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Contract No. DE-AC36-08GO28308

Algorithm for Screening 

Phasor Measurement Unit Data 

for Power System Events 

and Categories and Common 

Characteristics for Events Seen 

in Phasor Measurement Unit 

Relative Phase-Angle 

Differences and Frequency 

Signals

A. Allen

National Renewable Energy Laboratory

S. Santoso

University of Texas at Austin

E. Muljadi

National Renewable Energy Laboratory

Technical Report

NREL/TP-5500-58611

August 2013
NREL is a national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

Operated by the Alliance for Sustainable Energy, LLC

This report is available at no cost from the National Renewable Energy

Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

National Renewable Energy Laboratory

15013 Denver West Parkway

Golden, CO 80401

303-275-3000 • www.nrel.gov

Algorithm for Screening 

Phasor Measurement Unit Data 

for Power System Events and 

Categories and Common 

Characteristics for Events 

Seen in Phasor Measurement 

Unit Relative Phase-Angle 

Differences and Frequency 

Signals 

A. Allen

National Renewable Energy Laboratory

S. Santoso

University of Texas at Austin

E. Muljadi

National Renewable Energy Laboratory

Prepared under Task No. WE11.0825

Technical Report

NREL/TP-5500-58611

August 2013
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Cover Photos: (left to right) photo by Pat Corkery, NREL 16416, photo from SunEdison, NREL 17423, photo by Pat Corkery, NREL 

16560, photo by Dennis Schroeder, NREL 17613, photo by Dean Armstrong, NREL 17436, photo by Pat Corkery, NREL 17721.

Printed on paper containing at least 50% wastepaper, including 10% post consumer waste.
iii

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Acknowledgments

The authors acknowledge Dr. Mack Grady for his guidance during the development of 

this project. Doctors Wei-Jen Lee of the University of Texas at Arlington and Jamie 

Ramos of the University of Texas–Pan American provided a thorough review of this 

report and insightful comments and suggestions. We also acknowledge National 

Renewable Energy Laboratory colleagues Yih-Huei Wan, Yingchen Zhang, Vahan 

Gevorgian, and Mohit Singh, who supported this effort in many different capacities.
iv

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List of Acronyms

CSV comma-separated value

ERCOT Electric Reliability Council of Texas

FFT fast Fourier transform

PMU phasor measurement unit 

PSD power spectral density

RPAD relative phase angle difference

UT-Austin University of Texas at Austin

UTC Coordinated Universal Time

UTPA University of Texas–Pan American
v 

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Executive Summary

A network of multiple phasor measurement units (PMU) was created, set up, and 

maintained by professors and students from the University of Texas at Austin to obtain 

actual power system measurements for power system analysis. The network is now 

located and maintained at Baylor University in Waco, Texas. Power system analysis in 

this report covers a variety of time ranges, such as short-term analysis for power system 

disturbances and their effects on power system behavior and long-term power system 

behavior using modal analysis. Modal analysis is the analysis of power system dynamic 

behavior under excitation from changes in the power system. The PMU data examined in 

this report is archived at 30 samples per second and is continuously measuring and 

recording voltage phasor data. Because of the high volume of PMU data generated by the 

network, it is difficult to localize and analyze power system abnormal events (large 

disturbance events) of interest that have been recorded by the network. 

The first objective of this report is to screen the PMU data for events. An algorithm was 

created using a variety of methods to detect power system events. The algorithm uses fast

Fourier transform-, Yule-Walker-, and matrix-pencil-based methods to find events as 

well as a simple method to detect large swings in the PMU data. 

The second objective of the report is to identify and describe common characteristics 

extracted from power system events as measured by PMUs. The report describes 

category definitions based on visual analysis and extraction of numerical characteristics 

for each category. Category definitions based on visual inspection consist of two parts: 

events detected in voltage phase angle signals and frequency signals. In the voltage phase 

angle, events belong to one or more of the following proposed categories: impulse, 

transient, or step change. In the frequency, events belong to one or more of the following 

proposed categories: impulse, transient, or rise or drop in frequency. Some events belong 

to one category; some events belong to multiple categories, such as frequency drops 

caused by a sudden loss of generation that can also contain low-frequency oscillations. 

This type of event belongs to both the drop-in-frequency and transient categories. 

The numerical characteristics for each category and how these characteristics are used to 

create selection rules for the algorithm are also described. Trends in PMU data related to

different levels and fluctuations in wind power output are also examined. 
vi 

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Table of Contents

List of Figures............................................................................................................................................vii

List of Tables...............................................................................................................................................ix

1 Introduction (and Background) ........................................................................................................... 1

1.1 Independent Synchrophasor Network and PMU Data................................................................... 1

1.2 Screening Algorithm...................................................................................................................... 6

1.3 Categorization of Power System Events........................................................................................ 7

2 Screening Algorithm Development..................................................................................................... 8

2.1 PMU Data Format and Protocol .................................................................................................... 9

2.2 Event-Screening Methods............................................................................................................11

2.2.1 FFT ................................................................................................................................. 12

2.2.2 Matrix-Pencil ..................................................................................................................13

2.2.3 Yule-Walker Spectral .....................................................................................................15

2.2.4 Min-Max.........................................................................................................................16

2.3 Method Results for Marking Events............................................................................................16

3 Application and Demonstration.........................................................................................................18

3.1 Screening Results for a Systemwide Event Caused by Loss of Generation ................................18

3.2 Screening Results for Local Events With Unknown Causes.......................................................21

4 Event Categorization Based on Visual Analysis .............................................................................27

4.1 Event Categories..........................................................................................................................27

4.1.1 Voltage RPAD Event Categories....................................................................................27

4.1.2 Frequency Event Categories...........................................................................................35

5 Algorithm Development......................................................................................................................41

5.1 Extracted Characteristics for RPAD............................................................................................41

5.2 Extracted Characteristics for Frequency Data .............................................................................48

6 Influence of Wind Power on PMU Measurements ...........................................................................56

6.1 ERCOT Wind Power Data and Relationship to Voltage RAPD .................................................56

6.2 PMU Signal Mode Estimates.......................................................................................................58

7 Conclusion ...........................................................................................................................................67

8 References...........................................................................................................................................68
vii 

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List of Figures

Figure 1. Map of Texas PMU stations within the UT-Austin Independent Texas Synchrophasor 

Network .................................................................................................................................... 2

Figure 2. Map of wind farm locations in Texas [2]....................................................................................... 3

Figure 3. (Left) Equipment for each PMU station and (right) the phasor data concentrator and PC 

within the Independent Texas Synchrophasor Network........................................................... 4

Figure 4. Flowchart of the processes used to screen for events in PMU data ............................................... 8

Figure 5. Raw voltage phase angle for two PMU stations ..........................................................................10

Figure 6. RPAD between the same two PMU stations corrected by individually unwrapping and 

taking the difference ...............................................................................................................10

Figure 7. Voltage RPAD between UT-Austin and UTPA for 24 hours......................................................11

Figure 8. (Left) An illustration of a moving window applied PMU data and (right) a 10-second 

data window for analysis........................................................................................................11

Figure 9. Window of voltage RPAD ...........................................................................................................12

Figure 10. Amplitude of spectrum of voltage RPAD..................................................................................12

Figure 11. In the FFT method, data windows during which the peak magnitude exceeds three 

times the standard deviation of peak magnitudes for the entire hour are marked with 

an x. ........................................................................................................................................13

Figure 12. An example of the matrix-pencil method used to estimate parameters of the de-noised 

signal.......................................................................................................................................15

Figure 13. In the matrix-pencil method, data windows during which the peak magnitude exceeds 

three times the standard deviation of peak magnitudes for the entire hour are tagged...........15

Figure 14. Yule-Walker method power of frequency content in PMU signal during a large 

disturbance..............................................................................................................................15

Figure 15. In the Yule-Walker method, data windows during which the peak magnitude exceeds 

three times the standard deviation are tagged.........................................................................15

Figure 16. In the min-max method, data windows during which the difference between the 

minimum and maximum values in a 10-second data window exceeds three times the 

standard deviation are tagged. ................................................................................................16

Figure 17. Comparison of all the screening algorithms...............................................................................17

Figure 18. An entire day of PMU frequency from UT-Austin....................................................................17

Figure 19. Events detected in the UT-Austin PMU frequency for 23:00 UTC...........................................19

Figure 20. Events detected in the McDonald PMU frequency for 23:00 UTC ...........................................19

Figure 21. A large disturbance caused by a sudden 810-MW loss-of-generation impact on the UTAustin PMU and McDonald PMU frequencies......................................................................20

Figure 22. Events detected in the voltage RPAD between UT-Austin and McDonald PMU for 

23:00 UTC..............................................................................................................................21

Figure 23. A large disturbance caused by a sudden 810-MW loss-of-generation impact on the 

voltage RPAD between UT-Austin and McDonald................................................................21

Figure 24. Events detected in the UT-Austin PMU frequency for 17:00 UTC...........................................22

Figure 25. Events detected in the McDonald PMU frequency for 17:00 UTC...........................................22

Figure 26. A small-disturbance event detected in the UT-Austin PMU frequency but not in the 

McDonald PMU frequency ....................................................................................................22

Figure 27. A contour plot of the PSD (low-frequency content over time) shows (top) a 1-Hz 

oscillation present in the UT-Austin PMU frequency signal, but (bottom) the 1-Hz 

oscillation is absent in the McDonald PMU frequency signal................................................23

Figure 28. (Dotted line) A small-disturbance event detected in the McDonald PMU frequency but 

(solid line) not in the UT-Austin PMU frequency..................................................................24

Figure 29. Events detected in the UT-Austin to McDonald PMU voltage phase angle difference 

for 17:00 UTC ........................................................................................................................25
viii

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Figure 30. A contour plot of the PSD (low-frequency content over time) in the voltage RPAD 

over time shows a strong 1-Hz oscillation as well as another 0.6-Hz to 0.7-Hz 

oscillation. ..............................................................................................................................25

Figure 31. A small-disturbance event detected in RPAD between the UT-Austin and McDonald 

PMUs......................................................................................................................................26

Figure 32. An example of an RPAD single (large) impulse event (RPAD between UT-Austin and 

McDonald)..............................................................................................................................28

Figure 33. An example of an RPAD single (small) impulse event (voltage RPAD between UTAustin and UTPA)..................................................................................................................29

Figure 34. An example of an RPAD damped transient Event 1 (RPAD between UT-Austin and 

Waco) .....................................................................................................................................30

Figure 35. An example of an RPAD damped transient Event 2 (RPAD between UTPA and Waco).........30

Figure 36. An example of an RPAD damped transient Event 3 (RPAD between UTPA and Waco).........31

Figure 37. An example of an RPAD sustained transient (RPAD between UT-Austin and 

McDonald)..............................................................................................................................32

Figure 38. A detailed example of an RPAD sustained transient (RPAD between UT-Austin and 

McDonald)..............................................................................................................................32

Figure 39. A contour plot of the PSD (low-frequency content over time) for a voltage RPAD 

sustained transient event (RPAD between UT-Austin and McDonald) ................................. 33

Figure 40. An example of an RPAD sustained step change event (RPAD between McDonald and 

Waco) .....................................................................................................................................34

Figure 41. An example of an RPAD momentary step change event (RPAD between UT-Austin 

and Waco)...............................................................................................................................34

Figure 42. An example of a frequency impulse Event 1 .............................................................................36

Figure 43. An example of a frequency impulse Event 2 .............................................................................36

Figure 44. An example of damped transient event......................................................................................37

Figure 45. An example of a sustained transient event.................................................................................37

Figure 46. A contour plot of the PSD (low-frequency content over time) for a sustained-frequency 

transient event.........................................................................................................................38

Figure 47. An example of a sudden rise in frequency.................................................................................39

Figure 48. An example of a sudden drop in frequency ...............................................................................39

Figure 49. A systemwide frequency event seen by all PMUs.....................................................................40

Figure 50. A local frequency event that occurs only in the McDonald PMU .............................................40

Figure 51. A flowchart for the algorithm to categorize RPAD events........................................................42

Figure 52. An example of a PMU RPAD oscillation event.........................................................................43

Figure 53. An example of an oscillation-event PSD ...................................................................................44

Figure 54. An example of a non-oscillation-event PSD..............................................................................44

Figure 55. An event is detected in the RPAD signal...................................................................................45

Figure 56. Methods to detect an impulse event using the differentiated RPAD signal...............................45

Figure 57. The start and end times and the ramping period of the detected impulse event are 

shown for the RPAD signal....................................................................................................45

Figure 58. The (green) pre-event period and (red) post-event period are used to calculate the 

change in RPAD. ....................................................................................................................46

Figure 59. (Left) Examples of a momentary step change event and a (right) sustained step change 

event in the RPAD signal .......................................................................................................47

Figure 60. A flowchart for the algorithm to categorize frequency events...................................................49

Figure 61. (Left) The impulse event and (right) the differential of the signal exceeds the selected 

thresholds, indicating a Level 1 impulse event is detected.....................................................50

Figure 62. (Left) The impulse event and (right) the differential of the signal exceeds the selected 

thresholds, indicating a Level 2 impulse event is detected.....................................................50
ix

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Figure 63. (Left) The impulse event and (right) the differential of the signal exceeds the selected 

thresholds, indicating a Level 3 impulse event is detected.....................................................51

Figure 64. (Left) An oscillation event and (right) the spectral analysis showing that the frequency 

content for the signal exceeds the threshold, indicating a detected event. .............................51

Figure 65. From a 400-second window of frequency data, it is difficult to visually detect events.............52

Figure 66. An example of a frequency-rise event .......................................................................................52

Figure 67. An example of a frequency-drop event......................................................................................53

Figure 68. Another example of a frequency-drop event, on January 25, 2012, 7:13 UTC .........................53

Figure 69. A detailed view of the frequency-drop event shows the rapid drop in frequency at UTAustin and the oscillations at UT-Austin and UT-Pan American. .........................................54

Figure 70. The frequencies at each location begin to drop at different times, with UT-Austin 

dropping sooner and more rapidly..........................................................................................54

Figure 71. Aggregate wind power and wind power penetration within ERCOT on April 13, 2009 

(UTC) .....................................................................................................................................57

Figure 72. Voltage RPAD and wind power penetration on April 13, 2009 ................................................57

Figure 73. Modal frequency and damping estimates for low-wind conditions on April 13, 2009..............58

Figure 74. Modal frequency and damping estimates for high-wind conditions on April 13, 2009.............59

Figure 75. Voltage RPAD and wind power penetration on January 18, 2010 ............................................59

Figure 76. Modal frequency and damping estimates for high-wind conditions on January 18, 2010.........61

Figure 77. Modal frequency and damping estimates for low-wind conditions on January 18, 2010. 

