2784 ieee transactions on power systems, vol. 29, no. 6 ...le.xie/papers/dimentionality... · 2786...

2784 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 29, NO. 6, NOVEMBER 2014

Dimensionality Reduction of Synchrophasor Datafor Early Event Detection: Linearized Analysis

Le Xie, Member, IEEE, Yang Chen, Student Member, IEEE, and P. R. Kumar, Fellow, IEEE

Abstract—This paper studies the fundamental dimensionality ofsynchrophasor data, and proposes an online application for earlyevent detection using the reduced dimensionality. First, the dimen-sionality of the phasor measurement unit (PMU) data under bothnormal and abnormal conditions is analyzed. This suggests an ex-tremely low underlying dimensionality despite the large number ofthe raw measurements. An early event detection algorithm basedon the change of core subspaces of the PMU data at the occurrenceof an event is proposed. Theoretical justification for the algorithmis provided using linear dynamical system theory. Numerical simu-lations using both synthetic and realistic PMU data are conductedto validate the proposed algorithm.

Index Terms—Dimensionality reduction, early event detec-tion, phasor measurement unit, principal component analysis,visualization.

I. INTRODUCTION

T HIS paper is motivated by the need for real-time analyticsto make better use of the streaming data collected from the

increasing deployment of phasor measurement units (PMUs).Given the strong capability of the synchrophasor measurementsfor security assessment [1]–[3], a large number of other intelli-gent electronic devices (IEDs) with PMU functionality, such asfrequency monitoring network (FNET) [4] and frequency dis-turbance recorder (FDR) [5], are rapidly being brought online.As an illustration, China has coverage from about 1717 PMUsas of 2013 [6]; in the United States, there were about 500 PMUsinstalled by July 2012, and another 800 are anticipated by theend of 2014 [7], [8].There have been numerous discussions about utilizing

PMUs to improve wide-area monitoring, protection and control(WAMPAC) [9]–[11]. For example, the Lyapunov exponentsof the voltage phasors are utilized to monitor the short-termvoltage stability [12]. A PMU-based adaptive technique fortransmission line fault detection and location is proposed usingthe discrete Fourier transform [13], [14]. The phasor anglemeasurements are employed together with the system topologyto detect line outages [15]. ABB produces a monitoring system

Manuscript received July 30, 2013; revised December 06, 2013 andFebruary 14, 2014; accepted March 21, 2014. Date of publication April30, 2014; date of current version October 16, 2014. This work was sup-ported in part by Bonneville Power Administration Technology InnovationGrant, NSF ECCS Grant# 1150944, CPS-1239116, CPS-1232601, CPS-1232602, and NSF Science & Technology Center Grant CCF-0939370.Paper no. TPWRS-00983-2013.The authors are with the Department of Electrical and Computer Engineering,

Texas A&M University, College Station, TX 77843 USA (e-mail: [email protected]; [email protected]; [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TPWRS.2014.2316476

that can monitor phase angle stability, line thermal limits,voltage stability and power system oscillations using PMUmeasurements [16]. Given the increasing amount of PMU data,it has become a challenge to determine how to best manage andleverage the increasing amount of data from synchrophasors forreal-time operational benefits. Just one phasor data concentrator(PDC) collecting data from 100 PMUs of 20 measurementseach at 30-Hz sampling rate generates over 50 GB of data oneday [17].From a research perspective, large deployment of syn-

chrophasors raises several open questions: 1) What is the un-derlying dimensionality of the massive PMU data in wide-areapower systems? 2) Does the underlying dimensionality changeas the system operating conditions change? 3) Can such achange of dimensionality indicate the occurrence of an event inpower system real-time operations? 4) Is there any fundamentalconnection between the PMU data-driven analytics and themodel-based analysis of power systems? These are the newquestions that conventional model-based approaches alonecannot address.In this paper, by exploring the underlying dimensionality of

