster. The Parttonng Around Medods (PAM) algorthm s used n ths paper, whch s one of the most popular realzatons of the k-medods clusterng []. The overall goal s to mnmze an absolute error crteron presented n (), where e s the sum of absolute error for all objects p of the data set, o s the representatve object of the cluster C and dst s the selected dstance measure whch n ths case s the Eucldean dstance. Intally, a representatve object for each cluster s chosen ether arbtrarly or as n ths paper followng the k-means++ algorthm to speed up the process [3]. An teratve approach s followed n a greedy manner by changng the representatve object of a cluster and calculatng whether the absolute error s reduced or not. At each teraton the representatve object s modfed to the new one f the error s reduced, otherwse the same representatve object s used. k = p C ( ) e dst po, () = D. Sldng Wndow Method The ntal selected sgnal tme wndow T w s assumed long enough to contan most of the sgnal energy assocated wth the system oscllatory modes [8]. However, by applyng the above procedure only to T w, t may lead to the elmnaton of mportant low/negatvely damped oscllatory modes, characterzed by low energy durng ths perod. To overcome ths ssue, the MP and surplus mode flterng procedures can be addtonally appled to consecutve sldng sgnal wndows of length T w. As the energy of these modes ncreases wth tme, ther dentfcaton can be eventually successful at a later tme step and the updated lst of poorly damped modes provded to the clusterng algorthm. E. Probablstc Oscllatory Behavour In order to account for the ncreasng uncertanty n modern power system operaton, a probablstc approach s followed to nvestgate the probablstc oscllatory behavour of the system as well as of ndvdual generators. The uncertanty of the ntermttent behavour of RES and system loadng s taken nto consderaton to produce a number of TD dynamc MC smulatons for dfferent operatng condtons. The number of smulatons requred s defned accordng to the requred error of the sample mean shown n (3), where - s the nverse Gaussan cumulatve dstrbuton functon (CDF) wth a mean value of zero and standard devaton one, s the varance of the sampled random varable X, s the confdence level (.e.. for ths study) and MC the number of MC samples [5]. e X = δ s X Φ ( X ) III. TEST SYSTEM, UCERTAITIES AD SIMULATIOS MC (3) A. System Under Study Dynamc smulatons are used to substtute measurement data. The test network used s a modfed verson of the IEEE 68 bus, 6 machne reduced order equvalent model of the ew England Test System and the ew York Power System (ETS YPS). The conventonal part of the test network s adopted from [9] and RES are added at the buses shown n Fg.. Two types of RES unts are connected on each bus: Doubly Fed Inducton Generators (DFIGs), representng wnd generators (WGs) and Full Converter Connected (FCC) unts, representng both WGs and photovoltac (PV) unts. The dynamc performance of the system s analyzed by means of RMS smulatons usng DIgSILET PowerFactory software [6]. Standard 6 th order models are used for all synchronous generators ncludng ether slow IEEE DCA dc excters or fast actng statc excters type IEEE STA and generc governors, representng gas, steam and hydro turbnes. Generator G9 s also equpped wth a Power System Stablzer (PSS). A generc type 3 model, sutable for large scale stablty studes, s used n ths paper to represent DFIGs and a type 4 WG model s used to represent all FCC unts (both WGs and PVs). The models have a structure smlar to the one proposed by WECC [4] and IEC [5], and are avalable n DIgSILET PowerFactory [6], whereas all RES unts are (c) 8 IEEE. Personal use s permtted, but republcaton/redstrbuton requres IEEE permsson. See for more nformaton.