The 2-Hz oscillations are still present, even though the wind penetration levels were 

low. .........................................................................................................................................61

Figure 78. Modal frequency and damping estimates for high-wind conditions on January 27, 

2012, 9:00 to 11:00 UTC........................................................................................................62

Figure 79. Modal frequency and damping estimates for high-wind conditions on November 8, 

2010, from 4:00 to 6:00 UTC................................................................................................. 63

Figure 80. Modal frequency and damping estimates for high-wind conditions on October 7, 2011, 

from 8:00 to 10:00 UTC.........................................................................................................63

Figure 81. Modal frequency and damping estimates for high-wind conditions on October 7, 2011, 

from 19:00 to 21:00 UTC.......................................................................................................64

Figure 82. Modal frequency and damping estimates for high-wind conditions on November 1, 

2011, from 00:00 to 02:00 UTC.............................................................................................64

Figure 83. Comparison of modes during high-wind conditions in April 2009 and January 2010 ..............65

Figure 84. Comparison of modes during high-wind conditions in April 2009 and November 2010..........65

Figure 85. Comparison of modes during high-wind conditions in April 2009 and October 2011 (a).........65

Figure 86. Comparison of modes during high-wind conditions in April 2009 and October 2011 

(b) ...........................................................................................................................................65

Figure 87. Comparison of modes during high-wind conditions in April 2009 and November 2011..........66

Figure 88. Comparison of modes during high-wind conditions in April 2009 and January 2012 ..............66

List of Tables

Table 1. An example of Type 1 PMU Data in CSV Format for Two PMU Stations With the 

Magnitude, Angle, and Frequency for Each Station Grouped Together .................................. 9

Table 2. An Example of Type 2 PMU Data in CSV Format for Three PMU Stations With the 

Frequencies for Each Station Listed in the Last Columns........................................................ 9

Table 3. An Example of the Protocol Function Output...............................................................................10

Table 4. Categories Presented for PMU RPAD and Frequency Events......................................................27

Table 5. Summary of Characteristics From Events Detected in RPAD Data .............................................47

Table 6. Summary of Characteristics from Events Detected in Frequency Data ........................................55
1

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1 Introduction (and Background)

Wide-area monitoring systems based on phasor measurement units (PMUs) collect large 

amounts of power system data in the form of phasors. Wide-area monitoring systems are 

intended for use across large geographical areas. With these actual power system 

measurements, it is possible to identify system trends and behavior such as power system 

frequency and voltage phase angle responses to factors such as increasing load or 

increasing penetrations of renewable energy resources. PMUs generate high precision 

data typically at a rate of 30 observations per second, resulting in large volumes of phasor 

data. In larger wide-area monitoring systems containing a large number of PMUs, the 

amount of data generated can be difficult to handle. Eventually, PMU data and wide-area 

monitoring systems can be used to help power system operators make better-informed 

decisions to keep the power system stable and operational. However, before this can 

occur, power system behavior as seen through PMU data must be understood.

The purpose of the research presented herein is to better understand power system 

behavior by detecting power system events of importance and also to begin examining 

trends and the behavior of the power system under different operating conditions.

Algorithms are created to screen the large volumes of PMU data for power system 

events. The algorithms are applied to many days of PMU data so that many events are 

detected during different operating conditions (different times of the day and different 

seasons) and at different locations within the PMU network. These events are analyzed

and placed into categories based on similar visual characteristics. The research presented 

here also describes common quantitative characteristics in each event category and the 

ranges of characteristics for each event category. Eventually, conditions before and after 

each event type will be examined to determine which event categories could cause 

changes in power system behavior.

In the future, power system operators will be alerted through real time detection of 

harmful events that are occurring and/or incoming on the system. The stability margin 

will be gauged more accurately, and possible remedial actions could be prescribed ahead 

of time. 

All data used in this research are real power system measurements taken from PMUs.

The following sections describe the PMU network and data, screening algorithms to 

detect power system events in the data, and categorization of events based on common 

characteristics.

1.1 Independent Synchrophasor Network and PMU Data

Synchronized voltage measurements taken by PMUs allow for wide-area monitoring of 

the electric power system. However, the placement of PMUs and use of PMU data are 

generally controlled by utilities and the independent system operators that install them.

Data are not always readily available for research. To overcome this obstacle, the 

University of Texas at Austin (UT-Austin) introduced an independent synchrophasor 

network to monitor events and analyze low-frequency oscillations from the electric 

power grid through PMU measurements taken at the customer-level voltage (120 V). 
2

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PMUs can now be placed virtually anywhere throughout the electric power system, and 

measurements are freely available to use for power system analysis. A map of the 

locations of the Independent Texas Synchrophasor Network PMUs within the Electric 

Reliability Council of Texas (ERCOT) is shown in Figure 1. PMU stations were placed 

within different zones of ERCOT: the Waco PMU station is located in the North Zone;

the UT-Pan American and UT-Austin PMU stations are located in the South Zone; the 

Schweitzer Engineering Laboratories, Inc. (SEL) – Houston PMU station is located in the 

Houston Zone; and the McDonald Observatory PMU station is located in the West Zone.

The McDonald Observatory PMU location was selected also because of its proximity to 

wind farms in West Texas, as shown in Figure 2. Information on transmission level 

power system event and behavior is clearly captured by 120 V PMUs as shown in [1].

Figure 1. Map of Texas PMU stations within the UT-Austin Independent Texas 

Synchrophasor Network
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Figure 2. Map of wind farm locations in Texas [2]

A diagram of equipment at each PMU location and central phasor data concentrator

within the synchrophasor network is shown in Figure 3. All equipment was donated by 

Schweitzer Engineering Laboratories, Inc. As shown in Figure 3, each PMU station has 

an antenna to receive a global positioning system signal. This global positioning system

signal is the common time reference required to make synchronous phasor measurements.

The global positioning system signal is sent to the global positioning system receiver,

where it is converted to Coordinated Universal Time (UTC) and used by each PMU to 

time stamp the measured phasor quantity. The time-stamped phasor from each PMU 

station is sent either through public internet or serial cable to the phasor data 

concentrator. The phasor data concentrator waits for data from all PMU locations and 

sorts the PMU data once it is received. The collected data is sent to a dedicated desktop 

PC, where software provided by Schweitzer Engineering Laboratories, Inc., archives the 

PMU data and displays it in real time.
4

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Figure 3. (Left) Equipment for each PMU station and (right) the phasor data concentrator 

and PC within the Independent Texas Synchrophasor Network

The synchronized phasor measurements and calculated frequency are stored at a rate of 

30 data points per second. Because the data has a 30-Hz sampling rate, only lowfrequency oscillations (below 15 Hz) can be analyzed. Events such as capacitor bank 

switching, which induces oscillations on the order of a few hundreds of hertz to 1.5 kHz,

are not visible in the PMU data. Even with a sampling rate of 30 Hz, the archived hourly 

reports are very large. For one PMU, an hourly report of the voltage phase angle data 

consists of 108,000 data points. Because there are three signals for each PMU station 

(voltage phase angle, voltage magnitude, and frequency), each PMU station generates 

324,000 data points each hour. These data points are stored hourly in a comma-separated 

value (CSV) format. A network with five PMU stations generates hourly CSV reports 

that are 13.8 MB in size. The synchrophasor network is in operation at all times.

Since the network was set up in the fall of 2008, it has been continuously generating data.

Because so much data is being generated, it is difficult to detect events of interest and 

analyze them for power system studies. Resources such as ERCOT’s Daily Grid 

Operations Reports [3] provide information on sudden losses of power above 450 MW 

caused by generating unit trips and information on line contingencies. (Total peak 

generating capacity in ERCOT is above 65 GW.) In addition, it is generally 

straightforward to visually detect large, sudden imbalances in generation and load by 

monitoring frequency. However, information related to events such as transmission line 

reclosing and trips and other equipment trips is not readily available. The research 

presented herein examines if these system events are visible in the PMU data and if it is

possible to automatically detect events of interest.

In this report, the voltage phase angle difference between two PMU locations is used to 

detect power system events that are visible in the voltage phase angle signal. However, 
5

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ideally when there are a large number of PMUs installed in the system, a common 

reference phase angle for all PMUs is desired. This reference phase angle can be 

determined by using a center-of-gravity concept to PMU-derived local frequencies. A 

common phase angle reference can then be subsequently obtained from this center-ofgravity frequency. Any PMUs located within the interconnected system can be referenced 

to this center-of-gravity derived reference frequency or reference phase angle. There are 

many power system measurements available to estimate center of gravity, as is well 

known in the literature [4] and will not be discussed here.

Data from five PMUs are available at five separate locations, with the distance between 

any two PMUs being very large. For example, the shortest geographical distance between 

two PMUs is approximately 105 miles; the closest two PMUs in the network are Waco 

and UT-Austin. The longest distance between two PMUs is between McDonald (Ft. 

Davis) and the University of Texas–Pan American (UTPA) (Edinburg); the geographical 

distance between these two PMUs is approximately 560 miles.

These PMUs are located among many generation buses (many of which are PV buses)

that maintain the scheduled generation and scheduled bus voltage (V = 0.95 p.u. to 1.05 

p.u.). The McDonald PMU is located among wind power plants that are operated as PQ 

buses (delivering power at specified real and reactive power; many wind plants are 

operated at unity power factor). When two PMUs are installed at buses located at 

opposite ends of a transmission line, the voltage phase angle difference and power 

transfer between the two adjacent buses can be measured and computed. However, when 

there are many generators and loads connected to the network between two PMUs at 

opposite ends of the power system network, the measured data between them cannot be 

used to directly measure the voltage phase angle difference or the power transfer.

The voltage phase angle difference between any two PMUs available in this project 

cannot be used to estimate the power transfer; instead, the PMUs are used to measure 

power system oscillations and other power system events. Two different PMU signals—

voltage phase angle and frequency—are used to screen for power system events. As 

previously stated, because of limited numbers of PMUs installed in this area, the centerof-gravity concept is not applied; instead, the difference in phase angle between two 

PMUs (relative phase angle difference, RPAD) is used as a sensing variable to detect 

power system events. Note that the frequency is computed at each PMU.

Although the frequency is calculated by the PMU, different categories of events are 

visible in the frequency data that are not easily detected in the RPAD. Also, the 

frequency is taken from a single location requiring only a single PMU measurement;

whereas the RPAD is actually the angle difference between two separate PMU locations.

Some events that occur closer to one PMU location are stronger in the measured signal of 

that PMU, and therefore may be more easily detected in the frequency signal. The event

in the measured RPAD signal may be drowned out by the voltage phase angle from the 

opposite PMU location. Also, the RPAD may reveal possible event sources that are not as 

obvious in the frequency signal. One possible drawback is the difficulty to diagnose and 

categorize events in case there are two independent events occurring at the same time at 
6 

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two different locations. However, if this happens, other PMU signals can collectively 

help decipher the event. 

1.2 Screening Algorithm

The term event in the report is used to describe large disturbances on the power system 

and sudden changes in power output at wind farms. Large disturbances include but are 

not limited to short circuits on transmission lines; protective relay actions required to 

clear the fault, such as transmission line trip and reclosing actions; or a large and sudden 

loss of generation or load. A sudden change in renewable energy includes but is not 

limited to large ramping up or down of wind farm power output. Large disturbances 

excite a single or multiple modes within the power system; these can be measured as 

oscillations in PMU voltage data. These oscillations typically consist of one strong mode 

in which the frequency of the oscillation is between 0.1 Hz and 2.0 Hz, the amplitude of 

the oscillation is typically higher than oscillations induced by random load switching, and 

the oscillation is quickly damped out if the system is stable. For example, a lowfrequency oscillation of 0.3 Hz with a damping constant of 10% has a time constant of 

5.3 seconds (the signal would drop to 37% of its original value after 5.3 seconds). This 

information is used to detect events in the PMU data. However, it is difficult to verify the 

cause of many of the detected events. The root cause of a few of the detected events can 

be identified; however, not all causes are known because information on power system 

disturbances is not always available or shared. Most of the guessed causes of events are 

based on clues present in the PMU data. Also, wind power-induced events are difficult to 

describe because detailed measurements of renewable generation power output is 

necessary for a thorough analysis. 

The purpose of the PMU network is to conduct analysis on transmission system behavior, 

but because the measurements are taken at the customer-level voltage of 120 V, events on 

distribution system may be measured and recorded as well. However, the voltage 

magnitude at the customer level is more heavily impacted by events that occur on the

distribution system. Also, large events that occur on the transmission system are visible at 

multiple PMU locations rather than at a single PMU location as is the case for 

distribution events. If it is unclear if a detected event occurred on the distribution system 

or the transmission system, the data from multiple PMUs can be compared during the 

time of the event and the voltage magnitude can be checked as well. If the event appears 

at only one PMU location and the voltage magnitude drops significantly (to 95% or less 

of rated voltage), then the event should not be considered a transmission system event. 

This type of event should be attributed to distribution system changes and should not be 

considered for transmission system analysis. Therefore, by using the guidelines above, it 

is important to distinguish between these two types of events so that distribution system 

events are not incorrectly identified and interpreted as transmission system events. 

In Section 2, an algorithm to read PMU data from CSV data files is described as well as 

methods used to correct PMU data before analysis can begin. Section 2 also describes the 

algorithm implemented to screen PMU data for events. The algorithm includes multiple 

methods that analyze data for possible events and displays the detected events. Section 3

describes results of the application of the algorithm to PMU data and gives examples of 
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different types of events that were detected. For example, a large event visible at multiple 

PMUs is analyzed as well as smaller events visible at only one PMU location. Both the 

PMU measured voltage phase angle and PMU calculated frequencies are used to detect 

events. 

1.3 Categorization of Power System Events

Events in the PMU RPAD and frequency signals detected by the screening algorithm are 

analyzed further. To extract common characteristics, the events detected by the screening 

algorithm are placed into event categories. Event categories are created for events 

detected in the RPAD signal and for events detected in the frequency signal. In Section 4, 

a description of how these categories are created based on common visual characteristics 

is provided. Examples of events in the voltage phase angle and frequency signals are 

provided and described in Section 4.1.1 and Section 4.1.2, respectively. These categories 

were selected after examining many events that occur at different times of the day, 

seasons, and are measured at different locations within the PMU network. A variety of 

methods are applied to the data to extract different characteristics from each group. The 

numerical characteristics from each event category are described in Section 5. The ranges 

for each type of event are described for RPAD and frequency events in Section 5.1 and

Section 5.2, respectively. 
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2 Screening Algorithm Development

This section describes the algorithm developed to screen PMU data taken from PMUs 

within the UT-Austin Independent Texas Synchrophasor Network for power system 

events. The PMU synchrophasor data consist of voltage magnitude, phase angle, and 

frequency for each PMU station and are saved hourly in CSV format. All PMU 

frequencies and all possible voltage phase angle separations between PMU stations are 

analyzed. A flowchart describing the algorithm is shown in Figure 4. In the flowchart, the 

signal to be analyzed for the hourly PMU file uploaded is assigned to the variable y. The 

algorithm does not analyze the entire hour of data at once, but instead analyzes a window 

of PMU data, assigned to the variable yWindow. The subroutine analysis on the window 

of data yWindow is applied for each moving window of data until the end of the entire 

hour of the signal y is reached.

Select Date and 

Hour of PMU 

Data to be 

Analyzed

Protocol and Data 

Processing

Select PMU Signal, 

y, to analyze

Create 10 sec Data 

Window, yWindow, for 

analysis

Subroutine 

Analysis on 

yWindow

End of y 

Reached?

Event Detection 

Subroutine

Have any Events 

been detected?

Plot and Save 

Detected Events

Have all PMU 

quantities been 

analyzed?

