Online Estimation of Oscillatory Stability Using a Measurement-based Approach

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1 Onlne Estmaton of Oscllatory Stablty Usng a Measurement-based Approach Ce Zheng, Member, IEEE, Vuk Malbasa, Member, IEEE, and Mladen Kezunovc, Fellow, IEEE Dept. Electrcal and Computer Engneerng Texas A&M Unversty College Staton, TX , U.S.A. zhengce@neo.tamu.edu Abstract Evaluaton of oscllatory stablty n power systems tradtonally reles on model-based analyss. Recent nterest has shfted towards the measurement-based technques such as rngdown analyzers and mode meters. These approaches have lmtatons when nose s present n measurements or short wndows of tme-seres data are analyzed, respectvely. In ths paper we show how to overcome these dsadvantages by usng decson trees to drectly map synchrophasor measurements to one of four predefned stablty states. The proposed approach s llustrated usng synthetc data from smulatons on an IEEE test system, and PMU measurements collected from feld substatons. Decson tree performance s compared to that of artfcal neural networks and support vector machnes. Results ndcate that the proposed measurement-based approach complements the tradtonal model-based approach, enhancng stuatonal awareness of control center operators n real tme stablty montorng and control. Index Terms--Decson tree, electromechancal oscllaton, PMU, power system stablty, synchrophasor measurement I. INTRODUCTION Power system oscllatory stablty assessment s the task of montorng the rotor angle synchronsm of generators at dfferent locatons [1-2]. The recent trend n the electrc power ndustry s to nterconnect transmsson lnes lnkng small autonomous systems nto large ntegrated systems, some of whch span the entre contnent. For example, n the Unted States and Canada generators whch are located thousands of mles apart are operated smultaneously and synchronously. As a consequence nter-area electromechancal oscllatons are becomng a more common occurrence. Snce modern systems are optmally run near ther stablty threshold, the estmaton of the dstance of an operatng pont from nstablty regon s crtcal for stable operaton. Tradtonal oscllatory stablty assessment methods may not satsfy the onlne montorng requrements because: 1) they are based on tme-doman model smulatons whch are computatonally ntensve and tme-consumng; 2) they use data collected from Supervsory Control and Data Acquston (SCADA) systems, or state estmaton functons, both of whch are updated relatvely nfrequently. Wth mproved data acquston technology, such as temporal synchronzaton of measurements at dfferent locatons, t may be possble to detect the onset of nstablty more accurately. The ablty of synchrophasors to capture system-wde dynamcs shows ther potental n real-tme system stablty montorng applcatons [3]. The advantages of a measurement-based approach nclude lower computatonal complexty, reduced knowledge requrements about system model parameters, and the potental to provde system stablty assessment n real tme. Most measurement-based approaches use approprate sgnal processng or spectral analyss technques to extract nformaton from perodcally collected power systems data. One such method s Prony analyss, whch has been nvestgated by Kumaresan et al. n exponentally damped sgnal analyss [4-5], and later appled to power systems by Hauer et al. n oscllatory stablty assessment [6-7]. Prony analyss s a powerful tool for mode parameter dentfcaton of electromechancal oscllatons. However, f nose s present n measurements t performs poorly [5]. Another shortcomng of Prony s method s that t s only sutable for transent, or rngdown, data analyss, and cannot be appled to ambent data such that the system s excted by random load varatons [8]. Therefore t s termed a rngdown analyzer that operates specfcally on transent porton of a measured sgnal. Alternatvely, several mode meters, such as the Yule- Walker method [8], autoregressve movng average (AR/ARMA) model [9], and subspace estmaton method [10-11], have been extensvely studed n the past two decades n order to estmate mode parameters from both ambent data and transent data. Whle n prevous efforts accurate estmaton has been acheved for oscllaton mode frequency, the problem of dentfyng mode dampng, a more mportant task n terms of stablty assessment, has not been satsfactorly resolved, although encouragng results were reported under certan test scenaros [6-12]. Ths work s supported by Power System Engneerng Research Center (PSerc) under the project S-44 ttled Data Mnng to Characterze Sgnatures of Impendng System Events or Performance Usng PMU Measurements, and n part by Texas A&M Unversty.