6 Ths artcle has been accepted for publcaton n a future ssue of ths journal, but has not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TPWRS , IEEE > REPLACE THIS LIE WITH YOUR PAPER IDETIFICATIO UMBER (DOUBLE-CLICK HERE TO EDIT) < 5 consdered wth Fault Rde Through (FRT) capabltes. The number of the connected RES corresponds to % of the total nstalled generatng capacty of the system, 66.67% of whch are type 3 DFIGs and 33.33% FCC unts. FCCs are further consdered to be 3% WGs and 7% PV unts. B. Modellng of Uncertantes The tme frame for the consdered uncertantes n ths study s one day. Therefore, daly loadng and PV curves are ntally used and the hour of the day s sampled randomly followng a unform dstrbuton to determne the pu values for all the loads and PV unts. For every hour wthn the day, the correspondng uncertantes are also modeled usng a normal dstrbuton for the system load and a beta dstrbuton for PV generaton. Therefore, an extra uncertanty scalng factor for loads and PVs s ntroduced, whch s eventually multpled wth the correspondng value from the daly loadng or PV curve, respectvely. The normal dstrbuton for the system loadng uncertanty has mean value pu and standard devaton 3.33% and the beta dstrbuton a and b parameters are 3.7 and.3, respectvely. The uncertanty of the wnd speed s modelled usng a Webull dstrbuton wth parameters =. and k =. [3]. EW EGLAD TEST SYSTEM G6 6 G9 9 9 G G5 G3 G 3 G Fg.. Modfed IEEE 68 bus test network. G G L43 L44 L45 36 L4 EW YORK POWER SYSTEM C. Smulaton Procedure After consderng the uncertantes, Optmal Power Flow (OPF) s solved to determne the conventonal generators dspatch. The nomnal capacty of each generator s then adjusted to take nto consderaton the dsconnecton of conventonal generaton due to both load varatons and RES penetraton. A constant amount of 5% spare capacty s consdered for each smulated case as n [7]. Snce the generators are consdered as aggregated unts, reducng the nomnal power s equvalent to a reducton n the moment of nerta of the power plant and an ncrease n the generator reactance. Three phase self-clearng faults are consdered as dsturbances n ths study. However, the smulaton database could be extended to nclude any other dsturbances as well. A unform dstrbuton s used to model the fault locaton whch means that the fault may happen wth equal probablty at any lne of the test network and at any pont along the lne. A normal dstrbuton wth mean value of 4 cycles and standard devaton 6.67% s used to model the fault duraton. TD dynamc RMS smulatons are performed afterwards for the operatng condtons resultng from OPF and the selected L4 G G G L7 L66 G L69 G6 5 G5 4 G contngences explaned above, n DIgSILET PowerFactory [6]. For the examned system the number of requred MC smulatons ( MC ) s 6 to lmt the error of the sample mean descrbed n (3) to 5% [5]. IV. CASE STUDIES The selected tme wndow (after the fault s cleared) n studes carred out to llustrate the proposed methodology s approxmately 8 seconds,.e. 77 samples wth a samplng tme of cycle (n 6 Hz). The order for the adopted MP method s, resultng n the dentfcaton of 5 oscllatory modes. Ths model order s selected to ensure that the medan of the R values for all generators and for all smulated cases s hgher than 95%. The frequences of nterest n ths study are those >. Hz to focus on electromechancal modes. A. Applcaton to Representatve Cases Two representatve Test Cases (TCs) of generator oscllatory behavour obtaned from MC smulatons are shown n Fg. 3. In the frst case,.e. TC, all generators exhbt well damped oscllatory behavour, whle n TC some generators exhbt negatvely damped oscllatons wth slowly growng ampltudes. The least damped modes of each generator are ntally dentfed and afterwards used as nputs for the k-medods algorthm. Rotor angle (deg) Rotor angle (deg) b) a) Samples Fg. 3. Representatve responses for a) well damped (TC) and b) negatvely damped (TC) response. The dentfed least damped modes for TC are presented n Fg. 4a. The clusters obtaned by applyng the k-medods algorthm are also marked n Fg. 4a along wth the representatve object of each cluster. For TC, the least damped modes for all generators have postve dampng rato and therefore both resultng groups exhbt stable oscllatory behavour. Each group s related to a representatve generator (defned as the representatve object of the cluster followng the k-medods clusterng algorthm), whch descrbes the oscllatory behavour of the generators that belong to each group,.e. G5 (dampng rato 3.87% and frequency.86 Hz, representng the group of G8) and G (dampng rato 4.3% and frequency.57hz, representng the group of G-G7 and G9-G4) n ths case, respectvely. The physcal meanng of G G G3 G4 G5 G6 G7 G8 G9 G G G G4 G5 G (c) 8 IEEE. Personal use s permtted, but republcaton/redstrbuton requres IEEE permsson. See for more nformaton.

