1654 ieee transactions on smart grid, vol. 5, no ...1654 ieee transactions on smart grid, vol. 5,...

1654 IEEE TRANSACTIONS ON SMART GRID, VOL. 5, NO. 4, JULY 2014

Multiple Event Detection and RecognitionThrough Sparse Unmixing for High-Resolution

Situational Awareness in Power GridWei Wang, Student Member, IEEE, Li He, Student Member, IEEE, Penn Markham, Student Member, IEEE,Hairong Qi, Senior Member, IEEE, Yilu Liu, Fellow, IEEE, Qing Charles Cao, Member, IEEE, and

Leon M. Tolbert, Fellow, IEEE

Abstract—A situational awareness system is essential to provideaccurate understanding of power system dynamics, such thatproper actions can be taken in real time in response to systemdisturbances and to avoid cascading blackouts. Event analysishas been an important component in any situational awarenesssystem. However, most state-of-the-art techniques can only handlesingle event analysis. This paper tackles the challenging problemof multiple event detection and recognition. We propose a newconceptual framework, referred to as event unmixing, where weconsider real-world events mixtures of more than one constituentroot event. This concept is a key enabler for analysis of events togo beyond what are immediately detectable in a system, providinghigh-resolution data understanding at a finer scale. We interpretthe event formation process from a linear mixing perspective andpropose an innovative nonnegative sparse event unmixing (NSEU)algorithm for multiple event separation and temporal localization.The proposed framework has been evaluated using both PSS/Esimulated cases and real event cases collected from the frequencydisturbance recorders (FDRs) of the Frequency MonitoringNetwork (FNET). The experimental results demonstrate that theframework is reliable to detect and recognize multiple cascadingevents as well as their time of occurrence with high accuracy.

Index Terms—Event detection and recognition, linear unmixing,nonnegative sparsity constraint, power grid, wide-area situationalawareness.

I. INTRODUCTION

I T has become essential that wide-area situational aware-ness (WASA) systems can enable the monitoring of bulk

power systems and provide critical information for under-standing and responding to power system disturbances andcascading blackouts. Work first began in the 1980s on closelysynchronized measurements that would allow direct measure-ment of voltage phase angle at transmission level. As a result,

Manuscript received December 30, 2012; revised August 09, 2013 andNovember 21, 2013; accepted March 22, 2014. Date of current version June18, 2014. This work was supported in part by the Engineering ResearchCenter Program of the National Science Foundation and the Department ofEnergy under NSF Award Number EEC-1041877, in part by the CURENTIndustry Partnership Program, and in part by NSF-CNS-1239478. Paper no.TSG-00890-2012.The authors are with the Department of Electrical Engineering and

Computer Science, University of Tennessee, Knoxville, TN 37996 USA(e-mail: [email protected]; [email protected]; [email protected]; [email protected];[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/TSG.2014.2314116

Phasor Measurement Units (PMU) [1], [2] have been graduallyinstalled in substations that measure phasors at high voltagelevels. As a member of the PMU family, the Frequency Distur-bance Recorder (FDR) was developed at Virginia Tech in 2003.The FDR collects instantaneous voltage phasor and frequencymeasurements at low-voltage distribution level using ordinary120-V wall outlets. It then transmits the measured frequencydata remotely via the Internet. Based on these low-cost FDRs,a US-wide Frequency Monitoring Network (FNET) has beenimplemented [3]–[5]. FNET serves the entire North Americanpower grid through advanced situational awareness techniques,including, for example, real-time event alert, accurate eventlocation estimation, animated event visualization, and postevent analysis [6].When an event occurs in a power grid, a sudden imbalance

between generation and load consumption causes frequencychanges within the system that can be used as an indicator forevent disturbance. There have been a couple of works reportedso far conducting event analysis using data collected fromFNET [6]–[11]. Although successful, these state-of-the-arttechniques can only handle disturbances caused by a singleevent. If multiple cascading events are involved, existing tech-niques can only detect frequency disturbances caused by theinitial event, and the frequency disturbances from successiveevents might be overshadowed by continued frequency fluctua-tion from the initial event. The system disturbance reports fromthe North American Electric Reliability Corporation (NERC)[12] have made it obvious that major disturbances typicallyinvolve a number of unlikely, unplanned events. When multipleevents occur in cascading fashion, the electromechanical wavesgenerated will interfere with each other, and the measurementtaken at a FDR would more than likely be a “mixture” ofmultiple frequency signals. Thus, how to determine the numberof events that occurred and identify the types of events thatoccurred with precise estimation of occurring time using simplythe observed mixture is a very challenging problem.In this paper, we focus on the problem ofmultiple events de-

tection, recognition, and temporal localization. The main contri-butions of the paper are threefold: 1) the formulation of the mul-tiple event analysis problem using a linear mixing model, 2) theconstruction of the signature dictionary that incorporates tem-poral information to reflect the event dynamics in power grid,and 3) the validation of the proposed approaches using exten-sive simulations and real case studies.