End of Event 

Detection 

Algorithm

Load CSV PMU 

File into Matlab

Yes

No

Yes

No

Yes

No

Figure 4. Flowchart of the processes used to screen for events in PMU data

In Section 2.1, the PMU CSV format and the protocol created to organize and label PMU 

data for analysis is described. Section 2.2 describes the methods used to screen for events 

in the data. Four different methods were used because each method is able to detect 

different types of events. The methods are fast Fourier transform (FFT); matrix-pencil, an 

analysis based on the difference between the minimum value and maximum value within 

a window of data (min-max method); and Yule-Walker. FFT and Yule-Walker are 

spectral methods, whereas matrix-pencil is parametric. All methods are applied to a 

window of PMU data where resulting peak values from each method applied to the data 

window are saved. The peak values from each data window for the entire PMU file are 

used to detect events. Any peak magnitudes greater than three standard deviations are 

marked as possible events. Section 2.3 describes how the results from each of the 

methods are used to detect events. If two or more methods detect an event in the same 
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data window, that window is marked as containing an event. The event is plotted and data 

saved for further analysis. The algorithm was developed in Matlab and uses functions 

from the Signal Processing Toolbox and user-defined functions [5].

2.1 PMU Data Format and Protocol 

New PMU stations are installed and removed from the network for various reasons,

causing the format of the archived hourly PMU files to constantly change. The grouping 

of PMU quantities for each station changes as well, resulting in two types of data files.

The two types of data files are shown in Table 1 and Table 2. The voltage magnitudes 

were arbitrarily selected. All measurements are taken at customer-level voltage of 120 V.

Table 1. An example of Type 1 PMU Data in CSV Format for Two PMU Stations With the 

Magnitude, Angle, and Frequency for Each Station Grouped Together

t

MAG1 

(V)

ANG1 

(deg)

FREQ1 

(Hz)

MAG2 

(V)

ANG2 

(deg)

FREQ2 

(Hz)

... ... ... ... ... ... ...

24:26.7 79924.90 120.18 59.98 40.80

-

10.12 60.02

24:26.8 79930.60 119.89 59.98 40.81 -9.91 60.02

24:26.8 79933.17 119.60 59.98 40.82 -9.70 60.02

Table 2. An Example of Type 2 PMU Data in CSV Format for Three PMU Stations With the 

Frequencies for Each Station Listed in the Last Columns

t

MAG1 

(V)

ANG1 

(deg) MAG2 (V)

ANG2 

(deg) MAG3 (V)

ANG3 

(deg)

FREQ1 

(Hz)

FREQ2 

(Hz)

FREQ3 

(Hz)

... ... ... ... ... ... ... ... ... ...

08:38.6 41.192

-

22.827 79166.508 -45.7 73482 99.924 59.949 59.947 60.008

08:38.7 41.192

-

23.457 79141.992 -46.3 0 0 59.948 59.947 0

08:38.7 41.187

-

24.068 79138.844 -46.9 73484.742 100.14 59.948 59.948 60.009

Because of the two file types and the large variety in the number and location of stations 

in operation, it is cumbersome to read PMU data and begin analysis of the data. Without 

an automated method, it is first necessary to open the PMU file and count the number of 

stations and the order of the stations to conduct an accurate analysis. In addition, dropped 

data points appear in the voltage magnitude and frequency as zeros and need to be 

removed before analysis can begin.

A protocol was created to analyze the PMU data files and indicate the type of file format, 

the number of PMU stations, and the quality of the PMU data. The file format type 

indicates if the PMU frequency for each station is grouped with the other PMU station 

data or if all PMU frequencies are grouped together, as shown in Table 1 and Table 2,

respectively. The number of PMU stations provides the number of PMU stations in 

operation at the time the data was archived. The quality of the PMU data is “true” if the 
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PMU station contains zero or a limited number of dropped data points and “false” if the 

data contains many dropped data points or if the PMU station is not sending data to the 

phasor data concentrator. The Protocol function determines the PMU file type and the 

number of PMU stations. It also indicates the column locations for each PMU station’s

magnitude, angle, and frequency data, and if the PMU data is “false” or contains missing 

data. An example is shown in Table 3. This information is used to determine how to label 

the data type and how to label the data by PMU location.

Table 3. An Example of the Protocol Function Output

Type

Number of 

Measurement 

Points

(NMP)

NMP 1

Mag Ang Freq

Col 

Index Fault

Col 

Index Fault

Col 

Index Fault

2 6 1 “true” 2 “true” 13 “true”

After the file format type is known, the columns of the PMU data are identified and the 

voltage phase angle data is modified before analysis begins. Because the rotation of the 

voltage phasors is not constant and not at nominal frequency (60 Hz), the voltage phase 

angle increases or decreases depending on if the speed of rotation is greater or less than 

nominal. When the voltage phasor is rotating at greater-than-nominal speed and crosses 

from 180 to -180 degrees, the voltage phase angle jumps, as shown in Figure 5. The 

voltage phase angle at each PMU station is unwrapped before the difference in the 

voltage angle between the two stations is taken. The unwrapped RPAD is shown in 

Figure 6 and can now be screened for events. All possible RPAD combinations are 

considered for each PMU file.

Figure 5. Raw voltage phase angle for 

two PMU stations

Figure 6. RPAD between the same two 

PMU stations corrected by individually 

unwrapping and taking the difference

To illustrate the amount of information present in PMU data, an entire day of PMU 

RPAD data between UT-Austin and McDonald is plotted in Figure 7. Each PMU RPAD

and frequency data set is screened for possible events. Section 2.2 describes the methods 

used to screen for events in the PMU data.

12 14 16 18 20 22 -200

-150

-100

-50

0

50

100

150

200

Time, minutes

Voltage Phase Angle, degrees

Raw Voltage Phase Angle

UT-Austin PMU

McDonald PMU

12 14 16 18 20 22 -0.76

-0.74

-0.72

-0.7

-0.68

-0.66

-0.64

-0.62

-0.6

-0.58

-0.56

Time, minutes

Voltage Phase Angle, degrees

'Unwrapped' Relative Phase Angle Difference (RPAD)
11

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Figure 7. Voltage RPAD between UT-Austin and UTPA for 24 hours

2.2 Event-Screening Methods

To screen for events within each hourly PMU file, an overlapping, moving window is 

applied to the PMU data. The window size is 10 seconds long and overlaps half of the 

previously windowed data. The moving window method is illustrated in Figure 8.

tWindow

...

Figure 8. (Left) An illustration of a moving window applied PMU data and (right) a 10-

second data window for analysis

Each window of data is analyzed for possible events by applying the four different 

detection methods mentioned. All methods except for the min-max are based on the 

strength of the estimated frequency content. Only frequencies below 2 Hz are examined 

(the frequency range of inter- and intra-area oscillations [6]). Each method is described in 

detail below.

0 5 10 15 20

15

20

25

30

35

40

45

50

Time, hours

Phase Angle, degrees
12

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2.2.1 FFT

Before the method is applied, the data window is differentiated using the Matlab function 

diff to remove dc offset in the data to facilitate the detection of events in the lowfrequency range below 1 Hz. Differentiating the data increases the noise in the data;

however, it has been found that the magnitude of frequencies associated with events in 

the data tend to be very high. Therefore, increased noise is not a concern for this analysis.

The FFT utilizes the Matlab function fft to detect events in the PMU data. This 

function returns the discrete Fourier transform calculated using the FFT algorithm. The 

discrete Fourier transform is used to find the strongest frequency component within the 

data window. The maximum amplitude, |Y(f)|, is saved for frequencies in the range of 

0 < f ≤ 2 Hz. The method is applied to a data window of the voltage phase angle in 

Figure 9 containing oscillations induced by a large event. The discrete Fourier transform 

applied to the data window containing event information is shown in Figure 10. The 

Fourier transform in Figure 10 shows a strong 0.64-Hz component. In the algorithm, the 

peak magnitude, |Y(f)| = 0.03, would be saved for this data window.

Figure 9. Window of voltage RPAD Figure 10. Amplitude of spectrum of 

voltage RPAD

The FFT method is applied to each 10-second data window for the entire hour of PMU 

data. The average and standard deviation are calculated for all saved peak magnitudes.

Any saved magnitudes above three standard deviations are tagged as possible events.

Three standard deviations window was selected based on examples of detected events 

from the UT synchrophasor network data. A plot of the peak magnitudes from each 10-

second data window is shown for an hour of PMU frequency in Figure 11. The average 

and standard deviation of the peak magnitudes are indicated. The outliers, or possible 

events, are also marked in Figure 11. 

1928 1930 1932 1934 1936 1938 1940

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

Data Window During a Large Disturbance

Time, seconds

Voltage Phase Angle, degrees

0 1 2 3 4 5

0

0.005

0.01

0.015

0.02

0.025

0.03

Single-Sided Amplitude Spectrum of y(t)

Frequency (Hz)

|Y(f)|
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Figure 11. In the FFT method, data windows during which the peak magnitude exceeds 

three times the standard deviation of peak magnitudes for the entire hour are marked with 

an x.

2.2.2 Matrix-Pencil

The matrix-pencil method [7] fits a sum of damped sinusoids to evenly sampled PMU 

data. The amplitude, phase angle, frequency, and damping are the parameters of the 

damped sinusoids estimated to fit the PMU data. The mathematical representation of the 

sum of damped sinusoid estimates fitted to the sampled data is given in (1).

( ) ∑=

=

n

i

k

i i y k R z

1

(1)

where the discrete signal y(k ) in (3) is equal to the sum of the product of the residues or 

complex amplitudes R and the poles z. The parameter n is the number of sinusoids or 

modes to be estimated. The damping and frequency estimates of the signal can be 

extracted from each zi, as shown in (2).

( )

i i i

i i

j

z t

λ σ ω

λ

= ±

= exp ∆

(2)

This method also utilizes singular value decomposition to remove noise from the signal 

before the estimates are made. Because a matrix-pencil function is not available in 

Matlab, a user-defined function was created to calculate the parameters using the matrixpencil method and is described briefly by the following equations.

A matrix [Y] is created from the noisy PMU data y(k ), as shown in (3).

0 500 1000 1500 2000

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

FFT Method Data Window Peak Magnitudes

Time, seconds

|Y(f)|

Peak Magnitudes > 3*std

Peak Magnitudes

Peak Magnitudes Mean

3*std

-3*std
14

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[ ]

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

























− − − −

+ =

1 1

1 2 1

0 1

y N L y N L y N

y y y L

y y y L

Y



   





(3)

The parameter L is the pencil parameter, and N is the total number of data points in y(k ).

Singular value decomposition is applied to [Y], as shown in (4).

[ ] H Y = UΣV (4)

The matrices U and V are unitary matrices, and the operator H is the conjugate transpose. 

The singular values of [Y] are located along the diagonal of matrix Σ in descending order.

A threshold value is selected so that the n singular values above the threshold are 

considered and used to create the following matrices. 

[ ] [ ]

[ ] [ ]

[ ] [ ]

H

H

n

Y U V

Y U V

V v v v

' '

' '

' , , ,

2 2

1 1

1 2

= Σ

= Σ

= 

(5)

The vs are the column vectors of V from (4), matrixΣ' is the first n columns of Σ , [ '] V1 is 

the matrix V with the final column removed, and [ '] V2 is the matrix V with the final row 

removed. Using the matrix-pencil as defined in [7], the matrices from (5) can be used to 

create the following new matrix-pencil definition for noisy data.

[ ] [ ] [ ] + +

= H H Y Y V ' V ' 1 1 2 1 (6)

The next step is to find the eigenvalues for [ ] H H +

V ' V ' 2 1 . The eigenvalues are used to solve 

for R from (1) and is rewritten in the following format.

( )

( )

( ) 















































=

























− − − −

n

N

n

N N

n

R

R

R

z z z

z z z

y N

y

y





   







2

1

1 1

2

1

1

1 2

1 1 1

1

1

0

(7)

The estimates for the damping and frequency are extracted from z, as shown in (2), and 

the amplitude is extracted from R.

The matrix-pencil method is applied to a 10-second window of PMU data. Figure 12

shows the reconstructed signal (solid line) using the estimated parameters compared to 

the original signal (dotted line). Because noise was removed using singular value 

decomposition, parameters were not estimated to fit the noise but only the “true” modes 

present in the data.
15

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Figure 12. An example of the matrixpencil method used to estimate 

parameters of the de-noised signal

Figure 13. In the matrix-pencil method, 

data windows during which the peak 

magnitude exceeds three times the 

standard deviation of peak magnitudes 

for the entire hour are tagged.

The values of the two highest estimated amplitudes are saved for each data window. The 

method is repeated for the entire hour of data. It is assumed that if an event is present in 

the data, the max amplitude would be significantly larger than the max amplitude from a 

data window without any events. After the two highest magnitudes are saved for all data 

windows, the averages and standard deviations for the highest and second highest 

magnitudes are calculated separately. Detection of possible events is similar to the FFT 

method; any magnitudes above three standard deviations are tagged as possible events, as 

shown in Figure 13.

2.2.3 Yule-Walker Spectral

The Yule-Walker spectral method is similar to the FFT method but utilizes the pyulear

function from the Matlab Signal Processing Toolbox [5]. The pyuler function 

calculates the power spectral density (PSD) using the autoregressive Yule-Walker 

method. The PSD for a data window containing an event is shown in Figure 14.

Figure 14. Yule-Walker method power of 

frequency content in PMU signal during a 

large disturbance

Figure 15. In the Yule-Walker method, 

data windows during which the peak 

magnitude exceeds three times the 

standard deviation are tagged.

0 2 4 6 8 10

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Time, seconds

Voltage Phase Angle (detrended), degrees

Matrix-Pencil

Original Signal

Estimated Signal

0 500 1000 1500 2000

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Matrix-Pencil Method Peak Amplitudes

Time, seconds

Amplitude, degrees

Peak Amplitude > 3*std

Peak Amplitude

Peak Amplitude Mean

3*std

-3*std

0 0.5 1 1.5

-90

-80

-70

-60

-50

-40

Yule-Walker Method

Frequency, Hz

Power, dB

0 500 1000 1500 2000

-90

-80

-70

-60

-50

-40

Yule-Walker Method Peak Magnitudes

Time, seconds

Peak Magnitudes (dB)

Peak Magnitudes > 3*std

Peak Magnitudes

Peak Magnitudes Mean

3*std

-3*std
16

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The peak value in the PSD in dB is marked. The peak values for each PSD of the data 

window are saved. This is repeated for the entire hour. The average and standard 

deviation of the maximum magnitudes are calculated. Magnitudes above three standard 

deviations are tagged as possible events, as shown in Figure 15.

2.2.4 Min-Max

For this method, the difference between maximum and minimum values within the data 

window is calculated. The difference for each data window for the entire hour is saved.

This method is sensitive because it also detects gradual changes in the signal above the 

10-second data window that are not caused by power system events. Possible events are 

detected by calculating the average and standard deviation for all the data window 

differences for the entire hour of PMU data. The differences that exceed three times the 

standard deviation are marked as possible events, as shown in Figure 16.

Figure 16. In the min-max method, data windows during which the difference between the 

minimum and maximum values in a 10-second data window exceeds three times the 

standard deviation are tagged.