7 Ths artcle has been accepted for publcaton n a future ssue of ths journal, but has not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TPWRS , IEEE > REPLACE THIS LIE WITH YOUR PAPER IDETIFICATIO UMBER (DOUBLE-CLICK HERE TO EDIT) < 6 ths groupng s that the generators can be splt n two groups based on the frequency and dampng rato of ther least damped mode due to more pronounced separaton n frequency of the crtcal modes. Snce n TC all generators exhbt stable oscllatory behavour no further control acton would be requred. In TC however, one of the groups, namely, the crtcal group, exhbts growng oscllatons. Ths crtcal group s represented by generator G6 (dampng rato -.6% and frequency.57 Hz) and ncludes G, G4, G7, G8 and G9. The rest of the generators exhbt stable oscllatory responses wthn ths tme wndow and belong to the group represented by G (correspondng to dampng rato 4.7% and frequency.53 Hz). B. Flterng of Artfcal Surplus Mode Fg. 5, shows an example of a representatve response of G, where artfcal low energy modes appear (as explaned n Secton II.B), whereas Table I summarzes the extracted modes from the applcaton of the MP method, wthout consderng surplus flterng. In Fg. 5a, the orgnal and reconstructed sgnals usng the MP method are compared. In Fg. 5b, the damped snusodal responses of each of the 5 dentfed modes are analyzed ndvdually. Although the ft between the two sgnals (R value of 98.4%) s very good, two of the extracted modes,.e. mode # and #5, are characterzed by very low energy (as shown n the zoomed verson of the plot) as well as by very low or negatve dampng as descrbed n Secton II.B. The normalzed energy of mode # and mode #5 s.9e - and.39e -5, respectvely and thus they wll be fltered out when calculatng the least damped mode, followng the proposed procedure. If these trval modes characterzed by very low energy (as can also be seen n Fg. 5b) were not fltered out, the least damped mode would end up beng mode #. Therefore, the proposed surplus mode flterng procedure acts as an addtonal measure to ensure that only the mportant modes are ncluded n the second step of the algorthm, whle the trval ones are fltered out. Frequency (Hz) Frequency (Hz) a) Dampng rato (%) b) G representatve object Dampng rato (%) G5 representatve object G6 representatve object G representatve object Fg. 4. Generator groups obtaned from k-medods clusterng for a) TC and b) TC. TABLE I G EXTRACTED MODES (WITHOUT SURPLUS MODE FILTERIG) Mode Frequency (Hz) Dampng Rato (%) ormalzed Energy G G G3 G4 G5 G6 G7 G8 G9 G G G G4 G5 G6 Rotor angle (deg) Rotor angle (deg) e-3.9e e e e Tme (s) b) Fg. 5. G response and obtaned modes from MP method. C. Applcaton of Sldng Wndow In some cases, certan generators mght start exhbtng oscllatory behavour after the selected tme wndow used n the system dentfcaton procedure. For ths purpose (as explaned n Secton II.C), a sldng wndow s appled. To hghlght the mportance of the sldng wndow technque the followng case s nvestgated. Let us assume that the wndow s of fxed length and moves by sample as each new measurement pont s receved. To llustrate ths, the response of G for TC presented before s shown n Fg. 6a for an overall duraton of 7 samples ( addtonal samples compared to Fg. 3). The sldng wndow, denoted wth the red box, has a duraton of 77 samples and as tme proceeds moves to the rght tmes for ths specfc case shown n Fg. 6. The method s therefore appled tmes as the wndow sldes. As tme goes by, generator G s exhbtng growng oscllatons whch were not ncluded n the ntal tme wndow (and therefore have not been dentfed by the MP method). Fg. 6b presents the least damped mode dentfed by applyng consecutvely the mode dentfcaton method as the wndow sldes. As mentoned above the method s appled tmes as each new sample s obtaned from the measurements. These generated ponts n Fg. 6b start from the left for the ntal wndow and move to the rght, as the wndow sldes. It can be seen that only after 46 samples (also denoted n Fg. 6b), the unstable mode correspondng to the growng oscllatons s successfully dentfed, jumpng from a postve dampng value close to 4% to a negatve dampng value close to -.9%. It should be noted that the least damped mode dentfed usng the ntal wndow s also of dfferent frequency,.e. approxmately.5 Hz, whle the unstable mode s close to.5 Hz, whch s the same frequency wth the group of unstable generators already dentfed before. Therefore, as a) MP reconstructed Orgnal Mode Mode Mode 3 Mode 4 Mode Tme (s) (c) 8 IEEE. Personal use s permtted, but republcaton/redstrbuton requres IEEE permsson. See for more nformaton.

