Tesing and Validaion of Phasor Measuremen Based Devices and Algorihms Final Projec Repor Power Sysems Engineering Research Cener Empowering Minds o Engineer he Fuure Elecric Energy Sysem
Tesing and Validaion of Phasor Measuremen Based Devices and Algorihms Final Projec Repor Projec Team Anurag K Srivasava, Projec Leader Saugaa S Biswas, Graduae Suden Washingon Sae Universiy A. P. Sakis Meliopoulos Evangelos Polymeneas, Graduae Suden Yonghee Lee, Graduae Suden Georgia Insiue of Technology PSERC Publicaion 13-44 Sepember 2013
For informaion abou his projec, conac Anurag K Srivasava, Projec Leader Assisan Professor, The School of Elecrical Engineering and Compuer Science Direcor, Smar Grid Demonsraion and Research Invesigaion Lab SGDRIL) Energy Sysems Innovaion Cener ESIC) Washingon Sae Universiy 355 Spokane S, Pullman, Washingon 99164-2752 Phone: 509-335-2348 Fax: 509-335-3818 Email: asrivas@eecs.wsu.edu Power Sysems Engineering Research Cener The Power Sysems Engineering Research Cener PSERC) is a muli-universiy Cener conducing research on challenges facing he elecric power indusry and educaing he nex generaion of power engineers. More informaion abou PSERC can be found a he Cener s websie: hp://www.pserc.org. For addiional informaion, conac: Power Sysems Engineering Research Cener Arizona Sae Universiy 527 Engineering Research Cener Tempe, Arizona 85287-5706 Phone: 480-965-1643 Fax: 480-965-0745 Noice Concerning Copyrigh Maerial PSERC members are given permission o copy wihou fee all or par of his publicaion for inernal use if appropriae aribuion is given o his documen as he source maerial. This repor is available for downloading from he PSERC websie. 2013 Washingon Sae Universiy and Georgia Insiue of Technology All righs reserved.
Acknowledgemens This is he final repor for he Power Sysems Engineering Research Cener PSERC) research projec iled Tesing and Validaion of Phasor Measuremen Based Devices and Algorihms projec S -45). We express our appreciaion for he suppor provided by PSERC s indusry members and by he Naional Science Foundaion under he Indusry / Universiy Cooperaive Research Cener program. We wish o hank our indusry advisors for heir suppor and help: Jeff Fleeman American Elecric Power), Evangelos Faranaos Elecric Power Research Insiue), Floyd Galvan Energy), Jim Kleisch American Transmission Company), Xiaochuan Luo ISO New England), Bill Middaugh Tri-sae Generaion and Transmission), Reynaldo Nuqui ABB), George Sefopoulos New York Power Auhoriy), and Sanjoy Sarawgi American Elecric Power). Special hanks o Souhern California Ediion o provide inernship opporuniy relaed o PMU performance esing o Saugaa Biswas. We would also like o hank graduae sudens Jeong Kim and Hyojong Lee as well as an undergraduae suden Rory Becksorm a Washingon Sae Universiy for heir help in PMU and PDC esing. Addiionally, we are graeful o Schweizer Engineering Lab, General Elecric, ALSTOM, ERLphase, PONOVO and RTDS, Inc. for heir suppor. i
Execuive Summary For upgrading he radiional elecric power sysem o a smar power grid, i is essenial o make several enhancemens a various levels of operaion and conrol, which includes he inegraion of Inelligen Elecronic Devices IEDs), synchrophasor devices, advanced communicaion infrasrucure and efficien monioring and conrolling algorihms ha would make opimum use of hese devices. The even of Augus 14, 2003 blackou in he norh easern Unied Saes and pars of Canada ha affeced almos 50 million people emphasized he need for real ime siuaional awareness, and hus advocaed he use of synchrophasor devices in he power sysem. PMUs enable he wide area visualizaion of a power sysem in real ime by capuring high speed ime-samped snapshos in he form of volage and curren phasors, frequency and rae of change of frequency a he rae of up o 120 frames/second. This kind of ime samping allows he measuremens from differen geographical locaions o be ime-aligned or synchronized, hus providing a precise and comprehensive view of he enire sysem. Synchrophasor echnology enables a good indicaion of he saus or condiion of power grid in real ime. However, before puing he smar devices and algorihms in use in he acual power grid, i is of umos imporance o es and validae heir capabiliies as well as heir accuracy. The moive is o ensure high accuracy of measuremens from synchrophasor devices and he validaion of developed algorihms uilizing synchrophasors, under differen operaing scenarios of he power sysem. This research projec repor mainly focuses on following goals, a) esing and validaion of synchrophasor devices; b) esing of phasor based volage sabiliy and sae esimaion applicaions uilizing a real ime hardware-in-heloop HIL) es bed; and c) uilizaion of PMUs for advanced proecion schemes wih emphasis on dynamic proecion algorihms for ransformers. To achieve hese goals, he esing faciliy based on Real Time Digial Simulaor RTDS) a Washingon Sae Universiy WSU) and WinIGS-T a Georgia Insiue of Technology GIT) were boh upgraded o perform esing of synchrophasor devices and applicaions. For synchrophasor device esing, es sysems and also library of es condiions were developed o simulae sysem scenarios as specified in IEEE C37.118.1 sandard. Tesing for number of phasor measuremen unis PMUs) have been performed agains modeled sandard PMU. Tesing for sofware and hardware phasor daa concenraors PDCs) have been also performed agains limied number of performance crierion. For real ime esing and validaion of phasor based applicaions, we focused on volage sabiliy, sae esimaors and dynamic proecion algorihms for ransformers. These applicaions were simulaed in lab environmen for some example algorihms o check performance and find poenial problems before insalling in indusry grade power sysem. Synchrophasor Device Tesing Tes condiions for PMU s include a) nominal and off-nominal frequency; and b) wih and wihou harmonics, under balanced seady sae condiions while magniude, phase angle and frequency are changed wihin ranges as specified in he IEEE C37.118.1 sandard. For dynamic esing, es condiions include, a) magniude, angle and frequency ii
sep change; b) frequency ramp change; and c) ampliude, phase and frequency modulaion. The ess reveal ha he performance of he differen PMUs esed in lab are excellen under seady sae condiions and near nominal frequency. The esed PMUs mee he IEEE Sandard permissible error of oal vecor error. However under dynamic and off nominal frequency here is grea variabiliy among he various manufacurers and he errors can be quie high. All performance daa do no idenify he specific device esed. Also, oal vecor error TVE) for curren is generally higher han volage TVE and TVE is no he same for each phase. Frequency error FE) and rae of change in frequency ROCOF) error RFE) is wihin limis for mos of he cases. For dynamic esing example of one specific PMU, magniude sep change and angle sep change mees he requiremen of response ime and peak overshoo bu no he delay ime. For frequency sep change, requiremens for frequency response ime and peak overshoo are me bu no he ROCOF response ime and delay ime. For, frequency ramp change, requiremens are no me for FE and RFE. For, ampliude phase and frequency modulaion es, PMU fails all performance crierion esing. Tes resuls for PDC show ha he esed PDCs shows saisfacory response in aligning daa and daa validaion es was also successful for differen duraions and reporing rae of daa sreaming, collecion and archival. There is no daa loss, if PMU direcly sreams daa o a PDC wihou going hrough a complex communicaion nework. However, when he PMU sends daa o he PDC via communicaion neworks, here is considerable daa loss. Daa laency, daa rae conversion, forma conversion, phase/ magniude compensaion were found saisfacory for esed PDC s. Synchrophasor Applicaion Tesing The es bed was modified o perform real ime esing of volage sabiliy algorihms using real ime conrollers and real ime digial simulaors. Volage sabiliy algorihm esed in lab shows performance as expeced for line ouages and change in loading condiions. Sae esimaion algorihm is dynamic and perform very well wih ransformer inrush curren, over-exciaion and wih faul condiions. The seing-less proecion approach based on dynamic sae esimaion for he 3-phase ransformer has been proven o be a reliable mehod o proec he ransformer agains inernal fauls. I was shown ha he relay does no rip during normal operaing condiions or fauls ouside he proecion zone. On he oher hand, a rip is decided during he inernal faul. The simulaion resuls verify he heoreical analysis. The compuaion ime needed is wihin he requiremens of he daa acquisiion scheme. Oucomes of his projec include a) Se of sandard accuracy and performance ess for PMUs; b) An enhanced es bed o demonsrae operaion of phasor devices for research/ educaional purposes; c) Evaluaion of PMU based applicaions including volage sabiliy and sae esimaion in real ime; and d) Beer dynamic proecion algorihm for ransformer. iii
Performance resuls repored here for PMU and PDC can be used o guide evoluion of he sandards and o provide insigh for manufacurer. Tes resuls also shows need for addiional algorihms o filer ou bad daa for applicaions relaed o ransiens and dynamics as well as real ime conrol. Dynamic proecion algorihms for ransformer proecion can be incorporaed in new relays wih PMU capabiliy. Projec Publicaions: [1]. Saugaa S. Biswas, Jeong Hun Kim and Anurag K. Srivasava, Developmen of a Smar Grid Tes bed and Applicaions in PMU and PDC Tesing, in Norh American Power Symposium NAPS), Urbana, IL, Sepember 2012. [2]. Saugaa S. Biswas and Anurag K. Srivasava, Real ime Tesing and Validaion of Smar Grid Devices and Algorihms, in IEEE PES General Meeing, Vancouver, CA, July 2013. [3]. Saugaa S. Biswas and Anurag K Srivasava, A Novel Mehod for Disribued Real Time Volage Sabiliy Monioring Using Synchrophasor Measuremens, IREP Symposium, Rehymnon, Cree, Greece, June 2013. [4]. Saugaa S Biswas and Anurag K Srivasava, A fas Algorihm for Volage Sabiliy Monioring of Power Sysems wih Consideraion of Load Models, IEEE IAS Meeing, Orlando, FL, Ocober, 2013. [5]. Saugaa S. Biswas, Ceeman B. Vellaihurai and Anurag K. Srivasava, " Developmen and Real Time Implemenaion of a Synchrophasor based Fas Volage Sabiliy Monioring Algorihm wih Consideraion of Load Models," submied o IEEE Transacions for Indusrial Applicaions. [6]. Sakis Meliopoulos, George Cokkinides, Zhenyu Tan, Sungyun Choi, Yonghee Lee and Paul Myrda, "Seing-less Proecion: Feasibiliy Sudy", proceedings of HICSS 2013, Maui, HI, January 2013 [7]. A. P. Meliopoulos, E. Polymeneas, Zhenyu Tan, Renke Huang, and Dongbo Zhao, Advanced Disribuion Managemen Sysem, IEEE Transacions on Smar Grid, acceped. [8]. Sakis Meliopoulos, G. J. Cokkinides, S. Grijalva, R. Huang, E. Polymeneas, Paul Myrda, Evangelos Faranaos, Mel Gehrs, Inegraion & Auomaion: From Proecion o Advanced Energy Managemen Sysems, IREP Symposium, Rehymnon, Cree, Greece, June 2013. Suden Theses: [1]. Saugaa Biswas, Developmen and validaion of real ime monioring and conrol algorihms for power sysem, Ph.D. hesis, Washingon Sae Universiy, May 2014. [2]. Yonghee Lee, Comprehensive Proecion Schemes of a Microgrid and Disribuion Sysems, Ph.D. hesis, Georgia Insiue of Technology, in progress. [3]. Sefan Nwoku, Dynamic Transformer Proecion: a Novel Approach Using Sae Esimaion, Georgia Insiue of Technology, Augus 2012. iv
Table of Conens 1. Inroducion... 1 1.1 Background... 1 1.2 Projec Objecives and Overview... 1 1.3 Repor Organizaion... 2 2. Synchrophasor Device Tesing... 3 2.1 RTDS Based Tesing Faciliy... 3 2.2.1 Descripion... 3 2.2.2 PMU Tesing... 4 2.2.3 PDC Tesing... 26 2.2 WinIGS-T based Tesing Faciliy... 35 2.2.3 Descripion... 35 2.2.4 PMU Tesing... 36 3 Validaion and Tesing of Synchrophasor Applicaions... 52 3.1 Volage Sabiliy Algorihms Based on Synchrophasor Daa... 52 3.1.1 Inroducion o Volage Sabiliy... 52 3.1.2 Tesbed for performing online simulaion of volage sabiliy algorihms... 53 3.1.3 Performance of online simulaions of volage sabiliy algorihm... 58 3.1.4 Conclusion from Tes Resuls... 66 3.2 Comparing Sae Esimaion Algorihms Using Synchrophasor Daa... 67 3.3 Dynamic Sae Esimaion Based Proecion Algorihms for Transformers... 70 3.3.1 Descripion of he approach... 70 3.3.2 Transformer Seing-less Proecion Approach Descripion... 72 3.3.3 Proecion Logic... 81 3.3.4 Transformer Seing-less proecion resuls... 83 3.3.5 Conclusions on DSE Based Transformer Proecion... 99 4 Conclusions and Fuure Research Direcion... 100 4.1 Conclusions... 100 4.2 Fuure Research Direcions... 101 References... 103 v
Lis of Figures Figure 2.1: Tes bed a Washingon Sae Universiy... 3 Figure 2.2: Example of a draf case for simulaing a PMU es condiion... 5 Figure 2.3: Example of RSCAD run case for obaining es measuremens... 6 Figure 2.4: Example of daa archival in sofware PDC... 7 Figure 2.5: Tes condiions for magniude change balanced, nominal)... 9 Figure 2.6: Error analysis for magniude change balanced, nominal)... 10 Figure 2.7: Tes condiions for magniude change balanced, off-nominal)... 11 Figure 2.8: Error analysis for magniude change balanced, off-nominal)... 11 Figure 2.9: Tes condiions for magniude change harmonics, nominal)... 12 Figure 2.10: Error analysis for magniude change harmonics, nominal)... 13 Figure 2.11: Tes condiions for magniude change harmonics, off-nominal)... 14 Figure 2.12: Error analysis for magniude change harmonics, off-nominal)... 14 Figure 2.13: Tes condiions for angle change balanced, nominal)... 15 Figure 2.14: Error analysis for angle change balanced, nominal)... 16 Figure 2.15: Tes condiions for angle change harmonics, nominal)... 17 Figure 2.16: Error analysis for angle change harmonics, nominal)... 18 Figure 2.17: Tes condiions for frequency change balanced)... 18 Figure 2.18: Error analysis for frequency change balanced)... 19 Figure 2.19: Tes condiions for frequency change balanced, harmonics)... 20 Figure 2.20: Error analysis for frequency change balanced, harmonics)... 20 Figure 2.21: Response during sep change in volage magniude... 21 Figure 2.22: Response during sep change in volage angle... 22 Figure 2.23: Response during sep change in frequency... 23 Figure 2.24: Response during ramp change in frequency... 24 Figure 2.25: Dynamic es condiions for change in modulaed signal... 25 Figure 2.26: Error analysis of he es PMU under given sysem condiion... 25 Figure 2.27: Tes bed for esing PDCs wihou communicaion modeling... 30 Figure 2.28: Tes bed for esing PDCs wih communicaion model... 30 Figure 2.29: Hardware configuraion for esing GPS-synchronized IEDs/ PMU... 37 Figure 2.30: Schemaic of sofware archiecure for GPS-synchronized IED esing... 38 Figure 2.31: Daa acquisiion sysem block diagram... 38 vi
Figure 2.32: Laboraory seup for PMU esing... 39 Figure 2.33: Laboraory seup for PMU esing... 39 Figure 2.34: Illusraion of Toal Vecor Error TVE)... 40 Figure 2.35: Illusraion of iming error measuremen... 41 Figure 2.36: Illusraion of phase error measuremen... 43 Figure 2.37: Tes B-1: Frequency ramp, no harmonics... 48 Figure 3.1: Smar grid es bed for simulaion of volage sabiliy algorihm... 57 Figure 3.2: Funcional block diagram for simulaion of volage sabiliy algorihm... 59 Figure 3.3: IEEE-14 bus es case modeled in RSCAD for real ime simulaion... 60 Figure 3.4: RSCAD volage magniude changes a Bus-12 for IEEE 14 bus... 61 Figure 3.5: RSCAD showing angle changes a Bus-12 for IEEE 14 bus... 61 Figure 3.6: VSAI leading o volage collapse from = 0 s o = 85 s... 62 Figure 3.7: IEEE-30 bus es case modeled in RSCAD for real ime simulaion... 63 Figure 3.8: RSCAD showing volage magniude changes a bus-30 for IEEE 30 bus... 64 Figure 3.9: RSCAD showing angle changes a bus-30 for IEEE 30 bus... 65 Figure 3.10: VSAI leading o volage collapse from = 0 s o = 95 s... 65 Figure 3.11: Fracional sample inegraion... 68 Figure 3.12: Quadraic approximaion of a funcion from hree successive samples... 69 Figure 3.13: Sandard PMU algorihm performance... 69 Figure 3.14: Archiecure of he dynamic sae esimaion based proecive relay... 70 Figure 3.15: Illusraion of ime samples for ieraion of he seing-less relay... 71 Figure 3.16: Overall algorihm of sae esimaion... 82 Figure 3.17: Tes scheme for verifying he proposed proecion mehod... 83 Figure 3.18: Tes sysem for he seing-less proecion... 84 Figure 3.19: Seings of he hree-phase ransformer under proecion... 84 Figure 3.20: Measuremen signals of he ransformer Tes A: normal operaion)... 85 Figure 3.21: Measuremen signals of he ransformer Tes B: energizaion)... 86 Figure 3.22: Measuremen signals of he ransformer Tes C: overexciaion)... 87 Figure 3.23: Faul locaion in he es sysem es D: hrough faul)... 88 Figure 3.24: Measuremen signals of he ransformer Tes D: hrough faul)... 88 Figure 3.25: Faul locaion in he es sysem Tes E: inernal faul)... 89 Figure 3.26: Measuremen signals of he ransformer Tes E: inernal faul)... 89 Figure 3.27: Confidence level of he DSE Tes A: normal operaion)... 90 vii
Figure 3.28: Curren measuremens, esimaed values, and confidence level Tes A)... 90 Figure 3.29: Volage measuremens, esimaed values, and confidence level Tes A).. 91 Figure 3.30: Confidence level of he DSE Tes B: ransformer energizaion)... 92 Figure 3.31: Curren measuremens, esimaed values, and confidence level Tes B)... 92 Figure 3.32: Volage measuremens, esimaed values, and confidence level Tes B)... 93 Figure 3.33: Confidence level of he DSE Tes C: ransformer overexciaion)... 94 Figure 3.34: Curren measuremens, esimaed values, and confidence level Tes C)... 94 Figure 3.35: Volage measuremens, esimaed values, and confidence level Tes C)... 95 Figure 3.36: Confidence level of he DSE Tes D: hrough faul)... 95 Figure 3.37: Curren measuremens, esimaed values, and confidence level Tes D)... 96 Figure 3.38: Volage measuremens, esimaed values, and confidence level Tes D).. 97 Figure 3.39: Confidence level of he DSE Tes E: inernal faul)... 97 Figure 3.40: Curren measuremens, esimaed values, and confidence level Tes E)... 98 Figure 3.41: Volage measuremens, esimaed values, and confidence level Tes E)... 99 viii
Lis of Tables Table 2.1: Library of es condiions for PMU esing... 5 Table 2.2: Tes resuls for response o magniude sep change... 22 Table 2.3: Tes resuls for response o angle sep change... 22 Table 2.4: Tes resuls for response o frequency sep change... 23 Table 2.5: Tes resuls for response o frequency ramp change... 24 Table 2.6: Library of PDC ess... 29 Table 2.7: Tes resuls for ime alignmen rae = 30 frames / second)... 31 Table 2.8: Tes resuls for ime alignmen rae = 60 frames / second)... 31 Table 2.9: Tes resuls for daa validaion rae = 30 frames / second)... 31 Table 2.10: Tes resuls for daa validaion dae = 60 frames / second)... 32 Table 2.11: Tes resuls for daa loss rae = 30 frames / second)... 32 Table 2.12: Tes resuls for daa loss rae = 60 frames / second)... 32 Table 2.13: Tes resuls for daa loss wih nework rae = 60 frames / second)... 33 Table 2.14: Tes resuls for daa laency... 33 Table 2.15: Tes resuls for repor rae conversion 60 o 30)... 33 Table 2.16: Tes resuls for repor rae conversion 30 o 60)... 34 Table 2.17: Tes resuls for forma & coordinae conversion polar o recangular)... 34 Table 2.18: Tes resuls for forma & coordinae conversion recangular o polar)... 34 Table 2.19: Phase angle adjusmen +5 degrees)... 34 Table 2.20: Phase angle adjusmen -5 degrees)... 35 Table 2.21: Magniude adjusmen +5%)... 35 Table 2.22: Magniude adjusmen -5%)... 35 Table 2.23: Tes condiions for seady sae performance... 45 Table 2.24: Tes condiions for frequency ramp es... 46 Table 2.25: Tes condiions for volage magniude es... 46 Table 2.26: Tes condiions for volage magniude sep change... 47 Table 2.27: Tes condiions for curren magniude... 47 Table 2.28: Tes condiions for volage and curren imbalance ess... 48 Table 2.29: Performance evaluaion - individual phase analysis - es signals A... 49 Table 2.30: Performance evaluaion - posiive sequence - es signals A... 50 Table 2.31: Performance evaluaion - individual phase analysis - es signals B... 51 ix