2.3 Method Results for Marking Events

After all methods have been used to screen for possible events in the PMU data, the time 

stamps of data windows marked as containing possible events are compared. Figure 17

shows an example of the results for possible events in the RPAD between UT-Austin and 

McDonald. If two or more methods detect a possible event in the same data window, that 

data window is marked as containing an event and the PMU data for that window is 

saved and plotted. In Figure 17, an event is detected at 1,285 seconds by both the matrixpencil and min-max methods. Another event is detected at 1,935 seconds by all four 

methods. This event is analyzed further in Section 3.1.

0 500 1000 1500 2000

-0.5

0

0.5

1

1.5

2

Min-Max Method

Time, seconds

Min-Max, degrees

Min-Max > 3*std

Min-Max

Min-Max Mean

3*std

-3*std
17

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Figure 17. Comparison of all the screening algorithms

Figure 18. An entire day of PMU frequency from UT-Austin

0 500 1000 1500 2000 2500 3000 3500 4000

Time, seconds

Comparison of Event Screening Methods (RPAD between UT-Ausitn - McDonald)

Yule-Walker

FFT

Min-Max

Matrix-Pencil (Amp 1)

Matrix-Pencil (Amp 2)

Event

0 5 10 15 20

59.75

59.8

59.85

59.9

59.95

60

60.05

60.1

60.15

60.2

60.25

Time, hours

Frequency, Hz

One Day of PMU Frequency from UT-Austin 
18 

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3 Application and Demonstration

The results from the algorithm are examined by screening 24 hours (00:00 to 23:59 UTC) 

of PMU data for power system events. The UT-Austin PMU and McDonald PMU were 

operational during this time period. The voltage RPAD between UT-Austin and 

McDonald and the frequencies at each location are analyzed. An example of 24 hours of 

UT-Austin PMU frequency is shown in Figure 18 to illustrate the difficulty of visually 

screening for events in PMU data. The PMU frequency is a calculated quantity that is 

based on the measured voltage phase angle [8] and differs slightly across the power 

system, as shown in the PMU frequencies in this section. High-precision PMU calculated 

frequencies also provide more information than a single-system frequency. 

Two types of events found in the data are described here to illustrate how the screening 

algorithm detects events. The first event (described in Section 3.1) was caused by a 

sudden loss of generation. The event occurred at 23:33 UTC (17:33 CST) and is visible in 

all three signals. The second event (described in Section 3.2) was probably caused by a 

recloser operation visible only in the McDonald PMU data. Strong oscillations visible 

only at the UT-Austin PMU are also examined in Section 3.2. The source of the 

oscillations in the UT-Austin PMU data is unknown. 

3.1 Screening Results for a Systemwide Event Caused by Loss 

of Generation

At 23:33 UTC, a generating unit tripped, resulting in a loss of 810 MW of generation and 

a frequency decline to 59.774 Hz. The ERCOT load at the time was 35,000 MW [3]. The 

frequency at UT-Austin and McDonald are screened for events using the methods 

described in Section 2. The results from the algorithm are shown in Figure 19 and Figure 

20. The generating unit trip was the only event detected in both PMU frequencies and 

was detected by all four methods in the UT-Austin PMU frequency, as shown in Figure 

19. As shown in Figure 20, the disturbance was detected and tagged in the McDonald 

PMU frequency, but the matrix-pencil method detected other possible events as well 

(represented in Figure 20 as □ and ). However, because the matrix-pencil method was 

the only method to detect a possible event, these data windows were not tagged as real 

events.

The PMU frequencies data window for the event is plotted in Figure 21. Both PMU 

frequencies decline to 59.76 Hz, which differs slightly from the ERCOT Grid Report [3]

frequency decline possibly because the PMU frequencies are taken at specific buses 

rather than representative of the system frequency. It is possible that the PMU data also 

has a higher resolution than the ERCOT data. 
19

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Figure 19. Events detected in the UT-Austin PMU frequency for 23:00 UTC

Figure 20. Events detected in the McDonald PMU frequency for 23:00 UTC

0 1000 2000 3000

Time, seconds

 

Yule-Walker

FFT

Min-Max

Matrix-Pencil (Amp 1)

Matrix-Pencil (Amp 2)

Event

0 1000 2000 3000 4000

Time, seconds

 

Yule-Walker

FFT

Min-Max

Matrix-Pencil (Amp 1)

Matrix-Pencil (Amp 2)

Event
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Figure 21. A large disturbance caused by a sudden 810-MW loss-of-generation impact on 

the UT-Austin PMU and McDonald PMU frequencies

The same generating unit trip was detected in the RPAD between UT-Austin and 

McDonald, as shown in Figure 22. An additional event was detected in the RPAD signal,

but it is not clear if it is an actual event or if the threshold values in the algorithm are too 

sensitive. The RPAD during the event is plotted in Figure 23. The voltage phase angle 

has an approximate initial upswing of 1.5 degrees. The amplitude of the oscillation is not 

very large, and it is possible that the location of the generating unit that tripped is located 

far from the UT-Austin and McDonald PMU stations. The oscillations in the voltage 

phase angle prior to and after the event are much smaller and have an amplitude between 

0.1 to 0.25 degrees. 

1930 1935 1940 1945

59.75

59.8

59.85

59.9

59.95

60

Time, seconds (of hour)

Frequency, Hz

Detected Event PMU Frequencies

UT-Austin PMU

McDonald PMU
21

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Figure 22. Events detected in the voltage RPAD between UT-Austin and McDonald PMU for 

23:00 UTC

Figure 23. A large disturbance caused by a sudden 810-MW loss-of-generation impact on 

the voltage RPAD between UT-Austin and McDonald 

The examples illustrate that the screening algorithm can very easily detect a large event 

in all the PMU signals analyzed. Screening for smaller events in the PMU data are 

examined next.

3.2 Screening Results for Local Events With Unknown Causes

The methods are further evaluated by screening PMU frequencies and RPAD data for 

smaller, local events. In this section, an hour of PMU data (17:00 UTC) is screened for 

possible events. The algorithm is applied to the UT-Austin PMU frequency, and the 

McDonald PMU frequency with results is shown in Figure 24 and Figure 25.

0 1000 2000 3000 4000

Time, seconds

Comparison of Event Screening Methods (UT-Ausitn - McDonald Phase Angle)

Yule-Walker

FFT

Min-Max

Matrix-Pencil (Amp 1)

Matrix-Pencil (Amp 2)

Event

1928 1930 1932 1934 1936 1938 1940

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

Time, seconds

Phase Angle, degrees
22

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Figure 24. Events detected in the UTAustin PMU frequency for 17:00 UTC

Figure 25. Events detected in the 

McDonald PMU frequency for 17:00 UTC

Many of the events detected in the UT-Austin PMU frequency were not detected in the 

McDonald PMU frequency and vice versa. In the UT-Austin PMU frequency, the events 

detected starting at approximately 1,750 seconds are strong oscillations that are not 

visible in the McDonald PMU frequency. For comparison, a 20-second window of 

frequency data is plotted in Figure 26. The UT-Austin frequency (solid line) has stronger, 

higher-magnitude oscillations, but it is difficult to identify the strength and frequency of 

the oscillations based on the plot.

Figure 26. A small-disturbance event detected in the UT-Austin PMU frequency but not in 

the McDonald PMU frequency

The PSD is calculated to analyze the strength and frequency of the oscillations present in 

the PMU data. The PSD is stored for each 10-second window and plotted as a contour 

plot to compare the frequency content of the UT-Austin and McDonald PMU signals. 

The contour plots are shown in Figure 27. From Figure 27, it is easy to see a strong, 1-Hz 

0 1000 2000 3000 4000

Time, seconds

Comparison of Event Screening Methods (UT-Austin PMU Freq)

FFT

Min-Max

Matrix-Pencil (Amp 1)

Matrix-Pencil (Amp 2)

Total Events

0 1000 2000 3000 4000

Time, seconds

Comparison of Event Screening Methods (McDonald PMU Freq)

Yule-Walker

FFT

Min-Max

Matrix-Pencil (Amp 1)

Matrix-Pencil (Amp 2)

Event

1880 1885 1890 1895 1900

60.02

60.022

60.024

60.026

60.028

60.03

60.032

60.034

60.036

Time, seconds

Frequency, Hz

Detected Events PMU Frequencies

UT-Austin PMU

McDonald PMU

1,750 sec

900 sec –

1,000 sec
23

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oscillation in the UT-Austin PMU frequency that is not visible in the McDonald PMU 

frequency for the same time period. The oscillation in the UT-Austin data is strongest 

from approximately 1,600 seconds to 2,000 seconds, as indicated by the dark red. This is 

approximately the same time period that the algorithm tagged as a possible event. A 1-Hz 

oscillation indicates intra-area oscillations [6] (usually associated with a single machine), 

but the exact cause of the 1-Hz oscillation is currently unknown. In the contour plot, the 

frequency on the y-axis is the frequency content of the PMU frequency signal. The PMU 

frequency is not measured, but calculated from the voltage angle.

Figure 27. A contour plot of the PSD (low-frequency content over time) shows (top) a 1-Hz 

oscillation present in the UT-Austin PMU frequency signal, but (bottom) the 1-Hz 

oscillation is absent in the McDonald PMU frequency signal.

Frequency, Hz

UT-Austin PMU Frequency

Time,seconds

1300 1400 1500 1600 1700 1800 1900 2000

0.5

1

1.5

-200

-180

-160

-140

Time,seconds

Frequency, Hz

McDonald PMU Frequency

1300 1400 1500 1600 1700 1800 1900 2000

0.5

1

1.5

-190

-180

-170

-160

-150

-140

-130
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Figure 28. (Dotted line) A small-disturbance event detected in the McDonald PMU 

frequency but (solid line) not in the UT-Austin PMU frequency

In the McDonald PMU frequency, the events detected starting at approximately 900 

seconds are damped oscillations that are not visible in the UT-Austin PMU frequency. A 

40-second window of frequency data is plotted in Figure 28. The (dotted line) McDonald 

PMU frequency contains many damped oscillations that are not present in the (solid line) 

UT-Austin PMU frequency. The cause of these oscillations will become apparent when 

examining the voltage phase angle.

The screening results for PMU RPAD data for one hour (17:00 UTC) is shown in Figure 

29. The algorithm is able to detect events that were seen in the McDonald PMU 

frequency at approximately 900 seconds to 1,000 seconds, shown in Figure 25 and Figure 

28. However, the events detected in the UT-Austin frequency at approximately 1,750

seconds to 2,000 seconds (refer to Figure 24) were not as clearly visible in the voltage 

phase angle. The FFT and matrix-pencil methods were able to detect the oscillation 

during the 1,750-second to 2,000-second time frame, but because these methods did not 

detect the oscillation simultaneously, they were not tagged as events in the results from 

the PMU RPAD analysis.

950 960 970 980 990

59.96

59.97

59.98

59.99

60

Time, seconds

Frequency, Hz

Detected Event PMU Frequencies

UT-Austin PMU

Events McDonald PMU
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Figure 29. Events detected in the UT-Austin to McDonald PMU voltage phase angle 

difference for 17:00 UTC

Figure 30. A contour plot of the PSD (low-frequency content over time) in the voltage 

RPAD over time shows a strong 1-Hz oscillation as well as another 0.6-Hz to 0.7-Hz 

oscillation.

The contour plot for the RPAD signal in Figure 30 indicates that the 1-Hz oscillation is 

strong during the same time period, as shown in (top) Figure 27, but contains an 

approximate 0.6-Hz to 0.7-Hz oscillation as well. The contour plot for the entire hour of 

data shows that the 1-Hz oscillation is not as strong at other times.

The events detected in the McDonald PMU frequency in Figure 28 were also detected in 

the PMU voltage phase angle. The RPAD between UT-Austin and McDonald for this 

series of events is plotted in Figure 31. The sudden change and return of the phase angle 

indicates multiple reclosing events. Because the oscillations are visible only in the 

McDonald PMU frequency, it is assumed that the event occurred near McDonald (local 

event). However, it is difficult to tell at what voltage level the recloser is located 

(distribution or transmission voltage level). It can be concluded that the recloser is most 

likely not located at a distribution feeder directly upstream from the PMU station, 

0 1000 2000 3000 4000

Time, seconds

Comparison of Event Screening Methods (RPAD between UT-Austin - McDonald)

FFT

Min-Max

Matrix-Pencil (Amp 1)

Matrix-Pencil (Amp 2)

Event

Time,seconds

Frequency, Hz

UT-Austin - McDonald PMU Voltage Phase Angle

1300 1400 1500 1600 1700 1800 1900 2000

0.5

1

1.5

-120

-110

-100

-90

-80

-70

-60
26 

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otherwise a reclosing event could cause the PMU to lose power and the PMU would be 

unable to measure and transmit voltage phasor data. The measured voltage magnitude at 

McDonald is too noisy to extract any conclusions. 

Figure 31. A small-disturbance event detected in RPAD between the UT-Austin and 

McDonald PMUs 

So far in this report, the algorithm used to screen PMU data generated by the UT-Austin 

synchrophasor network for power system events has been described. The algorithm uses 

four different methods to screen for possible events. Each method is applied to a moving 

window of PMU data. Any values from each method that exceed three standard 

deviations away from the mean are marked as possible events. A data window is marked 

as containing an event if two or more methods detect a possible event in the same data 

window. In the following sections, events detected using this method are examined 

further. The event-screening algorithm is applied to many days’ worth of PMU data, and 

all detected events are collected. Events are placed into categories based on common 

characteristics. These categories and common characteristics are examined further in 

Section 4 and Section 5. 

940 950 960 970 980 990 1000

9

9.5

10

10.5

11

11.5

Time, seconds

Voltage Phase Angle, degrees

Detected Event (RPAD between UT-Austin and McDonald)
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4 Event Categorization Based on Visual Analysis

This section discusses the categorization of events detected by the screening algorithm 

based on common visual characteristics. The event categorizes and examples from each 

are described and provided in Section 4.1. In Section 4.1.1 and Section 4.1.2, the events 

as seen in the RPAD and frequency data are described, respectively. Example events 

from the PMU data are provided as well.

4.1 Event Categories

The categories of detected events for RPAD and frequency signals are proposed in Table 

4 below. Events were extracted from nine days’ worth of data taken from different 

seasons of the year and from different years (from 2010 to 2012). Based on the types of 

events extracted from these days, the categories were selected using common visual 

characteristics (oscillations, impulses, step change, and rate of change). The RPAD has 

three categories with a total of seven subcategories. The frequency also has three 

categories with a total of seven subcategories. 

Table 4. Categories Presented for PMU RPAD and Frequency Events

Voltage RPAD Frequency

Category Subcategory Category Subcategory

Impulse

Single 

(Small) Impulse

Small

Single 

(Large) Large

Transient Damped Transient Damped

Sustained Sustained

Step 

Change

Momentary

(Small)

Rise or Drop 

in Frequency

Rise

Momentary 

(Large) Drop

Sustained Unit Trip

Although the main categories were based on visual inspection, the subcategories were 

created after the quantitative characteristics from each category were extracted. The 

subcategories allow for more precise selection of thresholds when determining the 

category and subcategory of an event in the PMU data. The categories and subcategories 

are explained in more detail for the RPAD and frequency in Section 4.1.1 and Section 

4.1.2, respectively. The typical ranges for each category are given in Section 5.1.1.1 and 

Section 5.2.1.1.