8 Ths artcle has been accepted for publcaton n a future ssue of ths journal, but has not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TPWRS , IEEE > REPLACE THIS LIE WITH YOUR PAPER IDETIFICATIO UMBER (DOUBLE-CLICK HERE TO EDIT) < 7 ) the wndow s movng, generator G wll eventually move to the unstable cluster. G rotor angle (deg) Frequency (Hz) After 46 samples Samples b) Fg. 6. a) G response and sldng wndow and b) least damped mode as wndow sldes. V. AALYSIS OF PROBABILISTIC OSCILLATORY BEHAVIOUR OF THE SYSTEM AD IDIVIDUAL GEERATORS The applcaton of the proposed methodology to the results of MC smulatons carred out to account for the uncertan power system behavor s llustrated below. A boxplot of the R values for all the smulated cases and all generators s shown n Fg. 7 to hghlght the performance of the mode dentfcaton method. The medan of the R s > 95% for all generators, rangng from 99.9% for G5 and 93.7% for G8. The R n most cases remans > 8% though n few cases the outlers wth low R values appear, especally for generators G and G8. The R though s < 5% only n.4% for G6 and.9% for G8 of the total number of smulated cases. Ths s manly caused by the fxed dentfcaton model order of the MP method used durng the mode dentfcaton step. In some cases though, a hgher dentfcaton model order mght be necessary to acheve hgher R value. A. Probablstc Assessment of Generator Groups The proposed methodology s also appled to all frst-swng stable cases,.e out of 6 performed smulatons. The resultng representatve objects of the two clusters for each case are summarzed n Fg. 8 (focusng on the range wth dampng between ±%). Blue crcles correspond to the representatve object of the group wth lower dampng, whle the green squares are the representatve objects correspondng to the well damped group. It should be noted that there are some cases where both groups mght exhbt stable or unstable oscllatory behavour. Observng the locaton of the representatve objects (.e. the dampng rato and frequency) s therefore mportant to draw conclusons regardng the oscllatory behavour of the generators belongng to each cluster. Addtonally, t helps n dentfyng the modes that mght cause unstable behavour of the system under uncertantes consdered (ntermttent nature of wnd generaton, PVs and system loadng n ths partcular case). It can be seen, for example, that some modes located n the a) Dampng rato (%) regon around.5 Hz can exhbt low (but postve) dampng and only n very few cases mght become unstable. On the other hand, some modes n the frequency regon close to. Hz tend to exhbt unstable behavour n several cases, followed by modes wth frequences rangng from. Hz to.6 Hz. In order to get a more detaled overvew of the dynamc behavour of the system, some representatve generator groupng patterns (possble cluster formatons wthn the smulated cases) are presented n Table II, along wth the number of occurrences of each pattern. The total number of the observed groupng patterns s 796 for the 5345 frst-swng stable cases of the examned dataset wth a large number of them occurrng less than tmes. However, as noted before, the exact locaton of the representatve cluster object (representatve generator) should be observed to get a more accurate descrpton of the cluster (whether t exhbts well or poorly damped oscllatons). Ths means, for example, that n some of the groupng patterns presented n Table II, both groups mght be well damped (wth one group beng less damped than the other). In ths way, the nformaton on the expected groupng patterns as well as on the frequency of ther appearance for a gven system s provded. Coeffcent of determnaton (R Generators Fg. 7. R for all cases for each generator. Fg. 8. Representatve cluster objects (c) 8 IEEE. Personal use s permtted, but republcaton/redstrbuton requres IEEE permsson. See for more nformaton.

