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Change-point detection-based power quality monitoring in smart grids

Xingze He, Man-On Pun and C.C. Jay Kuo

APSIPA Transactions on Signal and Information Processing / Volume 4 / 2015 / e7DOI: 10.1017/ATSIP.2015.7, Published online: 17 August 2015

Link to this article: http://journals.cambridge.org/abstract_S2048770315000074

How to cite this article:Xingze He, Man-On Pun and C.C. Jay Kuo (2015). Change-point detection-based power quality monitoring in smart grids.APSIPA Transactions on Signal and Information Processing, 4, e7 doi:10.1017/ATSIP.2015.7

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SIP (2015), vol. 4, e7, page 1 of 9 © The Authors, 2015.This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permitsunrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.doi:10.1017/ATSIP.2015.7

original paper

Change-point detection-based power qualitymonitoring in smart gridsxingze he1, man-on pun2, and c.c. jay kuo1

The enormous economic loss caused by power quality problems (more than $150 billion per year in USA) makes power qualitymonitoring an important component in power grid.With highly connected fragile digital equipment and appliances, Smart Gridhas more stringent timeliness and reliability requirements on power quality monitoring. In this work, we propose a change-pointdetection theory-based power quality monitoring scheme to detect the most detrimental power quality events, such as voltagesags, transients and swells in a quick and reliable manner. We first present a method for single-sensor detection scenario. Basedon that, we extend the scheme to multi-sensor joint detection scheme which further enhances the detection performance. Agroup of conventional power quality monitoring schemes (i.e. Root-mean-square, Short-time Fourier transform, MUSIC, andMBQCUSUM) are compared with the proposed scheme. Experimental results assert the superior of the proposed scheme interms of detection latency and robustness.

Keywords: Smart grid, Power quality, Change-point detection

Received 1 June 2014; Revised 15 June 2015; Accepted 16 June 2015

I . I NTRODUCT ION

It has been estimated by the U.S. Department of Energy thatmore than $150 billion economic loss is caused by powerquality problems each year in the USA [1, 2], and this num-ber is expected to continue increasing as the power demandincreases much faster than the power system capacity.In addition, power quality problems are main threats tonormal functioning of system equipments and end-user’sdevices. Even small voltage variations caused by powerquality problems (within one cycle, i.e. 1/60 s) are detri-mental enough to crash servers, computers, life-supportmachines and other microprocessor-based devices. To mit-igate these risks, modern smart grid systems distribute alarge amount of phasor measurement units throughout theentire power system for power quality monitoring. The sys-tem so-called Wide Area Measurement System is designedto provide real-time situational awareness which is essentialfor safe and reliable smart grid operations [3, 4]. How-ever, the real-time measurement system only is insuffi-cient to meet the power quality monitoring requirements.Advanced measurement data-processing techniques must

1Ming Hsieh Department of Electrical Engineering, University of SouthernCalifornia, Los Angeles, CA, USA2Huawei Technologies, Bridgewater, NJ, USA

Corresponding author:X. HeEmail: xingzehe@usc.edu

be designed to detect power quality problems in a fast andreliable manner.

The power quality monitoring generally consists of threesteps: detection, characterization, and classification. Thedetection step takes the measurement data as input andtriggers alarm when power quality problems are detected.The characterization step analyzes and extracts featuresfrom power quality problems data. Finally, the classificationprocess classifies power quality problems into predefinedcategories based on the features extracted in the charac-terization step. According to the classification result, corre-sponding amending operations are then taken to solve theproblem and mitigate the loss. Our focus in this work is onthe first step, power quality problem detection.

Based on the deviation magnitude, power quality prob-lems are generally classified into two categories, namelypower quality variations and power quality events [5]. Thepower quality variation is characterized by small deviationsfrom the nominal power line signal while the power qualityevent typically has large deviations with approximately mil-lion dollars damage per event. Major power quality eventsare voltage sags, swells, and transients. In this work, wemainly focus on the power quality events detection.