Table 2.32: Performance evaluaion - posiive sequence - es signals B... 51 Table 3.1: Series of evens leading o volage collapse in IEEE-14 bus es case... 60 Table 3.2: VSAI in real ime for each even leading o volage collapse... 62 Table 3.3: Propagaion delays beween subsaions and conrol cener... 63 Table 3.4: Series of evens leading o volage collapse in IEEE-30 bus es case... 64 Table 3.5: VSAI compued in real ime for each even leading o volage collapse... 66 Table 3.6: Propagaion delays beween subsaions and conrol cener for 30 bus... 66 Table 3.7: Phase error a sampling rae of 8 KHz... 69 Table 3.8: All sae variables of he hree-phase ransformer n = 5)... 73 Table 3.9: Acual across measuremens for he hree-phase ransformer... 76 Table 3.10: Acual hrough measuremens for he hree-phase ransformer... 77 Table 3.11: Virual measuremens for he hree-phase ransformer... 78 Table 3.12: Pseudo measuremens for he hree-phase ransformer... 80 Table 3.13: Transformer parameers idenical a all phases)... 85 x
1. Inroducion 1.1 Background Implemenaion of he fuure smar grid requires adoping number of new echnologies including inegraion of phasor based devices and new algorihms o uilize synchrophasor daa for various applicaions. These newly developed phasor based applicaions need o be validaed before acual implemenaion. In order o properly evaluae he applicaions, i is imporan o characerize he phasor measuremen unis PMUs) and he qualiy of daa obained wih he PMUs. Tesing of phasor based devices including PMUs and phasor daa concenraors PDCs) for echnical performance are required before insalling in real world applicaion. Uiliies need o assure he reliable operaion of PMUs wih high daa qualiy before hey will inves heavily in hem. PMU daa qualiy is criical especially for conrol applicaions. The updaed Synchrophasor sandard IEEE C37.118.1-2011 released in 2011) defines he requiremens for he PMU measuremens in erms of he seady sae performance evaluaion quaniies like Toal Vecor Error TVE), Frequency Error FE) and Rae of change of Frequency Error RFE), and dynamic evaluaion quaniies like peak overshoo, response ime and delay ime [1, 2]. The sandard specifies es condiions ha include various ranges of signal frequency, magniude and phase angle, as well as levels of harmonic disorion. Norh American Synchro Phasor Iniiaive NASPI) [3] has also addressed he issue of PMU esing o help wih developing echnical guidelines and educaional documens. There are oher parallel effors by researchers, bu PMU applicaions and devices have been evolving over he years and need o be esed wih new developmens. 1.2 Projec Objecives and Overview This research projec mainly focuses on a) esing of phasor devices like PMUs and PDCs; b) esing and validaion of phasor based volage sabiliy and sae esimaion applicaions uilizing an exising real ime hardware-in-he-loop HIL) es bed; and c) uilizaion of PMUs for advanced proecion schemes wih emphasis on dynamic proecion algorihms for ransformers. Two proposed es beds have been uilized, one based on he Real Time Digial Simulaor RTDS) a WSU [4, 5] and anoher based on a digial simulaor WinIGS-T) a GIT. Boh es beds uilize addiional hardware and sofware ools including Phasor Measuremen Unis PMUs), amplifiers, Synchrophasor Vecor Processor SVP), Phasor Daa Concenraors PDC) and Hisorians. Volage sabiliy and sae esimaion algorihms based on PMU daa have been addressed in several publicaions bu here is need for real ime validaion before implemenaion. Dynamic proecion algorihms are in heir infancy - ye hey offer grea promise o provide robus, reliable proecion schemes for he mos difficul proecion problems. The use of PMUs for dynamic proecion algorihms for ransformer proecion has been invesigaed in his projec. Transformer proecion is he bes candidae o es dynamic 1
proecion algorihms since inrush currens in ransformers have been known o impose compromises in differenial ransformer proecion. For insance, he many excellen schemes o deal wih inrush currens in ransformer proecion: he algorihms and hardware for idenifying inrush currens are no fully reliable or accurae and as a resul he seings are normally desensiized, proecion acion is delayed and ransformers are subjeced o abnormal condiions longer han necessary. I is generally acceped ha dynamic proecion algorihms have he capaciy o provide more robus, highly selecive and reliable algorihms. This projec provides several poenial benefis including a) Beer dynamic proecion algorihm for ransformer; b) Se of sandard accuracy and performance ess for PMUs and a guide for PMU real ime applicaions resuling in cos reducion and verifiable operaional performance; c) An enhanced es bed o demonsrae operaion of phasor devices for educaional purposes; and d) Evaluaion of PMU based applicaions including volage sabiliy and sae esimaion in real ime. Improved es bed can be used for educaional/ research purpose. 1.3 Repor Organizaion This repor has been organized in four secions. Secion 1 provides inroducion, projec objecives and overview of he problem. Secion 2 provides deails for esing of phasor measuremen devices and phasor daa concenraor using he enhanced es bed a WSU and GIT. Secion 3 presens es resuls for esing and validaion of hree differen phasor applicaions for volage sabiliy, sae esimaion and dynamic proecion. Secion 4 concludes he repor. 2
2. Synchrophasor Device Tesing 2.1 RTDS Based Tesing Faciliy 2.2.1 Descripion Real Time Digial Simulaor RTDS) is a power sysem simulaor ha simulaes a power sysem buil in RSCAD user inerface sofware in real ime. The RTDS works on he parallel processing echnology of digial signal processors and execues he program developed on is processors. The RTDS no only calculaes and shows he elecrical oupu values in he runime sofware, bu also produces scaled oupu signals digial as well as analog) hrough he oupu inerface cards incorporaed ino is sysem. Figure 2.1: Tes bed a Washingon Sae Universiy The RTDS faciliy insalled a he Smar Grid Demonsraion & Research Invesigaion Lab SGDRIL), WSU, consiss of one rack wih hree Giga Processor Cards GPCs) and wo PB5 Cards for processing required compuaions in real ime. Oher componens include: a) One Giga Transceiver Worksaion Inerface Card GTWIF) for inerfacing he RSCAD user sofware wih he GPC cards of he RTDS; b) one Giga Transceiver Digial Inpu Card GTDI) for aking in inpu digial signals from exernal devices like PMU/ relays; c) one Giga Transceiver Fron Panel Inerface card GTFPI) for aking in 3
inpu digial signals and giving ou oupu digial signals from and o hardware devices like relays; d) hree Giga Transceiver Analog Oupu Card GTAO) for providing analog oupu signals o hardware devices like PMUs for measuring elecrical quaniies; e) one Giga Transceiver Analog Inpu Card GTAI) for aking in analog inpu signals from hardware devices; f) one Giga Transceiver Nework Inerface Card GTNET) for inerfacing a number of differen nework proocols wih he RTDS simulaor; and g) one Giga Transceiver Synchronizaion Card GTSYNC) for synchronizing he RTDS simulaion ime sep o an exernal ime reference like he GPS clock. Addiionally, es bed consiss of number of PMU devices, phasor daa concenraors PDCs), synchrophasor vecor processors SVP), conrollers, and amplifiers. Fig. 2.1 shows he lab seup a WSU. 2.2.2 PMU Tesing 2.1.2.1 Inroducion PMUs enable he wide area visualizaion of a power sysem in real ime by capuring high speed ime-samped snapshos in he form of volage and curren phasors, frequency and rae of change of frequency a he rae of 30/60/120 Frames / second [6]. This kind of ime samping allows he measuremens from differen geographical locaions o be ime-aligned or synchronized, hus providing a precise and comprehensive view of he enire sysem. Hence, synchrophasor echnology enables a good indicaion of he saus or condiion of power grid in real ime. However, before puing he smar devices and algorihms in use in he acual power grid, i is of umos imporance o es and validae heir capabiliies as well as heir accuracy. The moive is o ensure high reliabiliy and accuracy of hese devices and he developed algorihms, under differen operaing scenarios of he power sysem. 2.1.2.2 Library of Tes Condiions IEEE Sandard for Synchrophasors C37.118-2011 [7] is he laes sandard ha provide he PMU performance conformance es deails. This Sandard has been divided ino wo pars - C37.118.1 and C37.118.2, where he former specifies he ess required for PMU measuremen performance conformance, while he laer specifies he ess required for PMU communicaion performance conformance. In his projec, he PMU measuremen performance ess have been performed as menioned in IEEE C37.118.1). Also addiional ess ha are no in he presen sandard have been performed, keeping in mind some of he realisic sysem condiions in which he PMUs are supposed o operae when deployed in subsaions. Thus, he specially designed es library performs a comprehensive performance analysis of he PMUs. The library of es condiions has been creaed in he RTDS using es case as shown in fig. 2.2. Individual es cases have been creaed in he RTDS Draf case so as o generae he es signals. The ideal PMU is he GTNET PMU available in he RTDS. The draf case is se up in such a way he es PMU is conneced o he same bus as ha of he GTNET PMU, so ha boh he PMUs ge he same measuremens as heir inpus. 4
Figure 2.2: Example of a draf case for simulaing a PMU es condiion Main Caegory of PMU Tesing Seady Sae Tess Dynamic Tess Table 2.1: Library of es condiions for PMU esing Quaniies Changed during Tesing Volage & Curren Magniude Sysem Condiions during Tesing PMU Performance Evaluaion Parameers TVE, FE, RFE TVE, FE, RFE Sysem is balanced Sysem is a off-nominal frequency Sysem has harmonics TVE, FE, RFE Sysem is a off-nominal TVE, FE, RFE frequency and has harmonics Volage & Curren Sysem is balanced TVE, FE, RFE Angle Sysem has harmonics TVE, FE, RFE Frequency Sysem is balanced TVE, FE, RFE Sysem has harmonics TVE, FE, RFE Volage Magniude Sysem is balanced, a nominal Response Time, Sep frequency, wihou harmonics Delay Time, Volage Angle Sep Frequency Sep Frequency Ramp Ampliude, Phase & Frequency Modulaion Sysem is balanced, a nominal frequency, wihou harmonics Sysem is balanced, a nominal frequency, wihou harmonics Sysem is balanced, a nominal frequency, wihou harmonics Sysem is balanced, a nominal frequency, wihou harmonics % Peak Overshoo Response Time, Delay Time, % Peak Overshoo Frequency Response Time, ROCOF Response Time, Delay Time, % Peak Overshoo FE, RFE TVE, FE, RFE 5
The able 2.1 shows he library of es condiions used for analyzing he performance of PMUs. I can be seen from he able 2.1 ha he PMU esing has been broadly classified as seady sae ess and dynamic ess. The basic ess menioned in he IEEE C37.118.1 Sandard have been performed, in addiion o which he ess have been performed under varying sysem condiions. I is imporan o es he PMU wih parameer changes under differen condiions, especially during he seady sae performance analysis, as i is of umos imporance o analyze he behavior of he PMU under such realisic sysem condiions, for insance volage and curren magniude changing when harmonics are presen a off-nominal frequency condiions. The ranges of parameer or quaniy variaion as menioned in he 2nd column of able 2.1) and he hresholds of performance evaluaion crieria as menioned in he 4h column of able 2.1) have been nearly kep he same as ha menioned in he sandard. The change of sysem parameers or quaniies) has been scriped in RTDS Runime as shown in fig. 2.3. Figure 2.3: Example of RSCAD run case for obaining es measuremens 2.1.2.3 Performance of PMU Tesing Once he library of PMU es condiions is creaed in he RSCAD-RTDS, he PMU esing is performed in several sages. These include he following Sep-1: Running he individual es cases in he RTDS The RTDS draf case has he GTNET PMU conneced in such a way ha i ges he same inpu measuremens as he es PMU. The es PMU ges he low level analog signals from he GTAO card of he RTDS. The GTAO card in urn ges he same inpu measuremens as obained by he GTNET PMU. Wih his configuraion, individual scrip files have been wrien in he RTDS ha keep changing he quaniies and 6
parameers auomaically as menioned in able 2.1. These measuremens obained by running he es cases are fed ino he GTNET PMU and he es PMU. Sep-2: Collecing he daa of he individual es cases in he PDC from he PMUs A PDC SEL-5073) has been used o collec all he es daa of seady sae ess and dynamic ess from he PMU under es and he ideal PMU i.e. he GTNET PMU in he RTDS) as shown in fig. 2.4. Following are he daa ha are archived in he PDC for he es PMUs and he GTNET PMU -> Time Samp in he PMU -> Volage Magniude of Phase A measured by he PMU -> Volage Angle of Phase A measured by he PMU -> Volage Magniude of Phase B measured by he PMU -> Volage Angle of Phase B measured by he PMU -> Volage Magniude of Phase C measured by he PMU -> Volage Angle of Phase C measured by he PMU -> Curren Magniude of Phase A measured by he PMU -> Curren Angle of Phase A measured by he PMU -> Curren Magniude of Phase B measured by he PMU -> Curren Angle of Phase B measured by he PMU -> Curren Magniude of Phase C measured by he PMU -> Curren Angle of Phase C measured by he PMU -> Frequency measured by he PMU -> ROCOF measured by he PMU Figure 2.4: Example of daa archival in sofware PDC 7
Sep-3: Analysis of he daa of he individual es cases based on IEEE-C37.118.1 Sandard Once all he daa is archived in he PDC, his archived daa is analyzed o find he conformance of he es PMU o he Sandard requiremens. The performance evaluaion parameers for each es as menioned in able 2.1) are compued for he es daa analysis as per he formulae menioned in he Sandard. Following is a brief descripion of hese performance evaluaion parameers - a) Toal Vecor Error TVE) - Where, X n) r and X ı n) are he sequences of esimaes given by he es PMU, and Xrn) and Xin) are he sequences of values of he measuremens a he insans of ime n) read by he ideal PMU GTNET PMU). b) Frequency Error FE) - Where, f rue is he frequency measured by he ideal PMU GTNET PMU), and f measured is he frequency measured by he ideal PMU. c) Rae of Change of Frequency or ROCOF Error RFE) - Where, df ) d rue is he ROCOF measured by he ideal PMU GTNET PMU), and df is he ROCOF measured by he es PMU. d ) rue d) Measuremen Response Time - Measuremen response ime is he ime o ransiion beween wo seady-sae measuremens before and afer a sep change is applied o he inpu. I shall be deermined as he difference beween he ime ha he measuremen leaves a specified accuracy limi and he ime i reeners and says wihin ha limi when a sep change is applied o he PMU inpu. This shall be measured by applying a posiive or negaive sep change in phase or magniude or frequency o he PMU inpu signal. The inpu signal shall be held a a seady-sae condiion before and afer he sep change. The only inpu signal change during his es shall be he parameer ha have been sepped. e) Measuremen Delay Time - Measuremen delay ime is defined as he ime inerval beween he insan ha a sep change is applied o he inpu of a PMU and measuremen ime ha he sepped parameer achieves a value ha is halfway beween he iniial and final seady-sae values. Boh he sep ime and measuremen ime are measured on he UTC ime scale. This measuremen shall be deermined by applying a posiive or negaive sep change in phase or magniude or frequency o he PMU inpu signal. The inpu signal shall be held 8
a a seady-sae condiion before and afer he sep change. The only inpu signal change during his es shall be he parameers) ha have been sepped. f) Peak Overshoo - This is he maximum value by which he measured value exceeds he final seady sae value when a posiive sep change is applied in phase or magniude or frequency o he PMU inpu signal. The inpu signal shall be held a a seady-sae condiion before and afer he sep change. The only inpu signal change during his es shall be he parameers) ha have been sepped. 2.1.2.4 Conclusion from Tes Resuls All he ess menioned in able 2.1 have been performed on PMUs from differen vendors. The naure of PMU behavior are mosly he same qualiaively amongs hose esed. In his secion, he es condiions and resuls of 1 es PMU "PMU-A" have been discussed, which is a qualiaive represenaion of he oher PMUs ha have been esed. Example of sysem es condiions in RSCAD is shown in fig. 2.5. A) Discussion on Seady Sae Tess - Volage & Curren Magniude Change during balanced sysem condiions: Figure 2.5: Tes condiions for magniude change balanced, nominal) 9
Figure 2.6: Error analysis for magniude change balanced, nominal) From fig. 2.6, when he sysem is balanced and is a nominal frequency wihou harmonics, following observaions can be made - i) The volage TVEs of all he 3 phases are much lesser han he hreshold value of 1%. ii) The volage TVEs of all he 3 phases are no he same. iii) The curren TVEs of all he 3 phases are very high above 1%) when he PMU measures curren phasors far below he nominal curren value. Gradually, as he curren measuremen approaches he nominal value, he TVEs decrease and go below he permissible hreshold of 1%. iv) The curren TVEs of all he 3 phases are no he same. v) On he whole, curren TVEs are found o be significanly higher han he volage TVEs. vi) FE is much below he permissible hreshold value. vii) RFE is also much below he allowed hreshold value. 10
Volage & Curren Magniude Change under Off-nominal sysem frequency condiions: Figure 2.7: Tes condiions for magniude change balanced, off-nominal) Figure 2.8: Error analysis for magniude change balanced, off-nominal) 11
Fig. 2.7 shows sysem es condiion in RTDS. As shown in fig. 2.8, when he sysem is balanced and is a off-nominal frequency 58 Hz) wihou harmonics, following observaions can be made - i) The volage TVEs of all he 3 phases are higher han he hreshold value of 1%. ii) The volage TVEs of all he 3 phases are no he same. iii) The curren TVEs of all he 3 phases are very much higher han he allowed hreshold of 1%. iv) The curren TVEs of all he 3 phases are no he same. v) On he whole, curren TVEs are found o be significanly higher han he volage TVEs. vi) FE is much below he permissible hreshold value, bu is a lile higher han he es condiion when he sysem frequency was a nominal value. vii) RFE is higher han he es case when he sysem frequency was a nominal value. I can be seen ha a some poin, he RFE also has exceeded he allowed hreshold value. Volage & Curren Magniude Change under when harmonics 3rd, 5h, 7h, and 9h orders) exis in he sysem: Figure 2.9: Tes condiions for magniude change harmonics, nominal) 12
Figure 2.10: Error analysis for magniude change harmonics, nominal) Fig. 2.9 shows he es condiions and fig. 2.10 shows error analysis. When he sysem is balanced and is a nominal frequency wih harmonics, following observaions can be made- i) The volage TVEs of all he 3 phases are much lesser han he hreshold value of 1%. ii) The volage TVEs of all he 3 phases are no he same. iii) The curren TVEs of all he 3 phases are very high above 1%) when he PMU measures curren phasors far below he nominal curren value. Gradually, as he curren measuremen approaches he nominal value, he TVEs decrease and go below he permissible hreshold of 1%. iv) The curren TVEs of all he 3 phases are no he same. v) On he whole, curren TVEs are found o be significanly higher han he volage TVEs. vi) FE is much below he permissible hreshold value. If a comparison is made wih he es cases when harmonics are no presen, i has been seen ha he average FE is much higher when harmonics are presen. This is an expeced behavior, because of which he IEEE Sandard has also increased he permissible hreshold value of FE when harmonics are presen. vii) RFE is also much below he allowed hreshold value. If a comparison is made wih he es cases when harmonics are no presen, i has been seen ha he average RFE is much higher when harmonics are presen. This is also an expeced behavior, because of which he IEEE Sandard has also increased he permissible hreshold value of RFE when harmonics are presen. 13
