A Novel Approach for Calibration of Instrument Transformers using Synchrophasors

Transcription

1 A Novel Approach for Calbraton of Instrument Transformers usng Synchrophasors Trupt P. Hnge College of Engneerng, Pune, Inda Emal: Sanay. S. Dambhare College of Engneerng, Pune, Inda Emal: Abstract Ths paper presents a novel approach for calbraton of Instrument Transformers (ITs) usng synchrophasor data. The proposed algorthm detects the presence of bad data usng Largest Normalzed Resdual (LNR) test n a step and dscards the correspondng measurements. Ths method s ntended to work as a flterng scheme that can sgnfcantly mprove the accuracy of Current Transformers (CT) and Capactve Voltage Transformers (CVT) measurements. Once calbrated, accurate measurements are avalable to execute State Estmaton (SE), to enhance dynamc securty of system, and analytcs for Wde Area Montorng Systems (WAMS). Case studes based on smulated data are presented to prove the effectveness of the proposed method. Index Terms Bad data estmaton and computaton, calbraton of CT and CVT, Largest Normalzed Resdual test, Least Square method, synchronsed measurements, transmsson lnes. I. INTRODUCTION The performance of the Wde Area Measurements (WAMs) based State Estmaton (SE), Dynamc Securty Assessment (DSA) and other analytcs depends upon the accuracy of measurements from CT and CVT. However, n real lfe CT and CVT measurements are prone to nose and errors due to prevalng burden, age, envronmental condtons, modelng restrctons etc., [], []. Further, the measurements are also prone to errors due to data converson abnormaltes, communcaton delays and sensor de-synchronzaton. If the measurements nvolves large errors, the accuracy of devsed SE algorthm deterorates substantally. Earler, n SCADA system, weghts were assgned to Instruments Transformers (ITs) consderng that the measurements from meters of known greater accuracy are treated more favorably than less accurate measurements [3]. Hence, t s well known that the measurement chan s not deal. Also, practcal Instrument Transformers (IT) always have Rato error (Rato Correcton Factors - RCF) and Phase Angle error (Phase Angle Correcton Factor - PACF). Ideally, as requred by IEEE standard [4], the Total Error Vector (TVE) between the measured phasor and ts estmated value should be well wthn % under steady state operatng condtons. Therefore, t s mportant to calbrate ITs usng approprate algorthms to correct erroneous measurements. Current Transformers (CT) and Capactve Voltage Transformers (CVT) are the eyes and ears of the power system /4/$3.00 c 06 IEEE whch are nstalled at the substatons. The CT and CVT measurements are used to execute control and protecton algorthms. Also, wth the avalablty of communcaton, GPS synchronzaton and Phasor Measurements Unt (PMU), tme synchronsed measurements are easly avalable at substatons. However, CT and CVT errors can not be gnored and are ncreasng wth operatng condtons, age, and other factors. If these errors are not compensated a pror then the algorthm whch uses these as an nput may malfuncton. CT and CVT outages for calbraton are also not permtted by system operator because of labor-ntensve and costly process. The frequent replacement of erroneous CT and CVT s not encouraged for economc consderatons. Hence, uncalbrated ITs degrade the performance of the system for SE and DSA. Many attempts have been made to detect and calbrate the errors n ITs [5], [6], [7], [8], [9]. Reference [5] analyze and compute multple bad data orgnated n voltage or current transformer usng Largest Normalzed Resdual test. Reference [6] descrbes a measurement calbraton method whch dentfes calbraton models for the uncalbrated measurements and estmate the calbraton model parameters along wth the system states usng multple scans of measurements. In recent past, synchrophasors (Phasor Measurement Unt- PMU) are deployed on many power systems to acqure tme synchronzed data of current and voltage. The data generated from PMU s used for CT and CVT calbraton [7]. In ths paper, the tme synchronzed phasor data of PMU, placed n the system optmally or otherwse s used to estmate error n ITs, non-teratvely. II. MOTIVATION Let us consder the two bus system wheren transmsson lne s represented by equvalent-π model of as shown n Fg.. Consder CT and CVT at node are accurate however CT and CVT at node are erroneous. Measurements of voltage at node and node are derved from PMU. In a large system, although PMUs are not placed on every bus, however data of respectve bus.e. currents and voltages can be computed from state estmators whch may be workng on synchrophasor data. The tme synchronzed data may be avalable from PMU or WAMS based state estmator. Therefore, postve sequence equatons for transmsson lne after