2 In ths paper, a data mnng approach s used to estmate oscllatory stablty n real tme. The decson tree (DT) method proposed by Breman et al. [13] s deployed to map system operatng pont at each moment to one of several predefned stablty states. Compared to prevous research [3] [14], the proposed approach casts the task as a mult-class classfcaton problem, as detaled n Secton III. In Secton IV we show the results of the proposed method usng the IEEE 39-bus test system. Fnally, the data mnng approach s evaluated on feld PMU measurements from Salt Rver Project (SRP), a publc electrcal utlty n Phoenx, Arzona, U.S.A. C. Mode Identfcaton wthout System Model In contrast to the model-based approach, the measurementbased approach does not requre detaled system model nformaton. Recent efforts take measurements from dfferent locatons durng the same perod of tme, and dentfy oscllaton mode parameters through sgnal processng technques. The mode parameters that can be estmated nclude frequency, f, dampng,, ampltude, A, and phase,, as shown n Fg. 1. II. THEORETICAL BACKGROUND A. Oscllatory Stablty Assessment Oscllatory stablty s related to Hopf Bfurcaton [1]. An nstablty event occurs when, followng a small dsturbance, the dampng torques are nsuffcent to brng the system back to a steady-state operatng condton, dentcal or close to the pre-dsturbance condton. Power system oscllatons may be classfed nto four categores n terms of frequency: 1) speed governor band, from 0.01 to 0.15 Hz; 2) nter-area electromechancal band, from 0.15 to 1.2 Hz; 3) local electromechancal band, from 1.2 to 5 Hz; and 4) torsonal dynamcs band, from 5 to 15 Hz. Ths work focuses on the second category: the low-frequency nter-area oscllatons. B. Model-based Analyss Tradtonally, the stablty of nter-area oscllatons s evaluated through modal analyss of the system s non-lnear dfferental algebrac equatons (DAE) usng detaled system model parameters [15], x f ( x, y, u), (1) 0 g ( x, y, u) where x s the state vector, y s the output vector, and u s the control vector. A lnearzaton of (1) wll result n x A x B u. (2) y C x D u From modal analyss theory, each par of complex conjugate egenvalues of matrx A stands for an oscllaton mode. For the th oscllaton mode the followng conjugate par may be termed, j (3) Then the mode s dampng rato (DR) s calculated as. DR. (4) 2 2 The nter-area oscllaton modes that carry sgnfcant amount of energy but wth nsuffcent DR are crtcal among all modes and need to be closely montored. Fgure 1. Mode parameters dentfed from power system measurements There are three types of relevant power system measurements: ambent data, transent (rngdown) data, and probng data. Fg. 2 shows the ambent and rngdown measurements. The probng data s beyond the scope of ths work and wll not be dscussed further. For ambent data an AR/ARMA model s used to derve mode parameters whle Prony analyss s used for rngdown data. Fgure 2. Model-based and measurement-based methods D. Data Mnng Approach The DT algorthm has been used as a classfcaton tool for onlne oscllatory stablty estmaton. The DT s created by sequentally splttng the tranng data set at each tree node,

3 startng from the root. The node splttng rule s determned by searchng all canddate attrbutes, and fndng the splt whch gves the largest decrease n class mpurty. A termnal node s reached when maxmum purty has been acheved. In the expermental secton we compared results obtaned usng DTs wth those obtaned usng artfcal neural networks (ANNs) and support vector machnes (SVMs). An ANN may be characterzed by the number of neurons and the weghts of connectons between them. The SVM and ts varants can make accurate predctons for non-lnear problems n kernel space, and s reslent to the presence of nose n data. Compared to ANNs and SVMs, the advantage of the DT method les n the relatvely smple model structure and fast analyss. The method s partcularly appealng because the DT uses a more transparent model whch makes the results easy to nterpret and replcate. The OP s related to ts stablty state through a unque top-down path. The splttng rule at each node that belongs to a gven path represents an operatonal threshold. Based on the combnaton of splttng rules along the path, preventve and correctve control strateges could be formulated and ntated. In ths work the commercal data mnng software CART [16] s used to tran the DTs. MATLAB [17] s used to mplement the neural networks and support vector machnes. Synchrophasors collected from Phasor Measurement Unts (PMUs) are used as the nput attrbutes to data mnng tools. A. Framework III. PROPOSED APPROACH A framework of the proposed measurement-based scheme s shown n Fg. 3. The model-based approach, whch was nvestgated by the authors n [3] and [18], s also shown n the fgure for comparson purposes. oscllatory stablty thresholds θ STB and θ ALT (θ STB > θ ALT ), operatng ponts (OPs) wll be labeled as Good