Volage & Curren Magniude Change under Off-nominal sysem frequency condiions when harmonics are also presen: Figure 2.11: Tes condiions for magniude change harmonics, off-nominal) Figure 2.12: Error analysis for magniude change harmonics, off-nominal) 14
Based on es condiion of fig. 2.11, and fig. 2.12, when he sysem is balanced and is a off-nominal frequency wih harmonics, following observaions can be made - i) The volage TVEs of all he 3 phases are higher han he hreshold value of 1%. ii) The volage TVEs of all he 3 phases are no he same. iii) The curren TVEs of all he 3 phases are very much higher han he allowed hreshold of 1%. iv) The curren TVEs of all he 3 phases are no he same. v) On he whole, curren TVEs are found o be significanly higher han he volage TVEs. vi) FE is much below he permissible hreshold value. If a comparison is made wih he es cases when harmonics are no presen, i has been seen ha he average FE is much higher when harmonics are presen. This is an expeced behavior, because of which he IEEE Sandard has also increased he permissible hreshold value of FE when harmonics are presen. vii) RFE is also much below he allowed hreshold value. If a comparison is made wih he es cases when harmonics are no presen, i has been seen ha he average RFE is much higher when harmonics are presen. This is also an expeced behavior, because of which he IEEE Sandard has also increased he permissible hreshold value of RFE when harmonics are presen. viii) Amongs all he es condiions discussed above when he volage and curren magniudes are changed, he performance of he PMU deerioraes he mos when he sysem is a off-nominal frequency and also has harmonics. Volage & Curren Angle Change under balanced sysem condiions: Figure 2.13: Tes condiions for angle change balanced, nominal) 15
Figure 2.14: Error analysis for angle change balanced, nominal) From fig. 2.13 and fig. 2.14, when he sysem is balanced and is a nominal frequency wihou harmonics, following observaions can be made i) The volage TVEs of all he 3 phases are much lesser han he hreshold value of 1%. ii) The volage TVEs of all he 3 phases are no he same. iii) The curren TVEs of all he 3 phases are lesser han he permissible hreshold of 1%. iv) The curren TVEs of all he 3 phases are no he same. v) On he whole, curren TVEs are found o be higher han he volage TVEs. vi) FE is much below he permissible hreshold value. vii) RFE is also much below he allowed hreshold value. Volage & Curren Angle Change under when harmonics 3rd, 5h, 7h, and 9h orders) exis in he sysem: From fig. 2.15 and 2.16 when he sysem is balanced and is a nominal frequency wih harmonics, following observaions can be made i) The volage TVEs of all he 3 phases are much lesser han he hreshold value of 1%. ii) The volage TVEs of all he 3 phases are no he same. iii) The curren TVEs of all he 3 phases are very high above 1%) irrespecive of he curren magniude. iv) The curren TVEs of all he 3 phases are no he same. 16
v) On he whole, curren TVEs are found o be significanly higher han he volage TVEs. vi) FE is much below he permissible hreshold value. If a comparison is made wih he es cases when harmonics are no presen, i has been seen ha he average FE is much higher when harmonics are presen. This is an expeced behavior, because of which he IEEE Sandard has also increased he permissible hreshold value of FE when harmonics are presen. vii) RFE is also below he allowed hreshold value. If a comparison is made wih he es cases when harmonics are no presen, i has been seen ha he average RFE is much higher when harmonics are presen. This is also an expeced behavior, because of which he IEEE Sandard has also increased he permissible hreshold value of RFE when harmonics are presen. Figure 2.15: Tes condiions for angle change harmonics, nominal) 17
Figure 2.16: Error analysis for angle change harmonics, nominal) Frequency Change under balanced sysem condiions: Figure 2.17: Tes condiions for frequency change balanced) 18
Figure 2.18: Error analysis for frequency change balanced) Based on es condiions in fig. 2.17 and error analysis from fig. 2.18, when he sysem is balanced wihou harmonics, following observaions can be made - i) The volage TVEs of all he 3 phases are much lesser han he hreshold value of 1% when he sysem is a nominal frequency 60 Hz). However, as he sysem frequency moves away from he nominal value boh, above and below, he TVEs sar increasing rapidly. I can be seen ha a 58 Hz and 62 Hz, he volage TVEs exceed he hreshold value of 1%. ii) The volage TVEs of all he 3 phases are no he same. iii) The curren TVEs of all he 3 phases are lesser han he hreshold value of 1% when he sysem is a nominal frequency 60 Hz). However, as he sysem frequency moves away from he nominal value boh, above and below, he TVEs sar increasing rapidly. I can be seen ha a 58 Hz and 62 Hz, he curren TVEs exceed he hreshold value of 1%. iv) The curren TVEs of all he 3 phases are no he same. v) On he whole, curren TVEs are found o be higher han he volage TVEs. vi) FE is much below he permissible hreshold value. vii) RFE is also below he allowed hreshold value. 19
Figure 2.19: Tes condiions for frequency change balanced, harmonics) Figure 2.20: Error analysis for frequency change balanced, harmonics) 20
From fig. 2.19 and fig. 2.20, when he sysem is balanced wih harmonics, following observaions can be made - i) The volage TVEs of all he 3 phases are much lesser han he hreshold value of 1% when he sysem is a nominal frequency 60 Hz). However, as he sysem frequency moves away from he nominal value boh, above and below, he TVEs sar increasing rapidly. I can be seen ha a 58 Hz and 62 Hz, he volage TVEs exceed he hreshold value of 1%. ii) The volage TVEs of all he 3 phases are no he same. iii) The curren TVEs of all he 3 phases are mosly higher han he hreshold value of 1% and are quie random independen of he frequency values unlike volage TVEs. iv) The curren TVEs of all he 3 phases are no he same. v) On he whole, curren TVEs are found o be higher han he volage TVEs. vi) FE is much below he permissible hreshold value. vii) RFE is also below he allowed hreshold value. B) Discussion on Dynamic Tess - Volage Magniude Sep Change: Figure 2.21: Response during sep change in volage magniude Following are he analyical resuls of he PMU performance during he sep change in volage magniude fig. 2.21) - 21
Table 2.2: Tes resuls for response o magniude sep change Evaluaion Parameers Resuls of he Tes PMU Allowable Values as per IEEE-C37.118.1 Response Time in seconds) 0.093 0.182 Delay Time in seconds) 0.065 0.008 % Peak Overshoo 0.279 10 From he resuls able 2.2, i can be seen ha he PMU under es - i) Mees he requiremen of response ime. ii) Does no mee he requiremen of delay ime iii) Mees he requiremen of % peak overshoo Volage Angle Sep Change: Figure 2.22: Response during sep change in volage angle Table 2.3: Tes resuls for response o angle sep change Evaluaion Parameers Resuls of he Tes PMU Allowable Values as per IEEE-C37.118.1 Response Time in seconds) 0.113 0.182 Delay Time in seconds) 0.045 0.008 % Peak Overshoo 2.561 10 22
From he resuls as shown in fig. 2.22 and able 2.3, i can be seen ha he PMU under es- i) Mees he requiremen of response ime. ii) Does no mee he requiremen of delay ime iii) Mees he requiremen of % peak overshoo Frequency Sep Change: Figure 2.23: Response during sep change in frequency Table 2.4: Tes resuls for response o frequency sep change Evaluaion Parameers Resuls of he Tes PMU Allowable Values as per IEEE-C37.118.1 Response Time in seconds) 0.267 0.305 ROCOF Response Time 0.4 0.314 in seconds) Delay Time in seconds) 0.08 0.008 % Peak Overshoo 0.042 10 From he resuls shown in fig. 2.23 and able 2.4, i can be seen ha he PMU under es - i) Mees he requiremen of frequency response ime ii) Does no mee he requiremen of ROCOF response ime iii) Does no mee he requiremen of delay ime iv) Mees he requiremen of % peak overshoo 23
Frequency Ramp Change: Figure 2.24: Response during ramp change in frequency Table 2.5: Tes resuls for response o frequency ramp change Evaluaion Parameers Resuls of he Tes PMU Allowable Values as per IEEE-C37.118.1 Maximum FE in Hz) 0.083 0.005 Maximum RFE in Hz/s) 0.457 0.1 From he resuls as shown in fig. 2.24 and able 2.5, i can be seen ha he PMU under es- i) Does no mee he requiremen of FE ii) Does no mee he requiremen of RFE Ampliude, Phase & Frequency Modulaion Changes: From fig. 2.25 and 2.26, when he ampliude, phase and frequency modulaion is done in he sysem, following observaions can be made - i) The volage TVEs of all he 3 phases are much higher han he hreshold value of 1%. ii) The volage TVEs of all he 3 phases are no he same. iii) The curren TVEs of all he 3 phases are much higher han he hreshold value of 1%. iv) The curren TVEs of all he 3 phases are no he same. 24
Figure 2.25: Dynamic es condiions for change in modulaed signal Figure 2.26: Error analysis of he es PMU under given sysem condiion 25
v) On he whole, curren TVEs are found o be higher han he volage TVEs. vi) FE is much higher han he permissible hreshold value. vii) RFE is iniially below he allowed hreshold limi. Bu as he frequency modulaion increases, he RFE goes on increasing rapidly, and exceeds he allowed hreshold value. From he analysis of he seady sae and dynamic ess, i can be seen ha he PMU under es behaves differenly under differen sysem condiions. The ess performed on he PMU under es provides a comprehensive coverage of he performance of he PMU. I has been seen ha he PMU under es saisfies mos of he es crieria as menioned in he sandard, bu fails some of hem. 2.2.3 PDC Tesing 2.1.3.1 Inroducion A Phasor Daa Concenraor PDC) works as a node in a communicaion nework where synchrophasor daa from a number of PMUs or PDCs is processed and fed ou as a single sream o he higher level PDCs and/or applicaions. Synchrophasor daa may include ime samped 3-phase volage magniudes, volage angles, curren magniudes, curren angles, frequency, rae of change of frequency ROCOF), real and reacive power, digial signals like circui breaker swich saus, ec. The PDC processes synchrophasor daa by imesamp o creae a sysem-wide measuremen se. PDCs can have several modes of operaion. For insance, he local PDCs aggregae and ime-align synchrophasor daa from muliple PMUs in a subsaion and feed he daa o applicaions. Mid-level and higher-level PDCs collec synchrophasor daa from muliple PDCs, conduc daa qualiy checks, ime align he daa and feed he daa o applicaions. The PDCs may be recognized as a funcion raher han as a sand-alone device or hardware/sofware package, and can be inegraed ino oher sysems and devices. A srucured hierarchy of disribued PDCs may be formed o serve a hierarchy of sysems: subsaion, uiliy, conrol area, reliabiliy coordinaor, and inerconnecion level. Disribued PDCs may also inerac wih each oher on a peer-o-peer basis among uiliies, conrol areas, and reliabiliy coordinaors. A PDC is expeced o perform some of he imporan funcions in he synchrophasor infrasrucure as saed below - a) Daa Aggregaion - This is he basic funcion of a PDC. I refers o he sreaming and accumulaion of he synchrophasor daa from he PMUs) in he PDC. The daa aggregaion funcionaliy of a PDC is required for real ime sysem monioring as well as pos-even analysis. Daa aggregaion funcion could be performed wih or wihou ime alignmen. I should preserve daa qualiy, ime qualiy, and ime synchronizaion indicaions from each signal, and include he daa qualiy informaion assigned by he individual sending devices o he oupu daa frames. 26
Daa coming ino a PDC has been ime samped by he PMU wih a ime referenced o UTC, absolue ime. Daa aggregaion wih ime alignmen refers o waiing for daa wih a given imesamp from all sources, placing ha daa in a packe, and forwarding i. The PDC aligns he daa received from PMU/PDC according o heir imesamps, no heir arriving order or arriving ime. Time alignmen o absolue ime refers o waiing no more han a specified absolue wai ime afer a imesamp ime for daa wih ha imesamp. This requires ha he PDC is synchronized o UTC. Time alignmen o relaive ime refers o waiing no more han a specified relaive wai ime afer an even. An even may be he arrival of he firs daa wih a specific imesamp. For some applicaions, i is desirable o receive a se of synchrophasor measuremens wih minimum laency. However, o reduce daa loss due o lae daa arrival, longer wai imes are needed, which in urn increase laency. To address hese conflicing requiremens i.e. no loss of daa due o lae arrival and minimum laency, a PDC could aggregae all he daa required for he oupu desinaion wihou ime alignmen and ransmi i periodically. b) Daa Forwarding - To minimize PDC laency, a PDC needs o suppor daa forwarding. Daa forwarding is performed eiher from one inpu o one oupu, or from one inpu o muliple oupus. No daa aggregaion is performed in his case. Daa forwarding can be performed wihou daa modificaion or wih daa modificaions ha may include daa forma and coordinae conversion, phase and magniude adjusmens for calibraion purposes), decimaion, inerpolaion, ec. c) Daa Validaion - A PDC is supposed o perform basic daa validaion and check he daa arriving a he PDC. This includes checking he ime qualiy of all PMUs as well as he daa saus flags. For his purpose, daa inegriy checks such as cyclic redundancy check [CRC] can be performed on all received daa. Any errors deeced and suspeced corrup daa should be flagged in oupu daa sreams). d) Daa Communicaion - This funcion allows a PDC o connec wih oher devices via serial and Eherne based communicaion neworks so ha he PDC can receive synchrophasor daa. The synchrophasor sysem communicaions include boh daa sreaming daa and configuraion informaion) and command communicaions. Daa ransfer is ypically clien-server based using eiher auo-iniiaion or a daa reques command. In he auoiniiaion mode, daa ransmission is implemened wihou waiing for any reques from any desinaion devices/applicaions for each individual daa poin in he series. In he daa reques command mode of operaion a clien he PDC) sends a daa reques command o he server a PMU or anoher PDC). The server hen responds wih he requesed daa. The daa communicaions in a synchrophasor sysem could be one-o-one i.e., from one source o one desinaion) and/or one-o-many i.e., from one source o muliple desinaions). Eiher mode may be implemened on Eherne based neworks, bu serial neworks are generally one-o-one unless he serial connecion is specially modified 27
o allow a one-o-many connecion. The command communicaions of a synchrophasor sysem includes various synchrophasor command frames. For example for IEEE Sd C37.118.2-2011, he synchrophasor command frames provide commands o he PMU o iniiae sreaming, o sop sreaming, o rerieve he header frame, o rerieve he configuraion frame, and o execue user-defined conrols. The command communicaions of a synchrophasor sysem may be one-o-one using serial or Eherne neworks. When using Eherne neworks, command communicaions ypically uses TCP over IP, bu can also use UDP over IP. Command communicaions are independen of he proocols used for he daa ransmission. e) Daa Transfer Proocols Suppor and Conversion - Synchrophasor daa from PMUs may be available in differen synchrophasor daa ransfer proocols such as IEEE Sandard C37.118, IEEE Sandard 1344-1995, IEC 61850-90-5, ec. A PDC should be able o suppor a leas one of hese proocols for seamless sreaming of daa from he PMUs) i is conneced o. If a PDC suppors muliple synchrophasor daa ransfer proocols, i should conver synchrophasor daa from one synchrophasor daa ransfer proocol o anoher o he exen possible. f) Daa Laency Compuaion - In a packe-swiched nework, daa laency is he ime delay beween a sender ransmiing a packe and a user receiving i. Because communicaion raffic volume and errors in ransmission can affec inermediae delays, laency is someimes no very predicable. Applied o he PMU/PDC sysem, here are muliple sources of synchrophasor daa laency could be due o he following reasons - i) Physical disance beween he wo ends of he sysem, ii) Processing of he packe in inermediae nework devices, iii) PMU calculaion and processing ime, iv) PMU PDC daa ransmission ime, v) PDC processing ime. Daa laency will be differen a differen poins in a hierarchical daa nework. I will increase cumulaively a successive daa desinaions such as he subsaion PDC, he TO conrol cener PDC, he ISO conrol cener PDC. g) Reporing Rae Conversion - The reporing rae conversion refers o he change of he reporing rae of a daa sream o be differen from he inpu daa sream e.g., 30 frames per second fps) o 15 fps, or 30 fps o 60 fps). Reporing rae conversion funcions are very useful for - i) Merging synchrophasor daa arriving a differen reporing raes from differen sources, ii) Convering available daa o a rae ha is mos suiable for a specific applicaion using synchrophasor daa. A PDC should ideally include boh down-conversion and up-conversion funcions. If his funcion is no provided, i should be clearly saed in he PDC s specificaion by he manufacurer. Along wih his, any limiaions in he conversion funcions should also be specified. The PDC should suppor inpu rae conversion from all raes specified in IEEE 28
Sandard C37.118.1-2011 o oupu sreams having any rae specified in IEEE Sd C37.118.1-2011. Reporing rae conversion should be user-configurable o accommodae he compaibiliy needs of all he devices and applicaions in he synchrophasor sysem, as well as all he applicaions ha migh be using he daa from he PDC. h) Daa Adjusmens - The PDC funcion requires he incoming daa o be eiher copied ino he oupu daa sream, or convered o a differen forma e.g., recangular/polar, floaing/fixed poin). The daa are expeced o be essenially unchanged. However, a imes, a PDC may be required o perform magniude or phase adjusmens on he incoming signal. There could be wo ypes of such adjusmens: i) Calibraion ype adjusmens, ii) Bulk ype adjusmens. Each of hese adjusmens is expeced o be se manually, based on calibraion facors, phase roaion sequence, ransformer raios, phase angles, ec. Calibraion ype adjusmens are hose ha require small changes o he magniude/phase of a signal, ypically wihin 5% of he magniude, or wihin 5 degrees of he phase. The purpose of calibraion adjusmens is o compensae for errors in he measuremen chain. These may be useful for a PDC, especially for a subsaion PDC, bu generally, his funcion is performed in a PMU. Bulk ype phase and magniude adjusmens are hose ha require large changes o he phase/magniude of a synchrophasor signal. These are useful, for example, when a signal needs o be referenced across a ransformer when he phase idenificaion of he desinaion sysem is differen ABC versus ACB) from he source sysem, or when he quaniies are being referenced across a wye-dela or sar-dela) ransformer. 2.1.3.2 Library of Tes Condiions Table 2.6: Library of PDC ess Tes No. PDC Funcionaliy Tes 1. Time Alignmen of Daa 2. Daa Validaion 3. Daa Loss 4. Daa Laency 5. Reporing Rae Conversion 6. Forma & Coordinae Conversion 7. Phase & Magniude Adjusmen IEEE Sandard for PDC esing C37.244-2013 specifies he ess ha need o be performed on PDCs. From he pool of ess, some of he imporan ess have been performed a SGDRIL, WSU. Table 2.6 provides he library of es condiions. The descripions of he funcionaliy ess have been provided in Secion 2.1.3.1. 29
