SYNCHROPHASOR TIME SKEW: FORMULATION, DETECTION

AND CORRECTION

By

QIANG ZHANG

A thesis submitted in partial fulfillment of

the requirements for the degree of

MASTER OF SCIENCE IN ELECTRICAL ENGINEERING

WASHINGTON STATE UNIVERSITY

School of Electrical Engineering and Computer Science

AUGUST 2014

ii

To the Faculty of Washington State University:

The members of the Committee appointed to examine the thesis of QIANG

ZHANG find it satisfactory and recommend that it be accepted.

______________________________________________

Vaithianathan Venkatasubramanian, Ph.D., Chair

______________________________________________

Anjan Bose, Ph.D.

______________________________________________

Anurag K. Srivastava, Ph.D.

iii

ACKNOWLEDGMENT

Thank you everyone, for your support and believing in me.

Special thanks go to my supervisor, Dr. Mani. He taught me that research should start

from experiments. His inspiration also greatly helped me get to where I am right now. His

patience with me is also the biggest bless to me.

I also greatly appreciate the inspiring conversations I had with our faculties at WSU: Dr.

Bose, Dr. Roy, Dr. Anurag, and my fellow students: Xunning Yue, Tao Yang, Xing Liu et.al.

I can never forget the tender loving support from my wife Winnie Chan, my parents and

my sister.

iv

SYNCHROPHASOR TIME SKEW: FORMULATION, DETECTION

AND CORRECTION

Abstract

by Qiang Zhang

Washington State University

August 2014

Chair: Vaithianathan Venkatasubramanian

The most critical part of the synchrophasor technology is the availability of accurate UTC

time. Usually an external GPS clock device feeds PMU with 1 pulse per second time signals.

During the second, PMU’s internal clock keeps the pace until the next time signal arrives.

Because of various reasons, time skews have been observed in some real life synchrophasor data.

Two fundamental types of time skews are identified and formulated in this thesis.

It is also recognized that synchrophasor time skew problem is fundamentally different

from that in SCADA systems. In SCADA systems, time skew simply means time shift, because

all measurements are scalar values. However, synchrophasor data with time skew could have

huge errors because time shift is translated into error in phase angle measurements and

subsequent errors in frequency and rate of change of frequency measurements.

Algorithms are developed to automatically detect time skews online and to estimate the

time errors. A correction method is also provided. Both simulated data and real life data are used

to verify that the proposed methods are effective and accurate.

v

TABLE OF CONTENTS

Page

ACKNOWLEDGMENT ............................................................................................................... iii

ABSTRACT .................................................................................................................................. iv

LIST OF TABLES ......................................................................................................................... vi

LIST OF FIGURES ...................................................................................................................... vii

CHAPTER

1. INTRODUCTION ...............................................................................................................1

2. TIME SKEW PROBLEM FORMULATION .....................................................................6

TYPE A TIME SKEW: INTERMITTENT GPS CLOCK SIGNAL ....................... 6

TYPE B TIME SKEW: DRIFTING INTERNAL CLOCK ................................... 10

3. TIME SKEW ONLINE DETECTION ALGORITHM .....................................................13

4. TIME ERROR ESTIMATION ..........................................................................................16

5. TIME SKEWED PMU DATA CORRECTION ................................................................18

6. CASE STUDIES ................................................................................................................20

REAL-LIFE PMU RECORDING ......................................................................... 20

SIMULATED PMU DATA .................................................................................. 24

7. CONCLUSION AND DISCUSSION ...............................................................................25

BIBLIOGRAPHY ..........................................................................................................................26

vi

LIST OF TABLES

1. Results of Real-life Case.....................................................................................................21

vii

LIST OF FIGURES

1. Figure 1; Typical PMU Measurement System Setup ........................................................ 3

2. Figure 2; Phase Angle Calculation in PMU ....................................................................... 4

3. Figure 3; Voltage Angles with and without Intermittent GPS Clock Signal ..................... 7

4. Figure 4; Frequency and ROCOF with and without Intermittent GPS Clock Signal ........ 8

5. Figure 5; Zoom-in Voltage Angle with Intermittent GPS Clock Signal ......................... 10

6. Figure 6; Phase Angle, Frequency and ROCOF with Drifting Internal Clock ................ 11

7. Figure 7; Time Skew Detection Logics ........................................................................... 15

8. Figure 8; Frequencies From Real-life PMU Recording .................................................. 20

9. Figure 9; ROCOFs From Real-life PMU Recording ....................................................... 21

10. Figure 10; ROCOF and Voltage Magnitude During the Real System Event .................. 22

11. Figure 11; Voltage Angle After Correction in Real-life PMU Case ............................... 23

12. Figure 12; Frequency After Correction in Real-life PMU Case ...................................... 23

13. Figure 13; Voltage Angle and Frequency After Correction in Simulated PMU Case ..... 24

viii

Dedication

To my wife, Winnie Chan, my parents and my sister.

