Estimation of Synchronous Generator Parameters from On-line Measurements

Transcription

1 PSERC Estmaton of Synchronous Generator Parameters from On-lne Measurements Fnal Project Report Power Systems Engneerng Research Center A Natonal Scence Foundaton Industry/Unversty Cooperatve Research Center snce 1996

2 Power Systems Engneerng Research Center Estmaton of Synchronous Generator Parameters from On-lne Measurements Fnal Project Report Project Team Gerald T. Heydt Elas Kyrakdes George Karady Keth Holbert Sandeep Borkar Wnter Gu Arzona State Unversty Vjay Vttal Iowa State Unversty Garng Huang K. Men Texas A&M Unversty PSERC Publcaton 5-36 June 25

3 Informaton about ths project For nformaton about ths project contact: Gerald T. Heydt, Ph.D. Arzona State Unversty Department of Electrcal Engneerng Tempe, AZ Tel: Fax: Emal: Power Systems Engneerng Research Center Ths s a project report from the Power Systems Engneerng Research Center (PSERC). PSERC s a mult-unversty Center conductng research on challenges facng a restructurng electrc power ndustry and educatng the next generaton of power engneers. More nformaton about PSERC can be found at the Center s webste: For addtonal nformaton, contact: Power Systems Engneerng Research Center Cornell Unversty 428 Phllps Hall Ithaca, New York Phone: Fax: Notce Concernng Copyrght Materal PSERC members are gven permsson to copy wthout fee all or part of ths publcaton for nternal use f approprate attrbuton s gven to ths document as the source materal. Ths report s avalable for downloadng from the PSERC webste. 25 Arzona State Unversty. All rghts reserved.

4 Acknowledgements The Power Systems Engneerng Research Center sponsored the research project ttled Extended State Estmaton for Synchronous Generator Parameters. The project began n 23. Ths s the fnal report for the project. We express our apprecaton for the support provded by PSERC s ndustral members and by the Natonal Scence Foundaton under grant NSF EEC-188 receved from the Industry / Unversty Cooperatve Research Center program. The authors thank all PSERC members for ther techncal advce on the project, especally Dale Krummen (AEP), Dale Bradshaw (TVA), Mke Ingram (TVA), Ralph McKoskey (TVA), Baj Agrawal (Arzona Publc Servce), Douglas Seln (Arzona Publc Servce), John Demcko (Arzona Publc Servce), and Bll Prce (GE Energy). Dale Bradshaw and Baj Agrawal served as the ndustry advsors for the work. An earler Masters thess was done at ASU, and the authors lberally used the work of Warren Rees. Mr. Rees s presently wth the U. S. Bureau of Reclamaton n Denver. The authors also acknowledge Drs. Al Abur and A. P. Saks Melopoulos of Texas A&M Unversty and Georga Tech respectvely who contrbuted techncal advce and data to ths work. Dr. S. Suryanarayanan, of Florda State Unversty, formerly of Arzona State, provded useful comments.

5 Executve Summary Ths s the fnal report on a research project on dentfcaton of synchronous machne parameters usng on-lne measurements. The concept s to utlze the dynamc operatonal data n combnaton wth manufacturers estmates of synchronous machne parameters to force the machne model to agree wth measurements. Park s model s used wth three damper wndngs. The method uses a mathematcal tool from state estmaton technology to formulate a mnmum squared error soluton. A partcular dffculty relates to modelng magnetc saturaton. A combnaton of classcal model wth a new approach s used so that saturated and unsaturated data are calculated. The mathematcal detals are gven n equatons and flow charts. Also, the method has been programmed n an object-orented Graphc User Interface (GUI) n whch the user attaches the machne measurement data fle, and manufacturers estmates. The calculaton s dsplayed on a GUI menu. The method has been tested wth data from approxmately sx large generatng unts (all machnes wth feld crcut brushes). Estmates of model resstances and unsaturated nductances agree wth manufacturers estmates as well as operatng data. The authors conjecture that the parameters calculated n ths way actually may be more accurate for the gven operatng condtons than the manufacturer s parameters whch may have been obtaned from stand-stll tests many years ago. Applcatons of ths work nclude: Utlzaton of accurate data and accurate models n transent stablty studes, thus allowng more accurate and safe operatng practces (e.g., machne loadng) The avalablty of a user frendly software tool to obtan synchronous generator parameters even f these are mssng from manufacturers data The ablty to track changes n machne parameters as the machne ages and undergoes normal wear from operaton. The brushless excter confguraton has been examned, but results were dsappontng. The results shown n Appendx F may ndcate that our estmaton method s not sutable for synchronous machne parameter estmaton for brushless excter nstallatons. The report also provdes ctatons to several longer reports and publshed techncal papers where addtonal project detals are gven.

