Synchrophasor Reference Algorithm For PMU Calibration System
Synchrophasor Reference Algorithm forPMU Calibration SystemCheng Qian, Graduate Student Member, IEEE, Mladen Kezunovic, Fellow, IEEEDept. of Electrical and Computer EngineeringTexas A&M University, College StationCollege Station, TX, USpeterqiancheng@tamu.edu, kezunov@ece.tamu.eduAbstract—This paper describes a reference algorithmspecifically designed for PMU Calibration System. Contrary toexisting DFT-based and curve fitting-based methods, which usea single signal model, the proposed algorithm applies anadaptive mechanism, and switches signal models according tospecific signal input. Signals are modeled with parameters withapparent and certain physical meaning, fundamentally avoidingerror magnification from derivative calculation for frequencyand rate of change of frequency estimation. LevenbergMarquardt algorithm is used for solving the signal parameters.The test results show that the proposed algorithm has a muchhigher accuracy than the requirements of IEEE standardC37.118.1, and hence can serve as a reference algorithm in aPMU Calibration MUcalibration system, reference synchrophasor algorithm,synchrophasor estimation, power system measurements.I. INTRODUCTIONSynchronized phasor measurements and phasormeasurement units (PMUs) have grown to enhance wide-areasituational awareness, and have gained wide application inmodern power system worldwide. An efficient method ofestimating phasor using Discrete Fourier Transform (DFT)was introduced in 1983 [1], and has gained prevalence thanksto its high computational efficiency. The prototype of PMUwas built in Virginia Tech, and the first PMU device was builtby Macrodyne in 1992. So far, there are more than 1000PMUs commissioned in the US electric power grid, creating acomplex wide-area measurement system. [2]Multiple versions of IEEE standards have been proposed.In 2011, the original IEEE standard was further revised, andseparated into two standards: IEEE C37.118.1-2011 [3] forsynchrophasor measurement, and IEEE C37.118.2-2011 [4],for synchrophasor data transfer. In the new standard, adynamic synchrophasor model with broader scope was used.The standard categorized the PMU into P-Class and M-Class,and added the requirements for PMU dynamic tests. Thestandards were amended by IEEE C37.118a-2014 [5] in 2014.This work was supported by the Power Systems Engineering ResearchCenter (PSERC) Project T-57HI “Life-cycle management of mission-criticalsystems through certification, commissioning, in-service maintenance,remote testing, and risk assessment”IEEE Synchrophasor Measurement Test Suite Specification [6]was published in 2014 as an unambiguous guidance of PMUtesting.Industry, academia and government are contributing tosynchrophasor development and PMU calibration systemstogether. North America SynchroPhasor Initiative (NASPI) [7]carried work under the auspices of the North AmericaReliability Corporation (NERC), and has proposed severalguides for PMU testing and certification [8]. Funded by theNational Institute of Standard and Technology (NIST), DOE,and DOC, SynchroMetrology Laboratory was established atNIST in 2006, the static PMU Calibration System was built in2008, and the dynamic PMU Calibration System isconstructed in 2009 [9]. Besides NIST, many universities andinstitutes are developing PMU calibration systems and testinglaboratories [10]-[13].A great number of papers have introduced synchrophasorestimation methods in the past three decades. References [14]and [15] proposed interpolated DFT method in frequencydomain by estimating the discrepancy between local maximaand DFT bins. This method works only for static multifrequency signal. Reference [16] analyzed the spectral leakageand averaging effect of DFT, concluding that frequencydomain methods cannot perform well if subject to dynamicinput. By introducing dynamic phasor model to improveestimation accuracy, references [17] and [18] used Taylorpolynomials to fit dynamic signals in time domain, and thencalculate synchrophasor using fitting parameters. Timedomain methods essentially acknowledge the dynamic natureof synchrophasor. The computational efficiency of thismethod was improved in [13] by introducing Legendrepolynomials. Moreover, Model-based Kalman filter was usedfor dynamic phasor estimation [19].The aforementioned methods are capable of performingwell under certain test signals, but none of them can keep highaccuracy for all test signals, which is required in a PMUcalibration system. The algorithm that we propose in thispaper, however, takes into account each test signal property,