1

CHAPTER ONE

INTRODUCTION

Synchrophasor technology [1], a.k.a. PMU technology, is a “new” measurement system

that supplements the traditional SCADA system. Traditional SCADA system only measures the

Voltage Magnitude (VM), Active Power (P), Reactive Power (Q) and Frequency (F) analog

values, as well as circuit breaker digital values in the Electric Power Grid; they are all scalar

values. Local substation may have 3 phase measurements, while regional control center only have

one phase data. SCADA data is updated every 2-10 seconds, depends on the type of device it

measures. Remote Terminal Units (RTUs) are used to take SCADA measurements. There is no

timestamp associated with the measurements, and there is no universal coordination on the

sampling time for RTUs across the grid either. Usually the data receiver, e.g., Energy

Management System (EMS), puts a receiving timestamp when writing them into the database.

Many RTUs are deployed over the years to ensure redundancy. SCADA system’s major function

is to provide a live static view of the power flow on the power grid, also provides input for the

EMS to calculate State Estimation (SE) results.

SCADA systems have proven to be very useful and reliable in basic steady state power

grid monitoring. However, the formation of large interconnections, growing demands and more

rapidly changing system conditions have made power system operations more complicated than

ever. System operators and study engineers are facing more challenges. Traditional day-ahead

study has proven to be not sufficient sometimes. Specifically, during August 14, 2003 northeast

blackout, operators were not able to quickly re-dispatch the system due to fast changing system

conditions and lack of real-time situational awareness tools [2].

2

To answer this need, various wide-area situational awareness tools have been developed

over the years, largely due to the development of synchrophasor measurement networks.

Synchrophasor technology features GPS synchronized timestamp, high data rate, and

synchronized phase angle measurements. These features made synchrophasors suitable for

monitoring electromechanical system dynamics like oscillations and disturbances, which are

necessary supplements to the static view provided by SCADA systems[3][4][5]. In recent years,

synchrophasor technology is maturing well and is becoming an essential part in building a future

smart grid.

Synchrophasors are produced by devices that can be broadly called PMUs. The actual

device could be protection relays, multi-function recorders, Digital Fault Recorders (DFRs), or

dedicated PMUs. All PMUs are time-synchronized using some kind of GPS time signals. This is

to ensure that samples taken in different geographic locations can be compared directly as long as

they have the same timestamp. In fact, this is the very reason why the phase angle information

becomes synchronously measurable or available for the first time because all PMU signals use the

same GPS time signal as the common time reference or equivalently as the common phase angle

reference.

Synchrophasor measurement system is a complex system including several elements, as

shown in Fig. 1 [6]. Every single element on the whole data chain can affect the synchrophasor

data quality. PMU devices are usually tested and calibrated before and during the commissioning

[7]. This is to eliminate errors introduced from PT/CT, cable, attenuator, configuration, PMU

device and communication. Enforcement of the standard PC37.242 [7] is crucial to this process.

3

Figure 1. Typical PMU Measurement System Setup

Due to the high date rate and strict synchronization requirements, synchrophasor

measurement networks are high maintenance systems, compared to SCADA. The most critical

part is the time. PMUs can get time signals through different ways. If a PMU is already equipped

with a GPS receiver, it can accept GPS antenna signals directly. In most existing setups, a GPS

clock device provides time for the whole substation, and a shared substation time server is used,

in which case IRIG-B [8] signal is usually used as the time code. GPS clock usually feeds PMU

with 1 Pulse Per Second (PPS) time signal at the Coordinated Universal Time (UTC) second

rollover. During the second, the PMU internal clock serves as the time source for sampling signal

and time stamping results, until it is calibrated again when next PPS arrives. Therefore the GPS

time signal and PMU internal clock together define the accuracy of the timestamp associated with

the synchrophasors.