PMU data, we propose theoretical justifications for an earlyevent detection algorithm, which lends itself to early anomalydetection. Based on principal component analysis (PCA),the dimensionality reduction analysis provides a significantlylower dimensional “signature” of the states in the overall powersystem [18]. At the occurrence of a system event, an alertfrom the early event detection algorithm is issued whenevera large value of the proposed event indicator, induced by thechange of the core subspaces of the PMU data, is detected. Thekey features of the proposed algorithm are: 1) it is an onlinedata-driven approach requiring no knowledge of the systemmodel/topology; 2) it implements the dimensionality reductionat the adaptive training stage to extract the key features of theembedded high-dimensional PMU data; 3) it performs eventdetection using a much reduced number of PMUs as “pilots,”which is computationally desirable in real-time operations;4) it is theoretically justified using linear dynamical systemtheory; 5) for the online event detection, it does not requirelengthy buffering of data, which is required in the alternativeapproaches based on frequency-domain analysis; and 6) it iscapable of detecting system events at an earlier stage thanwould be possible by monitoring the raw PMU data.This paper is organized as follows. Section II presents a linear

PCA-based approach to analyze dimensionality reduction ofsynchrophasor data. Based on the dimensionality analysis ofPMU data, an online early event detection algorithm is pro-posed in Section III, with theoretical justification using lineardynamical system theory. In Section IV, numerical examplesutilizing synthetic PMU data from power system simulator forengineering (PSS/E) and realistic PMU data from Texas and

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XIE et al.: DIMENSIONALITY REDUCTION OF SYNCHROPHASOR DATA FOR EARLY EVENT DETECTION: LINEARIZED ANALYSIS 2785

Eastern Interconnections are provided to validate the proposedalgorithm. Conclusions and possible future research directionsare presented in Section V.

II. LINEAR ANALYSIS OF SYNCHROPHASOR DIMENSIONALITY

Dimensionality analysis and reduction of PMU data havebeen studied in recent literature due to the increasing sizeof PMU data [18], [19]. As one of the most commonly usedlinear dimensionality reduction methods, PCA reduces thedimensionality by preserving the most variance of the originaldata [20], [21]. Its fast computation feature alone is greatly at-tractive in the areas of coherency identification [22], extractionof fault features [23], and fault location [24], aside from itsconsiderable benefits for visualization.In this section, we propose a PCA-based approach to reducing

the dimensionality of streaming PMU data.Let denote the number of available PMUs across the whole

power network, each providing measurements. It is antici-pated that there could be up to thousands of PMUs in intercon-nected power systems, with each PMU providing up to 20 dif-ferent measurements1 at each sample [7], [8], [17]. At each timesample, a total of measurements are collected, in-dicating the difficulty of online data analytics. For each PMU,the measurements could include a variety of variables, such asfrequency and voltage magnitude, etc. In this paper, we conductthe dimensionality analysis for each category of measurementsindependently. In other words, we assume that at each round ofanalysis, . Define the measurement matrix

containing the measurements. Each mea-

surement has past samples, i.e., ,. The PCA-based dimensionality analysis is de-

scribed as follows, with the flowchart shown in Fig. 1:1) Calculate the covariance matrix of : .2) Calculate the eigenvalues and eigenvectors of .3) Rearrange the eigenvalues in decreasing order, with theeigenvectors being the principal components (PCs).

4) Out of the PCs, select the highest , which preservea cumulative variance satisfying . is apre-defined variance threshold, and .

5) Form a new -dimensional subspace from the top PCs.6) Project the original variables onto the -dimensionalPC-based space. Among the pairs of pro-jected vectors, select vector-based variables toform the basis matrix ,such that ,

, i.e., the variables should be as orthogonal toeach other as possible. The variables are henceforth de-noted as the “pilot PMUs,2” which will be utilized duringthe online detection described in Section III. The remaining

PMUs are denoted as “non-pilot PMUs.”3 ,containing the pilot PMUs, forms a linear basis for eachof the original measurements.

1Considering the different numbers of measurements provided by differenttypes of IEDs, this paper utilizes the industry grade PMUdevices, which provide20 measurements at each sample [19].2Pilot PMUs correspond to the PCs that are preserved after the PCA-based

dimensionality reduction. In reality, some practical concerns could also be in-cluded in the determination of the pilot PMUs. For example, for some topolog-ically and physically significant buses, their installed PMUs can be enforced tobe pilot PMUs.3Excluding the pilot PMUs from the total available PMUs, the rest are

denoted as non-pilot PMUs. In reality, some PMUs can also be enforced to benon-pilot PMUs if they are historically eventful.

Fig. 1. Implementation of the early event detection algorithm.

7) Represent the non-pilot PMUs in terms of , whereand , . Let

be the vector of the linear regres-sion coefficients for the approximation, i.e.,

(1)

Considering the large number of training PMU data in thedimensionality analysis, it follows that . There-fore, using and from the training data, can becalculated by solving the over-determined problem (1) as

(2)

in which the squared approximation erroris minimized [25].