and matches the model to the signal parameters for that case,hence can achieve high accuracy for all test scenarios.PMU testing as long as the input signal type is controlled andknown in advance.The rest of the paper is organized as follows, Section IIreviews the structure of PMU calibration system that uses anew PMU algorithm as a reference. Nonlinear regressionmethods, especially Levenberg-Marquardt algorithm, areintroduced in Section III. In Section IV, a new referencesynchrophasor estimation method based on nonlinearregression method is presented. Algorithm implementationand test results are presented in Section V.Figure 2. Input and Output of a typical Reference PMUII. PMU CALIBRATION SYSTEM BASED ONREFERENCE PMUA. Requirement Specification of a Calibration SystemA PMU Calibration System is a platform for testing andcalibration of PMU devices before their commissioning in apower grid. Typically a PMU Calibration System consists ofthe following subsystems: signal generation, timing reference,PMU measurement receiver, PMU under test, synchrophasorreference source, and result documentation. Structure of aPMU Calibration system is shown in Fig. 1.Although there are various ways to implement the PMUCalibration System, the basic mechanism of PMU testing isusing the reference value to evaluate measurements fromPMU under test, and then by comparing reference values andmeasurements according to the corresponding timestamps.III. NONLINEAR REGRESSION METHODSIn 2011, a dynamic synchrophasor model is proposed inIEEE Standard C37.118-2011, as shown in (1).( )( ) (1)( )where instant phase angle ( )is ( )described as an offset from cosine wave at the nominalfrequency. From this definition, phase angle is anaccumulation of angular velocity deviation over time.In our approach, power system signals, which arecombination of nonlinear trigonometric functions, can bemodeled by (2),()(2)where b is the known data sample from one data window, t isthe unknown time vector corresponding to b, and x is theunknown fitting parameter vector. f represents the model ofpower system signals.Solving (2) is essentially a nonlinear regression problem.The objective function is given by (3),( )(3)where SSR, or Sum of Squared Residue, is given by (4),Figure 1. Structure of a typical PMU Calibraiton SystemB. Reference PMUAccording to [7], based on the choice of reference values,three methods can be applied to implement synchrophasorreference source: Direct Measurement, Inference, and TransferMeasurement. In Transfer Measurement method, a deviceswith higher accuracy, typically with a test uncertainly ratio(TUR) greater than 4, is utilized as the source of referencevalues. In this paper, Transfer Measurement is adopted wherethe Reference PMU algorithm serves as the synchrophasorreference. The accuracy of Reference PMU can be achievedby carefully choosing the correct hardware and implementinghigh precision synchrophasor estimation methods. The inputsand output of a Reference PMU are shown in Fig. 2.When utilizing a Reference PMU, test scenario input canbe used to identify test signal input so that Reference PMUcan select the most suitable signal model and algorithm foreach input signals to achieve highest estimation accuracy. Theproposed algorithm is suitable for either offline or online( )‖‖‖()‖(4)where the subscript opt indicates optimized values to beattained.A common strategy of solving nonlinear regressionproblems is to linearize (2) and then solve linear regressionproblems instead, which is much less complicated. Typicalnonlinear regression methods include Gauss-NewtonAlgorithm (GNA), method of gradient descent (also steepestdescent). GNA is not suitable for iteration when the initialcondition is far off from the actual value. This drawback canbe compensated by method of gradient descent. However,gradient descent method shows a poor converging qualityaround true value. Levenberg-Marquardt algorithm (LMA)[20] uses a damping factor µ to adjust iteration increment tofind a trade-off between GNA and gradient descent method.For a nonlinear equation (2), the increment of LMA is shownin (3).()[()()()(()())]()[(())](5)