To meet the stringent timeliness requirement, we pro-pose a novel detection scheme based on the change-pointdetection theory in this work. We first study the sta-tistical properties of normal power line signals and sig-nals of all power quality event types. Then, a detectionscheme based on the Cumulative Sum (CUSUM) approachis developed by exploiting the statistical properties. Finally,

1

2 xingze he et al.

amulti-sensor joint detection scheme is proposed to furtherimprove the detection speed.

The rest of the paper is organized as follows. Section IIbriefly discusses the previous work of power quality mon-itoring. Section III presents the single-sensor detectionscheme. The multi-sensor scheme is then discussed inSection IV. Section V provides experimental results and,finally, Section VI concludes this paper.

I I . REV I EW OF PREV IOUS WORK

Root-mean-square (RMS) voltage is a most widely usedapproach for power quality event detections in power sys-tem. The detector keeps track of the RMS value of thevoltage signal over a sliding window with size typically as1 cycle or 0.5 cycle. The likelihood of the power qualityevent is then evaluated according to the deviations from thenominal RMS value.

Another type of approaches utilizes either high-pass orbandpass filters, like Short-time Fourier transform [6, 7]and Wavelet filters [8, 9]. Since the normal power signalwaveform is only composed of harmonics of low-frequencycomponents, high-frequency components usually indicatesoccurrence of power quality events, e.g. transients.

The third type of methods decomposes the power linewaveform into a sum of damped sinusoids using super-resolution spectral analysis techniques (e.g., ESPRIT orMUSIC) [10–12]. Power quality events are then detectedby decomposing the measured signal and comparing withthose decomposed from normal signals.

Note that a sliding window is required by all of the threetypes of methods above to segment the power line signalwaveform into blocks before any transformation or decom-position. As a result, the time resolution of all thesemethodsis restricted.

Without the sliding window, Tartakovsky and Pol-unchenko [13] discussed a decentralized change-pointdetection scheme in distributed sensor network. Thescheme so-called MBQCUSUM using the binary quantiza-tion technique is proven to be asymptotically optimal at thereference points and rather efficient elsewhere.

I I I . S INGLE -SENSOR DETECT IONSCHEME

A) Problem formulationThe single-sensor detection problem is to detect the powerquality events as quickly as possible with only one sensordeployed in the target area. As shown in Fig. 1, given asequence of power line sensor measurements {Vi , i ≥ 0},where Vi is either voltage measurement in volts or currentmeasurement in ampere, the power quality event detectionmodule outputs di ∈ {0, 1} where 0 indicates the absence ofpower quality events while 1 indicates the detection of cer-tain type of power quality event. For simplicity, we considerthe single power quality event in our analysis.

Fig. 1. Single-sensor power quality event detection.

Given event occurrence time te and event detection timetd , the detection latency is then expressed as D = td − te ,where td ≥ te . The primary goal of the single-sensor detec-tion is to minimize the detection latency under constraintssuch as a given false alarm rate (FAR).

B) Proposed scheme1. OverviewThe proposed detection scheme is based on the change-point detection theorywhich provides optimal detection. Inthe scheme, we first model both of the pre-event (normal)and post-event power line signals. In the post-event signalmodeling, we consider all types of power quality events, i.e.voltage sags, swells, transients and interruptions. By settingup these models, the probability density function (PDF) ofboth pre-event and post-event signals are derived. Finally,the CUSUM-based detection algorithm is proposed.

2. Signal modelingAccording to the presence of the prior knowledge aboutthe potential power quality event types, two power qual-ity event modeling methods can be used: generic modelingand event-specific modeling. As the name suggests, genericmodeling uses a single generic formula to model all typesof power quality events by taking into account both addi-tive and multiplicative distortion. In contrast, the event-specific model is proposed to further simplify the modelingof specific power quality events.

a. Generic modeling

• Pre-event signalThe kth sample of the pre-event signal can be modeled as

y[k] = sθ0 [k] + n[k], t ≤ te , (1)

where n[k] is the additive white Gaussian noise with zero-mean and variance σ 2

n , denoted byN (0, σ 2n ), and

sθ0 [k] = a0 · sin (2π f0Ts k + φ0) , (2)

is the pure power line waveform signal with Ts being thesampling duration, θ0

def= [a0, f0, φ0]T , where a0 = 1 is the

signal amplitude gain, and f0 and φ0 are the fundamentalfrequency and the initial phase of the power waveform,respectively.