2.1.3.3 Performance of PDC Tesing Two differen es beds have been creaed for esing PDCs. Fig. 2.27 provides he funcional schemaic diagram of he es bed used for performing PDC ess where daa loss due o long disance communicaion issues has no been esed. This simulaes an environmen in which he PMU and he PDC are locaed in he same subsaion. Fig. 2.28 provides he funcional schemaic diagram of he es bed used for performing PDC ess where daa loss due o long disance communicaion issues has also been esed. This simulaes an environmen in which he PMU and he PDC are locaed in he differen subsaions or he PMU is sending daa from a subsaion o a PDC locaed in he conrol cener. Figure 2.27: Tes bed for esing PDCs wihou communicaion modeling Figure 2.28: Tes bed for esing PDCs wih communicaion model In fig. 2.28, NS3 i.e. Nework Simulaor 3 has been used o model long disance communicaion delays and laencies in a sysem nework. NS3 is a discree-even simulaor argeed primarily for research and educaional use and is an open-source projec. I is he successor o he highly popular NS2, bu NS3 has been wrien from scrach and no derived from NS2. I uses C++ for scriping wih pyhon bindings. NS3 suppors emulaion mode of operaion and has he abiliy o simulae communicaion issues in real ime. 30
2.1.3.4 Conclusion from Tes Resuls A) Discussion on Tes-1: Time Alignmen of Daa Table 2.7: Tes resuls for ime alignmen rae = 30 frames / second) Time Duraion of Daa Collecion in PDCs Number of Daa Frames Sreamed Number of Time Alignmen Errors in PDC-A Number of Time Alignmen Errors in PDC-B 30 minues 54000 0 0 1 hour 108000 0 0 6 hours 648000 0 0 12 hours 1296000 0 0 24 hours 2592000 0 0 Table 2.8: Tes resuls for ime alignmen rae = 60 frames / second) Time Duraion of Daa Collecion in PDCs Number of Daa Frames Sreamed Number of Time Alignmen Errors in PDC-A Number of Time Alignmen Errors in PDC-B 30 minues 108000 0 0 1 hour 216000 0 0 6 hours 1296000 0 0 12 hours 2592000 0 0 24 hours 5184000 0 0 From he resuls presened in able 2.7 and 2.8, i can be seen ha for differen duraions and reporing rae of daa sreaming, collecion and archival, he esed PDCs were able o align daa w.r.. he GPS clock ime signal referenced o he UTC. Boh he es PDCs passed he daa ime alignmen es. B) Discussion on Tes-2: Daa Validaion Table 2.9: Tes resuls for daa validaion rae = 30 frames / second) Level of Sysem Volage Simulaed using RTDS) Number of Daa Errors in PDC-A Number of Daa Errors in PDC-B 13.8 kv 0 0 138 kv 0 0 230 kv 0 0 500 kv 0 0 760 kv 0 0 31
Table 2.10: Tes resuls for daa validaion dae = 60 frames / second) Level of Sysem Volage Simulaed using RTDS) Number of Daa Errors in PDC-A Number of Daa Errors in PDC-B 13.8 kv 0 0 138 kv 0 0 230 kv 0 0 500 kv 0 0 760 kv 0 0 For Daa Validaion Tes, decimal poins of each daa should be idenical. Rounding off he daa wih higher number of decimal poins was used o solve his issue. Afer round off all daa validaion es wih CRC check was performed. From he resuls presened in able 2.9 and 2.10, i can be seen ha for differen reporing rae of daa sreaming, collecion and archival, he esed PDCs good performance wih daa errors. Boh he es PDCs passed he daa validaion es. C) Discussion on Tes-3: Daa Loss As discussed earlier, daa loss has been sudied using wo differen esbeds - one in a small nework where he PMU sreams daa direcly o a PDC hrough a nework swich, and he oher one in which NS3 nework simulaor) is used beween he PMU and he PDC o model communicaion issues in he sysem nework. Table 2.11 and 2.12 show he resuls of daa loss when he es is carried ou on a small nework wihou NS3 simulaor. Time Duraion of Daa Collecion in PDCs Table 2.11: Tes resuls for daa loss rae = 30 frames / second) Number of Daa Frames Sreamed Number of Daa los in PDC-A Number of Daa los in PDC-B 30 minues 54000 0 0 1 hour 108000 0 0 6 hours 648000 0 0 12 hours 1296000 0 0 24 hours 2592000 0 0 Time Duraion of Daa Collecion in PDCs Table 2.12: Tes resuls for daa loss rae = 60 frames / second) Number of Daa Frames Sreamed Number of Daa los in PDC-A Number of Daa los in PDC-B 30 minues 108000 0 0 1 hour 216000 0 0 6 hours 1296000 0 0 12 hours 2592000 0 0 24 hours 5184000 0 0 32
Table 2.13 shows he resuls of daa loss when he es is carried ou on a larger nework using NS3 simulaor. Table 2.13: Tes resuls for daa loss wih nework rae = 60 frames / second) Time Duraion of Daa Collecion in PDCs Number of Daa Frames Sreamed Number of Daa los in PDC-A Number of Daa los in PDC-B 1 hour 216000 2203 2131 From Tables 2.11 and 2.12, i can be seen ha when a PMU direcly sreams daa o a PDC such ha he daa does no need o go hrough any complex communicaion nework), here is no daa loss. However, when he PMU sends daa o he PDC via communicaion neworks, here is considerable daa loss. For PDC-A, here is 1.02% daa loss, whereas for PDC-B, here is 0.986% daa loss. Time Duraion of Daa Collecion in PDCs Table 2.14: Tes resuls for daa laency Number of Daa Frames Sreamed Average Laency for PDC-A Average Laency for PDC-B 30 minues 54000 51.1028 ms 51.0054 ms 1 hour 108000 49.5897 ms 49.7183 ms 6 hours 648000 38.8801 ms 49.7628 ms 12 hours 1296000 38.8650 ms 48.6893 ms 24 hours 2592000 38.8903 ms 50.0694 ms D) Discussion on Tes-4: Daa Laency Table 2.14 shows he daa laency when he PMU sends daa o a PDC hrough he communicaion nework as shown in figure 2.28. From he above able i can be seen ha for he same es seup, on an average PDC-A performs beer han PDC-B. E) Discussion on Tes-5: Reporing Rae Conversion Tables 2.15 and 2.16 show he performance of he es PDCs for reporing rae conversion comprising of down-rae conversion from 60 Frames / second o 30 Frames / second and 30 Frames / second o 60 Frames / second. Table 2.15: Tes resuls for repor rae conversion 60 o 30) Down-rae conversion from 60 F/s o 30 F/s) Funcion Suppored Funcion Suppored in PDC-A in PDC-B Saisfacory Saisfacory 33
Table 2.16: Tes resuls for repor rae conversion 30 o 60) Up-rae conversion from 30 F/s o 60 F/s) Funcion Suppored Funcion Suppored in PDC-A in PDC-B Saisfacory Saisfacory I can be seen from boh he above resul ables ha he es PDCs show saisfacory performance for his es. F) Discussion on Tes-6: Forma & Coordinae Conversion Tables 2.17 and 2.18 show he performance of he es PDCs for Forma & Coordinae Conversion from polar o recangular and recangular o polar respecively. Table 2.17: Tes resuls for forma & coordinae conversion polar o recangular) Polar o Recangular form) Funcion Suppored Funcion Suppored in PDC-A in PDC-B Saisfacory Saisfacory Table 2.18: Tes resuls for forma & coordinae conversion recangular o polar) Recangular o Polar form) Funcion Suppored Funcion Suppored in PDC-A in PDC-B Saisfacory Saisfacory I can be seen from boh he above resul ables ha he es PDCs show saisfacory performance for his es. G) Discussion on Tes-7: Phase & Magniude Adjusmen Tables 2.19 and 2.20 show he performance of he es PDCs for phase adjusmen of +5 degrees and -5 degrees respecively in he PDCs w.r.. he phase angle daa sreamed by he PMU. On he oher hand, Tables 2.21 and 2.22 show he performance of he es PDCs for magniude adjusmen of +5% and -5% respecively in he PDCs w.r.. he magniude daa sreamed by he PMU. These adjusmens are of high imporance when calibraion needs o be done a he PDC level. Table 2.19: Phase angle adjusmen +5 degrees) Funcion Suppored in PDC-A Saisfacory Funcion Suppored in PDC-B Saisfacory 34
Table 2.20: Phase angle adjusmen -5 degrees) Funcion Suppored in PDC-A Saisfacory Funcion Suppored in PDC-B Saisfacory Table 2.21: Magniude adjusmen +5%) Funcion Suppored in PDC-A Saisfacory Funcion Suppored in PDC-B Saisfacory Table 2.22: Magniude adjusmen -5%) Funcion Suppored in PDC-A Saisfacory Funcion Suppored in PDC-B Saisfacory I can be seen from boh he above resul ables ha he es PDCs show saisfacory performance for his es. All he ess in able 2.6 have been carried ou successfully. However, while carrying ou he ess, we realized no having performance evaluaion hreshold crieria for PDCs like wha is available for PMUs) in he IEEE Sandard for PDCs C37.244. 2.2 WinIGS-T based Tesing Faciliy 2.2.3 Descripion The purpose of his approach is o provide a high fideliy esing and characerizaion of he performance of PMU devices from several manufacurers ABB, Macrodyne, Arbier, GE, SEL, TESLA, ec.). The aim is o answer he following key quesions regarding PMU performance: How accurae are he currenly available PMU devices under differen operaing condiions boh magniude and phase wih accuracy of 0.001 pu and 0.01 degrees respecively)? Augmening relays wih PMU funcionaliy has been proposed. Are modern relays wih PMU funcionaliy able o deliver boh funcions proecion and GPS synchronizaion) reliably? Wha are he suggesed improvemens proposed for he nex generaion of PMU s? Wha is he mos appropriae esing framework for evaluaing he performance of curren PMU devices? Wihin his projec, we have recognized ha PMU esing and performance evaluaion is a difficul ask, because of he requiremen for high accuracy measuremens and iming 35
iming of a fracion of a microsecond is required). Hence, high accuracy equipmen and algorihms have been employed o ensure accurae characerizaion. Since i is unrealisic o creae devices ha generae phasors wih accuracy of 0.001 pu in magniude and 0.01 degrees in phase, we developed a differen approach: generae waveforms wih sandard waveform generaing equipmen, feed hem o he PMUs under esing and capure he inpu of he PMUs wih high precision daa acquisiion sysems. In order o compare he phasors provided by he PMU under esing i is necessary o develop a high accuracy phasor compuaion mehod. Such a mehod has been developed and we refer o i as he sandard PMU described in a laer secion. Thus, he proposed esing procedure is based on accuraely recording he inpu of he PMU and processing i wih he sandard PMU, which is an exremely accurae procedure o compue fundamenal frequency phasor wih zero leakage specrum. Subsequenly, he oupu of he sandard PMU is compared wih he oupu of he PMU being esed, yielding a performance evaluaion of ha device. One specific issue is o sudy he performance of PMU devices ha combine proecive relaying funcionaliies wih GPS synchronizaion, such as he G60, SEL-421, ec. In his projec, various faul scenarios are generaed by he signal generaor, including various faul condiions o which he relay is supposed o respond, esing boh he accuracy relay s proecive funcion and he accuracy of is PMU funcion, answering he quesion wheher relays wih PMU funcionaliy are able o combine he wo funcions accuraely. Finally, he uilizaion of GPS synchronized equipmen will mos likely be in subsaions in a muli-vendor environmen. I is imporan in his case o develop mehods for comparaive esing of GPS synchronized equipmen from differen vendors. Wihin he scope of his projec, he performance of PMU devices from various vendors has been evaluaed. Regarding PDC performance, of major imporance is a) he abiliy of he PDC o imealign PMU daa and combine hem ino one sream of daa, while minimizing laencies and b) he abiliy of he PDC o fully suppor he sandards so ha ineroperabiliy is achieved. Anoher desired characerisic is he abiliy of he PDC o monior he observed laencies and idenify he sources of laency, hus providing useful repors ha could be used owards PDC redesign. Finally, i is desired for he PDC o be able o inelligenly handle missing daa, e.g. by inerpolaing using available daa and assigning larger measuremen errors o inerpolaed daa. 2.2.4 PMU Tesing 2.2.4.1 Descripion of approach In order o accuraely es PMU equipmen, a measuremen accuracy beer han one microsecond is needed. However, i mus be noed ha creaing inpu waveforms of ha accuracy requires exremely expensive equipmen. Hence, he approach followed in his projec is o generae he inpu signals from inexpensive, and relaively low accuracy equipmen and subsequenly measure he waveforms in he inpu of he PMU devices being esed using a daa acquisiion sysem wih beer han one microsecond accuracy iming) and 0.001 pu magniude accuracy. Such daa acquisiion sysems are relaively inexpensive and available unlike equipmen ha is able o generae inpu signals of ha 36
accuracy). The end resul, however, is he same and accurae esing of he PMU devices is esablished. The approach is oulined in he sequel. Fig. 2.29 shows he esing approach followed in his projec. The hardware insallaion suggesed in fig. 2.29 has been insalled in he Power Sysems Conrol and Auomaion lab locaed in he ECE Van Leer building of he Georgia Tech Campus. The signal generaor is able o provide a hree phase volage and curren of conrollable magniude and frequency as an inpu o he GPS synchronized device being esed. Also, i is able o simulae unbalanced and fauled condiions. As menioned above, a very high precision 24 bi, 10Ms/s A/D digiizer, GPS synchronized is used o measure he generaed inpu waveforms. Simulaneously, he relay daa are capured hrough he communicaion channels of he relay, as shown in fig. 2.29 [8-9]. The accuraely measured device inpus and he device recording are supplied o a personal compuer for comparison Daa acquisiion compuer in fig. 2.30). The comparison of he wo daa ses is performed in he program WinXFM. This program is able o accuraely compare wo ses of daa namely phase difference up o 0.01 o and magniude error up o 0.005%). The overall approach is illusraed in fig. 2.29 and he specific ess are described nex. GPS Clock IRIG-B 1kPPS 1PPS Relay Under Tes PC 300Ms/s, 12 bi, 8 Channel Waveform.Gen. Digial Daa RS232 / Eherne ) Power Amplifier 300W/chan Audio Amps) Xfmr 10Ms/s, 16 bi, 2 Channel Digiizer Divider Figure 2.29: Hardware configuraion for esing GPS-synchronized IEDs/ PMU The daa acquisiion sysem is illusraed in more deail in fig. 2.31 in block diagram form. I consiss of a Naional Insrumens PXI plaform wih 8 channels of 24 bi A/D converers wih maximum sampling rae of 200 ksps. 37
Figure 2.30: Schemaic of sofware archiecure for GPS-synchronized IED esing Figure 2.31: Daa acquisiion sysem block diagram 38
The converer sampling clock is obained from a 10 MHz signal provided from an oven conrolled crysal oscillaor disciplined o he GPS 1-PPS signal Trimble Thunderbol-E uni). The A/D converers are riggered by a clock pulse generaed by a second GPS receiver locaed wihin he PXI plaform. This sysem achieves UTC synchronized sampling wih ypical accuracy of less han 100 nanoseconds. As a resul he sysem exceeds he accuracy sandard ha we se as he goal for his esing. Figure 2.32: Laboraory seup for PMU esing Figure 2.33: Laboraory seup for PMU esing The PMU performance evaluaion procedure oulined above has been implemened in he laboraory insallaion of he Power Sysem Conrol and Auomaion Lab in Georgia 39
Tech. The es seup has he capabiliy o generae up o 18 channels of arbirary volage and curren waveforms a he sandard levels for PMU inpus nominally up o 120 vols and 5A). Generaed waveforms can be reproduced from digiized daa sored as COMTRADE files or synhesized based on user defined mahemaical expressions. For he purpose of validaing he phasor sream generaed by he device under es, he es seup includes a reference high precision daa acquisiion sysem. This sysem includes 8 digial o analog converer channels wih sampling synchronized o UTC ime wihin 100 nanosecond accuracy. An overview of he laboraory seup is shown in fig. 2.32. A phoograph of he laboraory is shown in fig. 2.33. In order o achieve proper characerizaion of a GPS-synchronized device, he following feaures are esed: a) Error analysis of boh iming accuracy and magniude accuracy over a generally acceped range of operaing condiions defined in erms of: Frequency Frequency Rae of Change Volage Magniudes Curren Magniudes Harmonics Imbalances b) Abiliy o communicae using sandard proocols, especially conformiy wih he IEEE Sandard C37.118. Figure 2.334: Illusraion of Toal Vecor Error TVE) 40
There are no sandardized ess, bu a sandard is being developed for ha purpose by he NASPI group and adoped by IEEE. Under he IEEE sandard, PMU s should be benchmarked by he Toal Vecor Error TVE), shown in fig. 2.34. A TVE of 1% includes all phasors ha lie wihin a circle cenered a he correc phasor wih radius equal o 1% of he exac phasor magniude. However, his would imply a phase angle error of as much as 0.573 o, which severely underesimaes he angle measuremen accuracy of modern PMU s which is much greaer han he magniude accuracy). While we suppor his sandard, i is imporan o noe ha our esing goes furher han he sandard. Specifically, we separaely esed PMU performance wih accuracy beer han 0.001 pu in magniude and 0.01 degrees in phase or beer han 1 microsecond in iming). In oher words our esing is segregaed in magniude and iming. The specific es procedures are described in erms of merics ha define performance and inpu es waveforms. The following performance merics are evaluaed for error analysis: Time or Phase Accuracy Magniude Accuracy Frequency Accuracy Figure 2.345: Illusraion of iming error measuremen 41
Time or Phase Accuracy: The ime accuracy of a daa acquisiion device can be evaluaed in wo ways, depending on he ype of daa ha can be downloaded from he device under es: a) If sampled waveform daa are available poin on wave daa) he ime accuracy can be direcly deermined by comparison of he sample sequence obained from he device under es o he corresponding sample sequence obained from he reference daa acquisiion device. The ime accuracy is hen exraced from he sample sequences using an esimaion based approach. Le a k be he sample sequence obained from he device under es and b k he sample sequence from he reference device. Le Δ be a variable represening he ime error of he device under es, and c a variable represening he magniude error. The variables Δ and c can be deermined by minimizing an objecive funcion JΔ,c) wih respec o Δ and c, which is defined as follows: N J = a k 1 + c)b k ) 2 k=0 where b k-δ represens a re-sampled version of he original sequence from he device under es wih ime delay Δ. This procedure is illusraed in fig. 2.35. b) If he device under es generaes phasor daa such as a C37-118 synchrophasor sream) hen he iming accuracy is deermined by comparing he phasor phase angles. Fig. 2.36 illusraes his procedure. Magniude Accuracy: As wih ime accuracy, he magniude accuracy is measured eiher using poin on wave daa if available) or phasor daa. These wo approaches as described in he previous secion also provide magniude accuracy evaluaion. Frequency Accuracy: The frequency accuracy is measured as a percenage difference beween he frequency compued by he device under es and he known frequency of he inpu waveform. Noe ha he sandard PMU also accuraely racks he frequency of he sampled daa sequence a a rae equal o he phasor compuaion rae up o 60 imes per second). Noe ha racking waveform fundamenal period is necessary for accurae phasor compuaions. The frequency compuaion is performed by observing he rae of change of phase angle beween successive cycles. Specifically, he following expression yields he fundamenal frequency as a funcion of successively compued phase angle values: f k = f 0 1 + φ k φ k 1 2π where φ k an φ k-1 are wo successively compued phase angles, and f 0 is he nominal power frequency. The communicaions merics deermine wheher he device under es complies wih he IEEE Sandard C37.118 for synchrophasor communicaions. In addiion o ime ag, 42
frequency and phasor magniude and phase, C37.118 for synchrophasor frames conain addiional informaion such as reference clock accuracy and qualiy codes, and various user assignable configuraion parameers such as saion name, phasor, analog and saus channel names. Furhermore, mos PMUs eiher conain a buil in GPS receiver for obaining UTC ime reference, or accep a ime synchronizaion signal using he IRIG-B sandard proocol. Communicaion merics are defined which esablish ha he device under es performs as specified by he relevan sandards. Specifically, communicaions merics esing includes monioring he synchrophasor sream accuracy and clock qualiy codes for various GPS clock saes, such as low saellie signal o noise raio, loss of GPS ime lock for various duraions, recovery of GPS lock afer loss of lock ec. These condiions have been simulaed by simply disconnecing he GPS clock for PMUs wih exernal GPS clock) or by simply puing a meallic objec over he GPS anenna o limi he signal for PMUs wih inernal GPS clock. Figure 2.356: Illusraion of phase error measuremen 2.2.4.2 Tes Condiions In order o fully characerize PMU performance, he following ess are performed: Timing Accuracy: Deermine he iming accuracy of he digiized samples. The accuracy is expressed in erms of microseconds wih precision 0.5 microseconds. The iming accuracy direcly affecs he phase measuremen. For each one microsecond error in iming he phase has an error of 0.02 degrees. Frequency Tess: Deermine he frequency error over hree differen ranges defined below. Three ranges: Range 1: nominal ± 0.25 Hz Range 2: nominal ± 2.5 Hz 43