whereis the Jacobian matrix.The damping factor µ is chosen to be a relatively largevalue at the beginning of iteration, where the initial valuetends to be away from the real value. The iteration incrementis large, which is similar to gradient descent method, for afast approach of real value; then µ decrease and LMAbecomes similar to GNA, in order to get more accurate result.IV. SYNCHROPHASOR ALGORITHMS FOR REFERENCE PMUThe drawback of the existing curve fitting based, timedomain methods is that there is no physical meaning of thefitting parameters. The quantities with physical meaning,namely amplitude, phase angle, frequency, and rate of changeof frequency, are derived from the fitting parameters. As aresult, the input signal cannot be modeled in a way that themodel truly reflects the input signal. Moreover, usually thefrequency and rate of change of frequency (ROCOF) areacquired by taking the derivative and second derivative ofphase angle, respectively. This process, however, magnifiesthe error in phase angle estimation.A general rule of thumb is, the more information about thesignal to be estimated can be acquired, the more accurateestimation results can be expected. As stated above and shownin Fig. 2, Test Scenario should be considered as a knownparameter to the PMU Calibration System. The algorithmproposed in this paper employs the additional Test Scenarioinput to identify the test signals, and apply respective signalmodels for each scenario. Nonlinear least square method isused to calculate fitting parameters in the models.A. Procedure of Synchrophasor Estimation using ProposedAlgorithmAccording to IEEE standards, a PMU has to be subjectedto static and dynamic tests. Details of the test types as well asthe corresponding power system scenarios are listed in Table 1.Diagram of how the algorithm works as a reference algorithmis shown in Fig. 3.TABLE I.TEST SCENARIOS IN PMU TESTSTest TypesSignal frequency rangeSignal magnitude rangeStaticTestsDynamicTestsPower System ScenariosFrequency deviation undernormal conditionMagnitude levels undernormal conditionPhase angle rangeNormal condition featuring aslowly varying angleHarmonic distortionHarmonic infiltration frompower electronic devices, etc.Out-of-band interferenceTesting PMU anti-aliasingeffectivenessAmplitude modulationAmplitude oscillation, lowFrequency oscillationPhase modulationFrequency oscillation,subsynchronous resonanceFrequency rampGenerator out-of-stepInput step changeFaults in power gridsAs shown in Fig.3, during a PMU test, the proposedreference algorithm uses Test Scenario to identify inputsignal and select corresponding signal model, which isintroduced in the following sections. Then LMA performsnonlinear regression method to estimate model parameters.The signal model is chosen in an optimized way so that themost prior knowledge of input test signal is employed forimproved accuracy.Figure 3. Procedure of synchrophasor estimation with proposed algorithmB. Model for Static Signals and Frequency Ramp SignalsIn static and frequency ramp signals, the parameters ofparticular interest are: root-mean-square value, initialangleinstant frequency deviation from nominal frequency), and rate of change of frequency (ROCOF) .( )( )(6)wheredenotes nominal frequency. The correspondingsynchrophasor of signal in (6) is,(( ))(7)C. Model for Harmonic Distorted and Out-of-Band SignalsIn signal with harmonic distortion model, an additionalharmonic term is added to (6). The harmonic signal ismodeled as a single frequency sinusoid.( )( )( ) (8)where represents the order of harmonic, subscriptdenotes the parameters for harmonic signal.The corresponding synchrophasor for (8) is the same as(7), since harmonic signal is not taken into consideration insynchrophasor model.The out-of-band (OOB) test signals can also beconsidered as a signal harmonic input. IEEE standard requiresthat the PMU can withstand harmonics from 2nd order to 50thorder, and OOB signal from passband to 2nd harmonics. [5]D. Model for Modulation SignalsIEEE standard [5] specifies two types of modulation tests,amplitude modulation and frequency/phase modulation.Modulation parameters are added to (6).( )[ [()]()] (9)whereis the amplitude modulation level,is thefrequency modulation level,is modulation frequency.The corresponding synchrophasor model for (9) is,
