On Data Quality and Availability Modeling ofPower Grid Phasor Measurements

Karl Reinhard, Student Member, IEEE

Abstract—United States ’Smart Grid’ initiatives envi-sion very reliable, available synchro-phasor data as acornerstone for improving electric power grid efficiencyand reliability. However through early 2012, power systemoperators report that synchro-phasor data availability fallsshort of the levels required to realize the vision. This paperproposes phasor measurement unit (PMU) reliability andsynchrophasor data availability models, using reliabilityblock diagrams and Markov chains. These models highlightcauses for reduced synchrophasor data availability andsuggest approaches for assuring very high synchrophasordata availability.

I. INTRODUCTION

In 2007, the United States Congress enacted theEnergy Independence and Security Act (EISA), whichmandated modernizing the nation’s electric power infras-tructure. The law established national policy to supportthe modernization of the Nation’s electricity transmissionand distribution system, commonly referred to as the’Smart Grid,’ with emphasis on increasing digital infor-mation and control technology applications to improveelectric grid reliability, security, and efficiency. [1]

The phasor measurement unit (PMU) is a key enablingtechnology that records voltage, current, power, andassociated phase angles multiple times per 60 hertzelectrical cycle and time-stamps the measurements us-ing micro-second (or better) resolution Global Position-ing Satellite (GPS) timing signals. These precise time-stamped measurements are essential to synchronizingdata from widely-dispersed locations to enable the rapidand accurate calculation of the power system’s state [2].Phasor Measurement Units (PMUs) are envisioned toclose the information gap between electric power systemevents occurring on the ground and being known bypower system control centers. PMU data, also known assynchrophasor data, is envisioned to be useful not onlyfor monitoring steady state system performance but alsofor tracking dynamic system behavior, facilitating timelysystem control decisions, and validating power system

Karl Reinhard, reinhrd2@illinois.edu, is with the Department ofElectrical and Computer Engineering at the University of Illinois atUrbana-Champaign

models. Very high integrity PMU data with very highavailability rates is foundational to realizing this vision.

The synchrophasor data is passed to phasor dataconcentrators (PDCs) which receive synchrophasor datafrom multiple PMUs, assemble data by time stamp, andforward synchronized data either to higher level PDCsor to control centers. Widespread PMU deployment willenable monitoring:

• Phase and power angles• System oscillations that threaten system stability• Voltage stability• Line Thermal conditions

These measurements will increase the fidelity and timeli-ness of the control center’s awareness of the system’s ac-tual operating state – especially under stressed conditions[3]. This real/near-real time knowledge will facilitatedynamic system adjustments and enable the post-mortemanalysis of significant power system events.

At the North American SynchroPhasor Initiative(NASPI) Working Group Meeting in February 2011,system operators representing the Eastern and Westerninterconnects provided frank assessments of the syn-chrophasor data quality that they tracked. The GridProtection Alliance (Eastern Interconnection) reportedthat on a typical day in February 2011 only 47 (39percent) of its more than 130 PMUs provided valid datamore than 99 percent of the time; in contrast, 66 (46percent) reported valid data less than 50 percent of thetime. Similarly, the California Independent System Op-erator (CAISO, Western Interconnection) reported thattypically 10 of 56 (18 percent) of the PMUs that ittracks have either failed or are out of synchronization;significantly, the communications network provided 99.5percent synchrophasor data availability for functioningPMUs. [4]

Given the public’s high expectations of very reliable,on-demand electric power, the reported synchrophasorperformance clearly falls short of power system op-erator requirements for trustworthy information fromsynchrophasor networks. Improving synchrophasor dataavailability requires an understanding likely weaknessesin PMU reliability and the system that delivers the data

Author copy. Do not redistribute.

Fig. 1. NASPI Synchrophasor Network Data Flow. Synchrophasor errors can originate at any of 8 points in the data flow. [4]

to the operator. To date, there have been a handful ofreported efforts to model PMU reliability.

