An Adaptive Method for Detection and Correction of Errors in PMU Measurements

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

IEEE TRANSACTIONS ON SMART GRID 1

An Adaptive Method for Detection and Correction ofErrors in PMU Measurements

Di Shi, Student Member, IEEE, Daniel J. Tylavsky, Senior Member, IEEE, and Naim Logic, Senior Member, IEEE

Abstract—PMU data are expected to be GPS-synchronized mea-surements with highly accurate magnitude and phase angle infor-mation. However, this potential accuracy is not always achieved inactual field installations due to various causes. It has been observedin some PMU measurements that the voltage and current pha-sors are corrupted by noise and bias errors. This paper presents anovel method for detection and correction of errors in PMU mea-surements with the concept of calibration factors. The proposedmethod uses nonlinear optimal estimation theory to calculate cali-bration factor using a traditional model of an untransposed trans-mission linewith unbalanced load. Thismethod is intended to workas a prefiltering scheme that can significantly improve the accuracyof the PMU measurement for further use in system state estima-tion, transient stability monitoring, wide area protection, etc. Casestudies based on simulated data are presented to demonstrate theeffectiveness and robustness of the proposed method.

Index Terms—Bad data detection, bias errors, calibration factor,non-linear estimation theory, PMU measurements, transmissionline modeling.

I. INTRODUCTION

P HASOR measurement units (PMUs) sample analogvoltage/current values in power systems in synchronism

with a GPS-clock and produce the corresponding time-stampedphasor values. The potential application of PMUs in powersystems is promising as PMUs are becoming increasinglyimportant in system identification [1], [2], system monitoring[3], [4], relay protection [5], [6], improving state estimation[7]–[9], control applications [10], [11], etc. [3], [12]. As thegrid evolves to become smarter, PMUs are expected to bemassively used in future power systems.Ideally, PMUs are expected to generate highly accurate mea-

surements. As required by the IEEE standard [13], for example,the total vector error (TVE) between a measured phasor and itstheoretical value should be well within 1% under steady stateoperating conditions. However, this potential performance isnot always achieved in actual field installations due to unbiasedrandom measurement noise and biased errors from the instru-mentation channels [14], [15]. Fig. 1 shows the magnitude and

Manuscript received July 11, 2011; revised October 03, 2011, January 27,2012, and May 07, 2012; accepted June 29, 2012. This work was supported byfunding provided by the Salt River Project. Paper no. TSG-00239-2011.D. Shi and D. J. Tylavsky are with the School of Electrical, Computer and

Energy Engineering, Arizona State University, Tempe, AZ 85287-5706 USA(e-mail: [email protected]; [email protected]).N. Logic is with Salt River Project, Phoenix, AZ 85072-2025 (e-mail: Naim.

[email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TSG.2012.2207468

Fig. 1. Recorded magnitude and phase angle of a voltage phasor from a PMU.

phase angle plots of real PMU measurements. As shown in thetwo plots, 5400 samples (three minutes) of synchronized phasordata are contaminated with spikes and complex noise behaviors.Even though PMUs are expected to be highly accurate, they areonly accurate when calibrated properly.The promise of using PMUmeasurements in state estimation,

system control, and transient instability monitoring requires thePMU measurements to be very accurate [4]. Further, the accu-racy and the reliability of PMUs are critical factors in fulfillingthe promise of the smart grid. There are pressing needs to cali-brate the PMU measurements to reach the claimed accuracy.The recently revised IEEE standard [13] establishes the accu-

racy requirements on synchrophasor measurement and providesthe general guidelines on PMU testing. It also specifies methodsfor evaluating the PMU measurements for compliance with thisstandard under both steady-state and dynamic conditions. ThePerformance and Standards Task Team (PSTT) of North Amer-ican SynchroPhasor Initiative (NASPI) prepared a PMU systemtesting and calibration guide [16], which describes the PMUtesting environments and procedures in compliance with theIEEE standards.Some practical experience with PMU testing and calibration

are presented in [17]–[23]. In general, these methods requirecertain types of specialized test equipment (systems) whoseaccuracies are at least one level greater than the to-be-testedPMUs. The specialized equipment can either be highly accuratesignal generators or PMUs that have already been calibrated.Presently, the lack of such ready-made equipment may makethe practical implementation of these methods difficult.In [15], the authors propose the concept of a “super cali-

brator” for PMU calibration. The inputs of this “super cali-brator” include PMU data, SCADA data, a detailed three-phasemodel of a substation, etc. Despite the complexity of this cali-brator, the accuracy level of the SCADA data may add uncer-tainty into, or even degrade the PMU calibration. In [24], the au-thors propose a phasor-data-based state estimator which can cor-