9 Ths artcle has been accepted for publcaton n a future ssue of ths journal, but has not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TPWRS , IEEE > REPLACE THIS LIE WITH YOUR PAPER IDETIFICATIO UMBER (DOUBLE-CLICK HERE TO EDIT) < In Fg. 9, the representatve objects of the two clusters for pattern #5 of Table II are presented n a smlar manner to Fg. 8. For ths specfc pattern, the entre ETS area and one generator n YPS area (G-G) exhbt unstable oscllatory behavor wth frequency around. Hz whle the rest of the generators (G-G6) oscllate wth postvely damped oscllatons wth frequences that vary from.5 Hz to.9 Hz. B. Probablstc Dynamc Behavour of Indvdual Generators By observng the extracted least damped mode for a specfc generator for all cases, the ndvdual generator oscllatory behavour can be nvestgated. Results for G4 are presented n Fg. a. For ths specfc generator, the mode around. Hz mght cause unstable or poorly damped (dampng rato less than %) oscllatory behavour. Addtonally, t s less lkely for two modes wth frequency.4 Hz and.6 Hz to exhbt unstable oscllatons. Smlarly, results for G5 are presented n Fg. b revealng that ths generator exhbts unstable modes very rarely, and f so, mostly wth a frequency around. Hz. Most of the tmes, G5 oscllates wth frequences around.5 Hz and.8 Hz. Of the two, the.8 Hz mode s less damped and occasonally, though very rarely, mght exhbt poor dampng (less than % dampng rato). Pattern o TABLE II REPRESETATIVE GROUPIG PATTERS Groupng Pattern Less damped Better damped group group (G-G) (G4-G6) (G, G8, G9) (G-G7, G-G6) (G, G8, G9, (G-G7, G, G, G) G4-G6) (G9) (G-G8, G-G6) (G-G) (G-G6) 8 oscllatory behavour. In ths case, the system loadng s taken nto account as the only uncertanty consderng the operatng condtons of the network (fault locaton and duraton uncertantes reman as descrbed before), snce all RES unts are dsconnected. In Fg., the Cumulatve Dstrbuton Functons (CDF) of the dampng rato of the least damped mode for three representatve generators (G, G4 and G5) are compared for the cases wth and wthout RES. In general, there s hgher probablty that these three generators wll exhbt negatvely damped oscllatons after the dsturbance. More specfcally, G4 for whch the deteroraton s more evdent, has approxmately 34% probablty to exhbt negatvely damped oscllatons when RES are connected whle the same probablty s approxmately 8% wthout RES. Ths denotes a possble ncrease n the probablty of oscllatory nstablty followng connecton of RES of the specfc generator (and the system n general) for a set of consdered operatng condtons. umber of occurrences Fg.. Least damped dentfed modes for a) G4 and b) G G % RES.5.9 G wthout RES G4 % RES.4.8 G4 wthout RES G5 % RES.3.7 G5 wthout RES Cumulatve probablty. Frequency (Hz) Dampng rato (%) Dampng rato (%) Fg. 9. Representatve objects correspondng to a specfc groupng pattern. Fg.. CDFs of the dampng rato of the least damped mode for G, G4 and G5 wth and wthout RES. C. Effect of RES on Indvdual Generator Oscllatory Behavour An addtonal case study s performed, consderng specfcally the effect of RES unts on ndvdual generator D. Computatonal Burden Consderatons All computatons have been performed usng an Intel Core GHz wth 6 GB of RAM. Both MP mode dentfcaton and k-medods clusterng algorthms are mplemented n Matlab. For the st step (.e. mode dentfcaton) of the (c) 8 IEEE. Personal use s permtted, but republcaton/redstrbuton requres IEEE permsson. See for more nformaton.

10 Ths artcle has been accepted for publcaton n a future ssue of ths journal, but has not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TPWRS , IEEE > REPLACE THIS LIE WITH YOUR PAPER IDETIFICATIO UMBER (DOUBLE-CLICK HERE TO EDIT) < 9 proposed algorthm approxmately 55ms n total are requred for the extracton of the modes for all generators, after the measurements for the chosen tme wndow are obtaned. The nd step (.e. the clusterng algorthm) requres approxmately 5 ms. Therefore, for a sngle tme wndow calculaton of the generator clusters, less than 6 ms are requred, showng that the method s sutable for close to real-tme applcatons. VI. COCLUSIOS In ths paper, a two-step, measurement based method s proposed for the onlne dentfcaton and analyss of power system oscllatory behavour. The