• Post-event signalAs a genericmodel, the kth sample of the post-event signalcan be modeled as

y[k] = sθ1 [k] + n[k], t ≥ te , (3)

where sθ1 [k] consists of both additive and multiplicativedistortion terms in an approach commonly employed in

change-point detection based power quality monitoring in smart grids 3

the literature of time-series analysis [14]. sθ1 [k] has thefollowing form:

sθ1 [k] = a1 · sin (2π f1Ts k + φ1)︸ ︷︷ ︸Multiplicative

+ ξϕ[k]︸ ︷︷ ︸Additive

(4)

and θ1def= [

a1, f1, φ1, ϕT]T .

The above generic model can be used to model alltypes of power quality events with appropriate parameteradjustments. For instance, a voltage sags signal could bemodeled as a sudden drop in thewaveformamplitude gainwith a1 < a0, while setting f1 = f0, φ1 = φ0, ξϕ[k] = 0.In contrary, transient signal can be modeled with rela-tively large and fast-changing ξϕ[k].

b. Event-specific modeling

• Pre-event signalEvent-specific modeling adopts the same method ofgeneric modeling for the pre-event signal, as shown inequation (1).

• Post-event signalDifferent from the generic modeling, the post-event sig-nal is modeled according to the specific type of the powerquality event. We divide the three types of power qualityevents into two categories: sags/swells and transients.

For sags/swells, the voltage changes with possible phasedeviation, but the frequency during the event keeps same.Therefore, the kth sample of the post-event signal ismodeled as

y[k] = sθ0 [k] + ess [k] + n[k], t ≥ te , (5)

where ess [k], sample from the difference of two sinusoidalsignals with the same frequency but different phase, is uni-formly distributed in [−b, +b] where b is an unknownparameter. The uniform distribution assumption wasmade by assuming the two sinusoidal signals are stronglycorrelated. ess < 0 indicates a voltage sag event, whileess > 0 indicates a voltage swell event.

For transient, considering its damped oscillation dur-ing the event, the kth sample of the post-event signal isapproximately modeled as

y[k] = sθ0 [k] + eth[k] + n[k], t ≥ te , (6)

where eth[k], is a normal distribution random variablewith mean 0 and unknown variance σ 2

th . Note that, thenormal distribution is assumed by modeling the transientas sum of multiple sinusoidal signals [15].

3. PDF derivationWith the above statistical models, we are able to derive thePDF of both pre-event and post-event signals for furtheranalysis based on the change-point detection theory.

a. Pre-processingTo facilitate the PDF derivation, we first subtract the purepower line signal sθ0 [k] from the measured samples y[k].After the one-step pre-processing, the output signal isderived as

z[k] = y[k] − sθ0 [k], for all t. (7)

b. PDF derivation of generic modelingAfter pre-processing, the pre-event signal becomes

z[k] = n[k]. (8)

Therefore, the PDF of the pre-event signal can be derived as

pθ0(z) = 1√2πσ 2

n

exp−z2/2σ 2n . (9)

Similarly, the post-event signal becomes

z[k] = x[k] + w[k], (10)

where

x[k] = a1 · sin (2π f1Ts k + φ1) , (11)

w[k] = ξϕ[k] − sθ0 [k] + n[k]. (12)

By invoking the central limit theorem, the PDF of w canbe approximated as N(0, σ 2

w), where σ 2w = σ 2

ξ + σ 2n + 1

2a20 .