1949-3053/$31.00 © 2012 IEEE


2 IEEE TRANSACTIONS ON SMART GRID

Fig. 2. Proposed PMU measurement calibration procedure.

rect the bias error in the phase angle measurements. This methodneglects the possibility that the bias error may also exist in themagnitude component of the synchrophasor measurements.A novel PMU calibration procedure is proposed in this paper.

This procedure is relatively easy to implement in the sense thatno specialized testing equipment is required. A schematic dia-gram of this procedure is shown in Fig. 2. The proposed algo-rithm is employed to calculate a set of calibration factors (CFs)based on the raw PMU data and a measurement model. PMUcalibration is then achieved by multiplying the raw PMU datawith the calculated CFs. Once the PMU data are corrected, theycan be used for further applications, such as system state esti-mation, transient stability monitoring and various control appli-cations. It should be noticed that while the calibration factors,once calculated, are used on each PMU measurement, the cali-bration factors themselves only need be calculated rarely, onlyas often as the system operator determines is needed.The solid lines of Fig. 2 indicate signal flow that must occur

for every measurement, while the dashed arrows in Fig. 2 indi-cate the signal flow and calculations that must be performed tocalculate the CFs. Note that CFs are not adjusted for every datasample; they are adjusted in the field very infrequently sincethey are used to correct the bias errors in the measurements. Theobjective of the proposed algorithm is threefold: to eliminate theneed to use specialized equipment to calibrate PMUs; to give thefield engineering guidance in selecting the calibration settings;and to provide CFs for real-time correction of PMU data.In case of communication delays from the transducer output

to PMU input, such an error would show up as an angle biaserror, something that the propose algorithm is specifically de-signed to address. A method for simultaneously correcting boththe angle and magnitude bias errors in PMU data is presented.The remainder of this paper is organized as follows. In

Section II, formulation of the CF and its practical applicationare first introduced. Section III discusses the proposed measure-ment model and the optimal estimator used for the computationof the calibration factors. Section IV presents the case studiesthat validate the proposed method while conclusions are drawnin Section V.

II. CALIBRATION FACTOR AND ITS PRACTICAL APPLICATION

In this section, the concept and formulation of the calibrationfactor are introduced and its practical application is discussed.

Fig. 3. Concept of the calibration factor.

A. Formulation of the Calibration Factor

A CF is a vector (complex number) applied to the measuredsynchrophasor to correct its error by restoring it to the corre-sponding true value. Two formulations can be used for the CF:the rectangular coordinate formulation and the polar coordinateformulation. The latter is employed in the proposed method pre-sented below.Fig. 3 shows the concept of the calibration factor. In this

figure is the measured (voltage/current)phasor, is the corresponding true phasor,and is the calibration factor that corrects theerror in and restore it to .Quantities and vectors in Fig. 3 are related by the following

set of equations:

(1)

(2)

(3)

where is the phase angle of the calibration factor.As shown in (1), is the phase angle difference between the

true phasor and the measured one. Equation (2) indicates thatthe magnitude of CF is the magnitude of the true voltage phasordivided by the measured one. The calibration is done throughmultiplying the measured phasor by the calibration factor.In the ideal case, if there is no error in the measurement, the

CF is

(4)

which provides a good initial estimate of the CF for the non-linear optimal estimator discussed in section that follows.