Range 3: nominal ± 5 Hz The frequency ess revealed differences among he various manufacurers resuling from he algorihms hey use for phase and frequency measuremens. A fundamenal frequency, all algorihms provided he same resul bu a off-nominal frequencies, differences did exis. Frequency Ramp: Deermine he frequency ramp error over hree frequency ramp raes defined below. Three ranges: Range 1: 0.05 Hz per sec. for 5 sec. Range 2: 0.25 Hz per sec. for 10 sec. Range 3: 0.5 Hz per sec. for 10 sec. These ess revealed differences among manufacurers. In addiion o he algorihms menioned above, differences exised among various manufacurers because of using differen ime windows by various manufacurers and differen filers. Volage Magniude: Deermine he volage magniude error in he following volage magniude range. Range: nominal 25% o nominal +20% Volage Phase: Deermine he volage phase error in he following volage magniude range. Range: nominal 50% o nominal +30% The phase accuracy is direcly relaed o he iming accuracy. In addiion, anoher source of errors and differences is he fron end analog filers used as well as digial filers a he A/D converer level. Volage Magniude Sep Change: Deermine he volage magniude sep change error in he following sep volage change values. Tes 1: nominal 1% o nominal +1% Tes 2: nominal 5% o nominal +5% Tes 3: nominal 50% o nominal +10% Elecric Curren Magniude: Deermine he curren magniude error in he following wo elecric curren ranges: Two Ranges: nominal 80% o nominal + 100% non relaying devices) Two Ranges: nominal 80% o nominal + 2000% relaying devices) Elecric Curren Phase: Deermine he elecric curren phase error in he following wo elecric curren ranges. Two Ranges: nominal 80% o nominal + 100% non relaying devices) Two Ranges: nominal 80% o nominal + 2000% relaying devices) 44
Elecric Curren Imbalance: Deermine he elecric curren imbalance measuremen error in he following elecric curren imbalance ranges oal of four): Volage negaive sequence range: zero o 5% Volage zero sequence range: zero o 5% Curren negaive sequence range: zero o 20% Curren zero sequence range: zero o 20% Table 2.23: Tes condiions for seady sae performance Tes Designaion Fundamenal Frequency Toal Harmonic Disorion A-1 60.0 Hz 0 A-2 59.8 Hz 0 A-3 60.2 Hz 0 A-4 59.5 Hz 0 A-5 60.5 Hz 0 A-6 59.0 Hz 0 A-7 61.0 Hz 0 A-8 57.0 Hz 0 A-9 63.0 Hz 0 A-10 55.0 Hz 0 A-11 65.0 Hz 0 A-12 50.0 Hz 0 A-13 70.0 Hz 0 A-14 60.0 Hz 5 % A-15 59.8 Hz 5 % A-16 60.2 Hz 5 % A-17 59.5 Hz 5 % A-18 60.5 Hz 5 % A-19 59.0 Hz 5 % A-20 61.0 Hz 5 % A-21 57.0 Hz 5 % A-22 63.0 Hz 5 % A-23 55.0 Hz 5 % A-24 65.0 Hz 5 % A-25 50.0 Hz 5 % A-26 70.0 Hz 5 % Tesing of Relay/ PMU Devices: One addiional es was performed for dual funcion devices, i.e. PMU capabiliy and relay funcions. Presenly here are many dual funcion devices relays wih PMU capabiliy). For hese devices, wo series of ess have been performed: a) he GPS-synchronizaion funcion has been esed under heavy relaying aciviy. For his purpose, he inpu signals o he dual funcion device has been generaed by a power sysem simulaion program and conain muliple faul condiions. The mehodology ha we have developed can evaluae he iming errors under hese condiions. Because in his case he waveforms are no near quasi-seady sae, direc iming error measuremen are performed insead of phase error measuremen. b) he PMU funcions, as defined in he IEEE sandard 118, and he relaying funcions, as defined by he manufacurer, are esed under several scenarios of muliple faul aciviy. The following relay funcions have been included in he scenarios: 1) phase and ground 45
disance, 2) overcurren, 3) direcional overcurren, 4) ime overcurren and 5) ou of sep. For each of he scenarios he following are deermined: a) accuracy of he PMU reporing funcion as defined in he IEEE Sd C37.118, b) accuracy of he relay operaion as defined in he manufacurers manuals. Tes Signals: A number of es signals has been developed for performing he above menioned esing procedure. The es waveforms are described below. Tes A: Seady Sae Tess a Various Frequencies: The es waveform is a consan frequency periodic waveform wih various levels of harmonic disorion. For each es, he following parameers are measured: a) iming error, b) magniude error, and c) frequency error. The inpu es waveforms are defined in able 2.23. Tes B: Frequency Ramp Tess: The es waveforms are of consan ampliude and wih frequency increasing or decreasing a a consan rae of change. For each es, he following are parameers are measured: a) iming error, b) magniude error, and c) frequency error. The following es waveforms comprise he frequency ramp es se as given in able 2.24. Tes Designaion Table 2.24: Tes condiions for frequency ramp es Iniial Frequency & Duraion Ramp Rae & Duraion Final Frequency & Duraion Toal Harmonic Disorion Tes B-1 60 Hz, 5 sec +0.1 Hz/s, 5 s 60.5 Hz, 5 sec 0 Tes B-2 60 Hz, 10 sec 0.1 Hz/s, 5 s 59.5 Hz, 5 sec 0 Tes B-3 60 Hz, 10 sec +0.5 Hz/s, 10 s 65.0 Hz, 5 sec 0 Tes B-4 60 Hz, 10 sec 0.5 Hz/s, 10 s 55.0 Hz, 5 sec 0 Tes B-5 60 Hz, 10 sec +1.0 Hz/s, 10 s 70.0 Hz, 5 sec 0 Tes B-6 60 Hz, 10 sec 1.0 Hz/s, 10 s 50.0 Hz, 5 sec 0 Table 2.25: Tes condiions for volage magniude es Tes Fundamenal Magniude Designaion Frequency C-1 60.0 Hz 50 %, C-2 60.0 Hz 70 % C-3 60.0 Hz 130 % C-4 60.5 Hz 50 % C-5 60.5 Hz 70 % C-6 60.5 Hz 130 % C-7 59.5 Hz 50 % C-8 59.5 Hz 70 % C-9 59.5 Hz 130 % 46
Tes C: Volage Magniude Tess: A se of consan magniude and frequency sinusoidal waveforms a various magniudes and frequencies. For each es, he following are measured: a) iming error, b) magniude error, and c) frequency error. The following inpu es waveforms are used see able 2.25). Tes D: Volage Magniude Sep Change Tess: The es waveforms are sinusoidal, of consan frequency, and each conains six sep magniude changes 5 seconds apar. For each es, he following are measured: a) iming error, b) magniude error, and c) frequency error. Table 2.26 shows following inpu es waveforms defined: Tes Designaion Table 2.26: Tes condiions for volage magniude sep change Frequency Hz) Magniude %) Magniude %) Magniude %) Magniude %) Magniude %) Magniude %) Tes D-1 60.0 100 95 50 95 110 100 Tes D-2 60.5 100 95 50 95 110 100 Tes D-3 59.5 100 95 50 95 110 100 Tes E: Elecric Curren Magniude Tess: Consan curren periodic waveforms of various frequencies, magniudes, and harmonic disorions. For each es, he following are measured: a) iming error, b) magniude error, and c) frequency error. The following inpu es waveforms are used as given in able 2.27: Table 2.27: Tes condiions for curren magniude Tes Designaion Fundamenal Frequency Magniude % of Raing) Tes E-1 60.0 Hz 20 Tes E-2 60.0 Hz 50 Tes E-3 60.0 Hz 200 Tes E-4 60.0 Hz 800 Tes E-5 60.0 Hz 2000 Tes E-6 60.5Hz 20 Tes E-7 60.5Hz 50 Tes E-8 60.5Hz 200 Tes E-9 60.5Hz 800 Tes E-10 60.5Hz 2000 Tes E-11 59.5Hz 20 Tes E-12 59.5Hz 50 Tes E-13 59.5Hz 200 Tes E-14 59.5Hz 800 Tes E-15 59.5Hz 2000 The percenage values refer o he device raed curren 1A or 5A). 47
Tes Designaion Table 2.28: Tes condiions for volage and curren imbalance ess Fund. Frequency Posiive Sequence Volage Negaive Sequence Zero Sequence Posiive Sequence Curren Negaive Sequence Zero Sequence F-1 60.0 Hz 100 % 2 % 2 % 100 % 5 % 5 % F-2 60.0 Hz 100 % 5 % 5 % 100 % 20 % 20 % F-3 60.5 Hz 100 % 2 % 2 % 100 % 5 % 5 % F-4 60.5 Hz 100 % 5 % 5 % 100 % 20 % 20 % F-5 59.5 Hz 100 % 2 % 2 % 100 % 5 % 5 % F-6 59.5 Hz 100 % 5 % 5 % 100 % 20 % 20 % c:\000\neerac projec\es b-1 - Mar 15, 2008, 14:58:32.000000-6000.0 samples/sec - 90001 Samples 162.6 VAY V) -162.6 162.6 VBY V) -162.6 162.6 VCY V) -162.6 7.071 IAY A) -7.071 7.071 IBY A) -7.071 7.071 ICY A) -7.071 60.50 VA_FREQ Hz) 60.00 60.50 CA_FREQ Hz) 60.00 14:58:3214:58:3314:58:3414:58:3514:58:3614:58:3714:58:3814:58:3914:58:4014:58:414:58:4214:58:4314:58:4414:58:4514:58:46 Figure 2.37: Tes B-1: Frequency ramp, no harmonics 48
Tes F: Volage and Curren Imbalance Tess: Three phase volage and curren waveforms conaining various levels of imbalance defined in erms of sequence componens. For each es, he following are measured: a) iming error, b) magniude error, and c) frequency error. The following inpu es waveforms are used as shown in able 2.28. Tes G: Composie Waveform Tesing Tesing Under Faul Condiions of Relay/PMU Devices): The signals for his es include normal operaing condiions inerruped wih fauls ha are cleared. Muliple fauls are simulaed resuling in exposure of he device under es in muliple fauls. Tes Table 2.29: Performance evaluaion - individual phase analysis - es signals A Magniude Error %) Phase Error Deg) Toal Vecor Error %) VA VB VC VA VB VC VA VB VC A1 0.006485 0.04042 0.006136 0.222 0.193 0.2 0.388 0.339 0.348 A2 0.01116 0.04095 0.01272 0.232 0.193 0.205 0.187 0.414 0.427 A3 0.009431 0.04502 0.006583 0.236 0.201 0.205 0.412 0.352 0.357 A4 0.01146 0.03887 0.004913 0.227 0.192 0.196 0.396 0.337 0.343 A5 0.01393 0.05303 0.01454 0.248 0.211 0.207 0.434 0.37 0.362 A6 0.02747 0.04741 0.02658 0.268 0.212 0.224 0.467 0.373 0.391 A7 0.03025 0.06655 0.03087 0.233 0.201 0.207 0.407 0.354 0.361 A8 0.07736 0.05603 0.07475 0.243 0.213 0.221 0.425 0.372 0.388 A9 0.07914 0.0116 0.07749 0.251 0.222 0.44 0.385 0.388 0.848 A10 0.117 0.07501 0.124 0.253 0.221 0.232 0.449 0.388 0.41 A11 0.127 0.161 0.128 0.261 0.227 0.229 0.46 0.411 0.405 A12 2.471 2.487 2.479 10.64 10.61 10.63 18.48 18.32 18.45 A13 2.598 2.653 2.623 10.08 10.11 10.11 17.76 17.82 17.82 A14 0.01314 0.06095 0.02507 0.234 0.204 0.2 0.408 0.36 0.349 A15 0.02246 0.05622 0.0199 0.241 0.205 0.215 0.42 0.362 0.375 A16 0.03038 0.06609 0.02924 0.25 0.215 0.224 0.436 0.377 0.391 A17 0.01971 0.05776 0.01979 0.243 0.206 0.214 0.424 0.361 0.374 A18 0.03443 0.07088 0.03346 0.254 0.218 0.226 0.443 0.385 0.395 A19 0.02525 0.06172 0.02284 0.246 0.211 0.222 0.43 0.37 0.387 A20 0.04789 0.08359 0.04753 0.255 0.219 0.228 0.446 0.389 0.398 A21 0.0473 0.08456 0.052 0.253 0.219 0.227 0.443 0.389 0.397 A22 0.04797 0.08444 0.04734 0.255 0.219 0.228 0.445 0.389 0.399 A23 0.107 0.08478 0.109 0.271 0.233 0.246 0.478 0.407 0.436 A24 0.04741 0.08384 0.04811 0.251 0.215 0.226 0.438 0.382 0.395 A25 2.528 2.555 2.5 10.62 10.59 10.6 18.45 18.38 18.41 A26 2.637 2.51 2.432 10.3 10.43 10.58 17.98 17.83 17.91 49
For limiing he size of his repor, he signal waveforms are no included hey are however available in elecronic form - in COMTRADE forma). As an example, he waveform for Tes B-1 case is depiced in fig. 2.37 for Freq=60Hz for 5 secs, ramping rae +0.1 Hz/sec for 5 secs, Freq=60.5Hz for anoher 5 seconds. 2.2.2.3 Performance of PMU esing Table 2.30: Performance evaluaion - posiive sequence - es signals A Tes Maximum Magniude Error %) Maximum Phase Error Deg) Maximum TVE %) Frequency Error Hz) A1 0.04042 0.222 0.388 0.000284 A2 0.40400 0.339 0.357 0.000187 A3 0.04502 0.236 0.412 0.000147 A4 0.03887 0.227 0.396 0.000193 A5 0.05303 0.248 0.434 0.000537 A6 0.04741 0.268 0.467 0.000133 A7 0.06655 0.233 0.407 0.000364 A8 0.07736 0.243 0.425 0.000633 A9 0.07914 0.44 0.848 0.000289 A10 0.12400 0.253 0.449 0.000614 A11 0.16100 0.261 0.46 0.000437 A12 2.48700 10.64 18.48 0.000686 A13 2.65300 10.11 17.82 0.000685 A14 0.06095 0.234 0.408 0.000391 A15 0.05622 0.241 0.42 0.000116 A16 0.06609 0.25 0.436 0.000213 A17 0.05776 0.243 0.424 0.000383 A18 0.07088 0.254 0.443 0.000597 A19 0.06172 0.246 0.43 0.000108 A20 0.08359 0.255 0.446 0.000464 A21 0.08456 0.253 0.443 0.000546 A22 0.08444 0.255 0.445 0.000428 A23 0.10900 0.271 0.478 0.000649 A24 0.08384 0.251 0.438 0.00042 A25 2.55500 10.62 18.45 0.000647 A26 2.63700 10.58 17.98 0.000688 For keeping he repor concise, he deailed es resuls are no included here. Insead we provide represenaive performance repor for one device wihou idenifying he device. You will noe ha he performance daa are idenified by he es, i.e. es A-1, B-3, ec. The performance daa are expressed in erms of magniude error, phase error and oal 50
vecor error for individual phase phasors and for posiive sequence phasor as well as frequency error. Only represenaive es resuls are presened in able 2.29 o able 2.32. Table 2.31: Performance evaluaion - individual phase analysis - es signals B Phase Error Deg) Magniude Error %) Toal Vecor Error %) Tes VA VB VA VB VC VC VA VB VC B1 0.01398 0.05226 0.01442 0.234 0.202 0.2007 0.409 0.354 0.361 B2 0.01854 0.04265 0.01714 0.226 0.193 0.202 0.395 0.338 0.353 B3 0.159 0.197 0.16 0.262 0.231 0.233 0.466 0.419 0.414 B4 0.114 0.08605 0.116 0.277 0.241 0.254 0.484 0.422 0.443 B5 2.74 2.796 2.736 10.21 10.24 10.25 17.76 17.82 17.82 B6 2.471 2.5 2.443 10.61 10.58 10.59 18.42 18.37 18.4 Table 2.32: Performance evaluaion - posiive sequence - es signals B Tes Maximum Magniude Error %) Maximum Phase Error Deg) Maximum TVE %) Frequency Error Hz) B1 0.05226 0.234 0.409 0.000393 B2 0.04265 0.226 0.395 0.008391 B3 0.19700 0.262 0.466 0.000379 B4 0.11600 0.277 0.484 0.03835 B5 2.79600 10.25 17.82 0.000382 B6 2.50000 10.61 18.42 0.000682 2.2.2.4 Conclusion from Tes Resuls The ess reveal ha he performance of he various PMU esed are excellen under seady sae condiions and near nominal frequency. The esed PMUs mee he IEEE Sd permissible error of oal vecor error. However under ransien and off nominal frequency here is grea variabiliy among he various manufacurers and he errors can be quie high. All performance daa do no idenify he specific device esed. 51
3 Validaion and Tesing of Synchrophasor Applicaions 3.1 Volage Sabiliy Algorihms Based on Synchrophasor Daa 3.1.1 Inroducion o Volage Sabiliy Unil he las wo decades, power sysems could afford o be overdesigned. Bu now due o he increasing loads, environmenal limiaions on he expansion of ransmission sysem and high compeiion amongs he ransmission uiliies, he power sysems are being pushed o heir sabiliy limis. Due o hese facors, hey now operae under severely sressed condiions. This in urn has increased he chances of he power sysem o exhibi unsable behavior ha is ofen characerized by volage insabiliy, someimes even leading o a oal collapse or blackou). As numerous volage insabiliy incidens have occurred around he globe in recen years, volage sabiliy sudies have gained momenum. Volage sabiliy has now become one of he major concerns in he planning and operaion of all power sysems. A. Definiions of Volage Sabiliy There have been several revisions in he definiion of volage sabiliy and volage collapse over a period of years [10]. Following are he acceped definiions i) According o IEEE [1990]: Volage collapse is he process by which volage insabiliy leads o loss of volage in a significan par of he sysem. ii) According o CIGRE [1993]: Volage insabiliy is he absence of volage sabiliy, and resuls in progressive volage collapse or increase). iii) According o Kundur [1994]: Volage sabiliy is he abiliy of a power sysem o mainain seady accepable volage a all buses in he sysem a normal operaing condiions, and afer being subjeced o a disurbance. iv) According o IEEE / CIGRE Join Task Force [2004]: Volage sabiliy refers o he abiliy of a power sysem o mainain seady volages a all buses in he sysem afer being subjeced o a disurbance from a given iniial operaing condiion. I depends on he abiliy o mainain / resore equilibrium beween load demand and load supply from he power sysem. Insabiliy ha may resul occurs in he form of progressive fall or rise of volages of some buses. Volage collapse is he process by which he sequence of evens accompanying volage insabiliy leads o a blackou or abnormally low volages in a significan par of he power sysem. B. Classificaion of Volage Sabiliy Based on he naure of he phenomenon of volage sabiliy or insabiliy), following classificaion has been advocaed in [10] 52
i) ii) iii) iv) Large Disurbance Volage Sabiliy Refers o sysem s abiliy o mainain seady volages afer large disurbance such as sysem fauls, loss of generaion, or circui coningencies. Small Disurbance Volage Sabiliy Refers o sysem s abiliy o mainain seady volages when subjeced o small perurbaions such as incremenal changes in sysem load. Shor Term Volage Sabiliy Refers o a disurbance period of he order of several seconds. Long Term Volage Sabiliy Refers o a disurbance period of he order of several or many minues. C. A Brief Noe on Applicaion of Synchrophasor Technology for Volage Sabiliy Assessmen The even of Augus 14, 2003 blackou in he norh easern Unied Saes and pars of Canada ha affeced almos 50 million people, emphasized he use of ime-synchronized recording devices in he Repor of US-Canada Power Sysem Ouage Task Force. Such synchrophasor devices like Phasor Measuremen Unis PMUs) enable coninuous wide area visualizaion of a power sysem nework in he form of ime samped volage and curren phasors. Following are some of he benefis ha Synchrophasor echnology provides as compared o he radiional SCADA echnology i) PMUs can provide synchrophasor daa a he rae of 30/60/120 phasor daases per second as compared o 1 daase in 4 seconds as provided by SCADA echnology. ii) Synchrophasor echnology direc measuremen of volage and curren angles a he bus or a branch using ime reference UTC obained from GPS saellie clocks, and hus here is no need for calculaing hese values using a sae esimaor as required if SCADA echnology is used. iii) Synchrophasor echnology provides a wide area view of he power sysem in he form of ime synchronized measuremens from differen geographically locaed subsaions, as compared o local non-ime synchronized measuremens obained using SCADA echnology. Hence, synchrophasor echnology enables a good assessmen of power grid sress like volage insabiliy. 3.1.2 Tesbed for performing online simulaion of volage sabiliy algorihms This secion gives a brief descripion of each of he hardware devices and sofware used in he es bed a Smar Grid Demonsraion & Research Invesigaion Lab SGDRIL) a WSU, along wih each of heir poenial applicaions [5]. 53
Real Time Digial Simulaor Real Time Digial Simulaor RTDS) is a power sysem simulaor ha simulaes a power sysem buil in RSCAD user inerface sofware in real ime. The RTDS works on he parallel processing echnology of digial signal processors and execues he program developed on is processors. The RTDS no only calculaes and shows he elecrical oupu values in he runime sofware, bu also produces scaled oupu signals digial as well as analog) hrough he oupu inerface cards incorporaed ino is sysem. The RTDS presen in he SGDRIL, WSU, consiss of one rack wih hree Giga Processor Cards GPCs) for processing all compuaions in real ime; one Giga Transceiver Worksaion Inerface Card GTWIF) for inerfacing he RSCAD user sofware wih he GPC cards of he RTDS; one Giga Transceiver Digial Inpu Card GTDI) for aking in inpu digial signals from exernal devices like relays; one Giga Transceiver Fron Panel Inerface card GTFPI) for aking in inpu digial signals and giving ou oupu digial signals from and o hardware devices like relays; hree Giga Transceiver Analog Oupu Card GTAO) for providing analog oupu signals o hardware devices like PMUs for measuring elecrical quaniies; one Giga Transceiver Analog Inpu Card GTAI) for aking in analog inpu signals from hardware devices; one Giga Transceiver Nework Inerface Card GTNET) for inerfacing a number of differen nework proocols wih he RTDS simulaor; and one Giga Transceiver Synchronizaion Card GTSYNC) for synchronizing he RTDS simulaion ime sep o an exernal ime reference like he GPS clock. GPS Clock A GPS clock provides he ime synchronizaion signal o all he synchrophasor devices, so ha all hese devices are in ime sync wih each oher and he daa ime samping is done simulaneously irrespecive of heir geographical locaion. The requiremen of a GPS clock o send such ime signals is ha i mus lock wih 4 GPS saellies hrough he GPS anenna. This kind of precise ime synchronizaion amongs all he devices is criical for deailed even analysis. In SGDRIL, here are wo GPS clocks SEL-2407 and PONOVO PGPSO2. These devices provide IRIG-B ype ime pulse oupus for he synchrophasor device IRIG-B inpus. Relays / PMUs / DFRs These are he Inelligen Elecronic Devices IEDs) ha form he hear of he smar grid es bed. Advancemens in high speed and reliable microprocessor based programmable relays in conjuncion wih advanced communicaion echnology embedded in such devices make monioring and conrol asks much more efficien han heir predecessors. Many of hese relays have faul finding feaure, which reduces he faul finding ime by abou 50%. Many relay manufacurers also provide he synchrophasor measuremen module i.e. a PMU) along wih he relay module, which means he monioring as well as conrol module, boh are in he same device. Many of hese devices have even recording feaure for pos even analysis purposes. In he es bed, here are differen kinds of relays, mean for generaor proecion, moor proecion, ransmission line proecion, 54