f they satsfy DR crt θ STB ; Far f they satsfy θ STB > DR crt θ ALT ; Alert f they satsfy θ ALT > DR crt 0; and Unstable when 0 > DR crt. In practce, the values of θ STB and θ ALT are usually around 10% and 5% respectvely. Fgure 4. Classfcaton of oscllatory stablty states B. Mode Parameter Identfcaton Fg. 5 llustrates the onlne applcaton procedures of the proposed scheme. As the frst step, a knowledge base needs to be created n order to tran the classfcaton tree. Included n the knowledge base are the nput PMU measurements at each system operatng pont (OP), as well as the oscllatory stablty state correspondng to each OP. Real Tme PMU Measurements Correlated Actual System Performance Valdaton Valdaton Optmal Decson Trees Off-lne Tranng Generate Knowledge Database On-lne Applcaton Model-based Smulaton Predcted Performance or Events Compare Other Data Mnng Tools (LR, SVM, NN) System Model Data Estmated System Stablty Performance Generate Knowledge Database On-lne Applcaton On-lne Tranng Optmal Decson Trees Mode Parameters Identfcaton (nter-area mode dampng rato) Model-based Approach Measurement-based Approach Hstorcal PMU Data wth Correlated Known System Performance Fgure 3. Model-based (left) and measurement-based (rght) methods For each power system, several stablty thresholds are specfed wth respect to the typcal dampng rato of the crtcal oscllaton mode (DR crt ), and a set of stablty states s defned accordngly. As shown n Fg. 4, for the gven Fgure 5. Onlne applcaton of the proposed scheme The procedure s ntalzed wth a wndow scannng of the hstorcal PMU measurements. An Oscllaton Detector (OD)

4 s desgned to detect whether a transent event occurs by montorng the presence of a sudden devaton n recorded measurements. If there are no abnormal changes, the OD suggests that the system s operated under a steady state, and an AR/ARMA model s employed to estmate the mode parameters n a sldng wndow manner. The requred wndow length for ambent data analyss vares from 5 mnutes to half an hour, dependng on the varaton level of system loads. If a sudden devaton s detected, but only lmted to fewer than 5 data ponts, the correspondng measurements are consdered outlers caused by sensor or communcaton error, and are dscarded from consderaton. If a contnued devaton has been observed, the OD wll report that a transent process s potentally occurrng, and Prony analyss s appled to scan the transent data usng a sldng wndow wth a length of 5 to 10 seconds, dependng on the crtcal mode frequency of the nter-area electromechancal oscllaton. Fgure 6. One-lne dagram of IEEE 39-bus test system C. Classfcaton Tree for Stablty Assessment In order to overcome the lmtatons of Prony and ARMA methods, the rngdown data s pre-processed usng a low-pass flter, and the wndow length of AR/ARMA model s suffcently large to assure accurate estmaton. Once a suffcent number of cases have been accumulated, the knowledge base s used to tran the classfcaton trees. The derved optmal DT s then appled onlne. As shown n Fg. 5, new PMU measurements are dropped down through the tree to predct the oscllatory stablty status of each OP n real tme. One of the key challenges of embeddng DTs n onlne applcatons s the problem of evolvng system operatng condtons. Due to varatons n system generaton and loadng patterns, and changes n system topology, the DR crt of nter-area electromechancal oscllatons may also change. To deal wth ths eventualty, the classfcaton tree derved n CART needs to be perodcally refreshed n order to reflect the most current system operatng condtons. Ths s done by updatng the knowledge base usng the most recent PMU measurements, and re-tranng the DT. IV. CASE STUDY The IEEE 10-machne 39-bus test system (New England system) [19] s used to mplement the proposed scheme. Its one-lne dagram s shown n Fg. 6. Frstly the oscllaton mode parameters are estmated through model-based egenvalue analyss. They wll be used later to valdate the results of the measurement-based approach. The 39-bus system s modeled n MATLAB/SIMULINK. As shown n Fg. 7, the Network Soluton Module ntalzes the tme-doman smulaton, calculates power flow, and provdes real tme network solutons usng dynamc model parameters. Fgure 7. Smulnk model of the IEEE 39-bus test system The low-frequency oscllaton modes wth nsuffcent DRs are lsted n Table I. They are obtaned from modelbased egenvalue analyss of the IEEE 39-bus system. Also lsted n ths table are the domnant generators that partcpate n the correlated oscllaton modes. TABLE I. LOW-FREQUENCY OSCILLATION MODES OBTAINED FROM MODEL INITIALIZATION OF THE IEEE 39-BUS SYSTEM Frequency (Hz) Dampng Rato (%) Domnant Generator Mode #1 Mode #2 Mode #3 Mode #4 Mode # G1, G3 G4, G6 G3 G10 G2 In ths work the Mode #5 wth a frequency of 0.58 Hz s targeted for montorng. To smulate the load varatons, Gaussan nose wth Mean = 0.05 and Sgnal to Nose Rato (SNR) = 20 db has been ntroduced to four system loads. The tme-doman smulaton has been performed for 15 mnutes. To create transent sgnal, a fault that caused the lne between