Further, a first-order approximation of the PDF of x mod-eled asU (−a1, a1) is employed in the sequel to keep the fol-lowing derivation analytically tractable. Then, it is straight-forward to derive the post-event PDF as

pθ1(z) = 1

4 |a1|[erf

(z + |a1|√

2 · σw

)− erf

(z − |a1|√

2 · σw

)],

(13)

where a1 and σw are both unknown parameters.

c. PDF derivation of event-specific modelingSimilar to the generic modeling approach discussed above,the pre-event PDF of the event-specific modeling can bederived as equation (9). For the post-event signal, differenttypes of power quality events have different PDFs.

For sags/swells, the post-event signal after pre-processingis written as

z[k] = ess [k] + n[k]. (14)

It can be shown that the PDF of z[k] can be derived as

pθ1(z) = 1

4 |b|[erf

(z + |b|√

2 · σn

)− erf

(z − |b|√

2 · σn

)], (15)

where b indicates the value range of the uniformly dis-tributed ess as shown in equation (5).

4 xingze he et al.

For transients, the post-event signal after pre-processingis expressed as

z[k] = eth[k] + n[k]. (16)

The PDF of z[k] can then be derived as

pθ1(z) = 1√2π(σ 2

n + σ 2th)

exp−[z2/2(σ 2n +σ 2

th)], (17)

where σth is an unknown parameter.

4. Detection algorithmThe proposed detection algorithm is based on the CUSUMscheme [16, 17]. The basic CUSUMalgorithmfirst calculatesthe log-likelihood ratio of each sample as

s [k] = lnpθ1(z[k])

pθ0(z[k]). (18)

Due to the existence of the unknown parameters in thepost-event model, we calculate the weighted sum of thelog-likelihood ratios considering all possibilities. We thenextend equation (18) into the following form:

s [k] = ln

[∫A1

∫�w

pθ1(z[k])

pθ0(z[k])dF�w

(σw) dFA1 (a1)

],

(19)

where F∗(∗) indicates the cumulative distribution func-tion of the unknown parameter. Three different uncertaintymodels (i.e. Guassian, Gamma, and Inverse-Gamma) of theunknown parameters are used [18].

With accurate modeling and parameter estimation,pθ1(z[k]) is generally larger than pθ0(z[k]) during pre-eventphase while smaller than pθ0(z[k]) during post-event phase.As a result, s [k] is prone to be negative during pre-eventphase while more likely to be positive during post-eventphase. Then, we calculate the cumulative sum of the log-likelihood ratio as

S[k] =k∑

i=1

s [i]. (20)

Finally, according to the CUMSUM algorithm from thequickest detection theory [17], the stopping time can befound as

td = min{k : S[k] − min1≤ j<k

{S[ j ]} > h}, (21)

where h is the predefined threshold.

I V . MULT I - SENSOR JO INTDETECT ION SCHEME

A) Problem formulationIn multi-sensor scenario, multiple sensors within the tar-get geographical area are involved for the joint detection.

Fig. 2. Multi-sensor joint detection.

As shown in Fig. 2, each detector takes its correspondingsensor measurements {Vl

0 , Vl1 , Vl

2 , . . . }, 1 ≤ l ≤ L as inputsequence and outputs its processing result dl , 1 ≤ l ≤ L .These intermediate processing results are then sent to thefusion center through independent communication chan-nel. Finally, the fusion centermakes the final detection deci-sion, D ∈ {0, 1}, based upon the local processing results.

B) Proposed schemeGenerally, there are two ways to handle sensors’ measure-ments: one is to directly send the original measurements tothe fusion center for central processing; the other way is tosend the compressed measurements or local results to thefusion center for further processing. The latter one is usu-ally more practical due to the communication bandwidthconstraints.