ransformer proecion, capacior bank proecion, reacor proecion, ec. Relays/PMUs in he es bed include SEL-351 2 nos.) wih synchrophasor measuremen feaure for nondirecional and direcional overcurren proecion, enhanced breaker monioring, pilo proecion scheme, auoreclosure conrol, and under-frequency loadshedding; SEL-387 1 no.) for muli-winding curren differenial proecion, overcurren proecion, resriced earh faul proecion; SEL-421 2 nos.) wih synchrophasor measuremen feaure for high speed disance proecion, direcional overcurren proecion, for pilo proecion scheme, auoreclosure conrol, and breaker failure monioring and conrol; GE-D60 1 no.) wih synchrophasor measuremen feaure for 5-zone quad or mho ype disance proecion, direcional overcurren proecion, muliple sandard pilo proecion schemes, single pole or hree pole ripping applicaions, 4-sho auoreclosure conrol, synchronism check for dual breaker operaion, ou of sep ripping and power swing blocking operaions; MICOM Alsom P847 1 No.) mainly for synchrophasor measuremen purpose; and TESLA 3000 disurbance recorder from ERLphase 1 No.) wih synchrophasor measuremen opion mainly for recording power sysem daa in hree domains: high speed ransien fauls in seconds), low speed dynamic swing in minues), and coninuous rend 10 seconds o 1 hour inervals). Curren & Volage Amplifiers The RTDS produces low level signals a is oupu pors as menioned earlier in II. A) These low level signals are inadequae o rigger he funcioning of he Relays, PMUs and DFRs excep for he ones manufacure by SEL, which have a special low level inerface ha can accep low level signals for is operaion). Thus hese signals need o be amplified o ge he volage and curren wihin he accepable range of each device for i o funcion properly. In SGDRIL, WSU, here is one curren amplifier and one volage amplifier from PONOVO. The curren amplifier has 6 oupu curren channels of range 0-30A wih maximum oupu power of 210VA, and has a ypical curren accuracy of < 0.1%. The volage amplifier has 6 oupu volage channels of range 0-250V wih a maximum oupu power of > 75VA, and has a ypical volage accuracy of < 0.1%. Phasor Daa Concenraor A Phasor Daa Concenraor PDC) aggregaes synchrophasor daa from a number of PMUs and also from PDCs a he lower ier of daa acquisiion. Aggregaed daa will be correlaed wih idenical ime-ags o creae a sysem wide measuremen se and archived o rerieve and use for fuure work. PDC has addiional funcions as well. I performs real-ime daa qualiy checks and calculaions involving high daa acquisiion raes such as 30 samples per second or higher like 120 samples per second. Since real-ime daa qualiy checks and calculaions should be done before he nex daa se arrive, he speed of performance mus be very quick. Some PDCs can down-sample sored daa o feed hem direcly o applicaions such as SCADA ha use daa a slower sample raes. A PDC is abided by sreaming proocol sandards such as IEEE C37.118 for boh he phasor daa inpu and he combined daa oupu sream o inerface wih daa-using applicaions. PDCs are available as hardware as well as sofware. The PDC presen in he es bed of SGDRIL is of boh ypes hardware as well as sofware. The sofware PDC is SEL-5073 wih inegraed daa archiving feaure ha runs on Microsof Windows based compuing 55
plaform. Daa can be archived on a coninuous basis or on he basis of predefined riggers. This sofware PDC has he capabiliy of acquiring synchrophasor daa from more han 200 PMUs and suppors message raes of 240 messages per second. I can send concenraed synchrophasor daa o 6 cliens a he higher level of monioring and conrol. The hardware PDC in SGDRIL is SEL-3373 wih inegraed daa archiving feaure. There are wo main differences beween he hardware PDC and he sofware PDC. The hardware PDC allows saving of all PMU daa on he solid-sae drive SSD) in he secure daabase. This ensures ha no PMU daa is los if communicaion wih he subsaion is disruped. This is a clear advanage over he sofware PDC. However, he oher poin of difference beween he wo ypes of PDCs is ha unlike he sofware PDC, he hardware PDC can acquire synchrophasor daa from up o a maximum of 40 PMUs a he same message rae of 240 messages per second specific o SEL PDC). Synchrophasor Visualizaion Sofware Many a imes, i becomes imporan o have a visual inerpreaion of he synchrophasor daa o see he rends of he differen elecrical parameers in real ime. SEL SynchroWAVe Cenral Sofware SEL-5078 is used o ranslae synchrophasor daa ino visual informaion, hus providing beer siuaional awareness. Synchrophasor daa can also be archived for power sysem analysis. Synchrophasor Vecor Processor As aemps are being made o make he power grid smarer, a lo of imporance is being given o real ime conrol of power sysem on he basis of real ime sysem monioring. SEL-3378 Synchrophasor Vecor Processor SVP) is a Programmable Logic Conroller PLC) like real ime conrol device which akes in synchrophasor daa as is inpu eiher from PDCs, or direcly from he PMUs) and oupus conrol acions, based on he conrol algorihm in he SVP o he PDCs, Relays or oher inelligen conrol devices) for wide area proecion and conrol of he power sysem. The SVP has he abiliy o idenify power sysem oscillaions wih preconfigured modal analysis; measure volage, curren, phase angle, real and reacive power; improve he efficiency of he sysem by opimizing volages and minimizing loop flows; and conrol circui breakers, and/or saic VAR compensaors based on he conrol algorihm. Thus, he SVP is a very powerful ool in deecing and conrolling he sabiliy of a power sysem. Anoher applicaion of his device is for measuremen of he saes of he power sysem. I can screen bad daa obained from a saion and hen send he rue daa o he Energy Managemen Sysem EMS). Addiionally, i can also calculae he sae vecors of he surrounding saions so as o provide measuremen redundancy. Apar from conrol, he SVP can also be used o generae alarms o he sysem operaors if he se hreshold limis of he elecrical parameers are violaed. In SGDRIL, presenly he SVP is primarily being used for idenifying and conrolling volage insabiliy in real ime a one or more buses in he es case power sysem. Subsaion Auomaion Compuer SEL-3354 is a robus, compuer CPU hardware designed o operae in he harsh environmen of a subsaion. I can have eiher Windows or Linux as he operaing 56
sysem. I doesn have a fan or as such, any moving pars. I is designed o wihsand 15 kv elecrosaic discharge, overcurren, dielecric srengh, radiaed emissions, fas ransiens, and pulse magneic field disurbances. I mees IEEE 1613, IEEE C37.90, and IEC 60255 Proecive Relay Sandards. A field-programmable gae array FPGA) provides an exra level of compuer sysem reliabiliy wih a programmable sysem monior inerface and alarm configuraion. If his hardware CPU is conneced o a video monior, keyboard, and mouse, i can be used o provide a human-machine inerface HMI) for alarm annunciaion, local indicaion, conrol, and configuraion. This hardware has a 4GB RAM and a 60GB or 120 GB solid sae drive sorage and can be conneced o various local peripherals and high-speed nework inerfaces wih hree 10/100BASE-T Eherne fiber opional), six USB, and up o 16 EIA-232/EIA-485 pors. Several sofware programs can be insalled in SEL-3354 so as o inerface i wih he Inelligen Elecronic Devices IEDs) insalled in he subsaion. This device can hus be used o make relay seings, gaher, view, and analyze even repors generaed by subsaion relays. I can also be used o forward informaion o muliple maser daa users, such as SCADA. In SGDRIL, his hardware device has been used o suppor various inerfacing sofware programs required for communicaion wih relays/pmus, PDC, and SVP. NS3: NS3 is a discree even communicaion nework simulaor. In his work, we use NS3 o deliver daa beween conrol cener and subsaion while emulaing delays due o processing, ransmission, propagaion and queuing encounered in a real communicaion nework. Inegraion of all he sofware and hardware devices for carrying ou online simulaion of volage sabiliy algorihm Figure 3.1: Smar grid es bed for simulaion of volage sabiliy algorihm 57
All he hardware and sofware programs described in he previous secion have been inegraed o form a smar grid es bed, which has he capabiliy of supporing real ime hardware-in-loop simulaions and synchrophasor device esing. Fig. 3.1 shows he archiecure of he inerconnecions communicaions and hard wired) amongs he various devices. The compuer suppors all kinds of sofwares inerfacing and simulaion) and is conneced o he Eherne swich hub) so as o communicae wih all oher devices presen in he es bed. The relays / PMUs, SVP are all conneced hrough Eherne connecions o he Eherne swich for communicaion purpose. The relays / PMUs are conneced o he analog and/or digial oupu pors of he RTDS o receive low level signals obained during he real ime simulaion of he sysem buil in RTDS using RSCAD. Those relays which canno operae using low level signals have been provided wih volage and curren amplifiers, which amplify he signals suiably. The relays / PMUs, RTDS, PDC, and SVP have all been synchronized o he UTC using he GPS Clock. The PDC and SVP can ge daa from he relays / PMUs. 3.1.3 Performance of online simulaions of volage sabiliy algorihm The overall funcional block diagram of he smar grid es bed wih he communicaion nework opology used for an IEEE es case and he subsaion level views are shown in fig. 3.2. The subsaion view of slack bus represening node 0 in he communicaion nework shows a PDC concenraing local PMU volage phasor measuremen and sending hem o he moniored subsaion hrough NS3 emulaed communicaion nework. The subsaion view of his moniored bus represening a node in he communicaion nework shows a PDC concenraing daa from he local PMU and receiving volage phasor from slack bus hrough NS3. The arrangemen of obaining slack bus measuremens is essenial as he power flow angle of he moniored bus w.r.. he slack bus angle can only be obained if is synchrophasor angle which are referenced o he UTC) is adjused wih ha of he slack bus. Boh he PMUs are inerfaced wih he RTDS o receive measuremen signals. The daa rerieval scrip rerieves he required daa from he daabase and feeds i o he algorihm running on he subsaion compuer. The subsaion compuer compues he VSAI and sends i o he conrol cener for visualizaion hrough he emulaed communicaion nework. For online simulaion purpose using he above menioned es bed, a real ime volage sabiliy algorihm [5] has been coded in C-language and run on Linux plaform in he Subsaion compuer a he moniored bus in each of he esed sysems IEEE-14 Bus sysem and IEEE-30 Bus sysem). I has been found ha he algorihm runs exremely fas wih a guaraneed ime sep of 163 microseconds, hus making i highly suiable for real ime volage sabiliy monioring. As his algorihm is mean for volage sabiliy monioring of jus he subsaion ha is equipped wih a PMU, hence here are no scalabiliy issues. 58
Figure 3.2: Funcional block diagram for simulaion of volage sabiliy algorihm 59
3.1.3.1 Simulaion of a possible volage collapse scenario in an IEEE-14 Bus es case using he Real Time Tes Bed The IEEE-14 Bus es case has been modeled in RSCAD, in which Bus-12 has a PMU for real ime monioring of volage sabiliy. Figure 3.3: IEEE-14 bus es case modeled in RSCAD for real ime simulaion Table 3.1: Series of evens leading o volage collapse in IEEE-14 bus es case Even Even Descripion No. & Time 1 a Load a Bus-9 increases such ha he real power consumpion is 44.9 MW and he =25s reacive power consumpion is 25.2 MVAR. 2 a =35s 3 a =45s 4 a =55s 5 a =65s 6 a =75s 7 a =85s Base Case: 29.6 MW & 16.7 MVAR) Load a Bus-10 increases such ha he real power consumpion is 24.9 MW and he reacive power consumpion is 16 MVAR. Base Case: 9.1 MW & 5.9 MVAR) Load a Bus-14 increases such ha he real power consumpion is 24.9 MW and he reacive power consumpion is 8.3 MVAR. Base Case: 15 MW & 5.1 MVAR) Load a Bus-11 increases such ha he real power consumpion is 26.9 MW and he reacive power consumpion is 11.5 MVAR. Base Case: 3.6 MW & 1.9 MVAR) Inverse Time Over-curren relay hardware relay) rips he ransmission line connecing Bus-13 and Bus-6 due o loading of he line above he se pick up value. Load a Bus-12 increases such ha he real power consumpion is 11.9 MW and he reacive power consumpion is 3.1 MVAR. Base Case: 6.2 MW & 1.7 MVAR) Inverse Time Over-curren relay hardware relay) rips he ransmission line connecing Bus-12 and Bus-6 due o loading of he line above he se pick up value. 60
Table 3.1 shows he series of evens ha have been simulaed using he RSCAD es case in RTDS for a possible volage collapse scenario, assuming ha iniially he sysem is a base case. The Even-7 finally leads o a volage collapse. Fig. 3.4 shows he volage magniude a he Bus-12 and fig. 3.5 shows he volage angle a he Bus-12, as simulaed in real ime in RTDS runime. From fig. 3.4, i can be seen ha during he base case siuaion, he volage magniude a Bus-12 is around 1.05 p.u., whereas wih each even he sysem becomes more sressed and finally collapses, during which he volage magniude is 0.657 p.u. From fig. 3.5, i can be seen ha iniially he volage angle is -15.07 degrees, and which each even, he angle separaion sars increasing such ha during he collapse, he angle is as high as -38.36 degrees. Figure 3.4: RSCAD volage magniude changes a Bus-12 for IEEE 14 bus Figure 3.5: RSCAD showing angle changes a Bus-12 for IEEE 14 bus Figure 3.6 shows a screensho of he volage sabiliy visualizaion applicaion corresponding o he proposed algorihm) running in he compuer a he conrol cener. 61
I can be seen in fig. 3.6 ha a ime = 0 s, when he sysem is a base case, he VSAI of Bus-12 is 0.3203 i.e. near 0 ) signifying a volage sable scenario. However, when he series of evens as lised in able 3.1) ake place over a period of 85 seconds, a = 85 s, he VSAI shoos up o 1.08023 i.e. near 1 ), clearly indicaing a volage collapse scenario. Figure 3.6: VSAI leading o volage collapse from = 0 s o = 85 s Table 3.2: VSAI in real ime for each even leading o volage collapse Even No. & Time VSAI recorded during he Even a Bus-12 Volage Sabiliy Saus Base Case 0.32030 Sable 1 a =25s 0.34381 Sable 2 a =35s 0.36909 Sable 3 a =45s 0.38773 Sable 4 a =55s 0.39513 Sable 5 a =65s 0.43073 Sable 6 a =75s 0.48802 Sable 7 a =85s 1.08023 Unsable Table 3.3 shows he propagaion delays among he moniored bus, slack bus and he conrol cener as simulaed in he NS3 sofware. 62
Table 3.3: Propagaion delays beween subsaions and conrol cener From Propagaion To Gaeway Gaeway delay in ms) Bus 12 Bus 1 1.26955 Bus 12 Conrol Cener 1.46955 3.1.3.2 Simulaion of a possible volage collapse scenario in an IEEE-30 Bus es case using he Real Time Tes bed: The IEEE-30 Bus es case has been modeled in RSCAD, in which Bus-30 has a PMU for real ime monioring of volage sabiliy. Figure 3.7: IEEE-30 bus es case modeled in RSCAD for real ime simulaion Table-3.4 shows he series of evens ha have been simulaed using he RSCAD es case in RTDS for a possible volage collapse scenario, assuming ha iniially he sysem is a base case. 63
Even No. & Time 1 a =35s 2 a =50s 3 a =65s 4 a =80s 5 a =95s Table 3.4: Series of evens leading o volage collapse in IEEE-30 bus es case Even Descripion Load a Bus-24 increases such ha he real power consumpion is 25 MW and he reacive power consumpion is 19.2 MVAR. Base Case: 8.61 MW & 6.61 MVAR) Load a Bus-26 increases such ha he real power consumpion is 15 MW and he reacive power consumpion is 9.69 MVAR. Base Case: 3.51 MW & 2.21 MVAR) Load a Bus-29 increases such ha he real power consumpion is 7 MW and he reacive power consumpion is 2.4 MVAR. Base Case: 2.31 MW & 0.81 MVAR) Load a Bus-30 increases such ha he real power consumpion is 30 MW and he reacive power consumpion is 5.09 MVAR. Base Case: 10.51 MW & 1.81 MVAR) Inverse Time Over-curren relay hardware relay) rips he ransmission line connecing Bus-27 and Bus-30 due o loading of he line above he se pick up value. The Even-5 in he above able) finally leads o a volage collapse. Figure 3.8 shows he volage magniude a he Bus-30 and fig. 3.9 shows he volage angle a he Bus-30, as simulaed in real ime in RTDS runime. From fig. 3.8, i can be seen ha during he base case siuaion, he volage magniude a Bus-30 is around 1 p.u., whereas wih each even he sysem becomes more sressed and finally collapses, during which he volage magniude is 0.6511 p.u. From fig. 3.9, i can be seen ha iniially he volage angle is - 17.94 degrees, and which each even, he angle separaion sars increasing such ha during he collapse, he angle is as high as -40.61 degrees. Figure 3.8: RSCAD showing volage magniude changes a bus-30 for IEEE 30 bus 64
Figure 3.9: RSCAD showing angle changes a bus-30 for IEEE 30 bus I can be seen in fig. 3.10 ha a ime = 0 s, when he sysem is a base case, he VSAI of Bus-30 is 0.38107 i.e. near 0 ) signifying a volage sable scenario. However, when he series of evens as lised in able 3.4) ake place over a period of 95 seconds, a = 95 s, he VSAI shoos up o 1.09668 i.e. near 1 ), clearly indicaing a volage collapse scenario. Figure 3.10: VSAI leading o volage collapse from = 0 s o = 95 s 65
Table 3.5: VSAI compued in real ime for each even leading o volage collapse Even No. & Time Base Case 1 a =35s 2 a =50s 3 a =65s 4 a =80s 5 a =95s VSAI recorded during he Even a Bus-30 Volage Sabiliy Saus 0.38107 Sable 0.41658 Sable 0.46717 Sable 0.50554 Sable 0.80496 Sable 1. 09668 Unsable Table 3.6 shows he propagaion delays among he moniored bus, slack bus and he conrol cener as simulaed in he NS3 sofware. Table 3.6: Propagaion delays beween subsaions and conrol cener for 30 bus From Propagaion To Gaeway Gaeway delay in ms) Bus 30 Bus 1 1.85426 Bus 30 Conrol Cener 2.05426 3.1.4 Conclusion from Tes Resuls Increase in sysem loading has he poenial of causing a small disurbance ype volage insabiliy, whereas coningencies like ripping of ransmission lines have he poenial of causing large disurbance volage insabiliy. Boh hese sysem condiions have been simulaed in real ime using he RTDS. From he online resuls ha have been obained and presened above for differen IEEE es cases i.e. IEEE 14 Bus es case & IEEE 30 bus es case) under differen sysem condiions causing volage insabiliy problems, i can be seen ha he resuls are in accordance wih he saic heory of volage sabiliy analysis [4-5]. The same mehod of online simulaion using he RTDS and he hardware and sofware devices can be used for validaing he accuracy of differen online volage sabiliy algorihms. The volage sabiliy algorihm has also been implemened using Srucured Tex language a ype of PLC language) in he Synchrophasor Vecor Processor SVP) insead of he C-language on Linux plaform on he auomaion compuer, and exac same resuls have been obained. 66