5 Bus 26 and Bus 28 to trp has been smulated. The fault occurred at t = 700s, and lasted for 0.02s. The resultng measurements from all system buses are recorded. In partcular, the voltage magntudes and phase angles at Bus 7 and Bus 39 are shown n Fg. 8 and Fg Bus 39 Voltage Mag Bus 7 Voltage Mag Fgure 8. Voltage magntude sgnals x 10 4 Bus 39 Voltage Angle Bus 7 Voltage Angle Phase Angle dfference Fgure 9. Phase angles and ther dfference Prony analyss has been appled to the Bus 39 voltage magntude sgnal durng the transent process. The sldng wndow has a length of 5 seconds and the Prony model order s set to be N= x 10 4 have been deployed to compare the results. The mode dampng ratos estmated by AR of order N=60 are drawn n Fg. 10. The Mean of the dampng ratos estmated wth dfferent model orders have been summarzed n Table II. Table II shows that the mode frequency estmated from AR and Prony are very close to the egen-analyss results n Table I. The dampng rato estmated by AR s approachng the actual value when ncreasng the model order. The DR estmated by Prony analyss s dfferent due to the change n system topology. By varyng the load dsturbance level and fault scenaro, the tme-doman smulatons have been replcated and a total of 4938 OPs wth ther correspondng stablty states are ncluded n the knowledge base. A classfcaton tree has been developed n CART usng 80% of the cases, and the rest 20% has been used n new case testng. The classfcaton accuracy s evaluated as follows, Number of Correct Predcton Accuracy. (5) Total Number of Predcton The DT accuracy s summarzed n Table III. It s observed that an overall predcton accuracy as hgh as 98.38% has been acheved. TABLE III. CLASSIFICATION TREE PERFORMANCE Good Far Alert Accuracy Good Far Alert Accuracy V. APPLICATION TO FIELD PMU MEASUREMENTS Fgure 10. Dampng ratos estmated from ambent measurements TABLE II. ESTIMATE MODE #5 BY APPLYING AR TO AMBIENT DATA Order Frequency (Hz) Dampng Rato (%) N= AR N= N= Prony N= The AR model has been appled to the phase angle dfference between Bus 7 and Bus 39, whch s shown n Fg. 9. The ambent data before the fault are treated usng a sldng wndow wth a length of 10 mnutes. Dfferent model orders Fgure 11. Feld voltage magntude measurements from PMUs The feld PMU measurements receved from a publc electrcal utlty n Phoenx, Arzona, U.S.A., the Salt Rver Project (SRP), have been used to evaluate the proposed

6 scheme. The data nclude synchronzed voltage and current phasor measurements, under both ambent and transent condtons. The transent data recorded two consecutve brake nserton applcatons at a major transmsson substaton. The voltage magntude measured at another substaton has been dvded nto two 5-mnute sgnals as shown n Fg. 11. Each of the sgnals ncludes one transent process. A knowledge base has been created by applyng the same procedure ntroduced n Secton IV to the feld measurements from PMUs. The resultng DT performance has been summarzed n Table IV. Two other data mnng tools, the ANN and SVM, have also been used to compare the results. From Table IV, the DT-based predcton model acheved smlar accuracy to other data mnng tools. Compared to black-box models, the DT provdes a more transparent structure wth a clearer cause-effect relatonshp. Its pecewse structure and node splttng rules enable the dentfcaton of the crtcal varables and thresholds that should be analyzed to gan nsght nto the oscllatory stablty of a system. Data Mnng Tools TABLE IV. RESULTS COMPARISON Msclassfcaton Rate Good Far Alert Overall Accuracy DT ANN SVM VI. CONCLUSIONS The use of Decson Trees for onlne stablty assessment wthout the knowledge of system model parameters has been nvestgated n ths paper. Several conclusons have been reached: The proposed scheme s a measurement-based method that complements the tradtonal model-based approach. It s partcularly useful when system model parameters are not readly avalable; The proposed approach s able to provde control center operators wth real tme support by makng use of the quckly updated PMU measurements; Once traned usng the knowledge base, the DT-based predctor can acheve hgh accuracy n onlne oscllatory stablty estmaton; The data mnng tools are capable of reflectng the evolvng system operatng condtons when the most recent PMU measurements and correspondng knowledge base are used; Wth almost dentcal predcton accuracy, compared to ANNs and SVMs, the DT approach enables a more transparent model and provdes engneerng nsght n support of the decson-makng process. ACKNOWLEDGMENTS The authors gratefully acknowledge the Salt Rver Project (SRP) electrcal utlty for sharng the feld measurements from PMUs n support of the research durng PSerc project S- 44. 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