U.S. Government work not protected by U.S. copyright.

WANG et al.: MULTIPLE EVENT DETECTION AND RECOGNITION THROUGH SPARSE UNMIXING 1655

Fig. 1. Four categories of typical root events in power grid. (a) Generator trip. (b) Load shedding. (c) Line trips. (d) Oscillation.

The rest of the paper is organized as follows. Section IIformulates the event unmixing problem. Section III explainsthe rationale behind the linear mixing model. Section IV elabo-rates on the construction of the root event signature dictionary.Section V describes the nonnegative sparsity constrained un-mixing algorithm and detection strategies. Sections VI and VIIconduct performance evaluation using both simulated casesproduced by PSS/E and real multiple event data recorded fromFNET. Finally, we conclude the paper and discuss future workin Section VIII.

II. PROBLEM FORMULATION

Mixed measurements are frequently encountered in real-world applications. Because of the resolution issue associatedwith discrete sampling and the effect of unknown sources,the measurements can rarely be pure. The existence of mixedmeasurements has brought the decomposition or unmixingtechniques to a wide array of applications. For example, in thefield of remote sensing, due to the large footprint, a single pixelusually covers more than one type of ground constituent. Thus,the measured spectrum at a single pixel is a mixture of severalground cover spectra, where the pixel unmixing technique hasbeen applied to subpixel object quantification [13], mineralidentification [14], area estimation [15], etc. Another emergingapplication is in biological microscopy where multispectralfluorescence microscopy is analyzed to discriminate differentco-localized fluorescent molecules with highly overlappingspectra [16]. Using common microscopy methods, the numberof molecules that can be detected simultaneously is limited by

both spectral and spatial overlap. These issues can be tackledby applying linear unmixing, which extends the possibilitiesto distinguish multiple proteins, organelles or functions withina single cell [17].Similar to the ubiquitous existence of mixed measurements,

events might not occur in a pure and isolated fashion, especiallyin power grid. Taking the major U.S. western blackout in 1996as an example, at the very beginning of the blackout, two par-allel lines were tripped due to a fault and mis-operation of theprotective equipment, and consequently some generation wastripped as a special protection system (SPS) response. Then, athird line was disconnected due to bad connectors in a distancerelay. After about 20 seconds of these events, the last strawof the collapse occurred when the Mill Creek -Antelope linetripped due to an undesired operation of a protective relay. Afterthis line trip, the system collapsed within three seconds. There-fore, to be able to provide high-resolution understanding of thepower system dynamics, it is very essential to perform multipleevent analysis.Typical power system disturbances fall into one of the four

categories, including generator trip (GT), load shedding (LS),line trip (LT), and oscillation (OS), which we refer to as the“root events” or “pure events”. See Fig. 1 for the frequencyvariation patterns when each of the root events occurs. Denotethe frequency signal collected at a FDR as (also referred toas the measured signal) and the frequency variation pattern ofeach root event as (also referred to as the source signal). Wepropose a new conceptual framework for the study of multipleevent analysis, where we consider the disturbances sensed at


each FDR, , as a linear mixture of a limited number of rootevents . The formulation can thus be expressed as

(1)

where is the measured mixture and is the number ofmeasurements corresponding to the time over which an eventis measured. is the root event signature dictionarywhose columns, , correspond to different patternprofiles of root events, and is the mixing coefficient vector.The possible error and noise are taken into account by the -di-mensional column vector . This concept is the key to accurateevent analysis that goes beyond immediately detectable infor-mation in a system and uncovers the true cause(s) of multiplecascading events. To realize this framework, however, we haveto answer the following questions.1) Is it valid to use a linear mixing model to formulate themixture sensed at a FDR?

2) How can one obtain the profiles of root events given thecomplexity and dynamic nature of the power grid?

3) How can one incorporate the different starting times ofcascading root events in the construction of ? and

4) How can one solve for event detection and recognitionpurposes in an on-line fashion?

We defer the discussions of the first issue to Section III andthe second issue to Section IV. To resolve the other two issues,we construct an overcomplete signature dictionary to incorpo-rate pattern profiles of various types of root events as well astemporal information on how events cascade. In this way we cansimultaneously detect event type and event starting time in oneunmixing procedure. In addition, since the number of events ismuch less than the number of pattern profiles in the dictionary,the “sparsity” enforced on the coefficient vector becomes anappropriate constraint that not only reduces the solution space,making the problem well-posed, but it also helps in the identifi-cation of event type and precise starting time. The sparse repre-sentation of the measured mixture is achieved through solvingan -regularized least squares problem, which can be done ef-ficiently through convex optimization.To further improve the robustness, we also enforce the