3.2 Comparing Sae Esimaion Algorihms Using Synchrophasor Daa In performing PMU accuracy evaluaion in an absolue sense and under various condiions such as ampliude and frequency ransiens, waveform disorion ec.) i is imperaive ha he oupu of a PMU under es is compared o he oupu of a "Sandard PMU". Since he exising sandards do no presenly address his issue, a Sandard PMU was designed and implemened using Naional Insrumens daa acquisiion hardware and cusom sofware. The Sandard PMU sofware was implemened wihin he WinXFM program. Since he PMU capabiliy was added wihin he daa acquisiion sysem as an objec oriened sofware componen we refer o i as a "Virual PMU". The sandard PMU is used as a benchmark agains which he accuracy of he PMU under es is evaluaed. Therefore, i is necessary ha he sandard PMU provides accuracy ha exceeds he accuracy required by he sandards and remains accurae during ypical power sysem volage and curren ampliude and frequency ransiens and waveform disorion. PMU implemenaions are based on he direc evaluaion of he discree Fourier ransform: k 2 V = ω 2π a k cosωk ) v k i a k sinωk ) v k k=k 1 k 2 k=k 1 where a k are he waveform samples. The above expression yields he exac phasor of a sampled waveform only if he waveform period is an ineger muliple of he sampling rae, so ha he summaion index range spans an ineger number of fundamenal frequency periods. I also assumes ha no aliasing has occurred during he sampling, i.e. he original analog waveform does no conain any frequency componens higher han half he sampling rae). Since pracical daa acquisiion sysems operae wih a fixed sampling rae while he power sysem frequency varies, in general he waveform period is no an ineger muliple of he sampling rae. This resuls in a significan error in he phasor compuaion. A common approach o reduce his error is o apply low pass filering on he compued phasors. However, his approach inroduces large phasor compuaion errors during ampliude and frequency ransiens. In he sandard PMU, his issue is addressed using fracional sample inegraion. This mehod accuraely evaluaes he Fourier inegral by aking ino accoun he conribuions of he fracional end inervals ha occur whenever he waveform period is no an ineger muliple of he sampling rae. For example, consider he funcion illusraed in fig. 3.11. A single period of he funcion o be inegraed spans 17.5 sampling inervals. Compuing he inegral over a single cycle using rapezoidal inegraion requires he summaion of he 17 rapezoid areas locaed beween successive samples plus he area indicaed by he yellow rapezoid which spans a fracion of a sampling inerval. Using he rapezoidal approximaion, his area can be compued from he sampled values 67
brackeing he sampling inerval. This procedure resuls in a modified expression for he Discree Fourier ransform ha akes ino accoun fracional samples: k 2 V = ω 2π c ka k cosωk ) v k i c k a k sinωk ) v k k=k 1 k 2 k=k 1 where c k are coefficiens which depend on he duraion of he fracional samples. Figure 3.11: Fracional sample inegraion The fracional sample inegraion mehod can be also implemened using quadraic inegraion. For his purpose, he funcion o be inegraed is approximaed wih quadraic segmens where each segmen spans wo sampling inervals, as illusraed in fig. 3.12. The resuling expression is similar o he one derived using rapezoidal inegraion, bu wih differen c k coefficiens. In order o evaluae he performance of he sandard PMU algorihm boh rapezoidal and quadraic approaches were implemened and a parameric error analysis was performed. I was found ha he rapezoidal fracional inegraion mehod subsanially reduces he error ha occurs wih radiional DFT, while he quadraic mehod performs slighly beer han he rapezoidal mehod for sampling raes above 4 khz. The resuls of he parameric analysis are illusraed in fig. 3.13, which shows a plo of he phase angle error of a 60 Hz waveform versus he sampling rae. The plo includes races for he rapezoidal mehod blue race) and he quadraic mehod green race). I also includes he phase angle error occurring when no fracional sample error correcion is performed red race). Table 3.7 summarizes he resuls for a sampling rae of 8 khz. As i can be seen he esimaion of frequency and phasors wih he sandard PMU is highly accurae. The 68
sandard PMU is used for esing he performance of various commercially available PMUs as well as for various applicaions, such as disribued sae esimaion, sabiliy monioring, ec. Table 3.7: Phase error a sampling rae of 8 KHz Correcion Mehod Phase Error Degrees) None 0.2 Trapezoidal 0.00004 Quadraic 0.00002 Figure 3.12: Quadraic approximaion of a funcion from hree successive samples Figure 3.13: Sandard PMU algorihm performance 69
3.3 Dynamic Sae Esimaion Based Proecion Algorihms for Transformers In his secion, a new ransformer proecion approach based on dynamic sae esimaion and PMU synchronized daa has been developed and esed seing-less proecion). The ransformer models used, as well as he implemenaion issues of he mehod are discussed. 3.3.1 Descripion of he approach The archiecure of he seing-less proecion relay for a ransformer is shown in fig. 3.14. The relay requires he model of he ransformer as well as he model of he measuremens daa acquisiion sysem). The measuremens may consis of acual measuremens as well as derived, virual and pseudo measuremens. The ransformer model mus be cas in a sandard quadraic form, referred o as Algebraic Quadraic Companion Form AQCF), which is defined in his documen. Given he poiners ha connec he measured quaniies o sae variables of he ransformer model, he model equaions) for he acual, virual and pseudo-measuremens are auomaically obained. Given he sae equaions and a model ha links saes o measuremens, a dynamic sae esimaion is coninuously execued by he proecion relay, and from i he resuls regarding proecion decision rip/no rip) as well bad daa deecion and idenificaion can be obained.. Figure 3.14: Archiecure of he dynamic sae esimaion based proecive relay In his approach, he ime-domain componen model used is in AQCF. The AQCF is obained from he model of he ransformer described in erms of a se of linear and nonlinear algebraic and differenial equaions wih he following procedure: firs he model is quadraized wih he inroducion of addiional sae variables resuling in a se 70
of linear and quadraic algebraic and differenial equaions. Subsequenly he quadraized model is inegraed wih he quadraic inegraion mehod yielding he model in he form of a se of Algebraic Quadraic Companion Form AQCF). As a resul of he quadraic inegraion, he sae equaions are wrien in erms of he sae of he componen a wo consecuive ime seps namely and m ) and pas hisory values. Hence, as shown in fig. 3.15, he dynamic sae esimaion algorihm ha enables seing-less proecion operaes on measuremens z) of wo consecuive ime insances and m = - s noe ha s signifies he sampling period). For a sampling rae of 5000 samples per second, i is implied ha s is 200μs, which in urn implies ha he analyics of he seing-less proecion algorihm mus be performed as wo ses of new measuremens arrive) wihin an inerval of 400μs, before he nex se of daa arrives. As a goal for his projec, an execuion ime of 200μs has been argeed. The overall approach is illusraed in fig. 3.16. The deails of his approach as applied o he proecion of a ransformer is discussed nex. Figure 3.15: Illusraion of ime samples for ieraion of he seing-less relay 71
3.3.2 Transformer Seing-less Proecion Approach Descripion 3.3.2.1 Transformer Model A deailed ransformer model has been derived in ime domain and has been cas in AQCF using quadraic inegraion. Here we presen he final AQCF model of he hreephase, wo-winding, variable-ap, and saurable-core ransformer as follows: + = 3 ) ) ) ) ) ) ) ) ) ) 0 ) 0 ),2 3,1 3,2 3,1 3 3 3 42 41 32 31 22 21 12 11 3 3 3 3 44 43 42 41 34 33 32 31 24 23 22 21 14 13 12 11 3 m m m m m f f f f h y h v N N N N N N N N y v y v Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y i i φ φ φ φ φ φ φ φ φ φ φ φ 3.1) where: T N C B A c b a i i i i i i i i )] ), ), ), ), ), ), [ ) 3 = φ 3.2) = 44 43 42 41 34 33 32 31 24 23 22 21 14 13 12 11 Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y eq 3.3) T N C B A c b a v v v v v v v v )] ), ), ), ), ), ), [ ) 3 = φ 3.4) T C C C C LC LC C C mc B B B B LB LB B B mb A A A A LA LA A A ma z y y y i i e i z y y y i i e i z y y y i i e i y )] ), ), ), ), ), ), ), ), ), ), ), ), ), ), ), ), ), ), ), ), ), ), ), ), ), ), [ ) 3 2 1 3 1 3 2 1 3 1 3 2 1 3 1 3 λ λ λ φ = 3.5) = 42 41 32 31 22 21 12 11 N N N N N N N N N eq 3.6) = ) ) ) ) ) ) ) 1 7 1 1 2 1 1 1 1,1 3 x Q x x Q x x Q x f T T T φ φ φ φ φ φ φ 3.7) = ) ) ) ) ) ) ) 1 27 1 1 9 1 1 8 1,2 3 x Q x x Q x x Q x f T T T φ φ φ φ φ φ φ 3.8) The deailed derivaion of his model is no shown here in he ineres of space. The sae variables for a hree-phase, dela-wye ransformer n = 5) are 68 34 for ime sep and 34 for inermediae ime sep m ), as lised in Table 3.8. 72
Table 3.8: All sae variables of he hree-phase ransformer n = 5) Sae Type Time Descripion x 1 = v a ) Exernal Phase-a erminal volage a he primary side x 2 = v b ) Exernal Phase-b erminal volage a he primary side x 3 = v c ) Exernal Phase-c erminal volage a he primary side x 4 = v A ) Exernal Phase-A erminal volage a he secondary side x 5 = v B ) Exernal Phase-B erminal volage a he secondary side x 6 = v C ) Exernal Phase-C erminal volage a he secondary side x 7 = v N ) Exernal Neural erminal volage a he secondary side x 8 = i ma ) Inernal Magneizing curren a he primary-side, phase-a coil x 9 = e A ) Inernal Phase-a winding volage a he primary side x 10 = λ A ) Inernal Magneic flux linkage a he phase-a core x 11 = i 1LA ) Inernal Phase-a erminal curren a he primary side x 12 = i 3LA ) Inernal Phase-A erminal curren a he secondary side x 13 = y 1A ) Inernal Addiional sae for he nonlinear erm a phase a x 14 = y 2A ) Inernal Addiional sae for he nonlinear erm a phase a x 15 = y 3A ) Inernal Addiional sae for he nonlinear erm a phase a x 16 = z A ) Inernal Addiional sae for he nonlinear erm a phase a x 17 = i mb ) Inernal Magneizing curren a he primary-side, phase-b coil x 18 = e B ) Inernal Phase-b winding volage a he primary side x 19 = λ B ) Inernal Magneic flux linkage a he phase-b core x 20 = i 1LB ) Inernal Phase-b erminal curren a he primary side x 21 = i 3LB ) Inernal Phase-B erminal curren a he secondary side x 22 = y 1B ) Inernal Addiional sae for he nonlinear erm a phase b x 23 = y 2B ) Inernal Addiional sae for he nonlinear erm a phase b x 24 = y 3B ) Inernal Addiional sae for he nonlinear erm a phase b x 25 = z B ) Inernal Addiional sae for he nonlinear erm a phase b 73
Table 3.8 coninued Sae Type Time Descripion x 26 = i mc ) Inernal Magneizing curren a he primary-side, phase-c coil x 27 = e C ) Inernal Phase-c winding volage a he primary side x 28 = λ C ) Inernal Magneic flux linkage a he phase-c core x 29 = i 1LC ) Inernal Phase-c erminal curren a he primary side x 30 = i 3LC ) Inernal Phase-C erminal curren a he secondary side x 31 = y 1C ) Inernal Addiional sae for he nonlinear erm a phase c x 32 = y 2C ) Inernal Addiional sae for he nonlinear erm a phase c x 33 = y 3C ) Inernal Addiional sae for he nonlinear erm a phase c x 34 = z C ) Inernal Addiional sae for he nonlinear erm a phase c x 35 = v a m ) Exernal m Phase-a erminal volage a he primary side x 36 = v b m ) Exernal m Phase-b erminal volage a he primary side x 37 = v c m ) Exernal m Phase-c erminal volage a he primary side x 38 = v A m ) Exernal m Phase-A erminal volage a he secondary side x 39 = v B m ) Exernal m Phase-B erminal volage a he secondary side x 40 = v C m ) Exernal m Phase-C erminal volage a he secondary side x 41 = v N m ) Exernal m Neural erminal volage a he secondary side x 42 = i ma m ) Inernal m Magneizing curren a he primary-side, phase-a coil x 43 = e A m ) Inernal m Phase-a winding volage a he primary side x 44 = λ A m ) Inernal m Magneic flux linkage a he phase-a core x 45 = i 1LA m ) Inernal m Phase-a erminal curren a he primary side x 46 = i 3LA m ) Inernal m Phase-A erminal curren a he secondary side x 47 = y 1A m ) Inernal m Addiional sae for he nonlinear erm a phase a x 48 = y 2A m ) Inernal m Addiional sae for he nonlinear erm a phase a x 49 = y 3A m ) Inernal m Addiional sae for he nonlinear erm a phase a x 50 = z A m ) Inernal m Addiional sae for he nonlinear erm a phase a x 51 = i mb m ) Inernal m Magneizing curren a he primary-side, phase-b coil 74
Table 3.8 coninued Sae Type Time Descripion x 52 = e B m ) Inernal m Phase-b winding volage a he primary side x 53 = λ B m ) Inernal m Magneic flux linkage a he phase-b core x 54 = i 1LB m ) Inernal m Phase-b erminal curren a he primary side x 55 = i 3LB m ) Inernal m Phase-B erminal curren a he secondary side x 56 = y 1B m ) Inernal m Addiional sae for he nonlinear erm a phase b x 57 = y 2B m ) Inernal m Addiional sae for he nonlinear erm a phase b x 58 = y 3B m ) Inernal m Addiional sae for he nonlinear erm a phase b x 59 = z B m ) Inernal m Addiional sae for he nonlinear erm a phase b x 60 = i mc m ) Inernal m Magneizing curren a he primary-side, phase-c coil x 61 = e C m ) Inernal m Phase-c winding volage a he primary side x 62 = λ C m ) Inernal m Magneic flux linkage a he phase-c core x 63 = i 1LC m ) Inernal m Phase-c erminal curren a he primary side x 64 = i 3LC m ) Inernal m Phase-C erminal curren a he secondary side x 65 = y 1C m ) Inernal m Addiional sae for he nonlinear erm a phase c x 66 = y 2C m ) Inernal m Addiional sae for he nonlinear erm a phase c x 67 = y 3C m ) Inernal m Addiional sae for he nonlinear erm a phase c x 68 = z C m ) Inernal m Addiional sae for he nonlinear erm a phase c To implemen he seing-less ransformer proecion for a hree-phase dela/wye conneced ransformer, he following measuremens are defined: Acual measuremens six volages a ime phase a-n, phase b-n, phase c-n, phase A-N, phase B-N, and phase C-N) seven currens a ime phase a, phase b, phase c, phase A, phase B, phase C, and phase N) six volages a ime m phase a-n, phase b-n, phase c-n, phase A-N, phase B-N, and phase C-N) seven currens a ime m phase phase a, phase b, phase c, phase A, phase B, phase C, and phase N). 75
These measuremens have a measuremen error depended upon he accuracy of he meers used. We represen his error wih is sandard deviaion. Virual measuremens These include measuremens wih a value equal o zero a ime [8h- o 34h-row in equaion 3.1) and measuremens wih a value equal o zero a ime m 42h- o 68h-row in equaion 3.2). These measuremens represen he zero value on he lef hand side of he 8h- o 34h-row and 42nd- o 68h-row in equaion 3.2). The virual measuremens are known wih absolue precision and normally we should assign a measuremen error of zero. However he algorihm will suffer a singulariy if an error of zero is used. For his reason we use a sandard deviaion which is equal o 0.001pu. Table 3.9: Acual across measuremens for he hree-phase ransformer Type Name Measuremen Model Sandard Deviaion Across volage_an z 1 = v a ) v N ) 0.01 p.u.) * Vscaleh Across volage_bn z 2 = v b ) v N ) 0.01 p.u.) * Vscaleh Across volage_cn z 3 = v c ) v N ) 0.01 p.u.) * Vscaleh Across volage_an z 4 = v A ) v N ) 0.01 p.u.) * Vscalel Across volage_bn z 5 = v B ) v N ) 0.01 p.u.) * Vscalel Across volage_cn z 6 = v C ) v N ) 0.01 p.u.) * Vscalel Across volage_anm z 7 = v a m ) v N m ) 0.01 p.u.) * Vscaleh Across volage_bnm z 8 = v b m ) v N m ) 0.01 p.u.) * Vscaleh Across volage_cnm z 9 = v c m ) v N m ) 0.01 p.u.) * Vscaleh Across volage_anm z 10 = v A m ) v N m ) 0.01 p.u.) * Vscalel Across volage_bnm z 11 = v B m ) v N m ) 0.01 p.u.) * Vscalel Across volage_cnm z 12 = v C m ) v N m ) 0.01 p.u.) * Vscalel Pseudo measuremens These measuremens represen quaniies ha are normally no measured, such as ground volage and curren in he neural. Typically, i is assumed ha hese measuremens have a relaively large measuremen error wih sandard deviaion equal o 0.1pu. For his ransformer we define he following pseudo-measuremens: one volage a ime phase N-g) and one volage a ime m phase N-g). 76
Noe ha for his hree-phase ransformer, here are 26 acual measuremens, 54 virual measuremens, and 2 pseudo measuremens; here are a oal of 82 measuremens. I is noed ha here are 68 saes, and herefore, his provides a redundancy of 20.6% i.e., 82-68)/68). All across, hrough, virual, and pseudo measuremens ha are used for he dynamic sae esimaor are lised in Table 3.9, Table 3.10, Table 3.11, and Table 3.12, respecively. The sandard deviaions are given in % in a per-uni sysem ha uses he ransformer raed values as bases. I is imporan o poin ou ha when wo consecuive sampling poins are impored, he firs poin becomes a measuremen for he inermediae ime m, and he second poin becomes a measuremen for he curren ime. Table 3.10: Acual hrough measuremens for he hree-phase ransformer Type Name Measuremen Model Sandard Deviaion Through curren_a z 1 = i a ) = 1s-row in eq. 3.1) 0.01 p.u.) * Iscaleh Through curren_b z 2 = i b ) = 2nd-row in eq. 3.1) 0.01 p.u.) * Iscaleh Through curren_c z 3 = i c ) = 3rd-row in eq. 3.1) 0.01 p.u.) * Iscaleh Through curren_a z 4 = i A ) = 4h-row in eq. 3.1) 0.01 p.u.) * Iscalel Through curren_b z 5 = i B ) = 5h-row in eq. 3.1) 0.01 p.u.) * Iscalel Through curren_c z 6 = i C ) = 6h-row in eq. 3.1) 0.01 p.u.) * Iscalel Through curren_n z 7 = i N ) = 7h-row in eq. 3.1) 0.01 p.u.) * Iscalel Through curren_am z 8 = i a m ) = 35h-row in eq. 3.1) 0.01 p.u.) * Iscaleh Through curren_bm z 9 = i b m ) = 36h-row in eq. 3.1) 0.01 p.u.) * Iscaleh Through curren_cm z 10 = i c m ) = 37h-row in eq. 3.1) 0.01 p.u.) * Iscaleh Through curren_am z 11 = i A m ) = 38h-row in eq. 3.1) 0.01 p.u.) * Iscalel Through curren_bm z 12 = i B m ) = 39h-row in eq. 3.1) 0.01 p.u.) * Iscalel Through curren_cm z 13 = i C m ) = 40h-row in eq. 3.1) 0.01 p.u.) * Iscalel Through curren_nm z 14 = i N m ) =41s-row in eq. 3.1) 0.01 p.u.) * Iscalel 77
Table 3.11: Virual measuremens for he hree-phase ransformer Type Name Measuremen Model Sandard Deviaion Virual virual 1 z 1 = 0 = 8h-row in eq. 3.1) 0.001 p.u.) Virual virual 2 z 2 = 0 = 9h-row in eq. 3.1) 0.001 p.u.) Virual virual 3 z 3 = 0 = 10h-row in eq. 3.1) 0.001 p.u.) Virual virual 4 z 4 = 0 = 11h-row in eq. 3.1) 0.001 p.u.) Virual virual 5 z 5 = 0 = 12h-row in eq. 3.1) 0.001 p.u.) Virual virual 6 z 6 = 0 = 13h-row in eq. 3.1) 0.001 p.u.) Virual virual 7 z 7 = 0 = 14h-row in eq. 3.1) 0.001 p.u.) Virual virual 8 z 8 = 0 = 15h-row in eq. 3.1) 0.001 p.u.) Virual virual 9 z 9 = 0 = 16h-row in eq. 3.1) 0.001 p.u.) Virual virual 10 z 10 = 0 = 17h-row in eq. 3.1) 0.001 p.u.) Virual virual 11 z 11 = 0 = 18h-row in eq. 3.1) 0.001 p.u.) Virual virual 12 z 12 = 0 = 19h-row in eq. 3.1) 0.001 p.u.) Virual virual 13 z 13 = 0 = 20h-row in eq. 3.1) 0.001 p.u.) Virual virual 14 z 14 = 0 = 21s-row in eq. 3.1) 0.001 p.u.) Virual virual 15 z 15 = 0 = 22nd-row in eq. 3.1) 0.001 p.u.) Virual virual 16 z 16 = 0 = 23rd-row in eq. 3.1) 0.001 p.u.) Virual virual 17 z 17 = 0 = 24h-row in eq. 3.1) 0.001 p.u.) Virual virual 18 z 18 = 0 = 25h-row in eq. 3.1) 0.001 p.u.) Virual virual 19 z 19 = 0 = 26s-row in eq. 3.1) 0.001 p.u.) Virual virual 20 z 20 = 0 = 27nd-row in eq. 3.1) 0.001 p.u.) Virual virual 21 z 21 = 0 = 28rd-row in eq. 3.1) 0.001 p.u.) Virual virual 22 z 22 = 0 = 29h-row in eq. 3.1) 0.001 p.u.) Virual virual 23 z 23 = 0 = 30h-row in eq. 3.1) 0.001 p.u.) 78
Table 3.11 coninued Type Name Measuremen Model Sandard Deviaion Virual virual 24 z 24 = 0 = 31s-row in eq. 3.1) 0.001 p.u.) Virual virual 25 z 25 = 0 = 32nd-row in eq. 3.1) 0.001 p.u.) Virual virual 26 z 26 = 0 = 33rd-row in eq. 3.1) 0.001 p.u.) Virual virual 27 z 27 = 0 = 34h-row in eq. 3.1) 0.001 p.u.) Virual virual_m_1 z 28 = 0 = 42nd-row in eq. 3.1) 0.001 p.u.) Virual virual_m_2 z 29 = 0 = 43rd-row in eq. 3.1) 0.001 p.u.) Virual virual_m_3 z 30 = 0 = 44h-row in eq. 3.1) 0.001 p.u.) Virual virual_m_4 z 31 = 0 = 45h-row in eq. 3.1) 0.001 p.u.) Virual virual_m_5 z 32 = 0 = 46h-row in eq. 3.1) 0.001 p.u.) Virual virual_m_6 z 33 = 0 = 47h-row in eq. 3.1) 0.001 p.u.) Virual virual_m_7 z 34 = 0 = 48h-row in eq. 3.1) 0.001 p.u.) Virual virual_m_8 z 35 = 0 = 49h-row in eq. 3.1) 0.001 p.u.) Virual virual_m_9 z 36 = 0 = 50h-row in eq. 3.1) 0.001 p.u.) Virual virual_m_10 z 37 = 0 = 51s-row in eq. 3.1) 0.001 p.u.) Virual virual_m_11 z 38 = 0 = 52nd-row in eq. 3.1) 0.001 p.u.) Virual virual_m_12 z 39 = 0 = 53rd-row in eq. 3.1) 0.001 p.u.) Virual virual_m_13 z 40 = 0 = 54h-row in eq. 3.1) 0.001 p.u.) Virual virual_m_14 z 41 = 0 = 55h-row in eq. 3.1) 0.001 p.u.) Virual virual_m_15 z 42 = 0 = 56h-row in eq. 3.1) 0.001 p.u.) Virual virual_m_16 z 43 = 0 = 57h-row in eq. 3.1) 0.001 p.u.) Virual virual_m_17 z 44 = 0 = 58h-row in eq. 3.1) 0.001 p.u.) Virual virual_m_18 z 45 = 0 = 59h-row in eq. 3.1) 0.001 p.u.) 79