Using (2), each non-pilot PMU measurement vector can berepresented in terms of the pilot PMUs. The dimensionality ofthe PMUs across the whole network can therefore be reducedfrom to , where . In such a case, the indepen-dent system operators (ISOs) or the vendors can utilize the pilotPMUs to approximate some selected non-pilot PMUs and de-tect the changes of system operating conditions in real-timeoperations.

III. ONLINE EVENT DETECTION USING PMU DATA

If the massive PMU data essentially lie in a much reduceddimensional space, ISOs or vendors can leverage the change inthe underlying subspaces of the PMU data to visualize and de-tect system events at an early stage. A system event is definedin this paper as a change of system topology, operating condi-tions or control inputs. In this section, we propose such an al-gorithm with the following features: 1) only a reduced numberof PMUs are needed; 2) it is online implementable; 3) it is the-oretically justified using linear dynamical system theory; 4) theimplementation of the algorithm can be done without knowl-edge of any underlying physical model of the system; 5) it candetect a system event at a very early stage (within 100 ms in ourstudy). This proposed early event detection algorithm consistsof two parts as shown the flowchart in Fig. 1. Fig. 2 provides an


Fig. 2. Overview of the early event detection algorithm.

overview of the proposed early event detection algorithm to beimplemented in power systems.

A. Adaptive Training

The adaptive training utilizes the PCA-based dimensionalityreduction proposed in Section II to compute the linear coeffi-cients ’s in (2).Define the training period as . It is presumed to have

been taken in normal operating conditions. At the current time, the PMU data in , in the normal operating conditions,

are employed to form the measurement matrix fortraining.Denote the update period as . is a system-dependent

variable, and usually can be chosen as 3–5 min. The adaptivetraining mechanism is designed as follows:1) If there is no event occurring during a period of , thetraining procedure is adaptively updated every timeunits.

2) If an event is detected within , the training procedureis updated immediately after the system recovers from theevent.

B. Robust Online Monitoring

The robust onlinemonitoring utilizes the pilot PMUmeasure-ments at current time and the coefficients ’s calculated fromthe adaptive training to approximate the measurements of someselected non-pilot PMUs at the same time. Under normal op-erating conditions, the predictor coefficients ’s provide ac-curate approximations of non-pilot ’s because of the usageof normal-operating-condition data in the training procedure.Whenever an event occurs, the spatial dependencies inside thepower system will change, resulting in the deterioration of theapproximations, leading to large approximation errors. When-ever a significant approximation error is noticed, an event alertis declared for the purpose of corrective control.

Assume that the real-time approximation of the th non-pilotPMU is

(3)

where is the measured at time , and is fromthe adaptive training in Section III-A.Define the relative approximation error of the th non-pilot

PMU as

(4)

where represents the real-time measurement of theth non-pilot PMU at time , andis the absolute approximation error. The occurrence of eventscan be monitored by using of some selected non-pilotPMUs.Numerically, because of the per unit scale of power system

variables, ’s are too small to be accurately identified atthe occurrence of events.We therefore propose a real-time eventindicator for the th non-pilot PMU, for the purpose of earlyevent detection, as

(5)

where is the mean value of calculated undernormal operating conditions. Whenever becomes largerthan a pre-specified threshold , an event alert is issued. Giventhe fact that the PMU samples at a rate of 30 Hz or higher, analert can be issued only two samples after the occurrence of anevent. Such a swift alert is capable of quickly identifying systemevents in real-time situations.Proposition 1: Using the proposed event indicator (5), a

system event can be detected within 2–3 samples of PMUs, i.e.,within 100 ms, whenever, for some selected non-pilot PMU ,the event indicator satisfies

(6)

where is a system-dependent threshold that can be calculatedusing historical eventful PMU data.