2 compensatng lne chargng current s wrtten as where V V = Z () = I lne B V () s the seres branch current at node, that can be computed after removng lne-chargng currents from lne currents. I lne, I lne V, V Z B Smlarly, at node where Lne currents at bus and respectvely. Voltage at bus and respectvely. Impedance of transmsson lne Susceptance of transmsson lne V V = Z (3) = I lne B V (4) s the seres branch current at node, that can be computed after removng lne-chargng currents from lne currents. Addng () and (3), we get V V = (Iser I ser )Z Let us consder, the measurements error n CVT and CT V Node PMU wth accurate CT and CVT I lne I cap B/ GPS Z I ser I lne B/ I cap Node V PMU wth naccurate CT and CVT Fg.. Sngle lne representaton of equvalent-π model of three phase transposed transmsson lne at node as Me N and Ae B respectvely. Node currents and voltages are estmated from the postve sequence measurements avalable from PMU at node. Usng the erroneous measurements of node, voltage estmated V est at node as, V est = (I ser I lne P e Q )Z +V T e F (+ ZB 4 ) (6) Arrangng (6) V est = (I ser I lne P e Q )Z + V V + I ser Z (5) +V T e F (+ ZB 4 ) I ser Z Segregatng error terms, V est = V + I ser Z Therefore, I ser Z +V (T e F +T e F ZB 4 ) + Z (I ser I lne P e Q ) V est = V + e t (7) where, V s measurement of voltage at node wth accurate PMU, e t = V (T e F + T e F ZB 4 ) + Z (I ser I lne P e Q ) The numercal term e t n (7) ndcates an error n the estmaton of V. And, f these measurements are used for further computaton then subsequent computatons wll be populated wth multple errors. Hence, for the compensaton of CT and CVT errors, computaton and compensaton of errors are requred. Once the errors are estmated, CT and CVT are calbrated remotely usng proposed algorthm. Ths process s known as Soft Calbraton. Hence, the followng secton dscuss the proposed method for the Soft Calbraton of Instrument Transformers. A. Detecton of Bad Data III. PROPOSED METHOD Wth reference to Fg., Let Z t be a vector of postve sequence synchronsed measurements derved from lne current and bus voltage measurements for a partcular tme nstant t. V = V + e ; (8) I (ser) = (V V )Y + e (9) Therefore, [ ] [ V 0 I (ser) = Y Y ] [ ] V V (0) Hence, State Estmator model can be represented as follows: Z t = M t V t + e t () The modal Matrx M t s assembled from postve sequence data of transmsson lne. V t s the postve sequence bus voltage vector. e t s the error vector for measurement Z t. The least square estmate of V t s gven by V t est = M t + Z t () where M + s the pseudonverse of M. Here, t can be seen that, estmaton problem s solved n one step [0]. Thus, from (), the resdual vector s gven by r t = (I m M t M t + )Z t (3) where, r t s the postve sequence or three phase resdual vector of measurement vector Z t and I m s the m x m dentty

3 matrx and m s the number of measurement. The normalzed resdual vector s gven as follows: r n = (dag(r r )) / r t (4) where, R r = s the covarance matrx of the resdual estmate vector and s gven by R r = ( r t r t T M t Mt + ) If normalzed resdues are above standard devaton 3, then presence of bad data s detected [] and correspondng samples should be dscarded. But f normalzed resdue s below standard devaton 3 then we compute calbraton factors requred for CT and CVT measurements. B. Computaton of Calbraton Factors for CT and CVT Measurements n power system are avalable from secondary crcuts of Instrument Transformers.e. CT and CVT. An deal nstrument transformer always reflect prmary sgnal fathfully n secondary crcuts. However, practcal nstrument transformers are always assocated wth phase angle error and magntude error due to ageng of nstruments. Measurements from CT and CVT are utlzed to execute State Estmaton and Dynamc Securty Assessment at control center; so erroneous measurements may envsage nadvertent results n processes. Therefore, here we attempt to compute calbraton factors requred to correct measurements receved from CT and CVT. Consder n Fg., equaton for seres currents n case of no fault stuaton s gven by, = (5) Assumng error n CVT (complex) as (R + S), and that of CT (complex) as (A + B), substtutng () n (5) = [I lne (A + B) B V (R + S)] (6) Segregatng real (RE) and magnary (IM) components from above [ [ ] RE = [I ser ] RE A + [I ser ] IM B+ ] IM = [I ser ] IM A [I ser ] RE B+ [ B V ] R [ B RE V ] S (7) IM [ B V ] R + [ B IM V ] S (8) RE Smlarly, voltage at node n equaton (3) s rewrtten as, V (R+S) V = Z[I lne (A+B) B V (R+S)] (9) Segregatng real (RE) and magnary (IM) components from above [V ] RE = [V ] RE R [V ] IM S [I lne ] RE ZA+ [I lne ] IM ZB + [ B V ] ZR + [ B RE V ] ZS (0) IM [V ] IM = [V ] IM R + [V ] RE S [I lne ] IM ZA+ [I lne ] RE ZB + [ B V ] ZR + [ B IM V ] ZS () RE equatons (7), (8), (0) and () represents four complex equatons wth four unknown as A, B, R and S. Arrangng the same n matrx form.e. Z tt = M tt U t The soluton for unknown errors s obtaned usng Least Square estmate as U t = (M + tt M tt ) M + tt Z tt () where M tt + s the conugate transpose of M tt. The calbraton factors for CT and CVT are expressed as recprocals of P e Q, T e F respectvely and are computed n a step, non-teratvely from, P = A + B Q = arctan( A B ) T = R + S F = arctan( R S ) (3) IV. PROPOSED ALGORITHM The flowchart for bad data detecton and calbraton of CT and CVT s shown n Fg. and descrbed as follows: ) Input transmsson lne parameters, set bad data threshold=3. ) Acqure latest GPS-synchronsed tme-tagged samples of 3 phase voltages and currents.e. V (abc) and V (abc) (t), I lne(abc) (t), I lne(abc) (t) (t) from node and node of lne resp. Tme t ndcates an nstant correspondng to latest sample and a, b and c desgnate the three phases. 3) Obtan phasors usng Full Cycle Recursve Dscrete Fourer Transform (FCRDFT)[] of voltages and currents. 4) Compute and usng () and (4) 5) Estmate presence of bad data usng (4). 6) Check f : standard devaton of normalzed resdues > threshold If TRUE, then dscard the samples (as bad data) and goto to step else, goto to next step. 7) Compute calbraton factors usng () 8) Compensate error due to CT and CVT usng calbraton factor and ths accurate measurements can be used for State Estmaton, DSA and for other analytcs of WAMs. V. CASE STUDY Fg. 3 depcts the network topology of IEEE 4 bus system. System s modeled wth 00 MVA, 0 kv base, 50 Hz frequency. The system s smulated n ATP-EMTP envronment [3] wth samplng frequency as khz. Transmsson lnes

4 Accurate data from node Erroneous data from node Input the Transmsson Lne parameters, set bad data threshold=3 Compute phasors of bus voltages and lne currents, estmate I ser and I ser Estmate bad data usng (4) Is Bad data detected? No Yes Compute bas errors n CT and CVT usng () Dscard the measurements are represented by equvalent-π model wth 00 km length. Measurements avalable at Bus 3 are consdered as erroneous measurement n CT and CVT whle Phasor Measurement Unt wth accurate CT and CVT s located at Bus. ANSI 500:5, class C400 CT model and 50 kv:00 V CVT model have been used for obtanng realstc CT and CVT response durng ATP smulatons []. Voltages and currents at Bus s computed from the measurements obtaned from Bus 3, and bad data s detected and correspondng measurements are dscarded. Samples are obtaned from ATP-EMTP smulatons are consdered as GPS synchronsed tme-tagged and processed n MATLAB; phasors are estmated usng Full Cycle Recursve Dscrete Fourer Transform (FCDFT). The speed of computaton s less than 3sec on khz samplng frequency wth MATLAB R03a and Intel(R) Core(TM) CPU@ 3.40GHZ wth 3- bt operatng system, 4 GB RAM. Performance of proposed methods s evaluated for varous bas errors. In smulatons, mplementaton s carred out n three-phase doman whle for convenence, the proposed method s dscussed n postve sequence representaton. TABLE I ESTIMATION OF CALIBRATION FACTORS FOR CVT AND CT Compute calbraton factors Compensate the errors n the measurements Calbrated measurements are now avalable for SE, DSA and other analytcs of WAMS Fg.. Flowchart for bad data detecton and nstrument transformer calbraton Error CVT T e F n.e. Estmated Calbraton factor for CVT.e. T e F Error n CT.e. P e Q Estmated Calbraton factor for CT P e Q Table I presents the estmaton of calbraton factors for errors assocated wth CVT and CT. Frst and thrd columns ndcate the error n the measurement of CVT and CT respectvely, whereas second and fourth columns show that f for measurement errors vared from 0 to 0, then proposed algorthm computes calbraton factors accurately for CVT and CT. 5 4 VI. CONCLUSION PMU PMU Fg. 3. IEEE 4 Bus Test System 3 The algorthm proposed novel approach to detect and dscard bad data and calbrate the ITs usng synchronzed measurement. The computaton efforts are less as the algorthm do not need sequence components computaton and do not use teratve method. No extra efforts or specalzed equpments are needed to calbrate CT and CVT. Extensve smulatons studes demonstrate the merts of proposed scheme.