B. Practical Application

Considering the fact that a typical PMU has the capabilityof processing no less than 3 current inputs and 3 voltage inputs[30], [31], one PMU at each terminal of a transmission line (TL)will be needed to fulfill the data requirements of the proposedmethod.The proposed method will generate a set of CFs with one CF

for each of the 3-phase voltage/current measurement channels.The proposed method is different from a real-time state esti-mator in the sense that it is not run for every data sample but runvery infrequently. Once the CFs are determined by the proposed


SHI et al.: AN ADAPTIVE METHOD FOR DETECTION AND CORRECTION OF ERRORS IN PMU MEASUREMENTS 3

Fig. 4. Two levels of PMU calibration.

algorithm, they are inputted via the front panel of PMUs man-ually or through the calibration programs [30], [31], or storedin a phasor data concentrator (PDC) to be applied to the corre-sponding measurements. These calculated CFs are not updatedvery often since the bias errors tend to remain constant unlesschanges happen in the instrumentation channels.In particular, the proposed PMU calibration method can be

achieved at two different levels. Fig. 4 schematically shows thePMU communication system as well as levels of calibration.Typically, many PMUs located at various substations gatherphasors in real-time and send the data to a PDC at the utilitywhere data are aggregated.At the first level of the calibration, calibration can be con-

ducted locally at each individual PMU by compensating the am-plitude and phase angle of the measured phasors (voltage or cur-rent). Calibration at this level can be used to correct the inaccu-racy of the instrumentation channels [14]. The state-of-the-artsynchrophasor technology enables the calibration of each outputchannel of a PMU [31]. These calibration factors are settableby the users. As a result, the calibration factors obtained fromthe proposed method can be easily applied to each PMU by ap-propriately setting these parameters and no other software isneeded.At the second level, calibration is conducted remotely at the

PDC. This level of calibration can correct the inaccuracies notonly due to the instrumentation channel but also due to the dif-ferent phase angles in two systems, e.g. due to Y-Delta connec-tion of power transformers. In this case, the calibration factorsobtained from the proposed method should be stored at the PDCand be applied to the real-time phasor data received from corre-sponding PMUs. Calibration factors calculated by the proposedmethod need be applied at either level 1 or level 2 but not both.

III. PROPOSED METHOD

A. Proposed Measurement Model

The proposed method is based on a TL “full” three-phasemodel that is applicable to transposed and untransposed linesof any line length. As shown in [25], the TL impedance param-eters calculated using PMU measurements are very sensitive tosystem imbalance when only the positive sequence line modelis used. For an untransposed TL with an unbalanced load, ifonly the positive sequence line model is used, the calculationof the CFs will likewise be inaccurate. Employing the “full” TLmodel will eliminate this additional source of inaccuracy so that

Fig. 5. 3-phase transmission line PI model.

more accurate calibration can be achieved for the PMU mea-surements. Also, utilizing the full model will enable the calcu-lation of CFs for all 3-phase (3-sequences) of the PMUmeasure-ments, and, as a result, provide calibration factors to not only theerrors in the positive sequence measurements but also to errorsin the negative and zero sequence measurements.Fig. 5 shows the TL used for analysis in this paper. The

proposed method requires two assumptions. First, PMUs areinstalled at both terminals (S and R) of the TL and all the3-phase synchrophasor measurements are available. Second,the impedance parameters of the TL are known a priori.As shown in Fig. 5, the following notation is adopted:

sending (receiving) end 3-phasevoltage vector (3 by 1);

sending (receiving) end 3-phasecurrent vector (3 by 1);

3-phase shunt admittance matrix (3by 3);

3-phase series impedance matrix (3by 3);

mutual series impedance betweenphase and ;

mutual shunt susceptance betweenphase and .

It should be noted that the model shown in Fig. 5 works forboth the short TL (nominal pi model) and the long TL (equiv-alent pi model). It also works for transposed TLs and untrans-posed TLs which have different structures of and . Forthe sake of generality, the following discussions are based on anuntransposed TL with the equivalent pi model. The other cases,however, can be analyzed similarly with minor modifications.In the 3-phase TL nominal/equivalent pi model, neglecting

the shunt conductance

(5)

Based on nodal analysis, the following equations can be de-rived from Fig. 5.

(6)

(7)



where

and

In order to apply the concept of calibration factor to the PMUmeasurements in (6), (7), the following equations can be formu-lated:

(8)

(9)

(10)

(11)

where

measured 3-phasevoltage/current vectors (each is3 by 1);

calibration factor matrices (3by 3 diagonal).