( )[(()]())(10)Note that frequency deviationis added to take intoaccount the frequency error of signal generator. Frequency of(9) is the first derivative of the phase angle,( )( )() (11)ROCOF of (9) is calculated by taking the derivative of(11),( )()(12)E. Model for Input Step SignalsInput step test signals can be considered as aconcatenation of two steady state sinusoids. Therefore themodel in (6) is used.is needed to acquire the model parameters. LMA requiresiteration and initial values input of fitting parameter vector x,as in (2), and damping factor µ, as in (5). Flowchart ofiteration process is shown in Fig. 5.C. Test ConditionsWhile test signals specified in [6] are used, two set oftests are performed to evaluate the accuracy of the proposedreference algorithm. The first set of tests is theoreticalsimulation tests, where the algorithm is tested undertheoretical input in LabVIEW. The second set of tests isimplementation test, where white Gaussian noise (WGN) isadded to the theoretical signal to simulate the effect ofdigitization and sampling noise. An effective-number-of-bits(ENOB) of 14-bit is chosen to represent the actual 16-bitADC resolution, which is equivalent to a signal-to-noise ratioof 70dB WGN [18]. Sampling noise is modeled according to[21].However, input step tests focus on evaluating the responsetime and delay time of the algorithm, rather than theestimation accuracy. Hence, a Reference PMU should be ableto accurately detect and locate the moment of a step change.Since the transition time of an algorithm is usually equal tothe length of data used for estimation, shorter data window(preferably shorter than one cycle) should be used. Tocompensate the loss of available data, higher sampling rateshould be utilized.V. ALGORITHM IMPLEMENTATION AND TESTINGA. Reference PMU SetupThe Reference PMU implementation at Texas A&MUniversity is based on National Instruments PXI platform,which is composed of a 2.0GHz dual-core embeddedcontroller, analog acquisition card, and a timing card capableof decoding IRIG-B signal. Timing signal is provided bySymmetricom clock. Software for reference PMU, includingusers’ interface, reference algorithms, and hardwareconfiguration codes, is written in National InstrumentsLabVIEW. The hardware system is shown in Fig. 4.Figure 5. Flowchart of Reference AlgorithmIn the theoretical simulation test, the following testscenarios are considered: steady-state tests, harmonic test,out-of-band test, frequency ramp test, modulation test. Thesignal models are chosen according to Section IV.For the implementation test, same test scenarios are usedas the theoretical simulation tests. However, white Gaussiannoise is added to the input signals.Figure 4. Reference PMU Test System at Texas A&M UniversityB. Iteration FlowchartAs introduced in Section III and IV, the proposedsynchrophasor reference algorithm utilizes different nonlinearsignal models for respective input signals. As a result, LMAD. Theoretical Simulation Test ResultsAs is shown in Table II, the proposed reference algorithmpresents high accuracy in typical tests specified in IEEEstandards. Since frequency and ROCOF are specificallymodeled, they can present the same accuracy level asamplitude and angle estimation, which cannot be achieved bytraditional algorithms. Note that the algorithm is designed tocomply with requirements for M-class PMU, but for
Harmonic and OOB tests, only P-class ROCOF requirementsare available so far.E. Implementation Test ResultsAs is shown in Table III, the proposed referencealgorithm can remain adequate accuracy for PMU CalibrationSystem. Thanks to customized modeling of input signal,frequency and ROCOF estimation exhibits high accuracy. Formodulation test, ROCOF is not modeled as unknownparameter, thus it is calculated by taking the derivative offrequency, and this is how estimation error is magnified.TABLE II.Test TypeSteady-statetestHarmonic testOOB testFrequencyramp testModulationtestTABLE III.Test TypeSteady-statetestHarmonic testOOB testFrequencyramp testModulationtestALGORITHM ACCURACY IN THEORETICAL 1.3%10-5/0.00510-5/0.0052 10-5/0.4 (P)2 10-5/0.4 (P)5 10-4%/1%5 10-6/0.013 