Proof: Large-scale power systems can be described by acoupled set of nonlinear differential and algebraic equations(DAEs) [26]

(7)

(8)

where and represent the power system dynamic stateand input vectors, respectively. defines the algebraic vari-ables-real and reactive power injections. denotes the time in-variant system parameters. Differential (7) consists of all thesystem dynamics including generators, wind turbines, loads,etc. Algebraic (8) represents the real and reactive power bal-ance equations.We linearize the nonlinear DAEs (7)–(8) around one system

equilibrium point (one operating condition), and eliminate thealgebraic equations by Kron reduction [27]. The resulting con-tinuous linear time invariant (LTI) state space model is

(9)

(10)


where and are the state and measurement vectors, re-spectively, with corresponding system matrices , , , and, which usually satisfies in power systems. is

the augmented input vector including the original system in-puts with the net injections of real and reactive power[27]. and are assumed to beuncorrelated white noises representing the modeling and mea-surement errors, respectively.Assume: 1) A zero-order hold of ; 2) A continuous in-

tegration of ; 3) . The discretization of (9) and (10)with sampling time yields [28]

(11)

(12)

where

(13)

Recursively substituting (11) into (12), the general expressionfor the measurement column vector at time can be representedas

(14)

where stands for the first system state in the training data,and represents the inputs at each time step before time .To generalize the proof, we further assume: 1) Each measure-

ment represents one PMU; 2) A total number of measure-ments are analyzed, each having samples for training, i.e.,

. Therefore, the th sample/row of can berepresented as . Denote

the observation matrix as , where. is the total number of system states, usu-

ally huge and unknown in reality. Correspondingly,, .

In order to prove the capability of the early event detectionalgorithm for early event detection, assume: 1) All the PMUdata for adaptive training are under normal operating conditions.Equivalently, 1a) is a constant input vector for

; 1b) the initial condition stays the same; 1c)the system matrices , , and stay the same. 2) Only onesystem event4 occurs at time .Using (14), the general form for the th measurement/column

in can be represented as

......

...

4In this paper, we only consider the detection of a single event using the earlyevent detection algorithm. The analysis and detection of multiple events or cas-cading events is a future avenue of research.

......

......

. . ....

...

(15)

where .Without loss of generality, assume the basis vectors in

are the first columns in . Therefore, using (2) and (3),can be represented as

(16)

where . Equivalently

(17)

As stated in (2), the ’s are calculated by minimizing thesquared error. Assume the calculation of ’s is of absoluteaccuracy. Therefore, 1) the errors in the calculations of the ’sare zero; 2) in (5) is almost zero. Consequently, forhigh dimensional training data, the three terms in (17) can beassumed to be zero, respectively, i.e.,

(18)

Now using (17) and (18), we will prove the capability of theearly event detection algorithm to detect the following threetypes of system events:1) Control Input Changes: For the control inputs in

(17), there are linear equalities. These equalities, whichare not necessarily linearly independent, form an over-deter-mined condition. Under this over-determined condition, theinitial input vector can be theoretically calculated by mini-mizing the squared error. Under normal operating conditions,

holds from (18). When one of the control inputschanges, the new input vector will not lie in the nullspace of . Consequently, a large nonzero termwill violate the zero approximation of (17), and thus impact theapproximation error (4).2) Initial Condition Changes: Consider the term related toin (17). There are linear equalities to solve for , in

an over-determined manner, . Under normal operatingconditions, holds as assumed in (18). A changeof the initial condition will make the new condition lieoutside the null space of . This will result in a large nonzero


term , which violates the zero approximation of (17)and results in a large approximation error in (4).3) System Topology Changes: During normal operating con-

ditions, and can be theoretically calculated by the over-determined equalities. In other words, they liein the null space of and , respectively. A change oftopology from into will yield changes of and

, as shown in (15). These changes will further inducechanges in the corresponding null spaces, in which andwill consequently not lie. As a result, a large nonzero term

will violate the zero approxima-tion of (17), and the approximation error (4) will be large.For the above three types of system events, the occurrence

of any one event will result in a nonzero approximation error(4), which serves as the numerator of the event indicator in(5). With an almost zero denominator calculated fromnormal operating conditions, will become huge at the oc-currence of any one of the system events.For some selected non-pilot PMUs, historical data with

known system events can be utilized to calculate the system-de-pendent threshold . Whenever in (6), a systemevent will be issued, and an alert will be declared for thepurpose of further corrective control.Remark 1: As shown in Fig. 1, starting from time , if there

is no event detected during the updating period , i.e., thetime interval between the current time and satisfies

, then the adaptive training procedure is conductedby updating the measurement matrix with the latest sdata.

IV. NUMERICAL EXAMPLES

In this section, we illustrate the efficacy of the early event de-tection algorithm, including the dimensionality reduction, theadaptive training, and the early anomaly detection. Both syn-thetic and realistic examples are utilized. Siemens PSS/E [29]is utilized to generate the synthetic PMU data, and the realisticdata are provided by Texas and Eastern Interconnections.