It should be noted that the 4 calibration factor matrices above arediagonal matrices. For example, has the following form:

(12)

where , , and are the calibration factors for each

element of the vector , respectively.Combining (5)–(11), the model of the TL with calibration

factors taken into account is obtained:

(13)

(14)

After some simplification, (13) and (14) can be rewritten inmatrix form as

(15)

(16)

Each of (15) and (16) includes three complex equations, andfor the purpose of obtaining an optimal estimate of the calibra-tion factors, we need to expand these 6 complex equations into12 real equations. Noticing that the calibration factors are com-plex numbers, we make the following definition:

(17)

Due to limited space, these 12 real equations are not listed herebut they can be easily derived by equating both the real partsand the imaginary parts of the left hand sides of the six complexequations to be zero. The discussion below is based on these 12real equations.

B. Proposed Optimal Estimator

In order to obtain a simple yet uniform expression for theproblem, the following definitions are made:Define X to be the 24 element measurement vector, which

is made up of the voltage and current measurements from bothterminal of a TL. That is,

(18)

where and yield the real and imaginary part of theinput argument, respectively.Define to be the unknown parameter vector, which is com-

posed of the unknown calibration factors. That is,

(19)

Based on the definition of X and , the 12 real equations canbe written in a general form as

(20)

where . It should be noted that these functionsare nonlinear functions in terms of the unknown parameter .In order to estimate the calibration factors for all the PMUs,

data redundancy is needed. Define all of the PMUmeasurementstaken at one time instant from PMUs installed at each end of theTL as one sample of data. The relationships among the mea-surements in one sample are described by (20). That is, 12 realequations are needed to describe the interdependencies of one



sample of data. Using multiple samples of PMU measurements,the underdetermined set of equations, (20), becomes an overde-termined set of equations and nonlinear state estimation tech-niques can be used to estimate the CFs.We define to be a vector that is composed of multiple

copies of , the number of which is equal to the numberof samples taken. Assuming N samples of measurements areavailable, is defined by (21)

...

...

...

...

...

...

...

...

(21)

where is the measurement error vector, whose elements are as-sumed to have zero mean and characterized by variance matrixR.This parameter estimation problem can be formulated as a

minimization of the cost function of

(22)

This minimization problem is solved through linearization ofthe nonlinear functions followed by the Gauss-Newton iterationmethod [19], [20]. During each iteration, a linearized version of(21) is solved for the vector of increments, based on which theunknown parameters are updated. In general, we have at theiteration

(23)

(24)

...

......

......

......

(25)

where

the unknown parameter vector beforeand after the iteration, respectively;

vector update for the iteration;

Jacobian matrix of with respectto at the iteration.

This iterative process continues until convergence, that is, until

(26)

where represent the th element of the unknown parametervector at iteration .

C. Detection and Identification of Bad MeasurementThe Classical method [26]–[28] is used to detect and iden-

tify the bad data after the estimation process by checking thenormalized residuals of each measurement, which proceeds asfollows:1) Solve the weighted least square problem (22) and obtainthe measurement residual vector

(27)

2) Compute the normalized residual as

(28)

where is the diagonal element of the matrix

(29)

3) Find the largest normalized residual and check if itis larger than a prescribed identification threshold c, forexample 3.0

(30)

If (30) does not hold, then no bad data will be suspected;otherwise, the data sample corresponding to the largestnormalized residual is the bad data and should be removedfrom the data set.

4) If bad data is detected and removed from the data set, thealgorithm flowmust return to step 1) and the process abovemust be repeated. Otherwise, this process ends and solu-tions are found.

D. Limitation of the Proposed Method

Used in the calibration factor derivation is a transmissionline model that is valid when the power system is operated atnominal frequency and in the steady-state but possibly unbal-anced condition. Under transients and oscillations, the assump-tions used are violated. In this case, the inputs and outputs ofPMUs will not be sinusoidal and thus a more complicated elec-trical model would have to be used; however, as PMU calibra-tion need only be done rarely, obtaining a measurement data setwithout transient content is generally not a problem.

IV. CASE STUDIES

Case studies are presented in this section to show the proce-dure and validate the effectiveness of the proposed method incorrecting bias errors in the PMU measurements. Two sets ofcase studies are conducted based on simulated data.