In our proposed multi-sensor scheme, each remotedetector outputs its local decision dl

i ∈ {0, 1} made by thesingle-sensor detection scheme discussed in Section III.On the fusion center side, majority voting is adopted forthe joint decision making. Specifically, given a sequenceof local decisions from multiple sensors in the target geo-graphic area dl

i , i ≥ 0, 1 ≤ l ≤ L , where dli ∈ {0, 1} and L

indicates the number of sensors involved. The final decisionis made as

Dk =

⎧⎪⎨⎪⎩

1, ifL∑

l=1dl

k > L2 ,

0, otherwise,(22)

Suppose the FAR of the single-sensor detection schemeis predefined as α, the FAR of the multi-sensor scheme canbe derived as

αMVWCU SU M =L∑

q=L/2

(L

q

)αq (1 − α)(L−q). (23)

Fig. 3 shows the relationship between αMVWCU SU M andα. Inspection of Fig. 3 reveals that the FAR is signifi-cantly improved when α is smaller than 0.5. In addition,as more sensors are involved, better FAR improvement canbe achieved by the multi-sensor detection scheme. Sinceless time samples are required, such a multi-sensor schemecan effectively reduce the detection latency. According to

change-point detection based power quality monitoring in smart grids 5

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

FAR of Single Detection

FA

R o

f Maj

ority

Vot

ing

L = 3L = 10L = 20L = 30L = 40L = 50L = 1

Fig. 3. FAR improvement with multi-sensors.

Fig. 4. SimPowerSystem model for voltage sag event.

Fig. 5. SimPowerSystem model for voltage transient event.

Wald’s inequality [19], we have the relationship between thepredefined FAR α and the threshold h as

e−h = α. (24)

Then, we can choose

h = − ln α. (25)

In order to achieve the targeted FAR for various signalmod-els and power events, Monte Carlo simulation is performedto determine the optimal threshold for a given FAR.

V . EXPER IMENTAL EVALUAT ION

We use Matlab toolbox SimPowerSystems to model andsimulate electrical power systems for power quality eventsignal generation. For example, Figs. 4 and 5 are powersystem

6 xingze he et al.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2−1.5

−1

−0.5

0

0.5

1

1.5

Time/s

Am

plitu

de/p

u

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2−1.5

−1

−0.5

0

0.5

1

1.5

Time/s

Am

plitu

de/p

u

(a)

(b)

Fig. 6. 3-Phase power quality event generated from SimPowerSystems models. (a) Voltage Sag. (b) Transient.

models for voltage sags and voltage transient, respectively.As shown in Fig. 4, the voltage sag event is triggered bythe fault on one of the transmission lines. The voltage tran-sient event, shown in Fig. 5, is triggered by the connection oflarge capacitor banks in order to improve the system powerfactor. Fig. 6 shows the generated power quality event sig-nals. In this particular example, voltage sag event happensaround 0.06 s and lasts until 0.15 s, while transient eventoccurs at 0.06 s and ends soon.

To compare the performance, we define the followingaveraged mean squared error (MMSE) of the event detec-tion as the performance metric:

MMSE = E [E [(Te − Oe)2])], (26)

where Oe indicates the occurrence time of the power qualityevent and Te is the detected stopping time.

Fig. 7(a) shows the short-time Fourier transform (STFT)of the transient event signal. The appearance and disap-pearance of high-frequency components indicates the start-ing and ending times of the transient event, respectively.Fig. 7(b) shows the analysis result of the MUSIC method.The deformed spectrum indicates the occurrence of thepower quality event. Please note, Figs 7(a) and 7(b) showsresults of STFT andMUSIC on the pure transient event sig-nal, noise distortion is not included. Due to the periodicityof the sinusoidal power signal, the window size of STFT andMUSIC must be a multiple of the cycle and the sliding stepmust be a multiple of half cycle to output a steady resultduring the pre-event phase. Limited by the sliding windoweffect, both of the STFT and MUSIC method are restrictedby a fixed detection resolution (0.01 s). Therefore, neither ofthem provides quick detection for smart grid system.