“nonnegativity” constraint on the coefficient vector . Thereare two reasons for adding this constraint: first, from the energyperspective, physical laws govern the power flow in a gridwhere the mixture of electromechanical waves generated bymultiple disturbances should be only an additive combinationof the constituent components; second, since generator tripsgenerally cause a decrease in frequency while load sheddingsgenerally cause an increase in frequency, the nonnegativityconstraint on is especially helpful to eliminate error caseswhere a load shedding event is mistakenly recognized as agenerator trip in the reverse way.Based on the discussion above, we mathematically formulate

the event unmixing problem as below:

(2)

where represents -norm, which is defined as the numberof non-zero entries in vector . The proposed cost function

Fig. 2. Demonstration of validity of the linear mixing model. Top: frequencysignals of two single events. Bottom: frequency signals of simulated multipleevents and additive combination of the two single events.

consists of two components with one measuring approxima-tion error of the linear mixing model (i.e., ) and theother measuring sparsity of the coefficient vector, . We referto the proposed algorithm as nonnegative sparse event unmixing(NSEU) for detection, recognition, and temporal localization ofmultiple cascading events in power grid. In the following sec-tions, we will discuss solutions to the four questions raised inthis section.

III. LINEAR MIXING MODEL

In a power grid, since the total frequency change is propor-tional to the total generation/load loss [18], it is reasonable toapproximate the mixture of frequency signals as a linear addi-tion of frequency signals caused by each individual event.We validate the linearity of the mixing process through two

experiments carried out using the PSS/E simulation. PSS/E is acommercial software for simulating, analyzing, and optimizingpower system performance based on concrete system configura-tion, thus it can precisely reflect the dynamics of a real system.In the first experiment, we conduct two simulations, Simu1and Simu2. In Simu1, a generator producing 110 MW poweris tripped (GT1) at the 10th second, producing the frequencysignal with about ’s frequency drop. In Simu2,a generator producing 778 MW power is tripped (GT2) at the30th second, producing the frequency signal with about

’s frequency drop. In the second experiment, weconduct only one simulation, Simu3, where the two generatortrips are programmed as two cascading events occurred at the10th and the 30th second, sequentially, producing the frequencysignal . The validation is to see if approximates. As shown in Fig. 2, the top sub-figure displays measured

signals from the two single events, and , and the bottomsub-figure compares measured signal and summation of

. It is easily observed that accurately approximateswith the root mean squared error (RMSE) being only.

Therefore, it is reasonable to formulate the measured mixtureat a FDR using a linear mixing model. The effectiveness of the


model will be further demonstrated using both simulated andreal case studies, as discussed in Sections VI and VII.

IV. SIGNATURE DICTIONARY CONSTRUCTION

Both the second and the third questions raised in Section IIregarding the formulation of event unmixing are related to con-struction of the root event signature dictionary . The dictionaryconstruction involves two steps. First, the root event patternsare learned from the training data previously collected fromFDRs recording disturbances experienced during single events.Second, temporal information (i.e., event starting time) is incor-porated into dictionary by augmentation and padding with thelearned root event patterns.

A. Learning Root Event Patterns

As mentioned in Section II, typical power system distur-bances (events) fall into one of four categories, includinggenerator trip (GT), load shedding (LS, or load drop), linetrip (LT), and oscillation (OS). As described in [8], [19], [20],events of the same category generally share similar character-istics. For example, a generation trip always starts with a rapidfrequency drop while a load shedding always starts with a fre-quency increase. Meanwhile, events of the same category alsocontain a certain degree of differences because of the differentsetups of intrinsic parameters, including power flow output,consumption, etc. It is impractical to include every single eventpattern in the dictionary which would affect the performance ofonline processing, especially for large-scale systems, like thepower grid. We, instead, resort to machine learning approachesto find a representative set of root event patterns for each eventcategory. Hereinafter, we refer to these root event patterns as“root-patterns”.There are various methods that can be adopted for learning

the root-patterns, including, for example, K-means clusteringand dictionary learning [21], [22]. The K-means clustering ischosen in order to preserve the physical meaning of each el-ement (or column) of the dictionary such that it represents asignature profile of an actual root-pattern, facilitating the eventdetection and recognition process. Given a set of single eventobservations of the same event category col-lected from either recordings of a real system (e.g., FNET) orsimulation, K-means clustering aims to partition the obser-vations into subsets, so as to minimize the within-clustersum-of-squares error:

(3)

where refers to the set of learned root-patterns and is the centroid of cluster . Notice that be-fore performing K-means clustering on , eachvector should be normalized to have unit -norm, such thatthe scale ambiguity [23], [24] in learning root-patterns is elim-inated. In addition, when performing K-means clustering, in-stead of directly using the mean vectors as cluster centroids, weselect the nearest observation as the cluster centroid for theth cluster in the final loop. In this way, the learned root-patternsare closer to real data.

In the context of this paper, we expect to detect and recognizethree different types of events, i.e., GT, LS, and LT. If we set

for K-means clustering, then the number of root-patternswill be .

