1

Dimensionality Reduction and Early Event

Detection Using Online Synchrophasor DataYang Chen, Student Member, IEEE, Le Xie, Member, IEEE, and P. R. Kumar, Fellow, IEEE

Abstract—This paper proposes a novel approach to utilizinglarge online synchrophasor data for early event detection inpower systems. Based on principal component analysis (PCA),a linear basis of the massive online phasor measurement unit(PMU) data can be extracted to reduce the dimensionality. Usingthe linear basis with much reduced dimensionality, an earlyevent detection algorithm is proposed. This algorithm is capableof predicting the changes of system operating conditions bycomparing the error between PCA-projected and actual valuesfrom a few selected locations. Numerical case studies basedon both PSS/E simulation and actual PMU data from ElectricReliability Council of Texas are conducted to demonstrate theefficacy of this algorithm.

Index Terms—Dimensionality reduction, principal componentanalysis, early event detection, phasor measurement unit.

I. INTRODUCTION

THIS paper focuses on the new paradigm of improving

power system online monitoring by using massively

deployed synchrophasor data. While the synchrophasor data

offer many opportunities to improve the situational awareness

[1]–[4], it also becomes a major challenge for large-scale

power system operators to utilize the data in a timely manner.

As an example, with only 120 PMUs installed, the Tennessee

Valley Authority needs to manage 36 GB data per day [5]. It

becomes very difficult for the system operators to directly use

the raw data for real-time decision making.

Complementary to conventional model-based monitoring

and decision making tools available in the control room, the

deployment of PMUs offers opportunities for real-time data-

driven analytics for the system operators. As a first step, this

paper assesses the potential of dimensionality reduction using

the classic PCA methods. Preliminary results indicate that

for a large power system, the measurements obtained from

PMUs lie in a much reduced lower-order space. Starting from

this observation, we further propose an online algorithm for

early event detection. This algorithm uses only a very small

set of PMU measurements as base vectors and predicts the

measurements from other PMUs. The deterioration of the

quality of the prediction will then indicate the change of

system conditions, i.e., for event detection. Such an algorithm

requires no knowledge of system fundamental model, and

is shown to be effective with several different case studies.

These preliminary results show the great potential to explore

This work is supported in part by NSF ECCS Grant #1150944, CNS-1239116, CNS-1035340, and CNS-1035378.

The authors are with Department of Electrical and Computer Engineer-ing, Texas A&M University, College Station, TX, 77843 USA. Email:hebe.cheny@tamu.edu, lxie@ece.tamu.edu, prk@tamu.edu.

the fundamental connection between large systems theory and

data-driven computational sciences. In summary, this work

serves the following purposes: (1) it provides a significantly

lower dimensional “signature” of the states of the overall

power system; (2) it greatly simplifies the data analysis, by

getting rid of the inherent redundancy as well as the noise

in the data; (3) it thereby proves a capability for a very

rapid detection of events, within a few samples of their

occurrence; (4) it greatly reduces the need for and amount of

data storage; (5) it can be more readily and quickly digested by

system operators and thus potentially improve their situational

awareness.

The rest of the paper is organized as follows. Section II

presents a linear PCA-based dimensionality reduction tech-

nique. This is a prerequisite for the early event detection al-

gorithm proposed in Section III. In Section IV, two numerical

case studies are conducted to evaluate the efficacy of this

algorithm. Conclusions and remarks are given in Section V.

II. DIMENSIONALITY REDUCTION OF ONLINE PMU DATA

As the synchrophasor measurement technology exhibits

great superiority in enhancing system situational awareness,

more PMUs and similar functional devices, such as frequency

monitoring network (FNET) [6] and frequency disturbance

recorder (FDR) [7], are being brought online. Correspondingly,

the availability of massive data is increasing significantly [5].

It is therefore an urgent need to leverage inherent correlations

among the PMU data for dimensionality reduction.

The dimensionality reduction method has been recognized

recently in power systems for its adaptive machine learning

features. PCA, as one of the premier linear dimensionality

reduction methods, reduces dimensionality by preserving the

most variance of the original data [8], [9]. Its fast compu-

tation feature itself provides much attraction in the areas of

coherency identification [10], extraction of fault features [11],

and fault location [12]. In a very recent paper [5], PCA is

performed on synchrophasor data for dimensionality reduction.