4.1.1 Voltage RPAD Event Categories

The event categories in the voltage RPAD are presented here, with examples shown for 

each category. The RPAD is approximately proportional to the real power flow between 

two buses. A sudden change in the RPAD indicates a sudden change in power flow 

somewhere between the two buses. The events presented here are those in which the 

RPAD behavior suddenly changes. When this occurs, it is assumed that the power flow 
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somewhere between the two PMU measurements changes as well. In the case of an 

impulse event, the power flow change typically occurs near only one of the PMU 

stations, as explained in Section 4.1.2. This may be interpreted as a sudden surge or drop 

of power caused by the energizing of a motor or transformer or other switching event 

where the power quickly returns to pre-event conditions. Step change events may be 

interpreted as a shift in power caused by events such as a transmission line trip or a 

generating unit trip. The cause of transient events at this time is unknown, but one 

possibility is that they may be caused by some switching event that occurs at a distance 

from the PMU station and causes power flows throughout the system to oscillate with a 

higher magnitude change in the RPAD than during normal operating conditions. These 

oscillations are mostly within the mechanical time constant range of synchronous 

generator power plants within the area. The categories for the RPAD are examined in 

further detail below. 

4.1.1.1 Impulse 

The first event category is for an impulse event as detected in the RPAD signal. The 

duration of the impulse is very short and the change in the value of the RPAD varies. The 

rate of change of the RPAD during the impulse event is typically very high. Two 

examples of the event are presented below. The first impulse event, shown in Figure 32,

falls under the single (large) subcategory and has a duration of 0.33 seconds (20 cycles) 

and a magnitude of 1.7 degrees. The ramp-up and -down rates are 15.9 deg/sec and 8.5 

deg/sec, respectively. The ramp rates are approximations, and because of the 30-Hz 

sampling rate of the PMU data, higher frequency oscillations above 15 Hz are not 

recorded.

Figure 32. An example of an RPAD single (large) impulse event (RPAD between UT-Austin 

and McDonald)

This type of event occurs only at the McDonald PMU station, but the cause is unknown.

After recording the time stamps of the occurrence of seven days’ worth of impulse 

events, it was found that the event is not periodic. Impulse events seem to occur 

570 575 580 585

48.5

49

49.5

50

Time, seconds of hour

Voltage Phase Anlge, degrees
29

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randomly throughout the day. The impulse in the RPAD is thought to arise from a 

temporary imbalance in load and generation locally or might be caused by self-clearing 

faults. Analysis of probable causes of impulse events is described in Section 4.1.2 and 

Section 4.1.2.1.

Figure 33. An example of an RPAD single (small) impulse event (voltage RPAD between 

UT-Austin and UTPA)

The second type of impulse event falls under the single (small) subcategory and is usually 

located near a peak of oscillations in the RPAD and sometimes appears as a pair of 

impulse events. This may also indicate a switching or reclosing event. Referring to Figure 

33, the duration of the impulse event is 0.47 seconds (about 28 cycles) for the first 

impulse, occurring at 698.8 seconds; and 0.13 seconds (about 8 cycles) for the second 

impulse, occurring at 700.4 seconds. The change in angle is 0.25 degrees for the first 

impulse and 0.22 degrees for the second. The ramp-up and -down rates for the first 

impulse are 1.86 deg/sec and 0.64 deg/sec, respectively. The ramp-up and -down rates for 

the second impulse are 3.35 deg/sec and 2.44 deg/sec, respectively. 

The impulse events shown in Figure 32 and Figure 33 are not caused by dropped data. 

Dropped data are detected by the screening algorithm but are also easy to identify 

visually because of the smoothness of the data (the RPAD would remain constant for the 

duration of the dropped data). The dropped data points are recorded as zeroes in the 

frequency data, which can also be used as a way to check if the detected event is actually 

an error in the data. Successful fault clearing may produce the phenomena indicated in 

Figure 33: two sequential events occurring two seconds apart. 

4.1.1.2 Transient

The next event category is damped and sustained transients in voltage RPAD data. The 

causes of these events are unknown, but the common characteristic is higher magnitude 

oscillations compared to normal operating conditions. This low-frequency oscillation 

may indicate an oscillation between a large generator or group of generators near the 

690 695 700 705

-117.4

-117.3

-117.2

-117.1

-117

Time, sec of hour

Voltage Phase Angle, degrees
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PMU station and the rest of system. These types of events differ from typical damped 

oscillations known as ambient response of the system that is typically seen in PMU data. 

The amplitude is typically larger and the oscillations during a transient event are not as 

noisy as ambient data. The duration, amplitude, and smoothness of the detected damped 

oscillation events vary as well. Three examples of damped transients are given below. 

The first damped transient event in Figure 34 lasts 5.07 seconds, and the amplitude of the 

largest swing is 0.41 degrees. The frequency of the oscillation is 1.17 Hz. 

Figure 34. An example of an RPAD damped transient Event 1 (RPAD between UT-Austin 

and Waco)

In the damped transient event shown in Figure 35, the duration is 10.5 seconds and the 

largest swing is 1.01 degrees. The frequency of the oscillation is 0.59 Hz. 

Figure 35. An example of an RPAD damped transient Event 2 (RPAD between UTPA and

Waco)

645 650 655 660

-65.1

-65.05

-65

-64.95

-64.9

-64.85

-64.8

-64.75

-64.7

Time, sec of hour

Voltage Phase Angle, degrees

1805 1810 1815 1820

33.8

34

34.2

34.4

34.6

34.8

Time, sec of hour

Voltage Phase Angle, degrees
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In the damped transient event shown in Figure 36, the duration is 4.4 seconds and the 

largest swing is 0.96 degrees. The frequency of the oscillation is 0.59 Hz.

Figure 36. An example of an RPAD damped transient Event 3 (RPAD between UTPA and

Waco)

The detected frequencies in the signal that are of interest fall below 2.0 Hz. This range of 

frequencies is typical to inter- and intra-area oscillations [6]. It is thought that the cause 

of the oscillation is from system modes being excited by a switching event. However, for 

most cases, the root cause of each switching event is unknown. One example of a 

sustained transient event is provided in Figure 37. For a sustained transient event in the 

RPAD data, the signal is not as smooth because it contains other frequencies.

2340 2345 2350 2355

35.4

35.6

35.8

36

36.2

Time, sec of hour

Voltage Phase Angle, degrees
32

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Figure 37. An example of an RPAD sustained transient (RPAD between UT-Austin and 

McDonald)

A detailed view of the oscillation is provided in Figure 38, where the oscillations in the 

voltage RPAD are clear.

Figure 38. A detailed example of an RPAD sustained transient (RPAD between UT-Austin 

and McDonald)

A sustained transient event is easily identified when examining the PSD contour plot 

shown in Figure 39 starting at approximately 350 seconds. The frequency of this type of 

oscillation is approximately 2.8 Hz, higher than the frequencies seen in the damped 

transients shown in the previous examples. 

0 100 200 300 400 500 600 700

-8

-7.5

-7

-6.5

-6

-5.5

-5

Time, sec of hour

Angle, degrees

380 385 390 395 400

-7.8

-7.6

-7.4

-7.2

-7

Time, sec of hour

Angle, degrees
33

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Figure 39. A contour plot of the PSD (low-frequency content over time) for a voltage RPAD 

sustained transient event (RPAD between UT-Austin and McDonald)

4.1.1.3 Step Change in RPAD

The following events are categorized as step changes in the RPAD data. During a step 

change event, the RPAD suddenly changes from one value to another lower or higher 

value. The direction of the change depends on the reference point from which the phase 

angle is measured and the effect of the change of power flow caused by the event. The 

change in the RPAD can vary, from less than 1 degree to up to 10 degrees or more. Large 

system changes in power flow, such as a generator unit trip, can result in larger step 

changes. Although the exact cause is unknown, it is assumed that smaller RPAD step 

changes are caused by transmission line trip or reclose events and larger step changes are 

caused by generator unit trips. The step changes in the RPAD caused by generating unit 

trips can be confirmed in the ERCOT Daily Grid Reports when sudden-loss-ofgeneration events above 450 MW are reported [3].

Transmission line trips can occur when a fault is detected on the line. A line trip causes 

the redirection of power to surrounding transmission lines, causing a change in the 

measured RPAD. When an auto-reclosing practice is utilized, breakers on both ends of 

the line will reclose automatically, typically after a period of 2 seconds following the 

initial line trip. If the fault is temporary, the line reclosing operation will likely be 

successful and no further protective action is needed. As a result, power will return to its 

original value, and the RPAD will return to its pre-fault value as well. If the fault persists, 

breakers will trip the line again and the reclosing operation is repeated as necessary. 

However, reclosing events do not normally occur more than three times. For permanent 

faults, the last trip operation of the sequence will result in the protected line remaining 

offline. Depending on the utility, voltage level, and type of line, the number of trips and 

reclosing actions and the wait period between the reclose and trip actions will vary [9]. 

Figure 40 represents a sustained step change event. For this event, the RPAD drops from 

Time,sec of hour

Frequency, Hz

PSD for RPAD between UT-Austin and McDonald

0 100 200 300 400 500 600 700

0

1

2

3

4

5

-150

-100

-50
34

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-56.53 degrees to -56.85 degrees. The ramp rate is 4.86 deg/sec. The event here appears 

to be caused by a transmission line trip. 

Figure 40. An example of an RPAD sustained step change event (RPAD between McDonald 

and Waco)

In the second event, shown in Figure 41, a momentary step change occurs. The RPAD 

starts at −67.39 degrees and rises to −67.13 degrees before returning to −67.45

degrees. The duration of the event is 1.23 seconds (74 cycles), the ramp-up rate is 2.57 

deg/sec, and the ramp-down rate is 2.56 deg/sec. Again, because the RPAD suddenly 

switches to a new value and then returns to its approximate original value, it is assumed 

that the cause of the event is a transmission line reclose. 

Figure 41. An example of an RPAD momentary step change event (RPAD between UTAustin and Waco)

3575 3580 3585 3590

-57.1

-57

-56.9

-56.8

-56.7

-56.6

-56.5

-56.4

Time, sec of hour

Voltage Phase Angle, degrees

3265 3270 3275 3280

-67.5

-67.45

-67.4

-67.35

-67.3

-67.25

-67.2

-67.15

Time, sec of hour

Voltage Phase Angle, degrees
35

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4.1.2 Frequency Event Categories

The event categories seen in the frequency are presented here with examples shown for 

each category. Although the PMU frequency is calculated using the voltage RPAD data, 

some events are more easily detected in the frequency signal than the RPAD signal. For 

example, a sudden, large imbalance in load and generation caused by a generating unit 

trip would cause the frequency across the entire system to drop significantly. The drop in 

frequency and rate of change depend on the amount of power lost and the inertia of the 

system. The frequency drop during a generating unit trip is of significantly greater 

magnitude than the frequency during normal operating conditions and can easily be 

detected. 

Smaller systemwide imbalances in load and generation also cause sudden frequency rises 

and drops that are not visible in the RPAD. The frequency also shows events that are 

local to the PMU station and does not rely on the difference between two PMU stations 

such as is needed by the RPAD signals. If an event is detected in the frequency at only 

one PMU station and is not visible in any of the other PMU frequencies, it is likely that 

an event occurred near the PMU station where the event was detected. Impulse events are 

predominantly local events. Some transient events are local and are most likely caused by 

equipment or events located nearby. Local events do not indicate an imbalance in system 

load and generation.

4.1.2.1 Impulse

Impulse events seen in the frequency are presented here. The frequency impulse is similar 

to a high-frequency oscillation with duration of either one cycle or one-half of a cycle

and fall into the large-impulse or small-impulse subcategories. The events occur only in 

the McDonald frequency data, indicating that some sort of switching event or motor 

starting occurs near the McDonald PMU station on either the transmission or distribution 

voltage level. It is possible that these types of events cause a frequency event because of 

a sudden difference between the local load and generation. This type of event occurs 

frequently and may represent a temporary imbalance in load and generation locally. 

Another event that could cause a local imbalance includes a sudden trip and reclose of a 

large load (such as a processing plant). Impulse events seen in a PMU frequency are 

always seen in the corresponding RPADs. The frequency signals are used to determine at 

which station a local event occurs. The RPAD signal cannot be used to determine where a 

local event occurs because two PMU measurements are involved. For example, if an 

impulse event is detected in the frequency at McDonald, the same impulse event is seen 

in the McDonald-UTAustin and McDonald-UTPA RPADs. This always occurs 

specifically for impulse events but is not always true for other event categories. 

The first example, as shown in Figure 42, is of a “full-cycle” impulse and belongs to the 

large-impulse subcategory. The duration of the event is 0.47 seconds (28 “60-Hz” 

cycles), and the impulse magnitude is 42.3 mHz. The ramp rate from peak to peak is 

253.8 mHz/sec.
36

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Figure 42. An example of a frequency impulse Event 1

The second example, as shown in Figure 43, is of a half-cycle impulse and belongs to the 

small-impulse subcategory. The duration of the event is 0.4 seconds (24 “60-Hz” cycles),

and the impulse magnitude from peak to peak is 7.1 mHz. The ramp-down and -up rates

are 26.43 mHz/sec and 58.87 mHz/sec.

Figure 43. An example of a frequency impulse Event 2

4.1.2.2 Transient

Transient events in the frequency data are not as common as impulse events. An example 

of a damped oscillation is provided in Figure 44, in which the duration of the event is 5 

seconds. The largest peak-to-peak amplitude during the event is 10 mHz. The frequency 

0 100 200 300 400 500 600

59.97

59.98

59.99

60

60.01

60.02

Impulse Event 

Time, seconds

Frequency, Hz

0 100 200 300 400 500 600

60.024

60.026

60.028

60.03

60.032

60.034

60.036

60.038

60.04

Impulse Event

Time, seconds

Frequency, Hz
37

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of the oscillation is 1.23 Hz. The frequency of the oscillation falls within the intra-area 

oscillation range. Intra-area oscillations are caused by one synchronous machine 

oscillating against a group of machines in the area.

Figure 44. An example of damped transient event 

An example of a sustained transient event is shown in Figure 45. The sustained transient 

event is detected in the UT-Austin PMU signal but is not present in the McDonald PMU 

signal. 

Figure 45. An example of a sustained transient event 

Although it is clear in Figure 45 that the event occurs only at UT-Austin, the PSD 

contour plot provides a simpler way to visually detect sustained transient events,

650 655 660 665

60.012

60.014

60.016

60.018

60.02

Time, sec of hour

Frequency, Hz

334 336 338 340 342

59.988

59.99

59.992

59.994

59.996

59.998

Time, sec of hour

Frequency, Hz

UT-Austin

McDonald
38

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including when the transient begins and ends and the approximate frequency of the 

transient. The PSD contour plot is shown in Figure 46.