A. Case Studies With Bias Errors in the Measurements

Amodel (shown in Fig. 6) is built in the Alternative TransientProgram (ATP) [29] to simulate a transmission line of the Salt



Fig. 6. Simulation model built in ATP.

River Project (SRP). As shown in Fig. 6, a 3-phase ac voltagesources (object name: AC3PH) is employed in the model as anideal source for the system; load in the system is modeled as a3-phase constant impedance load with RLC components (objectname: RLC3). The small rectangular box between node “ ” and“ ” is an LCC (Line Constants, Cable Constants, or Cable Pa-rameters) object, which represents a 3-phase overhead TL usedin the simulation. In particular, the TL simulated is a 300-MVA,230-kV and 150-mile long TL with typical physical parame-ters (e.g., tower geometry, conductor type, sag) obtained fromSRP. These physical parameters (Appendix A) are inputted intothe LCC object and the corresponding TL impedance parame-ters are calculated by the supporting subroutine of ATP. PTs andCTs are simulated at both terminals of line . PMUs are notrepresented in this model but their outputs are estimated by pro-cessing the corresponding waveforms from PTs/CTs by a dis-crete Fourier transform (DFT).The system is simulated in the steady-state operating condi-

tions and therefore the outputs of the CTs and PTs are perfectlysinusoidal.The method we propose requires redundant PMU measure-

ments. These redundant PMU measurements are obtained byrunning the ATP simulation multiple times with each simulationconducted with a different loading level. Variation of the loadis achieved by adjusting each of the 3-phase RLC (resistance,inductance, and capacitance) parameters in the load model. Allof these loading levels are selected randomly but within a rangebounded between 20% and 80% of the TL’s capacity. Each runof the simulation lasts for 0.2 second and the adopted time step is0.166667 microsecond. During each run, the outputs from eachPT/CT are processed by a DFT to generate the correspondingvoltage/current phasors. Finally, the phasors calculated in allthese different runs are combined together to form the data setused in our tests described below. The advantage of using sim-ulated data is that we have control over the bias errors in thePMU measurements. This means that the theoretical CFs canbe calculated exactly.With the theoretical CFs as references, theeffectiveness of the proposed method can be validated by com-paring the calculated CFs with their corresponding theoreticalreferences. While we do believe that field testing does providevalue, the tests we have conducted here provide proof of prin-ciple.In the first experiment reported here, white noise with 0 mean

and a standard deviation of 0.002 pu is first simulated and addedto the set of current and voltage measurement reported by thePMU. Then a set of bias errors described in Table I are added tothe PMU measurements. Next, this set of synchrophasor mea-surements, along with the transmission line parameters, is used

TABLE IDESCRIPTION OF THE BIAS ERRORS

TABLE IICALCULATED CALIBRATION FACTORS

in the algorithm defined by (21)–(26) to calculate the calibrationfactors.As shown in Table I, all of the 3-phase synchrophasor mea-

surements are affected by bias errors, either in the phase anglecomponents or in the magnitude components. In fact, the pro-posed method has been tested successfully against different setsof bias errors: bias errors only in the phase-A measurements,bias errors in both phase-A and phase-Bmeasurements, and biaserrors in all the 3-phase measurements. This set of bias errorsrepresents a particularly severe out-of-calibration bias, selectedto show the robustness of the proposed method under conditionsmore extreme than are likely to be found in the field.The PMU measurements described above are processed by

the proposed method to calculate the calibration factors asshown in Table II and Table III.As Table II shows, the second and the third columns are

the theoretical and calculated CFs while the last two columnsare the errors in the calculated CFs as compared to theircorresponding exact theoretical values. For example, for thesending-end voltage measurements, since a 5% bias error isadded to their magnitude, the theoretical CF should be

(31)



TABLE IIITOTAL VECTOR ERROR (TVE) BEFORE AND AFTER CALIBRATION

where . As the fourth column shows, the errorsin the ’s are calculated using the following equation:

(32)

where and are the calculated and referencevalues for the corresponding measurements. Based on thisdefinition, the largest error is 0.429%, which appears in .Errors in the angle of the calculated calibration factors ( ’s)are calculated using

(33)