proposed method s appled n a close to real-tme manner (less than 6 ms), to provde addtonal actonable nformaton to system operators regardng the partcpaton of ndvdual generators n poorly or negatvely damped oscllatory modes. Frst, the MP method s appled to TD responses to extract the domnant modes contaned n both stable and unstable oscllatory responses of each generator n the system. ext, the least damped mode of each generator s used to cluster the generators n groups based on ther oscllatory behavour, usng the k-medods algorthm. A sldng wndow s used to capture possble growng oscllatons that could have been mssed usng the ntal fxed tme wndow as well as a surplus mode flterng approach to ensure consstency and automate the procedure when applyng the method on a large number of responses for dverse operatng condtons (motvated by the ntermttent behavour of RES). From the analyss performed, t can be concluded that the MP method can successfully and wth hgh confdence dentfy both, stable and unstable, oscllatory modes of each generator. Moreover, the clusterng analyss showed that generators can be successfully splt nto two dstnct groups, each represented by a generator hghlghtng the oscllatory behavour of the group. Addtonally, the applcaton of the method has been demonstrated for the analyss of system dynamc behavor consderng varous uncertantes ncludng the ntermttent behavour of RES. By applyng the method on a large number of MC smulatons, the oscllatory modes and generators that may cause nstablty of a system can be dentfed. Comparatve study wth and wthout RES showed that, for the specfc system under study and for the operatng condtons nvestgated, the probablty of the appearance of negatvely damped oscllatons for certan generators mght ncrease when RES are connected. REFERECES [] S. Rovnyak, S. Kretsnger, J. Thorp, and D. Brown, Decson trees for real-tme transent stablty predcton, IEEE Trans. Power Syst., vol. 9, no. 3, pp , 994. [] V. Vttal,. Senroy, and G. T. Heydt, Decson Tree Asssted Controlled Islandng, IEEE Trans. Power Syst., vol., no. 4, pp , 6. [3] Q. Gao and S. M. Rovnyak, Decson trees usng synchronzed phasor measurements for wde-area response-based control, IEEE Trans. Power Syst., vol. 6, no., pp ,. [4] M. He, J. Zhang, and V. Vttal, Robust Onlne Dynamc Securty Assessment Usng Adaptve Ensemble Decson-Tree Learnng, IEEE Trans. Power Syst., vol. 8, no. 4, pp , 3. [5] P.. Papadopoulos, T. Guo, J. V. Mlanovc, Probablstc Framework for Onlne Identfcaton of Dynamc Behavor of Power Systems wth Renewable Generaton, IEEE Trans. Power Syst., avalable onlne. [6] F. R. Gomez, A. D. Rajapakse, U. D. Annakkage, and I. T. Fernando, Support vector machne-based algorthm for post-fault transent stablty status predcton usng synchronzed measurements, IEEE Trans. Power Syst., vol. 6, no. 3, pp ,. [7]. Amjady, S. F. Majed, Transent stablty predcton by a hybrd ntellgent system, IEEE Trans. Power Syst., vol., no. 3, pp , 7. [8] S. Kretsnger, S. Rovnyak, D. Brown, and J. Thorp, Parallel decson trees for predcng groups of unstable generators from synchronzed phasor measurements, n Proc. Precse Measurements n Power Systems Conf.,Washngton, DC, USA, 993. [9] G. Rogers, Power System Oscllatons. Kluwer Academc,. [] M. Jonsson, M. Begovc, J. Daalder, A new method sutable for realtme generator coherency determnaton, IEEE Trans. Power Syst., vol. 9, no. 3, pp , 4. [] M. A. M. Arff, B. C. Pal, Coherency Identfcaton n Interconnected Power System An Independent Component Analyss Approach, IEEE Trans. Power Syst., vol. 8, no., pp , 3. [] P. Mcabb, D. Wlson, J. Balek, Classfcaton of mode dampng and ampltude n power systems usng synchrophasor measurements and classfcaton trees, IEEE Trans. Power Syst., vol. 8, no., pp , 3. [3] P.. Papadopoulos, J. V. Mlanovc, P. Bhu,. Senroy, Feasblty Study of Applcablty of Recurrence Quantfcaton Analyss for Clusterng of Power System Dynamc Responses, n ISGT Europe 6, Ljubljana, Slovena, ovember, 6. [4] J. F. Hauer, C. J. Demeure, L. L. Sharf, Intal results n Prony analyss of power system response sgnals, IEEE Trans. Power Syst., vol. 5, no., pp. 8 89, 99. [5] J. J. Sanchez-Gasca, Computaton of turbne-generator subsynchronous torsonal modes from measured data usng the egensystem realzaton algorthm, IEEE