B. Incorporating the Temporal Information

After learning the set of root-patterns from each category, thenext step is to incorporate the temporal information into con-struction of the root event signature dictionary, . We refer toeach column of that already embeds temporal information asthe “temporal root-pattern”. The reason for doing this is that anyevent, be it single or consisting of cascading events, can start atany time and can last for a different period of time. To ensurethat the unmixing algorithm always captures the entire durationof the root event for better recognition accuracy, the dictionaryneeds to contain the root-patterns starting at all possible times.Another reason for doing this is such that we obtain an overcom-plete dictionary and the sparsity constraint would enable extrac-tion of only a few large valued non-zero mixing coefficients in, reducing the false-alarm rate. In the following, we detail theconstruction process of the temporal root-patterns.Suppose the root-patterns last for at most seconds and the

sampling frequency is , then each root-pattern would havesamples. For an observation vector acquired from a FDR

that lasts for seconds, it can have samples starting fromthe pre-event steady state, like 60 Hz, to the post-event steadystate. The dimension of is always larger than or equal tothat of since is always true, i.e., a multiple-eventobservation always consists of at least one root event.From the temporal perspective, each root-pattern can start at

all possible sample points from the first one to the thduring the time period . To obtain the temporal root-patterns,we construct number of profiles for each root-pattern by shifting it from the first sample to theth sample. For instance, denote a root-pattern as ,

. If we want to construct one temporal root-pattern, occurring at the th sample point for, then can be calculated as:

forfor

(4)

where , is the Dirac delta functionand denotes the convolution process. Because we only ana-lyze frequency fluctuation of the signal for event unmixing pur-pose, the starting value of is 0 Hz (by removing the basefrequency 60 Hz). Therefore, the function of (4) actually padsthe samples before the selected th sample with zero and thesamples beyond with tail stable value of toform a temporal root-pattern. The whole formation of a groupof temporal root-patterns from one root-pattern is illustrated inFig. 3.

V. NONNEGATIVE SPARSE LINEAR UNMIXING

Once we have constructed the overcomplete dictionary , wecan apply it to estimate the coefficient vector and use forevent detection—coefficients of non-zero value indicate that the


Fig. 3. Example: Shifting and padding one root-pattern to be “temporal root-patterns”, bottom-left: one root-pattern, top: temporal root-patterns with differentstarting time, bottom-right: a set of temporal root-patterns to be contained in dictionary .

corresponding temporal root-pattern in the dictionary should beused to reconstruct the observation mixture, . Since the tem-poral root-pattern indicates event’s pattern occurred at a certaintime, by deriving , we can detect existence of multiple cas-cading events as well as their temporal locations (or startingtime). Given the overcomplete dictionary, traditional methodsfor coefficient estimation such as the Fully Constrained LeastSquares (FCLS) [25] or the Nonnegatively Constrained LeastSquares (NCLS) [26] would not work, since the estimated co-efficient by FCLS or NCLS may have non-zero values on eachroot-pattern which would not serve as suitable methods for de-tection purposes. Recall that the number of constituent eventsinvolved in a cascading incident is generally small.On the other hand, recent developments on sparse coding

techniques [27]–[29] would provide good solution to the pro-posed NSEU algorithm in (2). The sparse coefficient vector pro-duced by sparse coding is confined by the sparsity constraint thatonly a few elements of the vector are non-zero, indicating thatonly a few temporal root-patterns would be utilized to recon-struct the original signal . In the application of event detec-tion, it is equivalent to say that only a limited number of eventshave occurred. Although the sparse optimization problem in(2) is NP-hard in general, Donoho [30] suggested that as longas the desired coefficient vector is sufficiently sparse, it canbe efficiently recovered by instead minimizing the -norm, asfollows:

(5)

Equation (5) can also be expressed as

(6)

where balances the sparsity of the solution and the fidelityof the approximation to . The “feature-sign search algorithm”in [29] is revised to solve this sparse coding problem with thenonnegativity constraint added.

Event detection is mainly based on studying the non-zero co-efficients in the sparse coefficient vector, , as each coefficientcorresponds to the weight of each atom (or column vector in thedictionary) in forming the observation vector . The larger thecoefficient, the more contribution the root event has in makingthe mixture. We apply an empirically-determined threshold onwhere coefficients above the threshold would correspond to

the temporal root-patterns that occurred at a certain time.