4

According to IEEE Standard C37.118.1, phase angles are defined as the difference

between a cosine function at nominal system frequency and the actual wave [9], as shown in Fig.

2 [9]. To satisfy the accuracy requirements defined by the C37.118.1 standard, time signal has to

be accurate down to microseconds [9]. It is obvious that the accuracy of the time signal is one of

the most critical parts in the synchrophasor technology.

Figure 2. Phase Angle Calculation in PMU

It is worth noting that the phase angle calculated according to the standard is not strictly

defined, or “true”, phase angle [15]. However, this is another topic and is not covered by this

thesis. In this thesis, the phase angle definition still follows that in the C37.118 standard.

Although both GPS clocks and PMU internal clocks are designed and calibrated to

provide accurate time signals, time issues do happen in real life, especially as devices degrade

over time. Many time skew scenarios have already been observed in the literature [6] [10] [11]

[12] [14]. Different from SCADA systems, where time skew is simply a time shift, because

SCADA only measures scalar values. In synchrophasor systems, the time skew problems were

manifested through angle, frequency, and Rate of Change of Frequency (ROCOF) values, and

may cause issues for the applications whose analytical results rely on the quality of the data. Thus

5

there is an urgent need to detect time skew problems, and to further estimate the time error

embedded in the timestamp.

The time skew identified in [6] is due to long cable caused time delay, which is a static

one. It could be relatively easily rectified although hard to find. Another type of “live” time skew

is identified in [11] and Kalman filter was used to compensate the errors in phase angles.

However, data are all shown in large time scale and the nature of that time skew was not analyzed

carefully. [14] uses state estimation technique to estimate the angle bias, potentially caused by

time skew. However, the method requires a “correct” angle reference bus, relies on network

model correctness, and needs measurements redundancy. There was also a lack of detailed

analysis on the time skew problem. Other time related data quality issues were also observed in

real life [10] [12].

In this thesis, two fundamental types of time skews are identified and formulated in

Chapter 2. An online automatic time skew detection algorithm is proposed in Chapter 3. Chapter

4 introduces a straight forward and effective time error calculation method, and Chapter 5

provides a method to compensate the time skew in PMU data. Demonstrations of the methods on

one real-life case and one simulated case are provided in Chapter 6. Finally, Chapter 7 concludes

the study and provides some discussions [13].

Note that the “data rate” in this thesis refers to the synchrophasor data rate. For simplicity

and practical reasons, this study only discusses timestamp accuracy. Actual PMU devices sample

the electric signals with a much higher sampling rate and produce synchrophasors through a

filtering algorithm. Time accuracies related to the detailed sampling and calculation processes are

not the focus of this thesis; however, their side effects on the final timestamp accuracy are

considered.

6

CHAPTER TWO

TIME SKEW PROBLEM FORMULATION

Since there are essentially two clocks, GPS clock and PMU internal clock, involved in

the time synchronization process, fundamentally they are the two sources of time skew issues.

Therefore, two typical time errors can be formulated assuming one of them is not accurate.

Theoretically, anything could go wrong. However, for a properly installed and calibrated system,

the following two problems are indeed the most commonly seen ones in real life.

Type A Time Skew: Intermittent GPS Clock Signal

Assuming the PMU internal clock is accurate, i.e., the oscillator can keep the 1 second

evenly divided into n intervals, where n is the data rate, the whole system’s time accuracy will

mainly depend on the GPS clock’s time signal. In most cases, the GPS clock can still provide

accurate time; however, PMU may not receive the correct time signals.

As mentioned before, GPS clock sends out one pulse signal every second to PMU on the

UTC second rollover to calibrate the PMU’s internal clock. When time cable has a loose

connection to the PMU device, PMU will receive intermittent GPS time signals, or even wrong

time signals. A 10 seconds recording of three Voltage Angles (VAs) from two PMUs at the same

substation is shown in Fig. 3. VA1 and VA2 are from PMU A, VA3 is from PMU B, all with 30

Hz data rate. Note that the static angle difference is another issue discussed in [12], and is not the

focus of this thesis.

7

Figure 3. Voltage Angles with and without Intermittent GPS Clock Signal

Both VA1 and VA2 had intermittent angle jumps in the beginning of several seconds,

whereas VA3 had a smooth trend. Notice that between the jumps, VA1 and VA2 were able to

maintain the static angle differences and keep track of VA3.