Fig. 8(a) shows the detection result of the sample-by-sample RMS method on the transient event signal. Thedetection result is expressed in terms of detection metricderived from the signal amplitude according to variousdetection methods. The length of the sliding window is set

to be a cycle, i.e. 1/60 s. The prominent amplitude devi-ation around 0.06 s indicates the incidence of the powerquality event. Fig. 8(b) shows the detection results of

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−40

−20

0

20

40

60

80

100

120

140

Normalized Frequency (rad)

Pow

er (

dB)

Window [0,0.03]

Window [0.03,0.06]

Window [0.05,0.07]

Window [0.06,0.08]

(a)

(b)

Fig. 7. STFT and MUSIC results. (a) STFT result on transients event. (b)MUSIC result on transients event.

change-point detection based power quality monitoring in smart grids 7

0 0.02 0.04 0.06 0.08 0.10.6

0.62

0.64

0.66

0.68

0.7

0.72

0.74

0.76

0.78

Time/second

Det

ectio

n M

etric

0 0.02 0.04 0.06 0.08 0.1−3000

−2500

−2000

−1500

−1000

−500

0

Time/s

Det

ectio

n M

etric

Generic ModelEvent−Specific Model

10 15 20 25 3010−4

10−3

10−2

SNR/dB

MM

SE

RMSWCUSUMSTFT/MUSIC

(a) (b) (c)

Fig. 8. RMS versus WCUSUM. (a) RMS-based detection in the time domain. (b) WCUSUM-based detection with various modeling methods in the time domain.(c) Detection latency comparison of various detection methods.

10 15 20 25 3010

−4

10−3

10−2

SNR/dB

MM

SE

Generic ModelEvent−Specific Model

Fig. 9. Detection results of different modeling methods.

the proposed scheme using generic modeling and event-specific modeling respectively. The turning points shownin Fig. 8(b) indicates the occurrence of the power qualityevent. To further compare the performance, we plot theaveraged detection latency under different signal to noiseratio (SNR). The FARs of both schemes are predefined asα = 0.17%. As shown in Fig. 8(c), the proposed scheme isable to detect the power quality event faster under the fixedFAR.

Fig. 9 compares the averaged detection latency underdifferent noise levels. For a larger SNR, the event-specific

0 0.02 0.04 0.06 0.08 0.1−1000

−500

0

500

1000

1500

2000

2500

3000

3500

Time/second

Det

ectio

n M

etric

Gaussian Modeling (m=1, sd=1)Gamma Modeling (k=1,th=2)Inv−Gamma Modeling (alpha =3, beta=0.5)

8 9 10 11 12 13 14

10−3

10−2

SNR/dB

MM

SE

UniformGaussianGamma & Inverse Gamma

(a) (b)

Fig. 10. Detection results under different uncertainty models. (a) Detection curves. (b) Detection latency.

modeling slightly outperforms the generic modeling interms of the detection latency. In addition, with oneunknown parameter, the event-specific modeling is morecomputationally efficient than that of the genericmodeling.

Fig. 10 shows the detection results under different uncer-tainty models. The detection curves of an example eventsignal shown in Fig. 10(a) present similar performance.Fig. 10(b) further proves the observation.With a large noiselevel, there is not much performance difference among dif-ferent uncertainty models. When the noise level increases,however, uniformmodel andGaussianmodel offer superiorrobustness.

Similar to the single-sensor data generation, we use theSimPowerSystem for multi-sensor power quality event datageneration. We place multiple sensors along the transmis-sion line in different event models. For example, a gener-ated three-sensor voltage sag signals are shown in Fig. 11.The distance between two sensors is 150 km and sensorVM2 is the closest one to the actual event occurrencelocation.

The MBQCUSUM scheme and the proposed MVW-CUSUM scheme are applied to the above multi-sensorpower quality signals for event detection. We compare thedetection performance of the two schemes in terms ofdetection delay and FAR with fixed alarm threshold. Wecan see from Fig. 12(a) that the MBQCUSUM scheme canachieve slightly smaller detection delay (i.e. hundreds ofmilliseconds) than the MVWCUSUM scheme. According

8 xingze he et al.

0 0.05 0.1 0.15 0.2

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

1.2x 10

6

Time (second)

Vol

tage

(Vol

t)Power Signal at VM1Power Signal at VM2Power Signal at VM3

Fig. 11. Sag signals generated from multi-sensor model.