VI. EVALUATION WITH SIMULATED DATA

This section conducts a series of experiments to demonstratethe effectiveness of the proposed NSEU algorithm using simu-lated data. The simulations are done on a small synthetic powergrid model “savnw” using the software “Power System Simu-lator for Engineering (PSS/E)” [31]. The grid model “savnw” isan example bench case supplied with PSS/E, whose configura-tion is illustrated in Fig. 4. As shown in the figure, the modelincludes 6 generators, 17 branch lines, 7 loads, and 21 buses.Each type of single event will cause the system to arrive at anew steady state within 30 seconds. We thus use 30-second fre-quency fluctuation of single event for learning root-patterns. Be-cause this power grid model is quite small, we simply select 4generator trips (GT) and 1 load shedding (LS) as root-patterns.As for line trips (LT), we apply the K-means method to extract5 root-patterns using the training data collected from 17 lines.Since we have not collected data with oscillation, we omit theoscillation event for simplicity.The dictionary is thus built based on the 10 extracted root-

patterns. Suppose a multiple event case would last for 40 sec-onds and the sampling rate is set to 60 Hz, the dictionary willthen include temporal root-patterns. We also can improve the on-line performance by de-creasing the number of temporal root-patterns in by shiftingat every two or more samples, at the sacrifice of losing a bit oftemporal localization accuracy. In each test, the regularizationparameter of NSEU is selected as and the threshold isselected as 0.034.


Fig. 4. Configuration of the synthetic power grid model, “savnw”, in PSS/E. This grid model “savnw” is an example bench case model supplied with PSS/E.It includes 6 generators, 17 branch lines, 7 loads, and 21 buses. All the simulated cases are produced by manually generating events in this grid model.

Based on the grid model “savnw”, we have conducted exper-iments on 8 cases of single event (S1C), 10 cases of multipleevent with two constituent components (M2C), and 5 cases ofmultiple event with three constituent components (M3C). Weuse four metrics to measure performance, including detectionaccuracy, false alarm rate, root-pattern recognition rate (R-PRecog), and occurrence time deviation from the ground truth(OT-Deviation), as shown in Table I.Both detection accuracy and false alarm rate are used to eval-

uate detection performance of the NSEU algorithm. The detec-tion accuracy calculates the ratio between the number of cor-rectly detected root events and the number of total root eventsaccording to the ground truth. The false alarm rate calculatesthe ratio between the number of detected root events not re-

TABLE IQUANTITATIVE EVALUATION ON SIMULATED EVENT CASES

ally happen and the total number of root events according to theground truth. As indicated in Table I, we can find that the pro-posed NSEU algorithm can detect all constituent events with100% accuracy while with very low rate of false alarms.The root-pattern recognition rate (R-P Recog) is used to eval-

uate the recognition performance. It calculates the ratio betweenthe number of correctly identified events (i.e., events with cor-


Fig. 5. Simulated multiple-event of LT154-3008 at 1 s, LT151-201 at 8 s andGT3018 at 15 s, top: unmixed coefficients with events starting time, middle:original and reconstructed signal, bottom: event type classification indicatesthree events are from root-patterns 8&6&4, and ground truth is marked withblack squares.

rect type of root-pattern) and the number of correctly detectedevents. Table I indicates the averaged root-pattern recognitionrates are very high.The deviation between the detected occurring time and the

ground truth (OT-Deviation) is used to evaluate the temporallocalization performance. As shown in Table I, the averagedOT-Deviation values are all very small, indicating the high ac-curacy of temporal localization.In addition, the results also show that the NSEU algorithm

has strong capability of signal reconstruction based on the linearmixing model, where the averaged reconstruction MSE of the23 example cases is .We also visually show one simulated example case of three

cascading events: LT 154-3008, LT 151-201, and GT 3018 oc-curring at the 1st, 8th, and 15th second, respectively, with arecording length of 50 s. The frequency recording from a ran-domly selected bus is used to simulate data collected from anFDR. The unmixing results using the proposedNSEU are shownin Fig. 5. From the top sub-figure, we clearly see that there arethree events above the detection threshold that occurred around1.03 s, 8.04 s, and 15.05 s, respectively. The reconstructed signalshown in the middle sub-figure resembles the original inputsignal with just very small deviation. In the bottom sub-figure,we sum up all the coefficients that belong to the same root-pat-tern for recognition purpose, in order to identify what type ofevent has occurred. The indices for root-pattern 1 4, 5 9,10 represent generator trip, line trip, and load shedding, respec-tively, and the indices with black square is the ground truth.From this detection result we know that the first two events areline trips and the third event is a generator trip, which is exactlywhat happened according to the ground truth.

VII. EVALUATION WITH REAL EVENT DATA

For evaluation with real event cases, we take the same strate-gies as used for experiments on simulated cases. However, theroot-patterns utilized are learned from real data collected fromboth US-wide FNET (generator trip and load shedding events)and PSS/E (the line trip events).

A. Event Data and Preprocessing

Three real event cases are used for evaluation.Case 1) A single event (generator trip) happened at a power

plant on May 30, 2006, as shown in Fig. 6 (Left).We use the first 50-second data (which is providedat 0.1 s interval for a total of 500 samples). 10 FDRsat different locations are used for checking the de-tection repeatability.

Case 2) A multiple-event case (a generator trip and a linetrip) happened at Surry, VA on February 2, 2011, asshown in Fig. 6 (Middle). We use the first 50-seconddata and 18 FDRs are used for checking the detec-tion repeatability.