Using the participation weights and principal components

(PCs), the reconstruction errors are utilized in [5] to extract

correlations of different variables and therefore reduce the

dimensionality. The reconstruction accuracy will be very high

for the global variables like bus frequency, due to the globally

similar profiles. However, for some local variables, such as

voltage magnitude or reactive power, the reconstructions may

not exhibit high accuracy, under which condition, a new

algorithm for dimensionality reduction is of great need.

In this paper, we propose a PCA-based linear dimensionality

reduction algorithm using online PMU data. Instead of using

2

reconstruction as [5], we utilize only the first few PCs to form

a new space. The original PMU data are projected into the

new space to determine the basis matrix, which contains the

much reduced linear basis of the original data, and therefore

reduces the dimensionality.

Let p denote the number of available PMUs, each providing

ℓ measurements. p is expected to be of the order of 103 in the

near future [13], indicating the massiveness of the real-time

data handling problem. Typically, and as is true for the data

in this paper, ℓ = 3, corresponding to bus frequency, phase

angle, and voltage magnitude. At each time sample, therefore,

a total of N := pℓ measurements is collected. Consider a

set of n such samples, each taken a different time instant.

Define Yn×N = [y(1), . . . , y(N)] as the matrix containing N

measurements from PMUs. Each measurement, as noted, has n

samples constituting a time history, i.e., y(i) = [y(i)1 , . . . , y

(i)n ]T ,

i= 1, . . . , N. The procedure for the PCA-based dimensionality

analysis can be described as follows:

1) Calculate the covariance matrix of Y : C = Y Tn×NYn×N .

2) Calculate the N eigenvalues and eigenvectors of C.

3) Reorder the N eigenvalues of C from the highest to the

lowest, and the corresponding eigenvectors are the PCs.

4) Select the highest m out of N PCs based on a predefined

variance threshold, where m ≪ N.

5) Use the m PCs to form a new m-dimensional space, in

which the N original variables are projected.

6) Decide m′ out of the original N variables to keep, where

the m′ variables are selected as nearly orthogonal to each other

in the m-dimensional space as possible, and m′ ≤ m. This

step is a key to the utilization of the PCA method for power

systems, since it makes possible the notion of “pilot PMUs,”

as we detail in the sequel.

7) Define the basis matrix formed by the m′ variables as

YB := [y(1)b , . . . , y

(m′)b ] ∈ R

n×m′, where YB ⊆ Y .

The basis matrix YB contains the basis vectors, which can

form a linear basis for each of the original measurements.

Let v(i) = [v(i)1 , . . . , v

(i)m′ ]

T be the vector containing the linear

regression coefficients for approximating column y(i) ⊆ Y in

terms of YB, i.e.,

y(i) ≈m′

∑j=1

v(i)j y

( j)b = YBv(i). (1)

To solve the over-determined problem (1), v(i) is defined as

[14]

v(i) := (Y TB YB)

−1Y TB y(i), (2)

which aims to minimize the squared approximation error

‖y(i)−YB · v(i)‖2.

Using (2), each measurement in Y can be represented

in terms of the linear basis in YB. The dimensionality can

therefore be reduced from N to m′, where m′ ≪ N. More

importantly, the system operators can regard the PMUs whose

measurements are featured in YB as the “pilot PMUs” for pre-

dicting other non-pilot measurements and detecting changes of

system operating conditions in an online fashion. In the next

section, we propose an early event detection algorithm based

on these “pilot PMUs.”

III. EARLY EVENT DETECTION ALGORITHM

If massive PMU data indeed lie in a much reduced dimen-

sional space, system operators can leverage the low dimen-

sionality of PMU data for early event detection (EED). In

this section, we propose such an algorithm with the following

features: (a) only a reduced number m′ of PMUs are needed;

(b) it is implementable; (c) it can detect events at a very early

stage. A system event is defined in this paper as either a change

of model or a change of control inputs. The EED algorithm

is described as follows.

i) Offline Training: The training aims at computing the linear

representation (2). Assume an n-time-sample N-measurement

matrix Y is obtained from historical PMU data. Y can be bus

frequency, phase angle, or voltage magnitude. After perform-

ing the PCA-based dimensionality reduction algorithm, the

corresponding v(i) can be obtained for each y(i).

ii) Online Prediction: The prediction uses the recent mea-

surements at time t of the pilot PMUs and the predictor

coefficients v(i)’s to predict the measurements of all the

other PMUs at that time sample t. If a significant prediction

error is identified, an event alert will be declared. Under

normal conditions, the predictor coefficients v(i)’s are good

for predicting y(i), therefore, the prediction has high accuracy.