Wang, et. al. developed a hierarchical Markov modelfor PMUs that examined in minute detail the contributionof each component to reliability; the final result wasa two-state equivalent Markov model. Their analysispointed to GPS and central processing unit modulefailure rates as most important to determining PMU re-liability. [5] Aminifar, et. al. applied fuzzy set modelingtechniques to Markov PMU models to compensate forinput data uncertainties used in the reliability model. [6]

The continuing challenge is developing useful modelsthat aid understanding underlying causes of industryreported low synchrophasor data availability and thatprovide direction to improve data availability and quality.This paper describes a generic PMU and develops asimple hardware reliability model using reliability blockdiagram concepts. The paper then examines synchropha-sor data availability in the context of the synchrophasornetwork and develops a Markov model characterizingPMU data availability due to a single PMU. The re-mainder of the paper is organized as follows. Section IIprovides background on the PMU and the synchrophasornetwork. Section III is organized in two sub-sections; thefirst develops a PMU reliability block diagram to modelhardware reliability; and the second develops a Markovmodel for synchrophasor data availability. Section IVproposes methods for improving PMU system perfor-mance. Finally, conclusions are presented in Section V.

II. BACKGROUND ON PMUS AND THESYNCHROPHASOR DATA NETWORK

The synchrophasor data network is shown in Fig. 1.The PMU is installed at select power sub-stations whereit measures voltage and current and computes current andvoltage phasor data. The synchrophasor data is in turntransmitted via a communications network to a hierarchyof phasor data concentrators (PDCs) that integrate time-stamped data from multiple PMUs. Ultimately, region-wide synchrophasor data is assembled at the control

Power System

Comm SystemComm Module

Anti-AliasingFilters

GPS SatelliteSignal

Phasor Measurement Unit System

A/D Conversion

Phase-Locked Oscillator

GPSReceiver

Phasor Processor

InstrumentTransformers

Fig. 2. PMU system model [7].

center. Synchrophasor data can be lost or corrupted atany of the eight stages in the data flow, indicated by thecircled numbers.

A PMU’s nominal internal components are shown inFig. 2. The PMU receives analog voltage and current sig-nals through current and power transformers connecteddirectly to the power grid at the substation. The analogsignals are conditioned by anti-aliasing filters to removeunnecessary high frequency signal components beforedigital sampling occurs in the analog to digital (A/D)converter. In parallel, the PMU receives GPS signalsthat provide precise timing data. The timing data servesas (a) the reference for the phase-locked oscillator thatdetermines sampling times in the A/D converter and(b) the time-stamp for synchrophasor data. The phasorprocessor computes synchrophasor data from the digi-tized signal and GPS timing data. The communicationsmodule formats the data for transmission and finally in-jects synchrophasor data into the communications systemmultiple times per 60 hertz cycle.

The Internet is assumed to be a significant part of thecommunications system through which synchrophasordata will be predominantly transmitted. The Internet usescomplex schemes to compensate for lost data – but those

Satellite 1

Satellite 2

(a)

Satellite 3

(b)

da

p4

r4Satellite 4

(c)

Fig. 3. Global Positioning System timing signal generation (a) Two satellite signals intersect in a circle (b) The third satellite signal intersectsthe circle at 2 points (c) The fourth satellite signal enables timing error detection and correction. [8]

processes will delay assembling complete, time-criticalsynchrophasor data at control centers.

GPS timing data is critical to enabling the comparisonof precisely synchronized voltage and current data at lo-cations separated by thousands of miles. The conceptualfoundation for generating that data is shown in Fig. 3.At any given time and point on the earth’s surface, aGPS receiver will be in view of 6 to 12 satellites; 4good satellite timing signals are required to generate theGPS timing data. Each satellite transmits timing datathat includes i) precise message transmission time, ii)precise orbital information (ephemeris), and iii) generalGPS system health and all approximate satellite positions(almanac). As shown in Figs. 3a and 3b respectively,the intersection of 2 satellite signals is a circle, andthe third satellite’s signal intersects that circle at 2points. Given that precise time computation includes thespeed of light, c, and corrections for relativistic affects,small clock errors can result in timing data outsiderequired error tolerances. The timing signal from thefourth satellite enables the error correction essential toproducing the precise timing data. Ideally, the fourthsatellite signal would intersect at one of the two points(Fig. 3c); however, the computation normally results inthe calculated distance da (the difference between therange, r4, and the pseudo range, p4) between calculatedand actual receiver locations. Conceptually, the error iscalculated using da and c such that

e(t) =da

c. (1)

The error-corrected time is accurate to approximately 10nanoseconds. [8]

FilterGPS

ReceiverOscillator A/D

ConverterPhasor

ProcessorComm

SysCommModule

lf lr lo lad lp lcm lcs

Fig. 4. PMU Network block diagram reliability model.