Figure 46. A contour plot of the PSD (low-frequency content over time) for a sustainedfrequency transient event 

4.1.2.3 Sudden Drops or Rises in Frequency

Small drops or rises caused by sudden imbalances between load and generation are 

detected in the PMU frequency data. These types of events are also typically detected at 

all PMU locations at the time of the event. An example of an imbalance caused by higher 

generation compared to load (the frequency increases above 60 Hz) is shown in Figure 

47. The event does not have a duration, but the rate of change of frequency from the bend 

at the start to the peak before the frequency begins to drop is 5.22 mHz/sec, significantly 

slower compared to the impulse event in the frequency. This event category differs from 

the impulse-frequency event because these types of events occur throughout the entire 

system, whereas an impulse event occurs only at a single PMU location. An imbalance 

caused by higher load compared to generation (the frequency drops below 60 Hz) is 

shown in Figure 48. Frequency, Hz

UT-Austin

0 200 400 600 800 1000

0

1

2

3

4

-200

-180

-160

-140

-120

Time,sec of hour

Frequency, Hz

McDonald 

0 200 400 600 800 1000

0

1

2

3

4

-200

-180

-160

-140

-120
39

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Figure 47. An example of a sudden rise in frequency 

Figure 48. An example of a sudden drop in frequency

A broad view of the frequency shown in Figure 49 provides a clearer picture of how a 

frequency-rise or -drop event differs from normal operating conditions. During normal 

operating conditions, variations in the frequency are always occurring, but during a risein-frequency event (indicated by the red arrow), the frequency rises at a more rapid rate 

than is typical. Another systemwide frequency event occurs around the 1,300-second 

mark, when the frequency drop is of a lower magnitude (approximately 250 mHz).

2370 2375 2380 2385

59.985

59.99

59.995

60

60.005

60.01

60.015

60.02

60.025

Time, sec of hour

Frequency, Hz

0 3 6 9 12 15 18 21

59.98

59.99

60

60.01

60.02

60.03

Frequency Drop Event Detected

Time, seconds

Frequency, Hz
40

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Figure 49. A systemwide frequency event seen by all PMUs

Figure 50 presents how an impulse event is a local event and is visible only at a single 

PMU station. The event was detected in the McDonald PMU frequency but is not present 

in either the UT-Austin or UTPA PMU frequencies. These examples illustrate that a 

PMU frequency contains systemwide information as well as local information. The 

variation in PMU frequencies during a large loss of generation in Section 5.2 also 

illustrates how the frequency differs across the power system during a drop-in-frequency 

event.

Figure 50. A local frequency event that occurs only in the McDonald PMU

1050 1100 1150 1200 1250 1300 1350

59.98

60

60.02

60.04

60.06

Time, sec of hour

Frequency, Hz

UT-Austin

McD

UTPA

3490 3495 3500 3505

59.975

59.98

59.985

59.99

59.995

60

60.005

Time, sec of hour

Frequency, Hz

UT-Austin

McD

UTPA
41 

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5 Algorithm Development

After the events have been placed into the separate categories outlined in Section 4, the 

characteristics from each type of event are extracted to determine which numerical 

characteristics are common to each category. An algorithm is written that utilizes the 

common characteristics to automatically identify events. For example, if an event has a 

strong 0.56-Hz frequency, the event will be identified as a transient event. In this section, 

the RPAD categories are examined first, followed by the frequency categories. For both 

the RPAD and the frequency, the characteristics that are unique to each category are 

identified. A flowchart of the algorithm to automatically categorize events and the useful 

characteristics in each category is given for the RPAD and the frequency. 

5.1 Extracted Characteristics for RPAD

This section examines the characteristics that are common to categories in the RPAD data 

described in Section 4.1. The categories are impulse, transient, and step change. The 

methods that are used to extract these characteristics are similar to the methods described 

in Section 2 and Section 3 used to screen the PMU data for events. The methods are FFT, 

Yule-Walker, differential of the PMU data, and matrix-pencil. The FFT and Yule-Walker 

methods are spectral methods used to identify strong oscillations within the PMU data. 

The differential of the PMU data is used to detect sudden changes in the data. The 

matrix-pencil method can be used to identify the damping and strength of the oscillations 

in the PMU data. The following subsections describe the characteristics for each 

category.
42

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Yes

No

Yes

No

Yes

No

Read in 

data y

Spectral Analysis 

of Signal y

For freq <1.2 Hz

Is Y(f) > threshold?

Calculate diff(y)

Find Peaks of 

diff(y) > 0.5 deg/

sec

Is abs(y_pre_event -

y_post_event) > 

threshold

Is a second 

switching event 

detected afterwards?

Sustained Step 

Change Event 

Detected

Momentary Step 

Change Event 

Detected

Impulse Event 

Detected

Transient Event 

Detected

Is rate of change > 

threshold and is 

magnitude > 

threshold

Calculate 

y_pre_event and 

y_post_event

Calculate rate of 

change and magnitude 

for events

Yes

Figure 51. A flowchart for the algorithm to categorize RPAD events 

The flowchart for the algorithm for the categorization of events in the RPAD data is 

shown in Figure 51. It is assumed that each identified event falls into at least one of the 

categories: sustained step change event, momentary step change event, impulse event, or 

transient event. 
43 

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Figure 52. An example of a PMU RPAD oscillation event

Two functions are used to categorize the events based on the extracted characteristics. 

The first function determines if the event is a transient event by examining the peak 

power for frequencies below 1.2 Hz. If the detected peaks are above a selected threshold, 

the event is identified as a transient event. The power for an inter- or intra-area oscillation 

during a transient event is typically very high. To illustrate, an example of a transient 

event and its characteristics is provided. The detected event in the RPAD data is shown in 

Figure 52. The event was originally detected by the screening algorithm from Section 2 

and Section 3. After the event is detected, the algorithm examines the frequency content 

of the signal. The Yule-Walker method is used to find the strength of the frequency 

content in the signal. The frequency content below 1.2 Hz is examined, and if the peak 

power for a frequency below 1.2 Hz is above the selected threshold, the event is 

identified as an oscillation event. 

The Yule-Walker calculates PSD for frequencies below 1.2 Hz, as shown in Figure 53. 

The peak frequency of the 0.62 Hz indicated is well above the selected threshold of -80 

dB. For the algorithm, the threshold is selected based on examining multiple transient 

events that have been detected by the screening algorithm. For comparison, the YuleWalker calculates the PSD for a non-transient event, as shown in Figure 54. The peak 

dBs of frequencies of interest fall well below the -80 dB threshold. 

0 100 200 300 400 500 600

36.2

36.4

36.6

36.8

37

37.2

37.4

37.6

Oscillation Event Detected with freq 0.62256 Hz

Time, seconds

Voltage Phase Angle, degrees
44

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Figure 53. An example of an oscillation-event PSD

Figure 54. An example of a non-oscillation-event PSD

The second function identifies the detected event as either an impulse event, a momentary 

step change event, or a sustained step change event in the RPAD. The function uses the 

differential of the PMU RPAD signal to determine if the event is a possible step change 

or impulse event. The peaks in the differential of the signal are detected, and if the peaks 

cross a certain threshold, the event is tagged as a possible step change or impulse event 

and evaluated further. For the RPAD, the thresholds of the rate of change of RPAD for 

impulse and step change events are above 0.08 deg/sec and below −0.05 deg/sec. An 

example of an impulse event shown in Figure 55 illustrates how the function is able to 

categorize impulse events. The (left) differential in Figure 56 has two peaks with only 

one (indicated by a red diamond) exceeding the defined threshold. This detected peak 

time is marked as a possible impulse or trip event. The (right) possible event is indicated 

in the original plot of the data in Figure 56. At this step, the function has not yet 

identified the event as an impulse or step change event, but only as a possible impulse or 

a possible step change event.

0 0.5 1 1.5 2

-110

-100

-90

-80

-70

-60

-50

-40

Frequency, Hz

Power, dB

Yule-Walker PSD

0 0.5 1 1.5 2

-115

-110

-105

-100

-95

-90

-85

-80

-75

-70

Yule-Walker PSD

Frequency, Hz

Power, dB
45

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Figure 55. An event is detected in the RPAD signal

Figure 56. Methods to detect an impulse event using the differentiated RPAD signal

Figure 57. The start and end times and the ramping period of the detected impulse event 

are shown for the RPAD signal

0 100 200 300 400 500 600

-64.4

-64.3

-64.2

-64.1

-64

-63.9

-63.8

-63.7

-63.6

Impulse Event Detected

Time, seconds

Voltage Phase Angle Degrees

0 100 200 300 400 500 600

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Time, seconds

deg/sec

PMU Data

Detected Peak -Non Event

Detected Peak - Event

Positive Threshold

Negative Threshold

0 100 200 300 400 500 600

-64.4

-64.3

-64.2

-64.1

-64

-63.9

-63.8

-63.7

-63.6

Possible Events Detected

Time, seconds

Voltage Phase Angle, degrees

0 100 200 300 400 500 600

-64.4

-64.3

-64.2

-64.1

-64

-63.9

-63.8

-63.7

-63.6

Time, seconds

Voltage Phase Angle, degrees

PMU Data

Detected Ramp

Event Start Time

Event End Time
46 

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The possible event in the original data is analyzed further to determine if the event is an 

impulse or a step change. The algorithm identifies the start of the ramping period and the 

end of the ramping period. With the starting and ending points identified, the ramp rate of 

the event is calculated in degrees per second. For the example event, the ramp-down rate 

as calculated by the algorithm is 2.66 deg/sec and is highlighted in red in Figure 57. 

Next, to differentiate between step change or impulse events, the average value of 0.33

seconds (20 cycles) of the RPAD before the start point of the detected ramp, ypre_event, and 

the average value of 0.33 seconds of RPAD after the end point of the detected ramp, 

ypost_event, are compared. This step of the algorithm is illustrated in Figure 58, in which (in 

green) ypre_event and (in red) ypost_event are highlighted. If the event is a line trip, the RPAD 

prior to the event suddenly changes and remains at the new value. Therefore, if the 

difference between ypre_event and ypost_event exceeds the selected threshold, the event is 

tagged as a trip event. Otherwise, the event is considered an impulse event. In the 

example provided, the jump falls below the selected threshold and the event is correctly 

identified as an impulse event by the algorithm. 

Figure 58. The (green) pre-event period and (red) post-event period are used to calculate 

the change in RPAD. 

If the jump exceeds the threshold, the event is considered either a sustained or 

momentary step change event. To differentiate between sustained and momentary step 

change events, the number and time stamps of each detected ramp-up and ramp-down 

event are examined. For example, if a ramp-up time is quickly followed by a ramp-down 

time or vice versa, the event is tagged as a momentary step change event. If there is a 

single ramp-up or ramp-down event that is not an impulse, the event is a sustained step 

change event. Examples of a line reclose event (step) and line trip event (sustained) are 

shown in Figure 59. 

0 100 200 300 400 500 600

-64.4

-64.3

-64.2

-64.1

-64

-63.9

-63.8

-63.7

-63.6

Time, seconds

Voltage Phase Angle, degrees

PMU Data

Event Start Time

Event End Time

Pre-Event

Post-Event
47

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Figure 59. (Left) Examples of a momentary step change event and a (right) sustained step 

change event in the RPAD signal

5.1.1.1 Summary of RPAD Event Categories

After extracting common characteristics from 62 impulse events, 39 transient events, and 

87 step change events, an approximate range of the event characteristics was determined. 

The magnitude, ramp rate, duration, frequency, and step change content of the events 

were extracted and saved. Note that when using the RPAD, which is the voltage phase 

angle between two buses separated by an unknown network, the RPAD difference 

indicates the strength of the effective tie line between two buses. It also shows the 

measure of stability of power systems. A large value of RPAD indicates a weaker tie 

between the two areas. Table 5 summarizes available characteristics for each category.

Table 5. Summary of Characteristics From Events Detected in RPAD Data

Category Subcategory Magnitude 

(deg)

Ramp Rate 

(deg/sec)

Duration 

(sec)

Frequency

(Hz)

Step 

Change 

(deg)

Impulse Single 

(Small) 0.18–0.4 0.5–5.5 0.167–

0.5 - -

Single 

(Large) 1.4–1.7 7.0–16.0 0.167–

0.5 - -

Transient Damped 0.15–1.5 - <9 0.4–1.1 -

Sustained 0.1–1.6 - >9 0.8–3.0 -

Phase 

Angle 

Change

Momentary 

(Small) - 0.75–3.25 0.5–

1.5 - 0.2–0.6

Momentary 

(Large) - 2–10 0.5–1.5 - 0.95–

1.15

Sustained - 1–5 - - 0.15–

0.75

0 100 200 300 400 500 600

-64.75

-64.7

-64.65

-64.6

-64.55

-64.5

-64.45

-64.4

-64.35

Reclosing Event Detected (with Duration 1.33 s)

Time, seconds

Voltage Phase Angle, degrees

0 100 200 300 400 500 600

-66

-65.9

-65.8

-65.7

-65.6

-65.5

Trip Event Detected

Time, seconds

Voltage Phase Angle, degrees
48

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5.2 Extracted Characteristics for Frequency Data

A different algorithm is used for categorizing events in the PMU frequency data. The 

algorithm is similar to the algorithm used to categorize events in the RPAD data, with 

changes made to include events only present in the frequency signal and to create new

threshold values because fluctuations in frequency are smaller than fluctuations in RPAD. 

The category for events present only in the frequency is the sudden rise or drop in 

frequency. Step change events are not included because these types of events are present 

in the RPAD only. 

A flowchart for the frequency categorizing method is shown in Figure 60. The signal is 

examined by all functions because it is possible for an event to belong to multiple 

categories. The flowchart below shows how each of the tags for the three categories is 

decided. After the tags have been assigned, they are examined to determine the category 

or categories in which the event belongs.
49 

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Read in 

data y

Calculate diff(y) Calculate FFT

Peaks of delta 

0.01 hz/sec 

identified

Is array empty?

Level 1 Type 

Impulse

Impulse_Event = 1

No

Peaks of delta 

0.005 hz/sec 

identified

Is array empty?

Level 2 Type 

Impulse

Impulse_Event = 1

No

Peaks of delta 

0.0025 hz/sec 

identified

Level 3 Type 

Impulse

Impulse_Event = 1

Not an Impulse 

Event

Impulse_Event = 0

Is array empty? No

Yes

Oscillation

Oscillation_Event = 1

Frequency Rise

Freq_Event = 1

Frequency Drop

Freq_Event = 1

Y(f) for 

0.075<f<2.0 Hz

Max(Y(f)) > 

cutoff

Yes

Calculate max(y), 

min(y), t_max, and 

t_min

Calculate df/dt

t_max – t_min 

> 9 sec

df/dt > 0.002 

hz/sec

Is df/dt >0

Yes

No

Not an Oscillation 

Event

Oscillation_Event = 0

Not a Frequency 

Event

Freq_Event = 0

No

No

No

Yes

Yes

Figure 60. A flowchart for the algorithm to categorize frequency events
50

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In this section, examples of the events and the analysis used to identify the events are 

given. The first category that is examined is for impulse events, which can fall into two

different subcategories. The next event category is for transient events. The third event 

category is a rise or drop in frequency. For the first category, in which possible impulse 

events are identified, the differential of the PMU frequency signal is used. Peaks in the 

differential are identified at three different levels. The first level is for impulses with the 

highest magnitude. An example of the impulse in the frequency data is shown below in 

Figure 61. This type of event is only found at the McDonald PMU station and could be 

caused by equipment on the distribution side located near the station. For the first level, 

the peaks in the differential of the signal are identified when previous values exceed 0.01 

Hz/sec. An example of the peaks identified for the impulse event is shown in Figure 61. 