Case 3) A multiple-event case that happened on August 4,2007, comprised of multiple single-line-to-groundfaults on a 765-kV line and generator trip at two lo-cations. The Eastern Interconnection frequency thusdropped from 60 to 59.864 Hz, as shown in Fig. 6(Right). We use the first 60-second data becausemajor events occurred in this period of frequencytransition (from stable state 60 Hz to the next stable59.864 Hz) for event detection purpose. 18 FDRs atdifferent locations are used for checking the detec-tion repeatability.

Before applying the NSEU algorithm to detect each con-stituent event, it is necessary to eliminate noises in the frequencydata. There are, in general, two kinds of noises reside in a fre-quency signal, including white noise and impulsive noise.Elimination of these two kinds of noises is an intricate process[32]. We adopt the adaptive median filter designed in [7] fornoise removal. Fig. 7 shows an example of the filtering effect.We observe that the filter successfully removed white noiseand spikes in original frequency signal, preventing possibledetection error caused by undesired noises.

B. Root-Pattern Learning

1) Training Case Selection: In order to select appropriatetraining cases, real data obtained from FNET and simulated datafrom PSS/E are used for learning. As described in [20], signif-icant time was devoted for selecting the training cases. In theUnited States, the power system is divided into the Eastern (EI),Western (WECC), and Texas (ERCOT) interconnections, whichare not synchronized with each other.First, data from individual generation trip and load shedding

events are retrieved from the FNET database [33]. Since FNETdoes not currently detect line trips, there is no entries or corre-sponding data for this event type. PSS/E was instead used toperform time-domain simulations of line trips. A 16,000-busmodel of the Eastern Interconnection was used for simulations.


Fig. 6. Frequency plot of three real event example cases. Left, Case 1: single event of a GT (10 FDR signals); Middle, Case 2: multiple events of one GT withone LT (18 FDR signals); Right, Case 3: multiple events of two GTs and two or three LTs (18 FDR signals).

Fig. 7. Result of applying the adaptive median filter on a signal collected fromthe FDR 14 of Case 3. The filter successfully removed white noise and spikes,especially the large spike around the 32th second.

TABLE IIBREAKDOWN OF TRAINING CASE EVENT TYPES

Approximately 75 buses corresponding to actual FDRs were se-lected as measurement points, and lines adjacent to these buseswere tripped one at a time. A 20-second simulation was per-formed in each case, with measurement points being saved at0.1-second intervals to match the reporting rate used by FDRs.Finally, all the data selected from different sources for trainingis shown in Table II.2) K-Means: Next, K-means clustering algorithm is used for

root-pattern learning. We also used the adaptive median filter topreprocess the training data before applying K-means. We set

and six root-patterns are learned for each of the threeevent categories. As shown in Fig. 8, each root-pattern has 200data entries standing for 20 s data with 0.1 s interval. From thisresult we can confirm that the learned root event patterns ofeach category indeed share similar characteristics with a cer-tain degree of difference, as explained in Section IV-A. Otherclustering algorithms, such as expectation-maximization (EM)or Dirichlet Process (DP) may be used for clustering as well,however, those algorithms produce similar results.

C. Detection Result

The learned root-patterns fromK-means are used to constructtemporal root-patterns to form the dictionary . We set the de-tection threshold as 0.04. That is, a temporal root-pattern willbe selected if the value of its corresponding coefficient is abovethe threshold.1) Case 1: Recall that case 1 is a single event case. The

detection results, as shown in Table III, indicate that the NSEUalgorithm successfully detected a single generator trip of root-

TABLE IIIEVENT DETECTION RESULTS FOR CASE 1. ONE GENERATOR TRIP ACTUALLYHAPPENED IN THIS REAL EVENT. ALL THE FDRS SUCCESSFULLY DETECTED

THE GENERATOR TRIP

TABLE IVEVENT DETECTION RESULTS FOR CASE 2. ONE GENERATOR TRIP AND ONELINE TRIP ACTUALLY HAPPENED IN THIS REAL EVENT. ALL THE FDRSSUCCESSFULLY DETECTED ONE GENERATOR TRIP (ROOT-PATTERN 6) AND

ONE LINE TRIP (ROOT-PATTERN 8 OR 12)

pattern 1 from each signal of 10 FDRs at different locationswithout any false alarm.2) Case 2: It is a multiple-event case with one generator trip

followed by one line trip. The detection results are shown inTable IV. All of the signals from 18 FDRs successfully detectedone generator trip from root-pattern 6 and one line trip, althoughthe detected line trip may be from either root-pattern 8 or 12.This maybe because the line trip’s root-patterns learned basedon PSS/E simulations can not reflect very well the behavior ofreal line trip events.3) Case 3: Case 3 is another multiple-event case with two

generator trips and possibly two or three line trips involved,thus it is more complicated than cases 1 and 2. The detectionresults are shown in Table V. The results show that the NSEUalgorithm successfully detected two generator trips from 16 outof 18 FDRs and two line trips from 17 FDRs without any falsealarms. An example of the detected root-patterns and the recon-structed signal from FDR 14 are shown in Fig. 9. From the topsub-figure of sparse coefficients, it is clear that the algorithmdetects two generator trips and two line trips correctly. The re-constructed signal in the middle sub-figure is also very close tothe original signal.This result further confirms that the NSEU algorithm can

not only correctly detect single event, but it also can handlemultiple cascading events with accurate temporal localization.