The angle jumps in the beginning of the second are caused by GPS time signal errors.

And the fact that the PMU A’s angle trends can track the correct angle (PMU B) means that

PMU A’s internal clock is still accurate. Field investigation revealed a loose GPS clock cable.

Once the cable was securely connected, the angle jumps disappeared. Because frequency and

ROCOF values were derived from voltage angle, intermittent jumps were also observed in PMU

A, as shown in Fig. 4. It is worth noting that the angle jumps and the subsequent

8

frequency/ROCOF jumps are not clean; there is a transition period that lasts a few data points.

This will be explained later.

Figure 4. Frequency and ROCOF with and without Intermittent GPS Clock Signal

To formulate this problem, assuming PMU has a n Hz data rate, and number the data

points from 1 to n for one second, starting from the second rollover, we can define the following

quantities at data point i:

M

i : Measured voltage angle.

T

i : True voltage angle.

9

E

i : Voltage angle error due to time error.

i : Time error introduced in each data point.

ic : Coefficient that translates time interval into angle change in degrees,

360i ic f , unit: °/s (degree per second).

if : Actual system frequency.

For an isolated data point i, the following stands:

, 1:M T E T

i i i i i ic i n (1)

To simplify the formulation, assume 60i nominalf f Hz is a constant. Because ic is such

a big number, under normal system operating conditions (59.95 to 60.05 Hz) and for a short time

period (several data points during transition), this approximation is accurate enough compared to

the time error. Thus 360 60 21600c becomes a constant.

In the intermittent GPS clock signal case, time error is only introduced at the first data

point of the second, so define 1 , angle measurement at data point i can be expressed as:

1 , 1:M T E T

i i i c i n (2)

This is a simplified theoretical result. Actual VA measurements are generated through a

filtering algorithm that takes a time window containing several cycles of the wave. So, in reality

the angle changes are slower, can last a few data points as shown in Fig. 5. Formula (2) describes

the data points before and after this transition period.

10

Figure 5. Zoom-in Voltage Angle with Intermittent GPS Clock Signal

Type B Time Skew: Drifting Internal Clock

Another common time skew is reported in [11]. In this type, because PMU internal clock

is either slower or faster than real time, a constant time error is introduced in each data point

during the second. GPS clock signal is accurate, so the PMU internal clock is always calibrated

on top of the second when time signal arrives, making the first timestamp accurate. A simulated

30 Hz PMU data with a fixed frequency of 59.99 Hz and noise is shown in Fig. 6. A65 10 s

time delay on each data point effectively lowered its frequency to 59.981 Hz.

11

Figure 6. Phase Angle, Frequency and ROCOF with Drifting Internal Clock

Following the same variable definitions as the previous problem, drifting internal clock

problem can be formulated as the following:

2 2

, 1:i i

M T E T

i i j i j

j j

c i n

(3)

A simplified case is the linear drifting clock. Assuming the PMU internal clock can still

maintain a steady pace even though it is slower or faster than real time pace, the time error

12

introduced can be considered as having a linear growth. So define j as a constant for each

data point, we have:

2

( 1) , 1:i

M T E T

i i j i

j

c i i n

(4)

The above two types of time skews are formulated in principle and are simplified time

skew problems. Other subtypes and combination of various types can also be derived through

this framework.

It is worth noting that although the problem is called “time skew”, synchrophasor time

skew is fundamentally different from that of SCADA systems. In SCADA system, because

measurements are all scalar values, “time skew” simply means “time shift”. However, in

synchrophasor system, angle data and frequency/ROCOF, which are derived from angle, are

meaningless in case of “time skew”. A short explanation is: phase angle is defined in frequency

domain while wave is in time domain. Their relation is defined by the constant c in the above

formulae.

13

CHAPTER THREE

TIME SKEW ONLINE DETECTION ALGORITHM

Most time skews feature sudden voltage angle changes on top of the second. This is the

key signature that differentiates time skew from other phenomena, so the detection method should

be designed to detect this sudden change. One approach is to calculate the voltage angle changes

directly. However, there is an easier way because PMU has done that work for us.

Frequency value is calculated from the slope of the voltage angle inside PMU, so it

directly reflects the rate of change of voltage angle. Further, ROCOF measures the rate of change

of frequency data, so ROCOF could be seen as the second derivative of the voltage angle.

Therefore, ROCOF value can be used directly as the indicator of the voltage angle change, and to

detect time skew.