A. Dimensionality Reduction of Synchrophasor Data

In this section, the efficacy of the dimensionality reductionfor synchrophasor data will be illustrated. Synchrophasor datafrom normal operating conditions are utilized in the adaptivetraining procedure. Assume that the length of the training datais .51) Dimensionality Reduction of Synthetic PSS/E Data: A

23-bus 6-generator system in PSS/E is utilized to generate PMUdata. Fig. 3 serves as a demonstration of the system topology,which is not necessary in either part of the early event detectionalgorithm. Table I6 lists the dynamicmodels [29] for the 6 gener-ators employed in the PSS/E system. Assume each bus has onePMU installed, and the sampling rate is 30 Hz. To mimic theindustry-grade PMUs, noise is added to the synthetic trainingdata so that the signal-to-noise ratio (SNR) is 92 dB.

5In reality, more synchrophasor data under normal operating conditions couldbe utilized in the adaptive training to obtain more accurate and robust trainingmodels.6GENROU: Round rotor generator model. GENSAL: Salient pole generator

model. IEEET1: 1968 IEEE type 1 excitation systemmodel. SCRX: Bus or solidfed SCR bridge excitation system model. SEXS: Simplified excitation systemmodel. TGOV1: Steam turbine-governor model. HYGOV: Hydro turbine-gov-ernor model. N/A: No model for the component.

Fig. 3. Topology of PSS/E 23-bus system [29].

TABLE IDYNAMIC MODELS IN PSS/E SYSTEM

For bus frequency , the cumulative variance calculated fromPCA is shown in Fig. 4(a). The first two PCs alone preserve over99.99% of the variance. Similarly in Fig. 4(b), 2 PCs preserve80% of the cumulative variance for voltage magnitude . If

and are assumed, then

can be selected for both and .The corresponding basis matrices are

and .In order to illustrate the robustness of the proposed training

procedure, assume the resulting and areutilized for all the online synthetic cases before the first adaptivetraining takes place.2) Dimensionality Reduction of Realistic Texas Data: Seven

PMU data sets from Texas Interconnection are trained in thissection to serve for the online early event detection algorithm.No system topology could be provided due to the confidentialityof the interconnected areas and the modeling complexity of thesystem components. The cumulative variances for and areshown in Fig. 5. Assume and . Then

and can be chosen. The basis matrices areand .

It can be observed that the variance thresholds in the Texascase are less than those in the synthetic case, respectively, i.e.,

and . One reason is that even ifnoise with an SNR of 92 dB is added to the synthetic data, it is


Fig. 4. Cumulative variance preserved by PCs for PSS/E data. (a) Bus fre-quency . (b) Voltage magnitude .

still difficult to accurately mimic the changes of realistic systemoperating conditions.3) Dimensionality Reduction of Realistic Eastern Data:

Fourteen PMU data sets are provided by the Eastern Intercon-nection for bus frequency analysis, and 8 for voltage magnitude.The cumulative variances are shown in Fig. 6. For bus fre-quency , assuming with , thebasis matrix is . Assuming ,

is selected for voltage magnitude with basis matrix.

As can be noticed from Figs. 4–6, for both and , thedimensionality reduction can be achieved by the PCA-basedmethod proposed in Section II. Because of the localization prop-erty of voltage magnitude, the numbers of basis vectors forand usually satisfy .It is worthwhile to emphasize that we separately analyze the

dimensionality reduction of and using the PCA-basedmethod. As is well known, is a global variable, which has asimilar profile throughout the whole power grid, while is alocal variable because of the voltage-level difference. This prop-erty of and can be illustrated in the loading plots shownin Fig. 7 for the PSS/E data. In each of the loading plots, thelines demonstrate the projections of the original measurementvectors onto the PC-based space. The separation of the lines in-dicates how much the original vectors are correlated with eachother. As shown in Fig. 7, has a concentrated characteristic,while is much dispersed. Combining and in PCA willresult in combined dispersed characteristics. Consequently, theconcentrated properties of will be concealed by the dispersedproperties of , leading to further inaccuracy of the dimen-sionality analysis.

B. Online Event Detection Using the Early Event DetectionAlgorithm

In this section, both PSS/E data and Texas data are utilizedto validate online event detection using the proposed algorithm.The Eastern data will not be employed due to the fact that thedata as provided do not contain any events.