When events occur, the spatial dependencies inside the power

system change, and so the v(i)’s are not anymore good for

predicting the other PMU measurements, and this leads to a

large prediction error.

Now we precisely state the algorithm used. The real-time

prediction of the ith measurement is defined as

y(t)(i) := Y measB (t) · v(i), (3)

where Y measB (t) is the real-time measurement of the pilot

PMUs, and v(i) is directly from the training without timely

update.

Define the prediction error as

e(t)(i) :=

∣

∣

∣

∣

∣

y(t)(i)

y(t)(i),meas

∣

∣

∣

∣

∣

×100%, (4)

where

∣

∣

∣y(t)(i)

∣

∣

∣:=

∣

∣

∣y(t)(i)− y(t)(i),meas

∣

∣

∣is the absolute predic-

tion error, and y(t)(i),meas is the real-time measurement of

the ith PMU. The system/regional operators can monitor the

occurrence of events by using e(t) of selected non-pilot PMUs.

Numerically, due to the per unit scale of power system

variables, the prediction error can be very small and difficult

identify. We therefore define the performance index PI of the

ith variable for EED as

PI(t)(i) :=e(t)(i)

enormal, (5)

where enormal is the prediction error calculated when the

system is under normal operating conditions. Whenever PI

becomes larger than a pre-specified threshold, an event alert

will be issued. Given the fact that PMU samples at a rate of

30 Hz or higher, theoretically speaking, an alert can be issued

only two samples after the occurrence of an event. Such a swift

alert allows the system operators to quickly identify events in

real-time situations.

The flowchart of EED algorithm is shown in Fig. 1.

3

m PI

n NY

C

BY

!iv

N

m m N

! !

ˆi

y t

! !i

e t

! !i

PI t

YES

1t t !

NOY

Fig. 1. Implementation of EED algorithm.

IV. CASE STUDY

In this section, two cases are employed to illustrate the

proposed algorithm. Siemens PSS/E is utilized in Case A

to generate PMU data, with three events simulated. Case B

uses realistic data from the Electricity Reliability Council of

Texas (ERCOT). The algorithms in both cases are conducted in

Matlab. Due to the page limit, only bus frequency is analyzed

in this paper.

A. Simulation in PSS/E

A 23-bus 6-generator system in Siemens PSS/E is utilized

to generate PMU data with the system topology shown in Fig.

2. Assume each bus has one PMU, and only the bus frequency

ω is analyzed with the sampling rate of 30 Hz.

Three events, line tripping, unit tripping, and input change,

respectively, are simulated with details shown in Fig. 3.

1) Offline Training: The training contains PMU data of 250

seconds. The cumulative variance preserved by the number of

PCs for ω is shown in Fig. 4, which indicates that the first two

PCs preserve a high amount of variance (99.99%). According

to Section II, we select m = m′ = 2. The basis matrix is Y ωB =

[ω1, ω12], which stays unchanged for the three events.

2) Line Tripping Event: As shown in Fig. 3(a), two trans-

mission lines connecting buses 154 and 203, 152 and 153, are

assumed to have a line tripping event and followed by a line

closure event. The frequency profile for bus 154 is shown in

Fig. 5. Using equation (2), PIω s in (5) for bus frequencies are

depicted in Figs. 6 and 7.

Fig. 6 illustrates PIω of bus 154, near which the first line

tripping event happens. As one can observe, the PI proposed

in Section III can detect all the four line tripping events.

The zoomed-in figure is an illustration of the early detection

for the first event. The line between buses 154 and 203 is

tripped at t = 100 sec, with PIω154 > 500 at the same time

indicating a large prediction error of the linear representation.

However, using frequency profile in Fig. 5, only a 0.0001 pu

frequency deviation happens at t = 100.033 sec. This indicates

the advantage of the PIω for a quick detection of an event.