ROCOF value is derived from only one voltage angle; can it represent the whole PMU’s

time quality? Considering each PMU only has one internal clock and one GPS time source, time

skew should manifest through all measurements in the same PMU. And since each PMU only has

one frequency and one ROCOF value, ROCOF data can represent the whole PMU’s time quality.

Time skews were originally discovered offline by human inspections. However, once we

understand its signature and model it mathematically, we can detect them online automatically.

The following steps are proposed to detect time skew online:

Sudden change test: Using a time window of 1 second long, starting from half second

(Fig. 5.), updating every second, monitor ROCOFs from all PMUs. Set a threshold

that’s slightly larger than normal variation (e.g., 0.02 Hz/s), and mark the PMUs that

has large ROCOFs.

14

Compare through all PMUs: If there is a real system disturbance, a frequency change

will be seen in several PMUs. However, time skew usually happens in isolated PMUs

at the same time. Cross-check among all available PMUs will highlight the

troublesome PMUs.

Further exclusions:

Time skew does not change the voltage magnitude (VM) measurements; however

system events may do so. Magnitude change should be set as an exclusion condition

in the logic. E.g., during an one second window, VM range should be within 1kV for

345kV system.

Also, time skew will usually last much longer than real system events. Hysterisis

should be enabled in the settings.

These criteria can also be used to distinguish time skew from real system events.

The detection logics are shown in Fig. 7.

It can be easily implemented in Data Quality Monitoring System (DQMS) if required.

DQMS would loop through all PMUs, and mark the ones that have the signatures. If this

behavior lasts for minutes and is consistent compared with other PMUs, an alarm would be

issued to warn utility IT staff about the situation and the suspect PMUs. The detection process is

fully automated once the settings are tuned properly.

15

Yes

PMU i

Max(Abs()) > Threshold ?

ROCOF

Yes

Yes

VM

Yes

PMU i

has time skew

No

Yes

ΔVM < Threshold ?

Hysteresis Count > N ?

PMU Count < M ?

PMU j

Figure 7. Time Skew Detection Logics

This algorithm is simple and effective in the sense that it minimizes calculations by using

available PMU data, easy to program, and threshold settings are not sensitive to system

conditions.

Note that some PMU devices allow users to configure the window lengths used for

ROCOF calculation. Different window lengths will result in different ROCOF values – shorter

the window, larger the value. For slow dynamics monitoring purpose, usually the PMUs are

tuned to produce ROCOF values within ±0.01 Hz/s for noise under steady-state conditions.

Adjust the thresholds used in the above algorithms accordingly if the normal ROCOF values are

in different ranges.

16

CHAPTER FOUR

TIME ERROR ESTIMATION

Once time skew is detected, the next natural step is to identify the type and estimate the

time error. For the above two types, type A (intermittent GPS signal) features frequency sudden

changes with alternating signs, while type B’s (drifting internal clock) frequency changes usually

has the same sign. So calculate the average frequencyavgf for the time window that has large

ROCOF values, and pick out the data point if that has the largest deviation:

arg maxi

i avgf

f f (5)

If the sign of ( )i avgf f is consistent through several consecutive detected windows, it is

type B; otherwise it is type A.

To estimate the time errors introduced, we have to go back to the formulation in Section

II. The key is to estimate the angle shift on top of the second.

For type A time skew, time error is only introduced on top of the second, so theoretically:

1 1 1

E M T (6)

Because the true value is not known and the transition can last several data points, a

linear regression is used to estimate the angle shift. Assuming system is stable during a second

(which is true for most of the time; during real system events time skew detection is skipped), the

angle trend before and after the transition should be relatively stable. Perform linear regression

before and after the transition separately and name them 1L and 2L . Expand their time ranges to

meet at the beginning of the second (middle of the time window), then,

17

1 2

1 1 1

1 2

1 1 1/ ( ) /

E

E

L L

c L L c

(7)

For type A time skew, time errors have alternating signs, which means one of them is

error and the other is correction. However, since they are both equally present, it is almost

impossible to distinguish the error from correction. Fortunately, their magnitudes are identical, so

we can always estimate the absolute value .