20 22 24 26 28 301

2

3

4

5

6

7

8

9x 10

−4

SNR/dB

Det

ectio

n D

elay

(T

hres

hold

= 1

0)

MBQCUSUMMVWCUSUM

20 22 24 26 28 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

SNR/dB

Fals

e A

larm

Rat

e

MBQCUSUMMVWCUSUM

(a)

(b)

Fig. 12. Performance comparison of BQCUSUM and MVWCUSUM. (a)Detection latency. (b) FAR.

to Fig. 12(b), however, the proposedMVWCUSUM schemeis more robust compared with the MBQCUSUM scheme asthe noise level increases.

V I . CONCLUS ION AND FUTUREWORK

We propose a power quality event detection scheme forpower quality monitoring in Smart Grid. Based on thechange-point detection theory, we exploit both instanta-neous information (real-time power line signal samples)and historical statistics of power line signals to detect theoccurrence of power quality event in a quick and reli-able manner. We also present a multi-sensor joint detec-tion scheme to further improve the detection performance.We compared the proposed scheme with a group of con-ventional schemes and shows that our scheme outper-forms conventional schemes in detection latency, reliabilityand robustness. In the future work, we plan to have adeeper analysis of the theoretical properties of the proposedscheme.

ACKNOWLEDGEMENT

The research for this paper was financially supported by theMedia Communications Lab of the University of SouthernCalifornia.

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Xingze He received the B.S. and M.S. degrees in the Depart-ment of Communication and Information System at Xi’an Jiao-tong University, Xi’an, in 2007 and 2009, respectively. He is aPh.D. candidate in Ming Hsieh Department of Electrical Engi-neering at the University of Southern California (USC). Hiscurrent research interest is in the area of Smart Grids, includ-ing power quality problem detection, public key cryptography,and homomorphic encryption.

Man-On Pun received the B.Eng. (Hon.) in Electronic Engi-neering from the Chinese University of Hong Kong in 1996,the M.Eng. degree in Computer Science from University ofTsukuba, Japan in 1999 and the Ph.D. degree in Electri-cal Engineering from the University of Southern California(USC) in 2006, respectively. He joined Huawei Technologies

in Bridgewater, NJ in 2011. Prior to Huawei, he held researchpositions at Mitsubishi Electric Research Labs (MERL), Cam-bridge, MA and Princeton University. Dr. Pun received manyawards including three best paper awards from Infocom 2009,ICC 2008, and VTC-Fall 2006. He served as an Associate Edi-tor for the IEEE Transactions onWireless Communications in2010–2014.

C.C. Jay Kuo received the B.S. degree from the National Tai-wan University, Taipei, in 1980 and the M.S. and Ph.D. degreesfrom theMassachusetts Institute of Technology, Cambridge, in1985 and 1987, respectively, all in Electrical Engineering. He isthe Director of the Signal and Image Processing Institute (SIPI)and Professor of Electrical Engineering, Computer Science andMathematics at the University of Southern California (USC).His research interests are in the areas of digital image/videoanalysis andmodeling,multimedia data compression, commu-nication and networking, and multimedia database manage-ment. Dr. Kuo has guided 108 students to their Ph.D. degreesand supervised 23 postdoctoral research fellows. He is a co-author of about 200 journal papers, 800 conference papers, and10 books. He is a Fellow of AAAS, IEEE, and SPIE. He is theEditor-in-Chief for the Journal of Visual Communication andImage Representation, and Editor for 10 other internationaljournals. Dr. Kuo received the National Science FoundationYoung Investigator Award (NYI) and Presidential Faculty Fel-low (PFF)Award in 1992 and 1993, respectively. Hewas an IEEESignal Processing Society Distinguished Lecturer in 2006, therecipient of the Electronic Imaging Scientist of the Year Awardin 2010 and the holder of the 2010–2011 Fulbright-Nokia Dis-tinguished Chair in Information and Communications Tech-nologies.