10-5/0.25 10-5%/3%2 10-6/0.0610-3/2ALGORITHM ACCURACY IN IMPLEMENTATION 0.01%/1%0.0004/0.0055 /0.4 (P)10-3/0.4 (P)0.04%/1%0.002/0.014 10-4/0.20.09%/3%0.012/0.060.2/2VI. CONCLUSIONIn this paper, a reference synchrophasor algorithm forPMU Calibration System is presented. The conclusions are asfollows. Input test signals are modeled with parameters withspecific physical meaning for accurate description of testsignals. Test scenario is used as an additional known input toidentify and switch respective signal models, so that higherestimation accuracy can be achieved. Levenberg-Marquardt algorithm is adopted to performnonlinear parameter estimation. The proposed algorithm istested against an algorithm provided in the IEEE standard.Test results show high accuracy of the proposed algorithm. Differentiation of phase angles, which magnifies angleestimation error, is avoided during frequency and ROCOFestimation. Hence, higher accuracy of frequency andROCOF estimation is achieved. The proposed algorithm requires prior knowledge of testscenario and employs iteration method, which can be usedin a PMU Calibration System for online/offline PMUtesting with controlled signal input.REFERENCES[1]. A. G. Phadke, J. S. Thorp, and M. G. Adamiak, "A new measurementtechnique for tracking voltage phasors, local system frequency, and rateof change of frequency," IEEE Trans. Power Apparatus and Systems,vol. 102, pp. 1025-1038, May 1983[2]. NASPI. (2014, Mar.). PMUs and synchrophasor data flows in rid.gov/files/naspi pmu data flows map 20140325.pdf[3]. IEEE Standard for Synchrophasors Measurements for Power Systems,IEEE Std. C37.118.1-2011, Dec. 2011[4]. IEEE Standard for Synchrophasors Data Transfer for Power Systems,IEEE Std. C37.118.2-2011, Dec. 2011[5]. IEEE Standard for Synchrophasor Measurements for Power Systems,Amendment 1: Modification of Selected Performance Requirements,IEEE Std. C37.118.1a-2014, Mar. 2014[6]. A. 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Algorithm (GNA), method of gradient descent (also steepest descent). GNA is not suitable for iteration when the initial condition is far off from the actual value. This drawback can be compensated by method of gra
(PMU) in development. 2002 Electronic relays with built-in PMU functions. 2005. 2. nd. Standard IEEE C37.118. SEL standardized many relays with built-in PMU . 2011. 1,110 standalone PMUs, with tens of thousands of built - in PMU in relays. 2017. PXiSE uses PMU for control in all areas of the grid . 1982 - Standalone PMU. Very few used for .
quality" [9], PMU timing accuracy [11], real-time supervisory assessment of multiple PMU data streams [12], and latency [13]. The importance of rigorous testing of PMU-based systems is strongly emphasised in [14]. Utilities are already using PMU data as tools for visualisation and stability monitoring [15], but closed-loop control, i.e. where .
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Phasor measurement units (PMUs), a type of synchrophasor, are powerful diagnostic tools that can help avert catastrophic failures in the power grid. Because of this, PMU measurement errors are particularly worrisome. This report examines the internal and external factors contributing to PMU phase angle and
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method and linear estimation that utilizes PMU measurements. In [12], a real-time fault detection and faulted line identifi-cation functionality is proposed based on computing parallel synchrophasor-based state estimators. In addition to new techniques based on graph and PMU data analyses, power system security has been extensively
Phase measurement units (PMU) provide synchronized phasor measurements at the sampling rate of 30 or 60 sample per second; More than 2000 PMU are installed in the North America. PMU are generating large-scale of datasets in the power grid; Data-driven methods based on PMU data are promising to automatically locate and identify abnormal
quality" [9], PMU timing accuracy [11], real-time supervisory assessment of multiple PMU data streams [12], and latency [13]. The importance of rigorous testing of PMU-based systems is strongly emphasised in [14]. Utilities are already using PMU data as tools for visualisation and stability monitoring [15], but closed-loop control, i.e. where .