Figure 61. (Left) The impulse event and (right) the differential of the signal exceeds the 

selected thresholds, indicating a Level 1 impulse event is detected.

The next step is to determine if the detected peaks exceed the selected threshold values. 

In the case below, all the detected peaks exceed the threshold. Examples of Level 2 and 

Level 3 impulse events are provided in Figure 62 and Figure 63, respectively. The peak 

detection and threshold values are different for all impulse event levels. The first event 

level is an example of the large-impulse-event subcategory. The second and third levels 

are examples of the small-impulse-event subcategory.

Figure 62. (Left) The impulse event and (right) the differential of the signal exceeds the 

selected thresholds, indicating a Level 2 impulse event is detected.

0 100 200 300 400 500 600

59.97

59.98

59.99

60

60.01

60.02

Impulse Event Detected - Level 1

Time, seconds

Frequency, Hz

0 100 200 300 400 500 600

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

Time, seconds

df/dt, Hz/sec

PMU Signal

Detected Max Peak

Detected Min Peak

Positive Threshold

Negative Threshold

0 100 200 300 400 500 600

60

60.005

60.01

60.015

60.02

60.025

Impulse Event Detected - Level 2

Time, seconds

Frequency, Hz

0 100 200 300 400 500 600

-3

-2

-1

0

1

2

3

4 x 10-3

Time, seconds

df/dt Hz/sec

PMU Signal

Detected Max Peak

Detected Min Peak

Positive Threshold

Negative Threshold
51

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Figure 63. (Left) The impulse event and (right) the differential of the signal exceeds the 

selected thresholds, indicating a Level 3 impulse event is detected.

The next category that is analyzed is a transient event. The FFT of the PMU frequency 

signal is used to detect transient events. Transient events are typically excited by the 

switching of either equipment in the power system or of load or generation. Because of 

the structure of the power system network, the damped transient events of interest that are 

excited fall into the range of frequencies below 2.0 Hz. From examining the PMU data, 

frequencies above 2.0 Hz are present, but the cause and origin of these oscillations are 

not well understood at this time. These frequencies may be examined in future work and 

help categorize power system events further. An example of a transient event is shown in 

Figure 64 below. The FFT as applied to the differential of the frequency (to remove dc 

offset) is given as well. The peaks are detected in the 0.05- to 2.0-Hz frequency range,

and if the peaks fall above the selected threshold, the algorithm assigns a transient event 

tag.

Figure 64. (Left) An oscillation event and (right) the spectral analysis showing that the 

frequency content for the signal exceeds the threshold, indicating a detected event.

To illustrate the difficulty of visually screening PMU data for oscillation events, a broad 

view of the plot of the frequency containing the event during a period of 400 seconds is 

shown in Figure 65. The event starts at 255 seconds.

0 100 200 300 400 500 600

60.024

60.026

60.028

60.03

60.032

60.034

60.036

60.038

60.04

Impulse Event Detected - Level 3

Time, seconds

Frequency, Hz

0 100 200 300 400 500 600

-4

-3

-2

-1

0

1

2

3 x 10-3

Time, seconds

df/dt, /itHz/sec

PMU Signal

Deterected Max Peak

Detected Min Peak

Positive Threshold

Negative Threshold

0 100 200 300 400 500 600

60.01

60.012

60.014

60.016

60.018

60.02

60.022

60.024

60.026

Oscillation Event Detected (1.2305 Hz)

Time, seconds

Frequency, Hz

0 0.5 1 1.5 2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6 x 10-4

Frequency, Hz

Magnitude, Hz/sec

PMU Signal

Detected Peak

Threshold
52

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Figure 65. From a 400-second window of frequency data, it is difficult to visually detect 

events.

Next, to determine if the event is a rise or drop in frequency, the maximum and minimum 

values and the times at which these occur within a 20-second window are extracted. The 

time between the maximum and minimum values is calculated as well as the slope 

between the maximum and minimum. The first step examines if the time difference is 

greater than 9 seconds. This step eliminates events in which there are sudden, large 

changes in the signal, such as those that occur during impulse events. Next, if the slope is 

greater than 2 mHz/sec, the event is placed in the rise- or drop-in-frequency category. If 

the slope is too gradual, the event is most likely not a rise- or drop-in-frequency event. 

The sign of the slope is used to determine if the event belongs to a rise-in-frequency or a 

drop-in-frequency subcategory. If the event is a rise-in-frequency event, the frequency 

increases and the slope is positive. If the event is a drop-in-frequency event, the 

frequency decreases and the slope is negative. Examples of both types of events are 

provided in Figure 66 and Figure 67. The rises and drops presented in this section are 

from small, sudden imbalances between load and generation.

Figure 66. An example of a frequency-rise event

0 50 100 150 200 250 300 350 400

59.97

59.98

59.99

60

60.01

60.02

60.03

60.04

60.05

PMU Frequency

Time, seconds

Frequency, Hz

0 3 6 9 12 15 18 21

59.97

59.98

59.99

60

60.01

60.02

Frequency Rise Event Detected

Time, seconds

Frequency, Hz
53

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Figure 67. An example of a frequency-drop event

An example of a drop-in-frequency event is provided in Figure 68, when a sudden loss of 

large generation of 478 MW on January 25, 2012 at 7:13 UTC occurs.

Figure 68. Another example of a frequency-drop event, on January 25, 2012, 7:13 UTC

The event was detected at all PMUs in operation at the time of the event. The frequency 

at the time of the event is shown in Figure 68. A more-detailed view in Figure 69 shows 

the initial rate of change of frequency is much higher at UT-Austin, and the frequency 

begins to oscillate against the frequency at UT-Pan American. The initial rate of change 

of frequency is approximate 300 mHz/sec, and eventually the rate of change of frequency 

changes to approximately 22.4 mHz/sec (from the start of the event to the nadir). A 

detailed view of the beginning of the event is also shown in Figure 70. The frequency at 

UT-Austin begins to drop before the other frequencies at the other PMU locations. The

rate of change of frequency characteristic taken for unit trip events is measured by taking 

the frequency and time at the start of the event and the frequency and time at the 

minimum nadir of the event. 

0 3 6 9 12 15 18 21

59.98

59.99

60

60.01

60.02

60.03

Frequency Drop Event Detected

Time, seconds

Frequency, Hz

855 860 865 870

59.9

59.95

60

System Wide Event Detected

Time, seconds

Frequency, Hz

UT-Austin

McDonald

UT-Pan American
54

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Figure 69. A detailed view of the frequency-drop event shows the rapid drop in frequency 

at UT-Austin and the oscillations at UT-Austin and UT-Pan American.

Figure 70. The frequencies at each location begin to drop at different times, with UT-Austin 

dropping sooner and more rapidly.

The event is also tagged as an oscillation event in the UT-Austin (1.17 Hz) and UT-Pan 

American (0.70 Hz) frequency data. The events are also categorized as impulse events 

because of sudden changes in the frequency. 

5.2.1.1 Summary of Frequency Event Categories

After extracting common characteristics from 82 impulse events, 35 transient events, and 

93 rise or drop events, an approximate range for characteristics of these event categories

was determined. The magnitude, ramp rates, duration, frequency content, and change in 

frequency of the events were extracted and saved. Table 6 summarizes available 

characteristics for each category.

858.5 859 859.5 860 860.5

59.97

59.98

59.99

60

60.01

60.02

60.03

60.04

System Wide Event Detected

Time, seconds

Frequency, Hz

UT-Austin

McDonald

UT-Pan American

859.1 859.15 859.2 859.25 859.3 859.35 859.4

60.028

60.03

60.032

60.034

60.036

60.038

60.04

System Wide Event Detected

Time, seconds

Frequency, Hz

UT-Austin

McDonald

UT-Pan American
55 

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Table 6. Summary of Characteristics from Events Detected in Frequency Data

Category Subcategory Magnitude 

(mHz) 

Magnitude 

Peak to 

Peak (mHz)

Ramp 

Rate 

(mHz/sec) 

Ramp 

Rate Peak 

to Peak 

(mHz/sec)

Duration 

(sec)

Freq. 

(Hz)

Delta 

Freq. 

(Hz)

Impulse

Single 3–9 - 10–900 - 0.267–

0.5 - - 

Multiple 20–25, 3–

10 40–50 25–250 250–500 0.3–0.6333 - - 

Transient

Damped 5–325 - - - 0.4–7 0.3–

5.0 - 

Sustained 0.1–1.6 - - - >9 0.8–

3.0 - 

Rise or 

Drop in 

Frequency 

Rise - - 0.8–3 - - - 0.015–

0.04

Drop - - 2–8 - - - 0.02–0.1

Unit Trip - - 15–30 - - - 0.1–0.21
56 

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6 Influence of Wind Power on PMU 

Measurements

In this section, the relationship between wind power penetration levels and the voltage 

RPAD are examined. Initial observations, after estimates of modal content in PMU data 

are made, are that there is correlation between wind power penetration levels and the 

appearance of an approximately 2-Hz mode (strongest at McDonald, but visible 

throughout the system) [10] [11]. These observations were first made near the beginning 

of the synchrophasor network’s initiation (in early 2009). After examining many days of 

PMU and wind data, it was observed that a pattern of tightly clustered modes around 2 

Hz appears during high-wind scenarios prior to approximately mid-2009. However, the 

pattern of tightly clustered modes around 2 Hz began to change in late 2009 and early 

2010. The typical behavior from early 2009 is compared to typical behavior seen in early 

2010 to the present. The linear relationship between the voltage RPAD and wind power 

penetration is also explored. Even though the weak relationship between power transfer 

and the voltage RPAD across large distances was discussed previously in Section 1, the 

power transfer from wind power plants in West Texas to major load centers in Central 

Texas has a strong linear relationship to the measured voltage RPAD between McDonald 

(West Texas) and UT-Austin (Central Texas). In this section, examples of the 

relationship between wind power and the modal frequency in the PMU data are provided. 

However, after examining PMU data taken in late 2009 to early 2012, the relationship 

between the strength of the 2-Hz modal frequency and wind power penetration levels in 

the latter years is weak or nonexistent. Examples are provided to show how the 

relationship between wind power penetration and modal frequency has changed over 

time. In this section, the ERCOT wind power data and its linear relationship to the 

voltage RPAD data is examined in Section 6.1. The impact of wind power on modal 

frequency estimates extracted from the PMU data are examined in Section 6.2. 

6.1 ERCOT Wind Power Data and Relationship to Voltage RAPD

Wind power and generation data required for this research was captured from the 

ERCOT website (no longer available) from January 27, 2009, to November 6, 2010. The 

data on the website included the aggregate wind power, aggregate generation, aggregate 

load, system frequency, and zonal pricing (before ERCOT switched to nodal pricing) and 

was updated at one-minute intervals. The time stamp for this data employs Central 

Standard Time and is not synchronized with the global positioning system time stamp 

used to time stamp the PMU data. The collected data also has a lot of missing data points. 

Gaps range from a few hours in a day to months’ worth of missing data. Aggregate wind 

power and generation are now available online as hourly averages in PDF format. The 

resolution of this data is too low for thorough analysis. 

An example of one day of wind power and wind power penetration is provided in Figure 

71. The left y-axis corresponds to the wind power (MW) and the right y-axis corresponds 

to the wind power penetration (%). The wind power penetration within ERCOT is 

calculated using the aggregate wind power and total generation data. The time stamp is 

converted to UTC to match the PMU data time stamp for easy comparison to PMU data. 

During the date of the examples provided, the Central Standard Time conversion is 
57

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UTC – 5. For example, in Figure 71, the peak wind power of 4,330 MW occurs at 05:00 

UTC or at 00:00 CST.

Figure 71. Aggregate wind power and wind power penetration within ERCOT on April 13, 

2009 (UTC)

Initial observations also show that during higher levels of wind power penetration, the 

voltage RPAD between UT-Austin and McDonald is closely correlated to the wind power

penetration, as shown in Figure 72. This information reveals that the voltage PMU data 

can be used to study power flows over a large system. 

0 5 10 15 20 25

-20

0

20

40

60

Degrees

Time, Hour (UTC)

0

5

10

15

20

Wind Power Penetration

Voltage RPAD

Wind Power Penetration

1:00 – 3:00 

CST

11:00 – 13:00 

CST

Figure 72. Voltage RPAD and wind power penetration on April 13, 2009

The highlighted areas in Figure 72. Voltage RPAD and wind power penetration on April 

13, 2009Figure 72 show the periods of data to be evaluated for dynamic modal behavior 
58

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in Section 6.2. The time stamp converted to equivalent Central Time are provided for 

convenience as well. The blue highlighted area is the wind power penetration and voltage 

RPAD during a period of high wind and occurs at 1:00 to 3:00 Central Time (1:00 to 3:00 

AM). The time at which high wind penetration occurs during spring within Texas 

typically occurs late at night to the early hours of the morning. This is when the power 

output from wind power plants is highest and total generation in the system is lowest. The 

red highlighted area is the wind power penetration and voltage RPAD during a period of 

low wind and occurs at 11:00 to 13:00 Central Time (11:00 AM to 1:00 PM). 

6.2 PMU Signal Mode Estimates

The modal frequency and damping of low-frequency oscillations in the PMU data are 

made using the auto-regressive parameter estimation using the Yule-Walker method, 

available in the Matlab Signal Processing Toolbox [5]. The number of modes estimated is 

set to 32, but only modes with frequency under 3 Hz are examined in this section. 

Estimates are made for a moving window of 5 minutes of PMU data. The estimates from 

each window are saved and plotted over a period of 2 hours. The frequency estimates, 

plotted on the y-axis, and the damping ratio estimates, plotted on the x-axis, made during 

a period of low wind power penetration is provided in Figure 73. The data used for the 

analysis is the data highlighted in red in Figure 72. The estimates are made using data 

from 16:00 to 18:00 UTC (11:00 to 13:00 Central Time) when the wind power 

penetration is between 4.6% and 5%. The wind power during this time period is between 

1,500 and 1,620 MW. There are clusters around the 1-Hz and 0.5-Hz modes that are 

always present. Other modes are present from 1.5 Hz to 3 Hz but are not as tightly 

clustered. This type of pattern occurs during time periods when the wind power 

penetration levels are low during the early months of 2009. 

Figure 73. Modal frequency and damping estimates for low-wind conditions on April 13, 

2009

A time period of high wind power penetration is examined. The data used for the analysis 

is the data highlighted in blue in Figure 72. The data time period is from 6:00 to 8:00 

UTC (1:00 to 3:00 Central Time) when the wind power penetration is between 15% and 

18%. The wind power during this time period is between 3,425 and 3,940 MW. The same 

0 5 10 15 20 25 30

0

0.5

1

1.5

2

2.5

3

Damping Ratio %

Frequency, Hz
59

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clusters around 1 Hz and 0.5 Hz are present; however, the modes around 2 Hz and 1.5 Hz 

are more tightly clustered. This pattern is seen during periods of high wind in early 2009.