5 ACKNOWLEDGEMENT The work reported n ths paper has been supported by Center of Excellence n Smart Renewable Energy Systems (CoE SRES) under Techncal Educaton Qualty Improvement ProgrammeII (TEQIP II) at College Of Engneerng afflated to S. P. Unv. of Pune, Maharashtra, Inda. Ths support s gratefully acknowledged. REFERENCES [] Z. Wu, K. Thomas, R. Sun, V. Centeno, and A. Phadke, Threephase Instrument Transformer Calbraton wth Synchronzed Phasor Measurements, n IEEE PES Innovatve Smart Grd Technologes (ISGT), 0, Jan 0, pp. 6. [] S. Dambhare, S. Soman, and M. Chandorkar, Adaptve Current Dfferental Protecton Schemes for Transmsson Lne Protecton, IEEE Transactons on Power Delvery, vol. 4, no. 4, pp , Oct 009. [3] M. Asprou, E. Kyrakdes, and M. Albu, The Effect of Varable Weghts n a WLS State Estmator Consderng Instrument Transformer Uncertantes, IEEE Transactons on Instrumentaton and Measurement, vol. 63, no. 6, pp , June 04. [4] Ieee Standard for Synchrophasor Measurements for Power Systems, IEEE Std C (Revson of IEEE Std C ), pp. 6, Dec 0. [5] E. Caro, A. Coneo, R. Mnguez, M. Zma, and G. Andersson, Multple Bad Data Identfcaton Consderng Measurement Dependences, IEEE Transactons on Power Systems, vol. 6, no. 4, pp , Nov 0. [6] S. Zhong and A. Abur, Combned State Estmaton and Measurement Calbraton, IEEE Transactons on Power Systems, vol. 0, no., pp , 005. [7] A. Phadke, J. Thorp, R. Nuqu, and M. Zhou, Recent Developments n State Estmaton wth Phasor Measurements, n Power Systems Conference and Exposton, 009. PSCE 09. IEEE/PES, March 009, pp. 7. [8] A. Pal, P. Chatteree, J. Thorp, and V. Centeno, On-lne Calbraton of Voltage Transformers Usng Synchrophasor Measurements, IEEE Transactons on Power Delvery, vol. 3, no., pp , Feb 06. [9] D. Sh, D. Tylavsky, and N. Logc, An Adaptve Method for Detecton and Correcton of Errors n PMU Measurements, n IEEE Power and Energy Socety General Meetng (PES), 03, July 03, pp.. [0] P. V. Navalkar and S. A. Soman, Secure Remote Backup Protecton of Transmsson Lnes usng Synchrophasors, IEEE Transactons on Power Delvery, vol. 6, no., pp , 0. [] S. A. Soman, S. Khaparde, and S. Pandt, Computatonal Methods For Large Sparse Power Systems Analyss: An Obect Orented Approach. Sprnger Scence & Busness Meda, 0. [] S. A. Soman, A Web Course on Power System Protecton, [3] H. Dommel, Electromagnetc Transents Program (EMTP) Theory Book. Portland OR: Bonnevlle Power admnstraton, 986.