Table 3.11 coninued Type Name Measuremen Model Sandard Deviaion Virual virual_m_19 z 46 = 0 = 60h-row in eq. 3.1) 0.001 p.u.) Virual virual_m_20 z 47 = 0 = 61s-row in eq. 3.1) 0.001 p.u.) Virual virual_m_21 z 48 = 0 = 62nd-row in eq. 3.1) 0.001 p.u.) Virual virual_m_22 z 49 = 0 = 63rd-row in eq. 3.1) 0.001 p.u.) Virual virual_m_23 z 50 = 0 = 64h-row in eq. 3.1) 0.001 p.u.) Virual virual_m_24 z 51 = 0 = 65h-row in eq. 3.1) 0.001 p.u.) Virual virual_m_25 z 52 = 0 = 66h-row in eq. 3.1) 0.001 p.u.) Virual virual_m_26 z 53 = 0 = 67h-row in eq. 3.1) 0.001 p.u.) Virual virual_m_27 z 54 = 0 = 68h-row in eq. 3.1) 0.001 p.u.) Table 3.12: Pseudo measuremens for he hree-phase ransformer Type Name Measuremen Model Sandard Deviaion Pseudo volage_n z 1 = 0 = v N ) 0.1 p.u.) * Vscalel Pseudo volage_nm z 2 = 0 = v N m ) 0.1 p.u.) * Vscalel Noe ha if here is no acual hrough measuremen for he neural phase i.e., phase N), pseudo measuremens for he phase-n curren can be added wih a sandard deviaion of 0.1 per uni. The proposed proecion algorihm uses four ypes of measuremens: across measuremens, hrough measuremens, virual measuremens, and pseudo measuremens. I is imporan o poin ou ha all measuremens e.g., z 1, z 2,, z m ) can be expressed wih he funcions of sae variables [e.g., h 1 x), h 2 x),, h m x)] and measuremen errors e.g., η 1, η 2,, η m ), forming he following measuremen model: z = hx) +η 3.9) where: 80
z1 z2 z = z m 3.10) h1 x) h2 x) h x) = hm x) 3.11) η1 x) η2 x) η x) = η m x) 3.12) Using he AQCF model of he ransformer he measuremen model is expressed in he following sandard form: zm = c + aixi + bjk x jx k ηm 3.13) i where z m is he measured value, c is he consan erm, a i are he linear coefficien erms, b jk are he nonlinear coefficien erms i.e., quadraic erms), x i, x j, and x k are he sae variables, i, j, and k are he indices of summaion, and η m is he measuremen error. j k 3.3.2.2 Dynamic Sae Esimaion The dynamic sae esimaion is obained using a sandard weighed leas squares approach, which is relaively sraigh forward, once he sae equaions and measuremen models have been obained. A deailed oulined of he mehod is given in fig. 3.16. Dynamic sae esimaion is inspired by disribued sae esimaion work done earlier [11-12]. 3.3.3 Proecion Logic The enire proecion logic is based on he resuls of he dynamic sae esimaor. Once he microprocessor ges he measuremens from boh sides of a ransformer under proecion, he dynamic sae esimaion runs using he ransformer AQCF model. Then, he chi-square es is performed o provide he probabiliy ha all he acual values for measuremens fi o he ransformer model. The resuls of he chi square are used o compue he confidence level ha measuremens fi he ransformer model and herefore he ransformer is in a healhy saus. If he confidence level drops o a low value for several cycles, hen he measuremens do no fi he model, hus he inernal ransformer model is incorrec, indicaing an inernal faul. As a resul, he relay would acivae breakers and rip he ransformer immediaely. 81
Figure 3.16: Overall algorihm of sae esimaion Meanwhile, during he sae esimaion process, he operaing limi is being moniored so ha he ransformer will be ripped once i violaes he operaing limi. Sar Iniialize Pas Hisory 0 0 ) ) 3 3 h y h V φ φ Sreaming Measuremen a Time is Compleed Iniialize Saes = 0 0 0 0 ) ) ) ) 3 3 3 3 m m y V y V φ φ φ φ Conribue All Measuremens o Form H T WH and H T Whx)-z) Calculae Gauss-Newon Ieraive Algorihm ) ) ) 1 1 z x h W H WH H x x i T T i i = + 0.01 1 < i+ i x x Calculae Confidence Level ), Pr 1.0 ] Pr[ 1.0 ] Pr[ 2 2 ν ζ ζ χ ζ χ = = = = m i i i z i x h 1 2 ˆ) σ ζ n = m ν YES NO Proecion Logic If Confidence Level < 10%, hen Trip Breakers Updae Pas Hisory If Confidence Level > 10%, hen Else If Confidence Level < 10%, hen ) ) ) ) 3 3 3 3 y V h y h V φ φ φ φ 0 0 ) ) 3 3 h y h V φ φ Proceed o Nex Time Sep h + +1 i i 82
The above described ransformer proecion requires no seing. Time synchronizaion is quie imporan for he proposed proecion scheme since he algorihm requires synchronized measuremens. Therefore he applicaion of his algorihm requires he use of PMUs are equivalen. 3.3.4 Transformer Seing-less proecion resuls The above described seing-less relay for ransformers have been esed wih simulaed daa. Specifically a es sysem was used o creae a number of scenarios. For each scenario he sysem was simulaed and he measuremens of he relay were sored in a COMTRADE file. Device Model WinIGS Measuremens COMTRADE) Seing-Less Proecive Relay Tes Resuls COMTRADE) Figure 3.17: Tes scheme for verifying he proposed proecion mehod The simulaion was performed wih he program WinIGS-T. Boh measuremens and device model consiue he inpu daa o he seing-less proecive relay which in urn performs dynamic sae esimaion and he proecion logic. The proecive relay oupus include esimaed saes, esimaed measuremens, raw measuremens, residuals beween esimaed and measured values, normalized residuals, and he processing ime; hese resuls are also sored in COMTRADE forma for addiional analysis and performance evaluaion of he algorihm. Figure 3.17 describes he overall approach for he feasibiliy es of he seing-less proecion algorihm. The es sysem used for numerical ess is shown in fig. 3.18. The sysem consiss of a 15kV-150MVA-raed generaor, an 18kV-350MVA-raed generaor, a 15kV-200MVAraed generaor, ransformers, and ransmission lines ha connec load on each line. The hree-phase ransformer under proecion is locaed a he middle of he enire sysem see he red circle in fig. 3.18). Moniored are en volages and seven currens a boh he erminals of he ransformer. 83
Figure 3.18: Tes sysem for he seing-less proecion Figure 3.19: Seings of he hree-phase ransformer under proecion 84
The red area is he ransformer zone being proeced. As shown in he diagram, he measuremens of volages and currens on boh sides are provided by PTs and CTs. In his es, he exponen n, which expresses nonlinear characerisics beween he magneizing curren and he flux linkage of he ransformer core, is five, and he ransformer is dela-wye-conneced. The seings of he ransformer under proecion are shown in fig. 3.19. g g 188.7 k Volage_XFMR1_AG V) Volage_XFMR1_BG V) Volage_XFMR1_CG V) 63.14 k -62.45 k -188.1 k 94.26 k 31.39 k Volage_XFMR2_AG V) Volage_XFMR2_BG V) Volage_XFMR2_CG V) Volage_XFMR2_NG V) -31.48 k -94.35 k 395.2 Curren_XFMR1_A A) Curren_XFMR1_B A) Curren_XFMR1_C A) 131.0-133.3-397.5 806.6 269.3 Curren_XFMR2_A A) Curren_XFMR2_B A) Curren_XFMR2_C A) Curren_XFMR2_N A) -268.0-805.3 3.210 3.240 3.270 3.300 Figure 3.20: Measuremen signals of he ransformer Tes A: normal operaion) The acual parameers of he single-phase ransformer model are given in Table 3.13 he parameers are idenical o all phases of he ransformer.) Table 3.13: Transformer parameers idenical a all phases) Parameer Value Parameer Value r 1 2.3805 Ω r c 158700 Ω L 1 0.096822 H L m 420.964824 H r 2 0.198375 Ω i 0 0.002050 L 2 0.008068 H λ 0 0.862803 N 0.288675 85
Five ses of differen measuremen signals are illusraed and esed using he seing-less proecion scheme: Tes A: Normal operaing condiion Tes B: Transformer energizaion inrush curren) Tes C: Transformer overexciaion Tes D: Through faul condiion Tes E: Inernal faul condiion Tes A: Normal Operaing Condiion The es signals used in his case are shown in fig. 3.20. 286.4 k Volage_XFMR1_AG V) Volage_XFMR1_BG V) Volage_XFMR1_CG V) 73.12 k -140.1 k -353.3 k 167.9 k 55.14 k Volage_XFMR2_AG V) Volage_XFMR2_BG V) Volage_XFMR2_CG V) Volage_XFMR2_NG V) -57.67 k -170.5 k 909.2 Curren_XFMR1_A A) Curren_XFMR1_B A) Curren_XFMR1_C A) 267.6-373.9-1.015 k 1.593 k 368.2 Curren_XFMR2_A A) Curren_XFMR2_B A) Curren_XFMR2_C A) Curren_XFMR2_N A) -856.4-2.081 k 3.000 3.020 3.040 3.060 Figure 3.21: Measuremen signals of he ransformer Tes B: energizaion) Tes B: Transformer Energizaion Inrush Curren) For ransformer energizaion, he es sysem in fig. 3.18 is used. A se of measuremen signals moniored during he energizaion is shown in he fig. 3.21. 86
Tes C: Transformer Overexciaion A se of measuremen signals moniored during he overexciaion is shown in he fig. 3.22. g g 219.6 k Volage_XFMR1_AG V) Volage_XFMR1_BG V) Volage_XFMR1_CG V) 73.01 k -73.53 k -220.1 k 116.7 k 35.44 k Volage_XFMR2_AG V) Volage_XFMR2_BG V) Volage_XFMR2_CG V) Volage_XFMR2_NG V) -45.87 k -127.2 k 512.0 Curren_XFMR1_A A) Curren_XFMR1_B A) Curren_XFMR1_C A) 126.8-258.4-643.6 1.054 k 273.9 Curren_XFMR2_A A) Curren_XFMR2_B A) Curren_XFMR2_C A) Curren_XFMR2_N A) -506.4-1.287 k 3.060 3.080 3.100 3.120 Figure 3.22: Measuremen signals of he ransformer Tes C: overexciaion) Tes D: Through Faul Condiion For hrough faul condiion, he es sysem in fig. 3.18 is used, bu single-phase-oground faul is given a a cerain bus ouside he ransformer under proecion. The faul lass for 0.05 seconds, and hen i is cleared. In fig. 3.23, he fauled locaion is marked wih he red circle. 87
Figure 3.23: Faul locaion in he es sysem es D: hrough faul) A se of measuremen signals moniored during he hrough faul condiion is shown in he fig. 3.24. The single-phase-o-ground faul is given for 0.05 seconds, saring a 3.20 seconds. Figure 3.24: Measuremen signals of he ransformer Tes D: hrough faul) 88
Tes E: Inernal Faul Condiion For inernal faul condiion, he es sysem in fig. 3.18 is used. Figure 3.25: Faul locaion in he es sysem Tes E: inernal faul) Figure 3.26: Measuremen signals of he ransformer Tes E: inernal faul) 89
The single-phase-o-ground faul occurs a he phase-a erminal on he lef side of he ransformer for 0.05 seconds, and hen he faul is cleared. In fig. 3.25, he fauled locaion is marked wih he red circle. A se of measuremen signals moniored during he inernal faul condiion is shown in he fig. 3.26. To simulae he inernal faul condiion, he single-phase-o-ground faul is given inside he ransformer phase a) for 0.05 seconds, saring a 3.20 seconds. Figure 3.27: Confidence level of he DSE Tes A: normal operaion) g g 395.1 m ThroughMeasuremen_Curren_Esiamed_PhaseA_Side1_, A ka) ThroughMeasuremen_Curren_Measured_PhaseA_Side1_, A ka) -397.3 m 379.4 m ThroughMeasuremen_Curren_Esiamed_PhaseB_Side1_, B ka) ThroughMeasuremen_Curren_Measured_PhaseB_Side1_, B ka) -376.4 m 390.5 m ThroughMeasuremen_Curren_Esiamed_PhaseC_Side1_, C ka) ThroughMeasuremen_Curren_Measured_PhaseC_Side1_, C ka) -390.8 m 806.1 m ThroughMeasuremen_Curren_Esiamed_PhaseA_Side2_, A ka) ThroughMeasuremen_Curren_Measured_PhaseA_Side2_, A ka) -804.9 m 780.9 m ThroughMeasuremen_Curren_Esiamed_PhaseB_Side2_, B ka) ThroughMeasuremen_Curren_Measured_PhaseB_Side2_, B ka) -777.5 m 761.3 m ThroughMeasuremen_Curren_Esiamed_PhaseC_Side2_, C ka) ThroughMeasuremen_Curren_Measured_PhaseC_Side2_, C ka) -766.7 m 3.427 m ThroughMeasuremen_Curren_Esiamed_PhaseN_Side2_, N ka) ThroughMeasuremen_Curren_Measured_PhaseN_Side2_, N ka) -3.587 m 100.0 Confidence_Level %) 0.000 3.00 3.10 3.20 3.30 3.40 Figure 3.28: Curren measuremens, esimaed values, and confidence level Tes A) 90
Performance Resuls for Tes A: Normal Operaing Condiion For he normal operaing condiion, he confidence level obained by he developed dynamic sae esimaor has been shown in he fig. 3.27. The resul graph shows 100% confidence level all he ime, which means ha measuremens are consisen wih he model and here is no faul condiion during he simulaion. The measured and esimaed currens a he primary and secondary side are compared wih differen colors as shown in he fig. 3.28. The measured and esimaed volages are also compared in he fig. 3.29: Program XfmHms - Page 1 of 1 188.7 AcrossMeasuremen_Volage_Esiamed_PhaseAN_Side1_, A kv) AcrossMeasuremen_Volage_Measured_PhaseAN_Side1_, A kv) -187.3 187.4 AcrossMeasuremen_Volage_Esiamed_PhaseBN_Side1_, B kv) AcrossMeasuremen_Volage_Measured_PhaseBN_Side1_, B kv) -187.3 186.6 AcrossMeasuremen_Volage_Esiamed_PhaseCN_Side1_, C kv) AcrossMeasuremen_Volage_Measured_PhaseCN_Side1_, C kv) -188.0 94.24 AcrossMeasuremen_Volage_Esiamed_PhaseAN_Side2_, A kv) AcrossMeasuremen_Volage_Measured_PhaseAN_Side2_, A kv) -93.54 93.88 AcrossMeasuremen_Volage_Esiamed_PhaseBN_Side2_, B kv) AcrossMeasuremen_Volage_Measured_PhaseBN_Side2_, B kv) -94.34 93.17 AcrossMeasuremen_Volage_Esiamed_PhaseCN_Side2_, C kv) AcrossMeasuremen_Volage_Measured_PhaseCN_Side2_, C kv) -93.82 100.0 Confidence_Level %) 0.000 3.00 3.10 3.20 3.30 3.40 Figure 3.29: Volage measuremens, esimaed values, and confidence level Tes A) I can be concluded ha he esimaed volages and currens are exacly same as he measured ones during he normal operaion condiion. Performance Resuls for Tes B: Transformer Energizaion Inrush Curren) For he ransformer energizaion, he confidence level obained by he developed dynamic sae esimaor shows he fig. 3.30. The resul graph shows 100% confidence level all he ime, which means ha measuremens are consisen wih he model and here is no faul condiion during he simulaion. 91
Figure 3.30: Confidence level of he DSE Tes B: ransformer energizaion) The measured and esimaed currens a he primary and secondary side are compared wih differen colors as shown in he fig. 3.31. g g 907.1 m ThroughMeasuremen_Curren_Esiamed_PhaseA_Side1_, A ka) ThroughMeasuremen_Curren_Measured_PhaseA_Side1_, A ka) -486.3 m 536.6 m ThroughMeasuremen_Curren_Esiamed_PhaseB_Side1_, B ka) ThroughMeasuremen_Curren_Measured_PhaseB_Side1_, B ka) -373.3 m 438.1 m ThroughMeasuremen_Curren_Esiamed_PhaseC_Side1_, C ka) ThroughMeasuremen_Curren_Measured_PhaseC_Side1_, C ka) -1.012 876.6 m ThroughMeasuremen_Curren_Esiamed_PhaseA_Side2_, A ka) ThroughMeasuremen_Curren_Measured_PhaseA_Side2_, A ka) -2.076 1.305 ThroughMeasuremen_Curren_Esiamed_PhaseB_Side2_, B ka) ThroughMeasuremen_Curren_Measured_PhaseB_Side2_, B ka) -975.7 m 1.589 ThroughMeasuremen_Curren_Esiamed_PhaseC_Side2_, C ka) ThroughMeasuremen_Curren_Measured_PhaseC_Side2_, C ka) -785.9 m 47.88 m ThroughMeasuremen_Curren_Esiamed_PhaseN_Side2_, N ka) ThroughMeasuremen_Curren_Measured_PhaseN_Side2_, N ka) -37.51 m 100.0 Confidence_Level %) 0.000 3.00 3.05 3.10 3.15 3.20 Figure 3.31: Curren measuremens, esimaed values, and confidence level Tes B) The measured and esimaed volages are also compared in he fig. 3.32. 92
g g 254.8 AcrossMeasuremen_Volage_Esiamed_PhaseAN_Side1_, A kv) AcrossMeasuremen_Volage_Measured_PhaseAN_Side1_, A kv) -268.3 239.1 AcrossMeasuremen_Volage_Esiamed_PhaseBN_Side1_, B kv) AcrossMeasuremen_Volage_Measured_PhaseBN_Side1_, B kv) -214.9 286.1 AcrossMeasuremen_Volage_Esiamed_PhaseCN_Side1_, C kv) AcrossMeasuremen_Volage_Measured_PhaseCN_Side1_, C kv) -353.3 167.9 AcrossMeasuremen_Volage_Esiamed_PhaseAN_Side2_, A kv) AcrossMeasuremen_Volage_Measured_PhaseAN_Side2_, A kv) -170.3 127.2 AcrossMeasuremen_Volage_Esiamed_PhaseBN_Side2_, B kv) AcrossMeasuremen_Volage_Measured_PhaseBN_Side2_, B kv) -119.2 133.0 AcrossMeasuremen_Volage_Esiamed_PhaseCN_Side2_, C kv) AcrossMeasuremen_Volage_Measured_PhaseCN_Side2_, C kv) -153.7 100.0 Confidence_Level %) 0.000 3.00 3.05 3.10 3.15 3.20 Figure 3.32: Volage measuremens, esimaed values, and confidence level Tes B) I can be concluded ha he esimaed volages and currens are exacly same as measured ones during he normal operaion condiion. Performance Resuls for Tes C: Transformer Overexciaion For he ransformer overexciaion, he confidence level obained by he developed dynamic sae esimaor is shown in he fig. 3.33. The resul graph shows 100% confidence level all he ime, which means ha measuremens are consisen wih he model and here is no faul condiion during he simulaion. 93
Figure 3.33: Confidence level of he DSE Tes C: ransformer overexciaion) The measured and esimaed currens a he primary and secondary side are compared wih differen colors as shown in he fig. 3.34. g g 508.5 m ThroughMeasuremen_Curren_Esiamed_PhaseA_Side1_, A ka) ThroughMeasuremen_Curren_Measured_PhaseA_Side1_, A ka) -414.3 m 419.7 m ThroughMeasuremen_Curren_Esiamed_PhaseB_Side1_, B ka) ThroughMeasuremen_Curren_Measured_PhaseB_Side1_, B ka) -373.3 m 401.0 m ThroughMeasuremen_Curren_Esiamed_PhaseC_Side1_, C ka) ThroughMeasuremen_Curren_Measured_PhaseC_Side1_, C ka) -535.7 m 829.3 m ThroughMeasuremen_Curren_Esiamed_PhaseA_Side2_, A ka) ThroughMeasuremen_Curren_Measured_PhaseA_Side2_, A ka) -1.079 853.3 m ThroughMeasuremen_Curren_Esiamed_PhaseB_Side2_, B ka) ThroughMeasuremen_Curren_Measured_PhaseB_Side2_, B ka) -806.8 m 924.5 m ThroughMeasuremen_Curren_Esiamed_PhaseC_Side2_, C ka) ThroughMeasuremen_Curren_Measured_PhaseC_Side2_, C ka) -785.9 m 12.20 m ThroughMeasuremen_Curren_Esiamed_PhaseN_Side2_, N ka) ThroughMeasuremen_Curren_Measured_PhaseN_Side2_, N ka) -9.424 m 100.0 Confidence_Level %) 0.000 3.000 3.020 3.040 3.060 3.080 Figure 3.34: Curren measuremens, esimaed values, and confidence level Tes C) 94
199.6 AcrossMeasuremen_Volage_Esiamed_PhaseAN_Side1_, A kv) AcrossMeasuremen_Volage_Measured_PhaseAN_Side1_, A kv) -207.3 189.5 AcrossMeasuremen_Volage_Esiamed_PhaseBN_Side1_, B kv) AcrossMeasuremen_Volage_Measured_PhaseBN_Side1_, B kv) -188.8 210.4 AcrossMeasuremen_Volage_Esiamed_PhaseCN_Side1_, C kv) AcrossMeasuremen_Volage_Measured_PhaseCN_Side1_, C kv) -219.7 111.4 AcrossMeasuremen_Volage_Esiamed_PhaseAN_Side2_, A kv) AcrossMeasuremen_Volage_Measured_PhaseAN_Side2_, A kv) -107.4 97.29 AcrossMeasuremen_Volage_Esiamed_PhaseBN_Side2_, B kv) AcrossMeasuremen_Volage_Measured_PhaseBN_Side2_, B kv) -101.6 98.14 AcrossMeasuremen_Volage_Esiamed_PhaseCN_Side2_, C kv) AcrossMeasuremen_Volage_Measured_PhaseCN_Side2_, C kv) -106.7 100.0 Confidence_Level %) 0.000 3.000 3.020 3.040 3.060 3.080 Figure 3.35: Volage measuremens, esimaed values, and confidence level Tes C) The measured and esimaed volages are also compared in he fig. 3.35. I can be concluded ha he esimaed volages and currens are exacly same as measured ones during he normal operaion condiion. Figure 3.36: Confidence level of he DSE Tes D: hrough faul) Performance Resuls for Tes D: Through Faul Condiion For he hrough faul condiion, he confidence level obained by he developed dynamic sae esimaor is shown in he fig. 3.36. The resul graph shows 100% confidence level all he ime, which means ha measuremens are consisen wih he model and here is 95
no faul condiion during he simulaion. The measured and esimaed currens a he primary and secondary side are compared wih differen colors as shown in he fig. 3.37. Figure 3.37: Curren measuremens, esimaed values, and confidence level Tes D) The measured and esimaed volages are also compared in he fig. 3.38. 96
Figure 3.38: Volage measuremens, esimaed values, and confidence level Tes D) Performance Resuls for Tes E: Inernal Faul Condiion For he inernal faul condiion, he confidence level obained by he developed dynamic sae esimaor is shown in fig. 3.39. During mos of he ime, he confidence level is 100%, which means ha measuremens are consisen wih he model. However, a ime 0.2 second in fig. 3.39, he confidence level drops o 0%, which means ha an inernal faul has occurred somewhere in he ransformer. Then, he confidence level recovers 100% in 0.05s as he ransformer reurns o he normal operaing condiion. Figure 3.39: Confidence level of he DSE Tes E: inernal faul) 97
Figure 3.40: Curren measuremens, esimaed values, and confidence level Tes E) The measured and esimaed currens a he primary and secondary side are compared wih differen colors as shown in he following fig. 3.40. The measured and esimaed volages are also compared in he following fig. 3.41. Noe ha here is a specific duraion in which he confidence level is zero, and herefore, i can be concluded ha any inernal fauls have occurred in he ransformer under proecion during his period. 98