As shown in the third column of Table II, the largest error in thephase angles of the calculated CFs is 0.00096 rad.Based on the IEEE standard [13], the total vector error (TVE)

characterizes the difference (error) between a synchrophasormeasurement and its corresponding true phasor. Table III sum-marizes the TVEs of the PMU measurements before and afterapplying the calibration factors. In this table, the TVEs of themeasured phasors at a certain time instant before and after thecalibrations are evaluated by (34), (35), respectively,

(34)

(35)

where and are themeasured phasors at a giventime instant and its theoretical value, respectively; is theCF corresponding to the measurement. As shown in Table III,the TVEs for the PMU measurements are greatly reduced bythe proposed algorithm. In particular, after applying the CFs,the maximum TVE in the measurements are 0.4396%, which is

TABLE IVCALCULATED CALIBRATION FACTORS

smaller than the required 1% by the IEEE standard C37.118.1-2011.The simulation result shows that the proposed method is able

to identify and correct the bias errors in the PMUmeasurementsunder noisy conditions and simultaneous severe bias conditions.To validate the robustness of the method, multiple applicationsof the proposed method were conducted using random load pro-files in addition to a sinusoidal load profile while inserting setsof simultaneous random bias errors applied to randomly se-lected sets of phases. The selected bias errors were of the sameseverity level as those applied when generating the results ofTables II and III. All of these tests yield similar TVE values.

B. Case Studies With Large Phase Angle Errors

As shown in Fig. 1, there are abrupt jumps in PMU phaseangle measurements. The second study case is intended todemonstrate the effectiveness of the proposed method indealing with big phase angle errors. In the following study,no error is added to the magnitude of the PMU measurementswhile a 20 degree ( 0.349065 rad) bias error is added tothe phase angle of sending-end voltage at phase A. Using atest similar to the previous test, calculated CFs and the corre-sponding errors are shown in Table IV.As shown in the table, all the ’s have near unity magni-

tude values as they should since no bias errors are added to themagnitudes of the phasor measurements. The largest error inthe magnitude of the calculated CF is 0.346%, which appears in

.The variable is calculated to be 0.34889 rad, which cor-

responds to an error of 0.0018 rad with respect to its theoreticalreference. All the other values are (as they should be) veryclose to zero radians, with a maximum error of 0.00059 rad.



TABLE VTRANSMISSION LINE PHYSICAL PARAMETERS USED IN SIMULATIONS

system frequency is 60 Hz; all phase conductors are single-bundledconductors

Similarly, the TVE for each measurement at a selected timeinstant is calculated. Before and after calibration, the TVEs for

are 34.7296% and 0.0175%, respectively; the TVEs for allthe other measurements are smaller than 0.45%. The TVEs forthe calibrated synchrophasor measurements all comply with theIEEE standard [13].These simulation results show that the proposed method is

robust, able to identify and correct considerable phase angle biaserrors in PMU measurements, supporting the effectiveness ofthe proposed approach.

V. CONCLUSIONS

An algorithm is presented for identification and correctionof PMU calibration errors by utilizing the concept of calibra-tion factors (CFs) The proposed method is based on the non-linear state estimation techniques and assumes availability of re-dundant-over-time PMUmeasurements. Implementation of thismethod requires a total of two PMUs (one per measurementpoint) at two terminals of the transmission line (TL) as well as apriori knowledge of the TL impedance parameters. A TLmodelcapable of modeling both transposed and untransposed lines isemployed so that the bias errors brought in by system imbalanceare avoid and that the PMUmeasurements from all three phasescan be accurately calibrated. Numerical experiments in calcu-lating and applying the calibration factors for an untransposedtransmission line with unbalanced load provide encouraging re-sults. These numerical results show the robustness of the pro-posed method.It should be noted that in all SE approaches, if the line param-

eters are in error then the state estimates will be inaccurate; like-wise with this approach, if the line parameters are in error thenthe calibration factors will be inaccurate. What the relationshipis between parameter errors and calibration factor inaccuracy isan open question.

APPENDIX A

A 3-phase TL is simulated in ATP using the LCC object [29].The physical parameters of this TL are described in Table V. Inthis simulation, the soil resistivity is assumed to be 100 .

ACKNOWLEDGMENT

The authors thank Salt River Project for the support in car-rying out this research work.

REFERENCES[1] J. Zhu and A. Abur, “Identification of network parameter errors using

phasor measurements,” in Proc. Power Energy Soc. Gen. Meet., Cal-gary, Canada, 2009, pp. 1–5.