Fig. 5. Cumulative variance preserved by PCs for Texas data. (a) Bus fre-quency . (b) Voltage magnitude .

Fig. 6. Cumulative variance preserved by PCs for Eastern data. (a) Bus fre-quency . (b) Voltage magnitude .

1) Online Event Detection of Synthetic PSS/E Data: Threetypes of system events, line tripping, unit tripping, and con-trol input change, are simulated in the PSS/E 23-bus system,with the event details shown in Fig. 8. The control input changeevent is as in Section III-B1, and the line tripping and unittripping events correspond to the system topology changes inSection III-B3. The initial condition changes are not simulatedin this paper due to the difficulty of mimicing realistic systemoperating condition changes in PSS/E.In order to demonstrate the efficacy of the adaptive training,

assume: 1) The training procedure conducted in Section IV-A1works for all the three types of system events before the firstadaptive training takes place; 2) It takes 10 s for the systemto return to normal operating conditions after an event; 3) The


Fig. 7. 2-D loading plot of PSS/E data. (a) Bus frequency . (b) Voltage mag-nitude .

Fig. 8. Timeline of three simulated system events in PSS/E. (a) Line trippingevent. (b) Unit tripping event. (c) Input change event.

updating period is ; 4) If update is needed, the re-training period is the same as the original training period, i.e.,

.a) Line tripping event: As shown in Fig. 8(a), assume the

transmission line connecting buses 152 and 202 (Line 152–202)is tripped at , following by a closure of Line 152–202at . The total data length is 100 s.The bus frequency profile for bus 153 during the events

is shown in Fig. 9. As can be observed, it takes about 10 sfor the system to recover from either event, i.e., the systemrecovers to normal operating conditions at and

Fig. 9. profile during line 152–202 tripping and closure events in PSS/E.(a) Overall . (b) Zoomed-in during 1st event. (c) Zoomed-induring 2nd event.

, respectively. With , the training modelis updated at time with the latest 250 s data. Theupdated basis matrices are and

correspondingly. The Line152–202 closure event is detected using the updated basismatrices.Fig. 10 illustrates the event indicator of bus 153, which

can detect both events. A zoomed-in view of the early detectionof the tripping events is presented in Fig. 10(b) and (c), showingthe capability to detect the event almost instantly, within 40 ms.Line 152–202 tripping at results in a huge value of

at the next step . This indicates a large ap-proximation error of the linear representation. Comparatively,as can be seen from the frequency profile in Fig. 9(b), at time

, the bus frequency deviation is ,which is too small to be identified as an event. When a rela-tively large deviation is detected, it is al-ready 250 ms later than the occurrence time of the event. Sim-ilar results can be observed for the line closure event at time

. In this sense, the advantage of the proposed algorithmis illustrated.Another observation is from the comparison of

Fig. 10(b) and (c): the maximum deviation of the eventindicator in Fig. 10(c) is much smaller than that in Fig. 10(b).The reason comes from the adaptive training, i.e., the retrainingtakes the eventful data into consideration, and thereforeimproves the accuracy of the training model. However, fromFig. 10(c), the capability to early detect system events is notaffected by this improvement. In reality, two system eventswill not occur as close as those in this case. Therefore, theretraining data will not always contain the eventful data. Inaddition, by choosing an appropriate length of training data,this kind of improvement can also be avoided, and the trainingmodel can be accurate and robust enough to detect the event atan early stage, as shown in Fig. 10(c).


Fig. 10. Event indicator during line 152–202 tripping and closure eventsin PSS/E. (a) Overall . (b) Zoomed-in during 1st event. (c) Zoomed-in

during 2nd event.

Fig. 11. profile during unit 3011 tripping event in PSS/E. (a) Overall. (b) Zoomed-in .

b) Unit tripping event: As shown in Fig. 8(b), a unit at bus3011 is tripped at . Fig. 11 shows the bus frequencyprofile of bus 3002, with the event indicator in Fig. 12.In Fig. 11(b), from the bus frequency deviation

at , it is difficult to directly detect theunit tripping event. However, from Fig. 12(b), unit 3011 trippingyields a huge value of the event indicator provided bybus 3002 at . This clearly demonstrates that theproposed event indicator is capable of early event detection bymagnifying the difference between the quantities for the normalcondition and the contingency.