Fig. 7 shows PIω205 and PIω

3011, which are for a nearby bus

205 and a remote bus 3011 in the line tripping event. It can

101NUC-A

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102NUC-B

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228.6

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600.0

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AREA 1 (FLAPCO) AREA 2 (LIGHTCO)AREA 5 (WORLD)

564.8

130.9 MW

-538.3 Mvar

358.7 MW

184.0 Mvar

1000.0 MW

800.0 Mvar

Area 1 to 2 Interchange

Area 5 Generation

Bus 154 Load

PSS(R)E PROGRAM APPLICATION GUIDE EXAMPLE

153MID230

750.0

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0.0

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Bus - VOLTAGE (kV/PU)/ANGLE

Fig. 2. Topology of PSS/E 23-bus system [15].

time / sec250 0 100 200 300 450

Line tripping

154-203Training

Stage

Line closure

154-203

Line tripping

152-153

Line closure

152-153

(a) Line Tripping Event

time / sec250 0 100

Unit tripping

102Training

Stage

(b) Unit Tripping Event

time / sec250 0 100 200

Training

Stage

(c) Input Change Event

102

ref 0.01V !211

ref 0.01V ! "

Fig. 3. Timeline of three simulated system events.

0 5 10 15 20 2599.96

99.97

99.98

99.99

100

100.01

Number of PCs

%

Cumulative Variance for Bus Frequency

Fig. 4. Cumulative variance preserved by PCs of ω in Case A.

0 100 200 300 400 500 600

0.999

1

1.001

1.002

1.003

Time (s)

Bus F

requency (

p.u

.)

ω154

Profile During Line Tripping Event

Fig. 5. Frequency profile for ω154 during line tripping event.

99 99.5 100 100.5 101 101.5 102−500

0

500

Time (s)

PI

Zoomed−in PI of ω154

0 100 200 300 400 500 600−500

0

500

Time (s)

PI

PI of ω154

Fig. 6. PIω of line tripping event.

be observed that both PIω205 and PIω

3011 are capable to detect

4

0 100 200 300 400 500 600−500

0

500

Time (s)

PI

PI of ω3011

0 100 200 300 400 500 600−500

0

500

Time (s)

PI

PI of ω205

Fig. 7. PIω of nearby and remote buses in line tripping event.

the event at an early stage.

In summary the proposed PIω of any bus is shown to be

capable of detecting the line tripping event efficiently.

3) Unit Tripping Event: Generator 102 is assumed to be

tripped at time t = 100 sec, as shown in Fig. 3(b). The

frequency profile of bus 102 is depicted in Fig. 8, with the

PIω s shown in Figs. 9 and 10.

From Fig. 9, generator 102 tripped at t = 100 sec yields

PIω102 > 3000. From the frequency profile in Fig. 8, the

deviation of ω102 is only about 0.002 pu at t = 100 sec whereas

it is difficult to use ω102 directly to indicate a unit tripping

event. The proposed PI however is capable of magnifying

the difference between normal condition and contingency

quantities.

Fig. 10 shows PIω of buses which are nearby (bus 151) and

remote (bus 3018) to the unit tripping bus. The large values of

PIω s during the event suggest that PIω of any bus can detect

the unit tripping event quickly.

4) Control Input Change Event: As shown in Fig. 3(c), the

voltage regular set points of buses 102 and 211 are changed

by 0.01 pu at t = 100 sec and −0.01 pu at t = 200 sec,

respectively. The frequency profile of bus 211 is shown in

Fig. 11, with the PIω depicted in Figs. 12 and 13.

From Fig. 12, PIω211 provides a clear indication of both input

change events. From the zoomed-in figure, one can observe

that the first event is detected at time t = 100.033 sec, while

the frequency profile in Fig. 11 cannot provide such a clear

detection until t = 100.5 sec.

Fig. 13 shows PIω s of a nearby bus 201 and a remote bus

3018, and both events can be detected by either PIω201 or PIω

3018.

This again illustrates that PIω of any bus can detect control

input changes at an early stage.

B. Realistic PMU Data From ERCOT

In this case, we will demonstrate the proposed algorith-

m using the realistic PMU data from ERCOT, without the

knowledge of system topology. We note that the usability of

our method even without knowing the system topology is a

potentially very important capability of our EED algorithm.

Data of 7 PMUs on two separate days are utilized as the offline

training data and the online prediction data, respectively.

Fig. 14 indicates that there are 2 events in the real-time

system, happening around t = 354 sec and t = 1113 sec.

i) Offline Training: We perform PCA on the 7 bus frequency

data on the first day. The cumulative variance is shown in

0 50 100 150 200 250 300 3500.9

0.92

0.94

0.96

0.98

1

Time (s)

Bus F

requency (

p.u

.)