[2] D. Shi, D. J. Tylavsky, N. Logic, and K. M. Koellner, “Identifica-tion of short transmission-line parameters from synchrophasor mea-surements,” in Proc. 40th North Amer. Power Symp., Calgary, Canada,2008, pp. 1–8.

[3] E. O. Schweitzer, III and D. E. Whitehead, “Real-world synchrophasorsolutions,” in Proc. 35th Annu. Western Protective Relay Conf., Oc-tober 2008.

[4] A. P. S. Meliopoulos, G. J. Cokkinides, O. Wasynczuk, E. Coyle, M.Bell, C. Hoffmann, C. Nita-Rotaru, T. Downar, L. Tsoukalas, and R.Gao, “PMU data characterization and application to stability moni-toring,” in Proc. IEEE Power Syst. Conf. Expo., Atlanta, GA, 2006,pp. 151–158.

[5] J. S. Thorp, A. G. Phadke, S. H. Horowitz, and M. M. Begovic, “Someapplications of phasor measurements to adaptive protection,” IEEETrans. Power Syst., vol. 3, no. 2, pp. 791–798, May 1988.

[6] Y. Liao andM. Kezunovic, “Optimal estimate of transmission line faultlocation considering measurement errors,” IEEE Trans. Power Del.,vol. 22, no. 3, pp. 1335–1341, Jul. 2007.

[7] H. Wu and J. Giri, “PMU impact on the state estimation reliabilityfor improved grid security,” in Proc. 2005 IEEE Power Energy Soc.Transm. Distrib. Conf. Exhib., pp. 1349–1351.

[8] M. Zhou, V. A. Centeno, J. S. Thorp, and A. G. Phadke, “An alternativefor including phasor measurements in state estimation,” IEEE Trans.Power Syst., vol. 21, pp. 1930–1937, Nov. 2006.

[9] S. Chakrabarti and E. Kyriakides, “PMU measurement uncertaintyconsiderations in WLS state estimation,” IEEE Trans. Power Syst.,vol. 24, no. 2, pp. 1062–1071, May 2009.

[10] E. O. Schweitzer, III and D. E. Whitehead, “Real-time power systemcontrol using synchrophasors,” in Proc. 34th Annu. Western ProtectiveRelay Conf., Oct. 2007.

[11] E. O. Schweitzer, D. Whitehead, G. Zweigle, and K. G. Ravikumar,“Synchrophasor-based power system protection and control applica-tions,” in Proc. 63rd Annu. Conf. Protective Relay Engineers, CollegeStation, 2010, pp. 1–10.

[12] J. De La Ree, V. Centeno, J. S. Thorp, and A. G. Phadke, “Synchro-nized phasor measurement applications in power systems,” IEEETrans. Smart Grid, vol. 1, no. 1, pp. 20–27, June 2010.

[13] IEEE Standard for Synchrophasor Measurements for Power Systems,IEEE Std C37. 118. 1-2011.

[14] North American Synchrophasor Initiative, Performance and StandardTask Team, “Synchrophasor measurement accuracy characterization,”Tech. Rep., Dec. 2007.

[15] A. P. S. Meliopoulos, G. J. Cokkinides, F. Galvan, and B. Fardanesh,“GPS-synchronized data acquisition: Technology assessment and re-search issues,” in Proc. 39th Annu. Hawaii Int. Conf. Syst. Sci., Jan.4–7, 2006.

[16] North American Synchron Phasor Initiatibe (NASPI), Performance andStandards Task Team (PSTT), “PMU system testing and calibrationguide,” Nov. 5, 2007.

[17] P. Komarnicki, C. Dzienis, Z. A. Styczynski, J. Blumschein, and V.Centeno, “Practical experience with PMU system testing and calibra-tion requirements,” in Proc. IEEE PES Gen. Meet., 2008.

[18] K. Narendra, Z. Zhang, J. Lane, B. Lackey, and E. Khan, “Calibrationand testing of TESLA Phasor Measurement Unit (PMU) using doubleF6150 test instrument,” in Proc. iREP Symp. Bulk Power Syst. Dyn.Control—VII. Revitalizing Oper. Rel., Aug. 2007, pp. 1–13.