Fig. 8. K-means clustering results for root-pattern learning (all the patterns above are normalized after remove their mean value).

TABLE VEVENT DETECTION RESULTS FOR CASE 3. TWO GENERATOR TRIPS ANDMULTIPLE LINE TRIPS MAY HAVE HAPPENED DURING THIS REAL EVENT.MOST OF THE FDRS DETECTED TWO GENERATOR TRIPS (ROOT-PATTERNS 3& 6) AND TWO LINE TRIPS (ROOT-PATTERNS 8 & 12). THE GENERATOR TRIPROOT-PATTERN 3 WAS NOT DETECTED BY FDR 2 & 16 AND THE LINE TRIP

ROOT-PATTERN 12 WAS NOT DETECTED BY FDR 3

TABLE VIQUANTITATIVE EVALUATION ON REAL EVENT CASES

However, line trips in this case are not completely detected sinceone line trip is missed. As for the processing time, since thesampling cycle of the FDR sensors in FNET is 0.1 second, amultiple-event case from one stable state to another stable statelasted for 60 s will have 600 samples. Then, in our settings, thedictionary derived from 18 root-patterns will have the numberof profile columns no more than . TheNSEU algorithm only takes less than 1 second under Matlabusing an ordinary laptop with Intel i7 core 2.7G for processinga recording by one FDR sensor, and we can expect much shortercomputational time if programmed in C.

D. Summary of Unmixing Performance

In the three experiments with real event cases, we have an-alyzed frequency signals from 46 FDRs in total. As shown inTable VI, the proposed NSEU algorithm can detect constituentevents with 98.15% averaged accuracy for generator trips and

Fig. 9. Case 3 detection result using data from FDR 14, where two generatortrips are detected at 5.6 s and 7.0 s, and two line trips are detected at 7.4 s and8.0 s, respectively. Bottom: Four detected events include two GTs and two LTsfrom the third, sixth, eighth and twelfth root-pattern, respectively.

82.4% averaged accuracy for line trips without any false alarms(FA). Due to the lack of ground truth, we cannot evaluate per-formance of recognition or temporal localization.From the experimental results, it is easy to see the advan-

tage of the proposed NSEU algorithm over existing event de-tection techniques. In Fig. 6, we observe that there is no im-mediately perceivable difference between frequency signal of amultiple-event case and that of a single-event case, because thenature of the mixing process will occlude or degrade most of thefeatures from different root patterns. Most of the existing tech-niques based on immediately detectable information can onlydetect the starting time of the initial event involved in multiplecascading events. In contrast, the NSEU algorithm is able to un-cover the constituent root events with high detection accuracy,except for the line trip detection rate in Case 3. The difficultyfor line trip detection can be analyzed from three aspects: First,the root-patterns of line trip are learned based on simulation,


which might not reflect the dynamics of line trips that occurredin real world. Second, the frequency change of line trips is gen-erally smaller than that of generator trips, probably causing theunmixed coefficients on line trips to be smaller than that on gen-erator trips. Therefore, line trips might not be detected if usingthe same detection threshold for GTs and LSs. Third, the powerimbalance caused by some line trips is quite small that can beeasily adjusted by system’s self-resilience.

VIII. CONCLUSION AND FUTURE WORK

This paper presented a novel interpretation of the systematicsof frequency signal formation ofmultiple events in a power grid.Through analysis of the connection between frequency distur-bance of multiple events and frequency fluctuation of singleevent, we developed an effective and promising constrained“event unmixing” algorithm, NSEU, based on a simple linearmixture model for multiple cascading events detection, recog-nition, and temporal localization. The experimental results withboth simulated and real event cases demonstrated the effective-ness of the proposed algorithm. Benefited by the frequency datarecorded by FNET, this work provides a new and feasible way toobtain high-resolution situational awareness of the power gridsystem. The findings from this work would also benefit otherapplications, particularly for example, microgrids remote moni-toring, multiple events localization, and smart grid coordination.In order to further improve the performance of the NSEU

algorithm and extend its potential for situational awareness,we plan to conduct the following investigations in the future.First, to make the algorithm more robust to oscillations, we willconsider adding the oscillation root-events in the overcompletesource signature matrix, . Second, to improve performance ofline trip detection, we will design a “weighted” dictionary suchthat the unmixed coefficients of different root events would beat comparable scale. Third, as observed from Tables III andIV, different FDRs would report different starting times for thesame event. This can be further utilized for event localizationpurpose as described in [9], [11].