ω102

Profile During Unit Tripping Event

99 99.5 100 100.5 101 101.5 1020.96

0.97

0.98

0.99

1

1.01

Time (s)

Bus F

requency (

p.u

.)

Zoomed−in ω102

Profile

Fig. 8. Frequency profile for ω102 during unit tripping event.

0 50 100 150 200 250 300 350−5000

0

5000

Time (s)

PI

PI of ω102

99 99.5 100 100.5 101 101.5 102−5000

0

5000

Time (s)

PI

Zoomed−in PI of ω102

Fig. 9. PIω of unit tripping event.

0 50 100 150 200 250 300 350−5000

0

5000

Time (s)

PI

PI of ω3018

0 50 100 150 200 250 300 350−5000

0

5000

Time (s)

PI

PI of ω151

Fig. 10. PIω of nearby and remote buses in unit tripping event.

0 50 100 150 200 250 3000.9998

0.9999

1

1.0001

Time (s)

Bus F

requency (

p.u

.)

ω211

Profile During Input Change Event

99 99.5 100 100.5 101 101.5 1020.9998

0.9999

1

1.0001

Time (s)

Bus F

requency (

p.u

.)

Zoomed−in ω211

Profile

Fig. 11. Frequency profile for ω211 during input change event.

Fig. 15. We select m = m′ = 2, and the basis matrix is Y ωB =

[ω3, ω5].ii) Online Prediction: Using equation (2), PIω for the non-

pilot frequencies can be calculated. For illustration, PIω4 is

shown in Fig. 16. In the zoomed-in figures, the detection of

changes of system operating conditions can be achieved at

t = 354 sec and t = 1113 sec, respectively. However, from the

frequency profile in Fig. 14, the frequency deviation at t = 354

sec is only 0.0005 pu, which is too small to be detected. Again,

5

0 50 100 150 200 250 300−1000

−500

0

500

1000

Time (s)

PI

PI of ω211

99 99.5 100 100.5 101 101.5 102−1000

−500

0

500

1000

Time (s)

PI

Zoomed−in PI of ω211

Fig. 12. PIω of input change event.

0 50 100 150 200 250 300−1000

−500

0

500

1000

Time (s)

PI

PI of ω3018

0 50 100 150 200 250 300−1000

−500

0

500

1000

Time (s)

PI

PI of ω201

Fig. 13. PIω of nearby and remote buses in input change event.

0 200 400 600 800 1000 1200

0.996

0.998

1

Time (s)

Bus F

requency (

p.u

.)

ω1 Profile

Fig. 14. Frequency profile for ω1.

1 2 3 4 5 6 799.994

99.996

99.998

100

100.002

Number of PCs

Cumulative Variance for Bus Frequency

%

Fig. 15. Cumulative variance preserved by PCs of ω in Case B.

0 200 400 600 800 1000 1200

−500

0

500

Time (s)

PI

PI of ω4

353 353.5 354 354.5 355 355.5 356 356.5 357−500

0

500

Time (s)

PI

Zoomed−in PI of ω4 for 1

st Event

1112 1112.5 1113 1113.5 1114 1114.5 1115 1115.5 1116

−500

0

500

Time (s)

PI

Zoomed−in PI of ω4 for 2

nd Event

Fig. 16. PIω for ω4.

the efficacy of using PIω rather than ω itself is demonstrated.

V. CONCLUSION

In this paper, we present a PCA-based dimensionality reduc-

tion method for online PMU data. A linear representation of

the basis is first obtained by PCA in the offline training using

historical data. The pilot PMUs are then applied in the online

prediction. We propose a performance index PI based on the

prediction error to detect system events at an early stage.

Two simulated examples illustrate the efficacy of the pro-

posed EED algorithm. It has been shown that based on the

prediction error, the defined PIω ’s are capable to detect system

events at an early stage. Although only bus frequency is

analyzed in this paper due to page limitation, the phase angle

and voltage magnitude are also under analysis and results will

be included in our future work.

Further work will focus on the theoretical justifications of

the connection between the early detection of system events

and the prediction error from PCA-based learning. More realis-

tic data will be used to test the proposed algorithms. Nonlinear

methods such as embedding will be used and applied for

higher accuracy of early detection [16], [17].

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