[19] G. Stenbakken and T. Nelson, “Static calibration and dynamic char-acterization of PMUs at NIST,” in Proc. IEEE PES Gen. Meet., Jun.2007, pp. 1–4.

[20] G. Stenbakken and M. Zhou, “Dynamic phasor measurement unit testsystem,” in Proc. IEEE PES Gen. Meet., Jun. 2007, pp. 1–8.

[21] G. Stenbakken, T. Nelson, M. Zhou, and V. Centeno, “Referencevalues for dynamic calibration of PMUs,” in Proc. 41st Hawaii Int.Conf. Syst. Sci., Jan. 2008, pp. 1–6.

[22] Y. Hu and D. Novosel, “Progresses in PMU testing and calibration,”in Proc. 3rd Int. Conf. Elect. Util. Deregulation Restructuring PowerTechnol., Nanjing, China, 2008, pp. 150–155.



[23] K.Martin, J. Hauer, and T. Faris, “PMU testing and installation consid-erations at the bonneville power administration,” in Proc. IEEE PowerEng. Soc. Gen. Meet., Jun. 2007, pp. 1–6.

[24] L. Vanfretti, J. H. Chow, S. Sarawgi, and B. Fardanesh, “A phasor-data-based state estimator incorporating phase bias correction,” IEEETrans. Power Syst., vol. 26, pp. 111–119, Feb. 2011.

[25] D. Shi, D. J. Tylavsky, N. Logic, K. M. Koellner, and D. Wheeler,“Transmission line parameter identification using PMU measure-ments,” Eur. Trans. Electr. Power (ETEP), vol. 21, no. 4, pp.1574–1588, May 2011.

[26] D. C. Montgomery, E. A. Peck, and G. G. Vining, Introduction toLinear Regression Analysis. New York: Wiley, 2006.

[27] A. Abur and A. G. Exposito, Power System State Estimation—Theoryand Implementation. New York: Marcel Dekker, 2004.

[28] A. Monticelli, State Estimation in Electric Power Systems: A General-ized Approach. Norwell, MA: Kluwer, 1999.

[29] H. W. Dommel, Electromagnetic Transients Program ReferenceManual (EMTP) Theory Book. Portland, OR: BPA, 1986.

[30] Schweitzer Engineering Laboratory (SEL), Synchrophasor Prod-ucts-PMUs [Online]. Available: http://www.selinc.com/synchropha-sors/products/

[31] GE Multilin, N60 Network Stability and Synchrophasor MeasurementSystem [Online]. Available: http://www.gedigitalenergy.com/prod-ucts/manuals/n60/n60man-w1.pdf

Di Shi (S’08) received the B.S. degree from Xi’an Jiaotong University, Xi’an,China, in 2007 and the M.S. degree from Arizona State University, Tempe, in

2009, all in electrical engineering. He is now working towards the Ph. D. degreeat Arizona State University.

Daniel J. Tylavsky (SM’88) received the B.S., M.S.E.E., and Ph.D. degreesin engineering science from Pennsylvania State University, University Park, in1974, 1978, and 1982, respectively.From 1974 to 1976, he was with Basic Technology, Inc., Pittsburgh, PA, and

from 1978 to 1980, he was an Instructor of Electrical Engineering at Pennsyl-vania State. In 1982, he joined the Faculty in the School of Electrical, Computerand Energy Engineering, Arizona State University, Tempe, where he is currentlyAssociate Professor of Engineering.Dr. Tylavsky is a member of IEEE Power Engineering Society and Industry

Applications Society, and is an RCA Fellow and NASA Fellow.

Naim Logic (S’01–M’05–SM’09) graduated from the University of Sarajevoand received theM.S. degree from theUniversity of Zagreb and the Ph.D. degreefrom Arizona State University, Tempe.He is currently with the Power SystemOperations Department-Computer Ap-

plications Group of Salt River Project (SRP), Phoenix, AZ.Dr. Logic is a Registered Professional Engineer in the State of Arizona.

Date post:	02-Oct-2016
Category:	Documents
Upload:	naim
View:	212 times
Download:	0 times

An Adaptive Method for Detection and Correction of Errors in PMU Measurements

Documents