III. RELIABILITY AND AVAILABILITY MODELING

A. PMU Hardware Reliability Modeling

A reliability block diagram, Fig. 4, is used to modelPMU reliability. While the PMU system itself has com-ponents connected in both series and parallel, the blockdiagram has only series connections because the PMUsystem functions if and only if all of its componentsare functioning. During an electrical component’s usefullife, it is common and accurate to model the componentswith constant failure rates. [9] Assuming that each PMUsystem component has a constant failure rate, λ, thePMU system failure rate is the sum of the componentfailure rates.

λ = λf + λr + λo + λc + λp + λcom + λcs (2)

The PMU reliability function, R(t), the probabilitythat the PMU will provide synchrophasor data (i.e. thehardware will not fail), is given by

R(t) = e−λt. (3)

The block diagram is useful for conceptually iden-tifying components likely to make the most significantcontributions to data not being available. Based uponthe electronic circuit state of the art reliabilities, a welldesigned PMU is expected to have very high reliabilityrates.

However, previously cited power system operatorexperience is inconsistent with this expectation. Onepossible explanation is that the PMU system fails toreceive required inputs – either the voltage and currentmeasurements or four GPS satellite signals. The localcurrent and power transformers are likely to have veryhigh reliabilities. However, the reliability of receivingfour very low power GPS satellite signals (approximately10−16 watts [10]) every second without interruption,especially in noisy electromagnetic environments, is lesscertain.

B. Synchor-phasor Data Availability Modeling

A second situation exists when the synchrophasordata system (stages 3 to 8 in Fig. 1.) fails to de-liver synchrophasor data to the control center. For nearreal-time applications, the synchrophasor data networkmust transmit, receive, and order data very quicklythrough multiple system layers (PDCs) and communi-cations paths between the point of measurement and thecontrol center. The IEEE Standard for synchrophasorsallows either the Transmission Control Protocol (TCP)or the Universal Datagram Protocol (UDP) to be used totransmit synchrophasor data packets. The two protocolsprovide sharply contrasting reliability, ordering, control,and speed capabilities. TCP is a connection-orientedprotocol, which establishes two-way handshake com-munications between the transmitter and receiver; theconnection feature ensures reliability by ensuring mes-sages sent are received and properly ordered – providingvery reliable communications at the expense of very fastcommunications. In contrast, UDP is a connectionlessprotocol – meaning data is sent without a process forensuring that it is received or sequentially ordered;communications is fast at the expense of reliability anddata integrity. [11]

The PDCs also have an important role assembling andordering the data for retransmission that will introduceadditional delays and errors. The engineering trade-offin selecting the protocol depends upon how quickly thedata must be assembled at the control center to be useful.Real-time power system control requires that data beavailable at the control center in less than a second.At the other extreme, synchrophasor data for post eventforensic analysis need not be retrieved for hours or days.In the mid-range, it may be acceptable for synchrophasordata to be assembled in seconds to minutes to depict thepower system’s state. Thus synchrophasor network andcommunications system capabilities and limitations cansignificantly affect data availability.

Thus, the hypothesis advanced and modeled is thatunavailable PMU data is primarily attributable to GPSsignal or communications systems failure. These failuremodes are highlighted as the ‘GPS Receiver’ and ‘CommSys’ on block reliability diagram.

Markov modeling techniques provide an appealingalternative approach. Since, synchrophasor data is com-puted at set intervals, a discrete Markov chain is appro-priate. For the purpose of modeling data availability, thenetwork can be considered to be self-healing becausedata not being available is hypothesized to be dependentupon random processes outside the PMU itself ratherthan upon physical PMU network component failures.

Hence, the external conditions affecting data availabilityare subject to change with each measurement. Thecandidate Markov model is shown in Fig. 5. This four-state model includes a synchrophasor data available state(1) and three data not available states: GPS signal notavailable (2), communications system not available (3),and neither being available (4). The transition probabilitybetween states i and k at each discrete time step k de-noted by qij . The discrete difference equation is written

π1[k + 1]π2[k + 1]π3[k + 1]π4[k + 1]

=

q11 q12 q13 0q21 q22 0 q24q31 0 q33 q340 q42 q43 q44

π1[k]π2[k]π3[k]π4[k]

, (4)

where ∀i, j, qi,j ≥ 0 and πi[k] represents the probabilityof being in the state i at time k. The transition rate matrixQ is comprised of the transition rates between states, qij .Also note, that for ∀j,

∑j qi,j = 1 . The solution of this

discrete time equation is

π[k + 1] = Qk+1π[0]. (5)

Significantly as the number of iterations becomes verylarge, Qk will converge to steady state values, whichwill determine the long run probabilities of being in agiven state. The design objective is to design componentsand backup mechanisms that assure the desired long runprobabilities.