For type B time skew, time errors are introduced in each data point and are accumulated

until the last point of the second. On the contrary from type A, the time error is corrected on top

of the second:

M T

n n c n (8)

Same as type A, since the true value is not known and the transition may take several data

points, linear regression is used to estimate the angle correction. Following the previous

definition of 1L and 2L , we have:

1 2

1 1( ) / ( )L L c n (9)

Because type B angle shift is always in one direction, we can estimate both the magnitude

and the sign of the time error.

18

CHAPTER FIVE

TIME SKEWED PMU DATA CORRECTION

As mentioned before, synchrophasor time skew is fundamentally different from that of

SCADA system. In SCADA system, time skew simply means time shift, because all

measurements are scalar values. So for steady state analysis, time skew is acceptable in SCADA.

However, in synchrophasor system, because time skew changes phase angle calculation, the

resulted phase angle, frequency and ROCOF values could have huge errors. These data have to

be corrected before any use.

One compensating approach using Kalman filter is introduced in [11]. Below is a simpler

yet effective way of correcting data based on the formulation in previous sections.

For type A time skew, because of the alternating signs of the voltage angle changes, it’s

almost impossible to determine the sign of the time error. Fortunately, if static angle difference is

not a concern and dynamic is the focus of the study, we can simply assume one direction is the

error and we have:

1 2

1 1 1( ), 1:C M E M M

i i i ic L L i n (10)

This will be applied to only one direction and the time series afterwards, until next

change is detected. Actual transition may take several data points, use simple linear

interpolations to populate the data points in between.

There is no need to recalculate the frequency data for two reasons. First, the majority of

the frequency data are still correct, except during transition. Second, since system frequency

tends to change slowly in real system, and actual frequency data lacks accuracy anyway.

19

Simply replacing the frequency spikes with linear interpolation is good enough. ROCOF

data could be corrected too in a similar way if so desire.

For type B time skew, because errors are introduced in each data point during the second,

the whole second’s correction have to be distributed to each data point:

1 2

1 1

2

( 1)( ), 1:

iC M E M

i i j i

j

iL L i n

n

(11)

Same as type A, if transition lasts several data points, use interpolation to populate the

data points in between.

Because the frequency value is derived from a faulty voltage angle trend, for type B time

skew, frequency has to be recalculated. We can simply mimic the PMU algorithm to generate a

new set of frequency data. Following the definition of Discrete Rate of Change of Angle

(DROCOA) in [12]:

0( ) 360 /DROCOA f f n (12)

where n is PMU data rate and 0f is nominal system frequency (60 Hz), we have:

0/ (360 / )f DROCOA n f (13)

DROCOA can be calculated through linear regression of a short time window (several

VA data points around).

20

CHAPTER SIX

CASE STUDIES

To demonstrate the algorithm, two cases were used. First case is a real-life PMU recording

that contains a PMU with type A time skew problem, a control PMU without time skew, and has a

real system event. Second case is a simulated PMU data with type B time skew problem.

Real-life PMU recording

10 minutes data from the PMUs in Fig. 3, 4 was passed through the algorithm. PMU A

has time skew problem, and PMU B serves as a perfect control case since they are from the same

substation (Fig. 8, 9).

Figure 8. Frequencies From Real-life PMU Recording

21

Figure 9. ROCOFs From Real-life PMU Recording

It can be seen that due to time skew issues, PMU A’s frequency has frequent large spikes,

whereas PMU B’s frequency only has one spike which corresponds to a real system event.

Results are shown in Table I. Total of 66 ROCOF spikes were detected in 10 minutes, and 1 of

them is a common one so identified as a system event.

TABLE I. RESULTS OF REAL-LIFE CASE

PMU # of ROCOF Detection

Time Skew (#) VA (s) std (s)

A 66 Type A (65)

VA1 52.335 10 64.129 10

A VA2 52.337 10 64.167 10

B 1 None VA3 N/A N/A

22

For the spike in PMU B, because it is seen in many other PMUs, it is also the only spike

for a long time and the voltage magnitude changed, it was identified as a system event. ROCOFs

and VMs for that time window are shown in Fig. 10.

Figure 10. ROCOF and Voltage Magnitude During the Real System Event

After the correction, voltage angle and frequency data are shown in Fig. 11 and Fig. 12.

Compare with Fig. 3 and Fig. 4, we can see that the values in PMU A follows well with that of

PMU B; meaning the correction algorithm is effective.