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WeiWang (S’12) received the B.S. degree from Uni-versity of Science and Technology, Beijing, China, in2006 and the and M.S. degree from Beihang Univer-sity, Beijing, China, in 2009. He is currently pursuingthe Ph.D. degree in the Department of Electrical En-gineering and Computer Science, University of Ten-nessee, Knoxville, TN, USA.His research interests include signal/image anal-

ysis, pattern recognition, machine learning and smartgrid secure monitoring.

Li He (S’11) received the B.S. degree from ChinaUniversity of Geoscience, Beijing in 2005, the M.S.degree from Beijing Jiaotong University, Beijing,China, in 2008, and the Ph.D. degree from theUniversity of Tennessee, Knoxville, TN, USA, in2013.He is currently an Algorithm Engineer at

KLA-Tencor Corporation. His research interestsinclude machine learning, image processing, linearunmixing and color emotion.

Penn Markham (S’03) received the B.S.E.E fromVirginia Polytechnic Institute and State University,Blacksburg, VA, USA, in 2006 and the Ph.D. degreefrom the University of Tennessee, Knoxville, TN,USA, in 2012.He is now a Research Engineer in the Grid Oper-

ations and Planning group at the Electric Power Re-search Institute (EPRI) in Knoxville, TN, USA.

Hairong Qi (S’97–M’00–SM’05) received the B.S.and M.S. degrees in computer science from NorthernJiaoTong University, Beijing, China, in 1992 and1995, respectively, and the Ph.D. degree in computerengineering from North Carolina State University,Raleigh, NC, USA, in 1999.She is now a Professor in the Department of Elec-

trical Engineering and Computer Science at the Uni-versity of Tennessee, Knoxville. Her current researchinterests are in advanced imaging and robust collab-orative processing in resource-constraint distributed

environment and information unmixing.Dr. Qi is the recipient of the NSF CAREERAward. She also received the Best

Paper Awards at the 18th International Conference on Pattern Recognition andthe third ACM/IEEE International Conference on Distributed Smart Cameras.She recently receives the Highest Impact Paper from the IEEE Geoscience andRemote Sensing Society.

Yilu Liu (S’88–M’89–SM’99–F’04) received theB.S. degree from XiAn Jiaotong University, China,and the M.S. and Ph.D. degrees from the Ohio StateUniversity, Columbus, OH, USA, in 1986 and 1989,respectively.She is currently a Governor Chair Professor at the

University of Tennessee, Knoxville and Oak RidgeNational Laboratory. Prior to joining UTK/ORNL,she was a professor at Virginia Tech. She led the ef-fort to create the North American power grid moni-toring network (FNET) at Virginia Tech which is now

operated at UTK and ORNL as FNET/GridEye. Her current research interestsinclude power system wide-area monitoring and control, large interconnectionlevel dynamic simulations, electromagnetic transient analysis, and power trans-former modeling and diagnosis.

Qing Charles Cao (M’10) received the Master’s de-gree from the University of Virginia, Charlottesville,VA, USA, and the Ph.D. degree from the Universityof Illinois, Champaign, IL, USA.He is currently an Assistant Professor in the

Department of Electrical Engineering and Com-puter Science, University of Tennessee, Knoxville,TN, USA. His research interests include wirelesssensor networks, embedded systems, and distributednetworks.Dr. Cao is a member of IEEE, ACM, and the IEEE

Computer Society. He has published more than 50 papers in various journalsand conferences, and has served as technical committee members for more than30 conferences held by IEEE and ACM.

Leon M. Tolbert (S’88–M’91–SM’98–F’13)received the B.S., M.S., and Ph.D. degrees inelectrical engineering from the Georgia Instituteof Technology, Atlanta, in 1989, 1991, and 1999,respectively.He worked at Oak Ridge National Laboratory,

Oak Ridge, TN, from 1991 until 1999. He wasappointed as an Assistant Professor with the Depart-ment of Electrical and Computer Engineering, TheUniversity of Tennessee, Knoxville, in 1999. He iscurrently the Min Kao Professor in the Department

of Electrical Engineering and Computer Science, The University of Tennessee.He is the UTK Campus Director for the National Science Foundation/De-partment of Energy Research Center, CURENT (Center for Ultra-wide-areaResilient Electric Energy Transmission Networks). He is also a Senior ResearchEngineer with the Power Electronics and Electric Machinery Research Center,Oak Ridge National Laboratory.Dr. Tolbert received an NSF CAREER Award in 2001, the 2001 IEEE In-

dustry Applications Society Outstanding Young Member, and four prize paperawards from the IEEE Industry Applications Society and the IEEE Power Elec-tronics Society.

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