Power Eng. Soc. Wnter Meet., Columbus, USA,. [6] M. L. Crow, A. Sngh, The matrx pencl for power system modal extracton, IEEE Trans. Power Syst., vol., no., pp. 5 5, 5. [7] Z. Tashman, H. Khallna, V. Venkatasubramanan, Mult-dmensonal Fourer rngdown analyss for power systems usng synchrophasors, IEEE Trans. Power Syst., vol. 9, no., pp , 4. [8] T. A. Papadopoulos, A. I. Chrysochos, E. O. Konts, P.. Papadopoulos, G. K. Papaganns, Measurement-Based Hybrd Approach for Rngdown Analyss of Power Systems, IEEE Trans. Power Syst., vol. 3, no. 6, pp , 6. [9] "IEEE Standard for Synchrophasor Measurements for Power Systems," IEEE Std C pp. -6. [] J. Han, M. Kamber, J. Pe, Data mnng concepts and technques. Waltham, USA: Elsever,. [] IEEE Task Force on Identfcaton of Electromechancal modes, Identfcaton of electromechancal modes n power systems, IEEE Power & Energy Socety, Tech. Rep. PES-TR5,. [Onlne]. Avalable: []. Zhou, J. W. Perre, D. Trudnowsk, A Stepwse Regresson Method for Estmatng Domnant Electromechancal Modes, IEEE Trans. Power Syst., vol. 7, no., pp. 5 59,. [3] Arthur, Davd, and Serg Vasslvtsk. K-means++: The Advantages of Careful Seedng, n SODA 7: Proceedngs of the Eghteenth Annual ACM-SIAM Symposum on Dscrete Algorthms, pp. 7 35, 7. [4] WECC Wnd Power Plant Dynamc Modelng Gude, WECC Renewable Energy Modelng Task Force, 4. [5] Wnd turbnes - Part 7-: Electrcal smulaton models - Wnd turbnes, IEC 64-7-, 5. [6] DIgSILET-PowerFactory User Manual, DIgSILET GmbH, 4. [7] P.. Papadopoulos, J. V. Mlanovć, Probablstc Framework for Transent Stablty Assessment of Power Systems Wth Hgh Penetraton of Renewable Generaton, IEEE Trans. Power Syst., vol. 3, no. 4, pp , Panagots. Papadopoulos (S 5-M 4) receved the Dpl. Eng. and Ph.D. degrees from the Department of Electrcal and Computer Engneerng at the Arstotle Unversty of Thessalonk, n 7 and 4, respectvely. Snce 4 he has been postdoctoral Research Assocate at the Unversty of (c) 8 IEEE. Personal use s permtted, but republcaton/redstrbuton requres IEEE permsson. See for more nformaton.

11 Ths artcle has been accepted for publcaton n a future ssue of ths journal, but has not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TPWRS , IEEE > REPLACE THIS LIE WITH YOUR PAPER IDETIFICATIO UMBER (DOUBLE-CLICK HERE TO EDIT) < Manchester. He s currently a Lecturer n the Department of Electronc and Electrcal Engneerng at the Unversty of Strathclyde. Hs specal nterests are n the feld of power system modelng, smulaton and nvestgaton of dynamc behavour of power systems wth ncreased penetraton of non-synchronous generaton. Theoflos A. Papadopoulos (S -M 9-SM 8) receved the Dpl. Eng. and Ph.D. degrees from the School of Electrcal and Computer Engneerng at the Arstotle Unversty of Thessalonk, Greece, n 3 and 8, respectvely. He s currently Asst. Professor at the Power Systems Laboratory of the Department of Electrcal and Computer Engneerng of the Democrtus Unversty of Thrace, Greece. Hs specal nterests are power systems modelng, PLC and computaton of electromagnetc transents. He receved the Basl Papadas Award at the IEEE PowerTech 7 Conference. Andreas I. Chrysochos (S 8-M 6) receved the Dpl. Eng. and Ph.D. degrees from the School of Electrcal and Computer Engneerng at the Arstotle Unversty of Thessalonk, Greece, n 9 and 5 respectvely. From 5 to 7, he was a Research Fellow at the same school. Snce 7, he has been a Senor Engneer at the R&D Department of Cablel Hellenc Cables S.A., Vohalco Group. Hs specal nterests are power systems modelng, computaton of electromagnetc transents, and PLC. He was a scholar of the Alexander S. Onasss Publc Beneft Foundaton (-5, 6-7). Jovca V. Mlanovć (M'95, SM'98, F ) s a Professor of Electrcal Power Engneerng, Deputy Head of School and Drector of External Affars n the School of Electrcal and Electronc Engneerng at the Unversty of Manchester, U.K. Professor Mlanovc s a Chartered Engneer n the UK, Foregn member of the Serban Academy of Engneerng Scences, Fellow of the IET, Fellow of the IEEE, Dstngushed IEEE PES Lecturer and currently serves on IEEE PES Governng Board as Regonal Representatve for Europe, Mddle East and Afrca and on IEEE PES Fellows Commttee (c) 8 IEEE. Personal use s permtted, but republcaton/redstrbuton requres IEEE permsson. See for more nformaton.