c) Control input change event: As shown in Fig. 8(c), thevoltage regulator set-point of bus 211 is changed by 0.01 p.u.and 0.01 p.u. at and , respectively. In this

Fig. 12. Event indicator during unit 3011 tripping event in PSS/E.(a) Overall . (b) Zoomed-in .

case, the training models are updated at time withthe latest data. The updated basis matrices arecorrespondingly and

. The second event with isdetected using the updated basis matrices.In Fig. 14(a), the event indicator provided by bus 201 is

capable of indicating both events. From Fig. 14(b), the event ofcontrol input change by p.u. is detected around

with , while from the bus frequencyprofile in Fig. 13(b), the bus frequency deviation

at cannot be detected efficiently. Similarresults can be observed from Figs. 13(c) and 14(c).In this case, because of the adaptive training, the maximum

deviation of the event indicator in Fig. 14(c) is smaller than thatin Fig. 14(b). However, this does not impact the efficacy andcapability of the event indicator for the early event detection, asshown in Fig. 14(c).2) Online Event Detection of Realistic Texas Data: In this

case, we utilize the Texas data to demonstrate the early eventdetection algorithm with respect to its purely data-driven capa-bility, i.e., without the knowledge of system topology or model.Both bus frequency and voltage magnitude are analyzed in thiscase.As can be observed from Figs. 15 and 17, there are two unit

tripping events occurring around and .After the first event, it takes about 300 s for the system to re-cover to normal operating conditions. In this case, assume theupdating period is and the retraining period is

. Therefore, according to the early event de-tection algorithm, the adaptive training results in Section IV-A2will work only for the first event. The latest training model be-fore the second event will be updated at time withthe latest 250-s data. The detection of the second event will beachieved using the latest training model. In this case, the re-training data do not contain any events and therefore can betterdemonstrate the efficacy of the adaptive training.


Fig. 13. profile during bus 211 input change events in PSS/E. (a) Overall. (b) Zoomed-in during 1st event. (c) Zoomed-in during 2nd

event.

Fig. 14. Event indicator during bus 211 input change events in PSS/E.(a) Overall . (b) Zoomed-in during 1st event. (c) Zoomed-induring 2nd event.

The event indicator of bus 4 frequency, , is shown inFig. 16. In the zoomed-in Fig. 16(b) and (c), the changes ofsystem operating conditions can be detected atand , respectively. However, from the bus fre-quency profile in Fig. 15(b), the bus frequency deviation

at is too small to be detectedearly or accurately. Similar conclusions can be drawn for

at in Fig. 15(c).For the same two events, the event indicator of bus 4 voltage

magnitude, , is shown in Fig. 18. The changes of system op-erating conditions are detected at and ,respectively, as shown in Fig. 18(b) and (c). From the voltage

Fig. 15. profile during unit tripping events of Texas data. (a) Overall .(b) Zoomed-in during 1st event. (c) Zoomed-in during 2nd event.

Fig. 16. Event indicator during unit tripping events of Texas data.(a) Overall . (b) Zoomed-in during 1st event. (c) Zoomed-in during2nd event.

magnitude profile in Fig. 17(b), the voltage magnitude devia-tion at is not as noticeable,and neither is at . As can benoticed, there is a drop of value in Fig. 18(a) around .This is because of the update of the training model, and will notbe evaluated as an event.For both and , the advantages of the proposed event

indicator for early event detection are demonstrated throughFigs. 9–18.The comparisons of detection time for the simulated bus fre-

quency cases are summarized in Table II. As can be observed,the proposed algorithm is capable of detecting each of the sim-ulated events earlier than would be possible by only using thebus frequency profiles themselves. This will benefit the ISOs


Fig. 17. profile during unit tripping events of Texas data. (a) Overall .(b) Zoomed-in during 1st event. (c) Zoomed-in during 2nd event.

Fig. 18. Event indicator during unit tripping events of Texas data.(a) Overall . (b) Zoomed-in during 1st event. (c) Zoomed-in during2nd event.

and the vendors for real-time operations and to efficiently applythe corrective controls.