IV. IMPROVING SYNCHROPHASOR DATAAVAILABILITY

Proposed approaches to improving data availability areshown in Fig. 6. To address the hypothesized shortfall ofthe GPS signal being available, a backup clock providesthe time stamp, when needed; the backup clock’s oscil-lator must be sufficiently accurate to meet time stamp

Comm SysFailure

SystemOpn’l

GPSFailure

GPS &Comm Sys

Failure

q11

q21 q42

q12

q13

q31

q24

q34

q43

q22

q44

q33

1

2

3

4

Fig. 5. Markov model for synchrophasor data availability.

accuracy requirements for a specified period. The PMUsystem must sense GPS timing signal absence and switchthe backup clock into operation; similarly, the PMUsystem must sense and return to normal operation whenthe GPS timing signal becomes available again. Further,the PMU system must record and report the GPS timingsignal absence and backup clock activation.

Addressing absent synchrophasor data due to commu-nications system errors requires that synchrophasor databe stored locally – either by the PMU or by an on-sitePDC. When the PMU network recognizes the absenceof synchrophasor data for a particular period from aspecific PMU, PDCs (or higher echelons to the controlcenter) must be able to query the PMU for absent data.The consequent delay will diminish the recovered data’svalue for real time power system state awareness andcontrol; however, the data will be available for the post-mortem analysis of any significant system events thatmight have occurred.

These addition of new PMU components will intro-duce new states and hence new difference equations.The updated Q will result in a new long-run solutionto (5) with the expectation that reliability performancewill improve.

V. CONCLUSIONS

Synchrophasor data availability clearly can be mod-eled both with reliability block diagrams and discreteMarkov chains. Markov chains are preferred becausethey provide greater flexibility for modeling systembehavior – and consequently greater insight into factorsaffecting synchrophasor data availability. The anticipatedbenefit of applying Markov modeling techniques is arigorous analytical effort to understand raising PMUnetwork performance so that the data is reliably availableand viewed as trustworthy. The Markov chain model

Power System

Comm SystemComm Module

InstrumentTransformers

Anti-AliasingFilters

Phasor Processor

Data Storage

GPS SatelliteSignal

Phasor Measurement Unit System

A/D Conversion

Phase-Locked Oscillator

BackupClock

GPSReceiver

Fig. 6. PMU system model modified to increase synchrophasor dataavailability.

presented is based upon two hypothesized synchrophasorloss mechanisms – the absence of GPS timing data andthe communications system shortfalls. The anticipatedfollow-on effort is to test the hypotheses using measuredsynchrophasor data. A second possible line of effort isto develop reliability models that provide insights toimproving the synchrophasor data availability as it ispasses through intermediate PDCs and the communica-tions system.

REFERENCES

[1] Section 1301, Energy Independence and Security Act (EISA) of2007 [Public Law 110-140-Dec 19, 2007]. [Online]. Available:http://www.oe.energy.gov/DocumentsandMedia

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[3] K. Moslehi and R. Kumar, “Smart grid - a reliability perspective,”in Proc. Innovative Smart Grid Technologies (ISGT), 2005, pp.1–8.

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[6] F. Aminifar, S. Bagheri-Shouraki, M. Fotuhi-Firuzabad, andM. Shahidehpour, “Reliability modeling of pmus using fuzzysets,” vol. 25, no. 4, pp. 2384–2391, 2010.

[7] A. P. J. Thorp, Synchronized Phasor Measurements and TheirApplications. Springer Science+Business Media, LLC, 2008.

[8] Global Positioning System. http://en.wikipedia.org/wiki/Gps.Accessed 14 May 2011. [Online]. Available:http://en.wikipedia.org/wiki/Gps

[9] M. Rausand and A. Hoyland, System Reliability Theory: Models,Statistical Methods, and Applications, second edition ed., ser.Wiley Series in Probability and Statistics. Wiley-Interscience,2004.

[10] J. S. Warner and R. G. Johnston, “GPS spoofingcountermeasures,” Homeland Security Journal, 2003. [Online].Available: http://library.lanl.gov/cgi-bin/getfile?00852243.pdf

[11] Comparison of UDP and TCP.http://en.wikipedia.org/wiki/User Datagram Protocol. Accessed14 Jun 2011.