23

Figure 11. Voltage Angle After Correction in Real-life PMU Case

Figure 12. Frequency After Correction in Real-life PMU Case

24

Simulated PMU data

4 seconds simulation data with noise (Fig. 6) was passed through the algorithm. 3 Type B

time skews were detected and the estimated average time error is 64.99 10 , which is close to

the theoretical value of 65 10 used in the simulation. Corrected data is shown in Fig. 13.

Figure 13. Voltage Angle and Frequency After Correction in Simulated PMU Case

25

CHAPTER SEVEN

CONCLUSION AND DISCUSSION

Accurate UTC time synchronized timestamp enables effective phase angle comparison

across the electric power grid. Accuracy of the time signal is among the most critical parts of the

synchrophasor technology. Time skews have been observed in real-life synchrophasor data, and

two fundamental types are described and formulated in this paper: intermittent GPS clock signal

and drifting PMU internal clock. An automatic online detection method is proposed, with the

capability of estimating time error. Correction method is also provided to compensate time skews

in PMU data. Both simulated data and real-life PMU recordings verified the proposed methods.

This thesis only lays the foundation for formulating time skew issues. Other types of time

issues or combinations of the various time issues could be derived through the proposed

formulation and be detected using similar methods.

Note that the proposed compensation methods assume a linear system trajectory. The

corrected data can be used for steady-state analysis. Its influence on the oscillation detection and

other applications still needs to be evaluated in the future studies.

We also assume that PMU’s calculations on frequency and ROCOF are accurate.

However, that might not be the case. Other similar malfunctions could also happen in the PMU

device. In these situations, the proposed algorithm may still issue an alarm although it might

indicate a completely different issue. Therefore, the final diagnose may still need engineering

judgment, which is the case in the industrial practice.

26

BIBLIOGRAPHY

[1] A.G. Phadke, J.S. Thorp, Synchronized Phasor Measurements and Their Applications,

Springer, 2008.

[2] Final Report on the August 14, 2003 Blackout in the United States and Canada: Causes

and Recommendations, U.S.-Canada Power System Outage Task Force, Apr. 2004.

[3] Bose, “Smart Transmission Grid Applications and Their Supporting Infrastructure”,

IEEE. Trans. Smart Grid, vol.1, issue 1, pp. 11-19, 2010.

[4] V. M. Venkatasubramanian, X. Yue, G. Liu, M. Sherwood, Q. Zhang, “Wide-Area

monitoring and control algorithms for large power systems using synchrophasors,” in

Proc. 2009 Power Systems Conference and Exposition, pp.1-5.

[5] E. Litvinov. (2012 Sep.) New England’s Synchrophasor Initiative. IEEE Smart Grid

Newsletter.

[6] Synchrophasor Measurement Accuracy Characterization, Performance and Standard

Task Team (PSTT), North American Synchrophasor Initiative (NASPI), Aug. 2007.

[7] IEEE Draft Guide for Synchronization, Calibration, Testing, and Installation of Phasor

Measurement Units (PMU) for Power System Protection and Control, IEEE

PC37.242/D10, Sep. 2011

[8] IRIG Standard 200-04, IRIG Serial Time Code Formats, Sep. 2004.

[9] IEEE Standard for Synchrophasor Measurements for Power Systems, IEEE Std

C37.118.1-2011, Dec. 2011.

[10] Q. Zhang. (2012, Mar.). Synchrophasor Data Validation and Applications Test at ISO-

NE. Washington State University, Pullman, WA.

27

[11] Q. Zhang, V. Vittal, G. Heydt, Y. Chakhchoukh, N. Logic, S. Sturgill, "The time skew

problem in PMU measurements," in Proc. 2012 IEEE Power and Energy Society General

Meeting.

[12] Q. Zhang, X. Luo, D. Bertagnolli, S. Maslennikov, B. Nubile, "PMU Data Validation at

ISO New England," in Proc. 2013 IEEE Power and Energy Society General Meeting.

[13] Q. Zhang, V. Venkatasubramanian, Synchrophasor Time Skew Formulation, Detection

and Correction, unpublished.

[14] L. Vanfretti, J. H. Chow, S. Sarawgi, B. Fardanesh, “A Phasor-Data-Based State

Estimation Incorporating Phase Bias Correction”, IEEE Tran. Power System, vol. 26,

issue 1, pp. 111 – 118, 2011.

[15] H. Kirkham, J. Dagle, “Synchronous Phasor-Like Measurements”, in Proc. Innovative

Smart Grid Technologies Conference (ISGT), 2014.