V. CONCLUSION

In this paper, by exploring the dimensionality reduction ofthe PMU data, we have proposed an early event detection al-gorithm, along with theoretical justifications, to detect powersystem events at an early stage. A PCA-based dimensionalityreduction method for the PMU data is implemented with anadaptive training procedure. A basis matrix, consisting only ofthe pilot PMUs, can be employed to linearly approximate the

TABLE IICOMPARISON OF DETECTION TIME FOR BUS FREQUENCY CASES

non-pilot PMUs. The value of the approximation error is uti-lized to form an event indicator , which is designed for therobust data-driven early event detection in online monitoring.Both synthetic and realistic PMU data suggest the efficacy ofthe early event detection algorithm in detecting events in an on-line setting. Such detection is much faster than detection tech-niques that are based on direct frequency or voltage magnitudemeasurements.The presented work is only a first step towards understanding

and utilizing dimensionality reduction of online PMU data forreal-time monitoring. Much more research could be done alongthis direction. First, with the accumulation of more realisticevent data, we plan to continue investigating the efficacyand robustness of the proposed algorithm. Second, given thefundamental nonlinearity arising in power systems, nonlinearmethods will be further investigated for dimensionality analysis[30], [31]. Last but not least, online classification of particularcategories of events, such as inter-area oscillations, deservessignificant attention.

ACKNOWLEDGMENT

The authors would like to thank the Electric ReliabilityCouncil of Texas (ERCOT) and Pennsylvania-New Jersey-Maryland (PJM) Interconnection for the data provided. Theinformative discussion with engineers from Bonneville PowerAdministration (BPA), as well as with Prof. Y. Baryshnikovfrom the University of Illinois at Urbana-Champaign is alsoappreciated.

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Le Xie (S’05–M’10) received the B.E. degree inelectrical engineering from Tsinghua University,Beijing, China, the M.Sc. degree in engineeringsciences from Harvard University, Cambridge, MA,USA, in 2005, and the Ph.D. degree in electricaland computer engineering from Carnegie MellonUniversity, Pittsburgh, PA, USA, in 2009.He is currently an Assistant Professor with the

Department of Electrical and Computer Engineering,Texas A&M University, College Station, TX, USA.His research interest includes modeling and control

of large-scale complex systems, smart grid application with renewable energyresources, and electricity markets.

YangChen (S’12) received the B.E. degree in con-trol science and engineering in 2010 from HarbinInstitute of Technology, Harbin, China. She is pur-suing the Ph.D. degree in Department of Electricaland Computer Engineering at Texas A&M Univer-sity, College Station, TX, USA.Her industry experience includes an internship

(May to August 2013) with PJM Interconnection.Her research interests include data analyticsof phasor measurement units, power systemmodeling, analysis and control, voltage stability

monitoring and analysis.

P. R. Kumar (F’88) received the B.Tech. degreein electrical engineering (electronics) from I.I.T.Madras, India, in 1973, and the M.S. and D.Sc.degrees in systems science and mathematics fromWashington University, St. Louis, MO, USA, in1975 and 1977, respectively.From 1977–1984, he was a faculty member in

the Department of Mathematics at the University ofMaryland Baltimore County. From 1985–2011, hewas a faculty member in the Department of Electricaland Computer Engineering and the Coordinated

Science Laboratory at the University of Illinois. Currently he is at TexasA&M University, College Station, TX, USA, where he holds the College ofEngineering Chair in Computer Engineering. He has worked on problemsin game theory, adaptive control, stochastic systems, simulated annealing,neural networks, machine learning, queuing networks, manufacturing systems,scheduling, wafer fabrication plants and information theory. His currentresearch interests are in wireless networks, sensor networks, and networkedembedded control systems. His research is currently focused on wirelessnetworks, sensor networks, cyberphysical systems, and the convergence ofcontrol, communication and computation.Dr. Kumar is a member of the National Academy of Engineering of the USA,

and the Academy of Sciences of the DevelopingWorld. He was awarded an hon-orary doctorate by the Swiss Federal Institute of Technology (EidgenossischeTechnische Hochschule) in Zurich, Switzerland. He received the IEEE FieldAward for Control Systems, the Donald P. Eckman Award of the American Au-tomatic Control Council, the Fred W. Ellersick Prize of the IEEE Communica-tions Society, and the Outstanding Contribution Award of ACM SIGMOBILE.He was a Guest Chair Professor and Leader of the Guest Chair Professor Groupon Wireless Communication and Networking at Tsinghua University, Beijing,China. He is an Honorary Professor at IIT Hyderabad. He was awarded the Dis-tinguished Alumnus Award from IIT Madras, the Alumni Achievement Awardfrom Washington University in St. Louis, and the Daniel C. Drucker EminentFaculty Award from the College of Engineering at the University of Illinois.

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