Figure 74. Modal frequency and damping estimates for high-wind conditions on April 13, 

2009 

It is observed that this pattern of tightly clustered modes of 2 Hz during high-wind 

scenarios began to change in late 2009 and early 2010. To illustrate this, a day with a 

similar wind profile was found in early 2010. The wind penetration and voltage RPAD 

between UT-Austin and McDonald are shown in Figure 75. The wind power penetration 

and the voltage RPAD follow each other closely, especially during sudden ramping 

periods in wind power. 

0 5 10 15 20 25

-40

-20

0

20

40

Degrees

Time, Hour (UTC)

5

10

15

20

25

Wind Power Penetration

Wind Power Penetration

Voltage RPAD

2:00 - 4:00 

CST

10:00 - 12:00 CST

Figure 75. Voltage RPAD and wind power penetration on January 18, 2010

0 5 10 15 20 25 30

0

0.5

1

1.5

2

2.5

3

 

Damping Ratio %

Frequency, Hz
60

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The highlighted areas in Figure 72. Voltage RPAD and wind power penetration on April 

13, 2009Figure 75 show the periods of data to be evaluated for dynamic modal behavior. 

The time stamp converted to equivalent Central Time are provided for convenience as 

well. The blue highlighted area is the wind power penetration and voltage RPAD during a 

period of high wind and occurs at 2:00 to 4:00 Central Time (2:00 to 4:00 AM). The red 

highlighted area is the wind power penetration and voltage RPAD during a period of low 

wind and occurs at 10:00 to 12:00 Central Time (10:00 AM to 12:00 PM). 

The frequency and damping estimates in the voltage RPAD are saved for a period of two

hours during high wind power penetration. The data is taken from 8:00 to 10:00 UTC and 

the wind power penetration during this period is between 16.8% and 18%. The wind 

power during this time period is between 4,575 and 4,830 MW. However, in this case the 

frequency estimates are not as tightly clustered around 2 Hz as during the April 2009

case. Multiple days of data are examined to show that the relationship between the wind 

power and the clustering of the approximate 2-Hz mode is not as strong as would be 

expected from analysis of mid-2009 data. 
61

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Figure 76. Modal frequency and damping estimates for high-wind conditions on January 

18, 2010

Modal frequency and damping estimates are also made for a period of the same day when 

the wind power output is low, as shown in Figure 77. The data is taken from 16:00 to 

18:00 UTC, and the wind power penetration during this period is between 7% and 7.8%.

The wind power during this time period is between 2,275 MW and 2,625 MW. However, 

the approximate 2-Hz data is tightly clustered, which is the opposite of what occurred in 

the April 2009 case. 

Figure 77. Modal frequency and damping estimates for low-wind conditions on January 18, 

2010. The 2-Hz oscillations are still present, even though the wind penetration levels were 

low.

The two cases provided above show that the relationship between frequencies present in 

the PMU data and wind power penetration has changed over time. Possible reasons for 

these changes may include new transmission in wind-rich resource areas, new wind 

plants or conventional generators coming online, retirement of old generators, or other 

significant system changes. An annual report on the Electric Systems Constraints and 

Needs released at the end of December in 2010 includes a summary of major completed 

0 5 10 15 20 25 30

0

0.5

1

1.5

2

2.5

3

Damping Ratio %

Frequency, Hz

0 5 10 15 20 25 30

0

0.5

1

1.5

2

2.5

3

 

Damping Ratio %

Frequency, Hz
62

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transmission improvements [12]. In the summary is a list of improvements made in 2009 

and 2010, including some two-line rebuilds and a new autotransformer all located in 

West Texas. The same report for the following year shows upgrades to transmission lines 

in the northwest region of ERCOT that could also have an impact on the dynamic modal 

behavior of the system [13]. A few more examples of estimated modes during high wind 

power penetration are provided in Figure 78 to Figure 82 to illustrate that the cluster of 

modal estimates around 2 Hz is not always present. 

Figure 78. Modal frequency and damping estimates for high-wind conditions on January 

27, 2012, 9:00 to 11:00 UTC

In Figure 78, the wind power output during the duration of the analysis on January 27, 

2012, was 6,000 MW to 6,500 MW, and the wind power penetration was above 20% 

during this period. The wind data taken starting in August 2010 to the present can be 

found in ERCOT Wind Integration Reports [14]. The data was taken from 3:00 to 5:00 

Central Time or 9:00 to 11:00 UTC. The approximate 2-Hz mode at this time is spread 

out along both the y-axis and the x-axis, consistent with observations made that during 

high-wind conditions, the modal estimates do not cluster tightly around 2 Hz. 

0 5 10 15 20 25 30

0

0.5

1

1.5

2

2.5

3

 

Damping Ratio %

Frequency, Hz
63

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Figure 79. Modal frequency and damping estimates for high-wind conditions on November 

8, 2010, from 4:00 to 6:00 UTC

In Figure 79, the wind power output during the duration of the analysis on November 8, 

2010, was approximately 6,000 MW, and the wind power penetration was approximately

20%. The data was taken from 22:00 to 00:00 November 7, 2010, Central Time or 4:00 to 

6:00 November 8, 2010 UTC. The modal estimates are also not tightly clustered around 2 

Hz, even though the wind penetration is high. 

Figure 80. Modal frequency and damping estimates for high-wind conditions on October 7, 

2011, from 8:00 to 10:00 UTC

In Figure 80, the wind power penetration was above 20% and the wind power is 

approximately 7,000 MW at 9:00 UTC. The figure shows that the frequency estimates 

(the spread across the y-axis) are more tightly clustered, but the damping estimates 

change throughout the 2-hour window of data. Another change is that the modal 

frequency has shifted so that there is no longer a 2-Hz mode, but instead two neighboring

modes, located at 2.26 Hz and 1.74 Hz. Another example taken from the same day in 

Figure 81 shows modal estimates made during a new record for wind power when the

wind power output reached 7,400 MW at 20:06 UTC. The modal frequencies during this 

0 5 10 15 20 25 30

0

0.5

1

1.5

2

2.5

3

 

Damping Ratio %

Frequency, Hz

0 5 10 15 20 25 30

0

0.5

1

1.5

2

2.5

3

 

 

Damping Ratio %

Frequency, Hz
64

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time of the day have changed so that now there is a modal frequency at 2 Hz. The mode 

is not as tightly clustered as it was in the examples from early 2009. The change in modal 

frequency and the spread of the damping as well as the tightness of the clustering of the 

modal estimates indicates that a lot of different variables besides wind power and wind 

penetration could have an effect on the modes present in the power system.

Figure 81. Modal frequency and damping estimates for high-wind conditions on October 7, 

2011, from 19:00 to 21:00 UTC

A final example in Figure 82 is taken during a time when the wind power output of 3,000 

MW, which is approximately the same as the wind power output during the April 13, 

2009, case. However, here the wind power penetration is lower, at about 7% to 9%. 

Figure 82 shows the modal estimates from 00:00 to 02:00 UTC.

Figure 82. Modal frequency and damping estimates for high-wind conditions on November 

1, 2011, from 00:00 to 02:00 UTC

A comparison of all the modes during high penetration levels is shown in Figure 83 to 

Figure 88. Each comparison is of a typical high-wind modal behavior in April 2009 to 

high-wind modal behavior examples from January 2010 to January 2012. When 

comparing the modal behavior, it is easier to see how the modes have changed over time. 

0 5 10 15 20 25 30

0

0.5

1

1.5

2

2.5

3

 

 

 

Damping Ratio %

Frequency, Hz

0 5 10 15 20 25 30

0

0.5

1

1.5

2

2.5

3

 

 

Damping Ratio %

Frequency, Hz
65

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In all cases, the spread along the x-axis is greater and shifted toward the right, meaning 

the modes are better damped. When the oscillations are better damped, damping

estimates are more difficult to make because the oscillation in the signal has a shorter 

duration compared to a lightly damped oscillation. The frequency estimates also change, 

but these changes aren’t consistent and even change throughout the day. For example, the 

modes shown in Figure 85 and Figure 86 are both taken from the same day but the 

frequencies are different. Early in the day, as shown in Figure 85, there is a frequency 

below 2 Hz, but later in the day, as shown in Figure 86, there is a frequency at almost 

exactly 2 Hz. 

Figure 83. Comparison of modes during 

high-wind conditions in April 2009 and

January 2010

Figure 84. Comparison of modes during 

high-wind conditions in April 2009 and

November 2010

Figure 85. Comparison of modes during 

high-wind conditions in April 2009 and

October 2011 (a)

Figure 86. Comparison of modes during 

high-wind conditions in April 2009 and

October 2011 (b)

0 5 10 15 20 25 30

0

0.5

1

1.5

2

2.5

3

Damping Ratio %

Frequency, Hz

April 13, 2009

January 18, 2010

0 5 10 15 20 25 30

0

0.5

1

1.5

2

2.5

3

Damping Ratio %

Frequency, Hz

April 13, 2009

November 8, 2010

0 5 10 15 20 25 30

0

0.5

1

1.5

2

2.5

3

Damping Ratio %

Frequency, Hz

April 13, 2009

October 7, 2011 (8:00 UTC)

0 5 10 15 20 25 30

0

0.5

1

1.5

2

2.5

3

Damping Ratio %

Frequency, Hz

April 13, 2009

October 7, 2011 (19:00 UTC)
66

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Figure 87. Comparison of modes during 

high-wind conditions in April 2009 and

November 2011

Figure 88. Comparison of modes during 

high-wind conditions in April 2009 and

January 2012

These examples illustrate the power of PMUs to document changes in power system 

behavior over time. However, the data used to find the relationship between trends 

measured by PMUs and the wind power output for ERCOT is limited. At this time, it is 

not possible to make a conclusive statement about the effect wind power has on the 

power system as measured by PMUs. The ERCOT wind data is not always available, and 

is limited to less than two years of data taken at a rate of one sample per minute. ERCOT 

wind data is now only available in PDF format as hourly averages. The wind data used is 

aggregated wind power for all of ERCOT and does not take into account variation in 

output between wind resource regions. As more wind power plants are installed over a 

larger geographical area, it will become difficult to use the limited number of PMUs 

currently in the system to make accurate analysis on the effects of wind power on PMU 

measurements. As more PMUs are installed and more wind data becomes available, a 

more accurate analysis can be conducted, and PMUs will become a more valuable tool 

for tracking long term bulk power system behavior changes, particularly changes 

resulting from adoption of wind and other variable generation. 

0 5 10 15 20 25 30

0

0.5

1

1.5

2

2.5

3

Damping Ratio %

Frequency, Hz

April 13, 2009

November 1, 2011

0 5 10 15 20 25 30

0

0.5

1

1.5

2

2.5

3

Damping Ratio %

Frequency, Hz

April 13, 2009

January 27, 2012
67

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7 Conclusion

In this report, the algorithm used to screen PMU data generated by the UT-Austin 

synchrophasor network for power system events was described. The algorithm uses four 

different methods to screen for possible events. Each method is applied to a moving 

window of PMU data. The FFT and Yule-Walker methods are based on using the 

maximum magnitude of the spectral content of PMU signals to detect possible events.

The matrix-pencil method is a parametric method that estimates parameters to fit the 

PMU signal. The two maximum amplitudes are used to screen for possible events. The 

min-max method screens for large fluctuations in the PMU data. Results from the four 

methods are collected for one hour of PMU data. Any values from each method that 

exceed three standard deviations away from the mean are marked as possible events. A 

data window is marked as containing an event if two or more methods detect a possible 

event in the same data window.

The algorithm was applied to 24 hours of PMU data to analyze how well the algorithm 

was able to detect large and small events. A large event caused by a sudden loss of 

generation was easily detected in both the UT-Austin and McDonald PMU frequencies 

and the voltage phase angle separation between the two PMU stations. Two smaller 

events were present in the PMU data as well. In the UT-Austin PMU frequency, a strong 

oscillation at approximately 1 Hz was visible but was not present in the McDonald PMU 

frequency. A reclosing event was detected in the McDonald PMU frequency and voltage 

phase angle. However, it is difficult to determine if the reclosing event was located on the 

distribution or transmission system. Once an event is detected by the algorithm, the data 

window containing the event is saved for further analysis.

The events detected from a screening algorithm are placed into categories based on 

common characteristics. First, the events are placed into categories based on visual 

inspection. These categories are impulse, transient, and step change for RPAD events and 

impulse, transient, and change in frequency for frequency events. The characteristics are 

extracted from each category and used to write an algorithm that automatically identifies 

events in PMU data. 
68

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8 References

[1] Allen, A.J.; Sang-Wook Sohn; Grady, W.M.; Santoso, S., "Validation of distribution 

level measurements for power system monitoring and low frequency oscillation 

analysis," Power Electronics and Machines in Wind Applications (PEMWA), 2012 IEEE , 

vol., no., pp.1,5, 16-18 July 2012

[2] Office of the Governor, Economic Development & Tourism. “Wind Energy Potential 

in Texas” and “Wind Farm Locations in Texas.” Austin, TX: 2010. Accessed March 

2012: http://governor.state.tx.us/ecodev/business_research/maproom/.

[3] Electric Reliability Council of Texas (ERCOT). Daily Grid Operations Reports. 

Austin, TX: 2004–2010. www.ercot.com/gridinfo/congestion/operations/.

[4] Kundur, P. Power System Stability and Control. New York: McGraw, 1994.

[5] Matlab Version 7.12.0. Natick, Massachusetts: The Mathworks Inc.

[6] Rogers, G. Power System Oscillations.New York: Springer, 1999.

[7] Liu, G.; Quintero, J.; Venkatasubramanian, V., “Oscillation Monitoring System Based 

on Wide-Area Synchrophasors in Power Systems.” Bulk Power System Dynamics and 

Control—VII. Revitalizing Operational Reliability, iREP Symposium; 2007.

[8] Phadke, A.G.; Thorp, J.S. Synchronized Phasor Measurements and Their 

Applications. New York: Springer, 2008.

[9] Midwest Reliability Organization Protective Relay Subcommittee. Considerations for 

Transmission Reclosing Practices in the MRO Area. Roseville, MN: 2009. 

www.midwestreliability.org/03_reliability/studies_reports/transmission_reclosing_paper_

090302.pdf.

[10] Allen, A.J.; Santoso, S.; Grady, W.M. “Voltage Phase Angle Variation in Relation to 

Wind Power.” IEEE Power and Energy Society General Meeting Proceedings; July 25–

29, 2010; pp.1–7.

[11] Grady, W.M.; Costello, D. “Implementation and Application of an Independent 

Texas Synchrophasor Network.” 2010 63rd Annual Conference for Protective Relay 

Engineers Proceedings; March 29, 2010–April 1, 2010; pp.1–12.

[12] Electric Reliability Council of Texas. Report on Existing and Potential Electric 

System Constraints and Needs. Taylor, TX: December 2010. 

www.ercot.com/content/news/presentations/2011/2010%20Constraints%20and%20Need

s%20Report.pdf.
69

This report is available at no cost from the 

National Renewable Energy Laboratory (NREL) 

at www.nrel.gov/publications.

[13] Electric Reliability Council of Texas. Report on Existing and Potential Electric 

System Constraints and Needs. Taylor, TX: December 2011. 

www.ercot.com/content/news/presentations/2012/2011%20Constraints%20and%20Need

s%20Report.pdf. 

[14] Electric Reliability Council of Texas. ERCOT Wind Integration Reports Taylor, TX. 

www.ercot.com/gridinfo/generation/windintegration/.