6 Table of Contents Acknowledgements... Table of Contents... Table of Fgures...v Table of Tables...x Table of Tables...x 1 Modelng of Synchronous Generators Background and Motvaton Off ne Alternatves for Obtanng Synchronous Machne Model Project Objectves Techncal Documentaton of the Project Research Staff A Gude to the Appendces Analyss and Modelng of Synchronous Generators Estmaton of Parameters of Synchronous Generators Estmaton Technques Nose Flterng Magnetc Saturaton Organzaton of the Report Modelng of Synchronous Machnes Introducton Park s Model of a Synchronous Generator Development of an Observer for the Damper Wndng Currents Case Studes Usng a Damper Wndng Currents Observer Confguraton of the State Estmator Bad Data Detecton, Rejecton and Flterng Magnetc Saturaton Brushless excters Estmaton of Machne Parameters and Testng of the Algorthm Descrpton of a Testng Regmen Descrpton of Tests Results of Parameter Estmaton from Actual Measurements Multple Parameter Estmaton... 35

7 Table of Contents (contnued) 3.5 Applcaton of the Algorthm to Dfferent Machnes and Operatng Ponts Utlzaton of the Parameter Formulas to Obtan Machne Parameters Graphc User Interface Implementaton Usng Vsual C A Graphc User Interface A Sample Input / Output Dalog And Estmator Confguraton stng of the Code and Flow Charts Conclusons and Comments General Comments Comments from Industry Research Conclusons Future Steps...53 Appendx A Constructon of a Damper Current Observer A.1 Introducton...55 A.2 Development of an Observer for Damper Wndng Currents A.3 Case Studes Usng a Damper Wndng Currents Observer A.4 Confguraton of The State Estmator Appendx B Bad Data Detecton, Rejecton and Flterng... 6 B.1 Introducton...6 B.2 Transformaton / Flterng Sequence... 6 B.3 Implementaton of a Butterworth Flter Appendx C Magnetc Saturaton C.1 Magnetc Saturaton n Synchronous Machnes C.2 Improved Modelng Appendx D Data Acquston Detals D.1 Introducton...64 D.2 Synchronous Machne Mathematcal Model D.3 Park s Transformaton D.4 Movng Average Flters D.5 Dgtal Flterng D.6 Butterworth Flter D.7 Chebyshev I Flters D.8 Ellptc Flters... 7 v

8 Table of Contents (contnued) D.1 Data Acquston and Processng: A Test System D.11 Bad Data Rejecton D.12 Data Flterng Analyss D.13 Estmated and Expected Results D.14 Summary Appendx E Zero Phase Flterng and Park s Transformaton E.1 Introducton...88 E.2 Measured Data Processng Block E.3 Zero-phase Flterng Technque... 9 E.4 Analyss of Park s Transformaton E.5 Processng of Harmoncs of Dstnctve Sequence E.6 Smulaton Results E.7 Implcatons to Post Transform Flterng Strategy E.8 Phase Sgnal Flterng and Results E.9 Conclusons Appendx F The Brushless Excter Case F.1 An Approach to Brushless Excter Models and Identfcaton F.2 Selecton of Excter Model F.3 Input-Output Data Collecton F.4 Parameter Estmaton wth near Functons F.5 Parameter Estmaton wth Nonlnear Functons F.6 Estmaton Results F.7 A Hypothetcal Example F.8 Conclusons Drawn for the Brushless Excter Case REFERENCES v

9 Table of Fgures Fg. 1.1 Synchronous generator operaton and graphc user nterface mplementaton... 4 Fg. 1.2 Sample saturaton curve for a synchronous generator Fg. 2.1 Schematc dagram of a synchronous machne Fg. 2.2 Concept of an observer for a dynamc system Fg. 2.3 Smulated and estmated damper current D usng transent data Fg. 2.4 Smulated and estmated damper current G usng transent data Fg. 2.5 Smulated and estmated damper current Q usng transent data Fg. 2.6 Magnfcaton of porton of Q to demonstrate the dfference between the smulated and observed sgnals Fg. 2.7 Block dagram for observer mplementaton and parameter dentfcaton algorthm Fg. 2.8 Flterng and bad data detecton/rejecton confguraton Fg. 2.9 Unfltered drect axs voltage n the tme doman Fg. 2.1 Fltered drect axs voltage n the tme doman Fg. 3.1 Algorthm for estmator mplementaton for actual measurements Fg. 3.2 Change of AD wth operatng pont for Redhawk gas turbne generators Fg. 3.3 Saturated and unsaturated values of AD for Redhawk gas turbne generators 42 Fg. 3.4 Change of AQ wth operatng pont for Redhawk gas turbne generators Fg. 3.5 Saturated and unsaturated values of AQ for Redhawk gas turbne generators 43 Fg. 4.1 Input wndow of the estmator Fg. 4.2 Output wndow of the estmator Fg. A.1 Concept of an observer for a dynamc system Fg. A.2 Block dagram for observer mplementaton and parameter dentfcaton algorthm Fg. B.1 Flterng and bad data detecton/rejecton confguraton... 6 Fg. B.2 Unfltered drect axs voltage n the tme doman Fg. B.3 Fltered drect axs voltage n the tme doman Fg. D.1 Synchronous machne model Fg. D.2 Template of magntude response of desgned IIR flters Fg. D.3 Frequency response of the Butterworth flter for ncreasng orders Fg. D.4 Frequency response of the Chebyshev I flter for ncreasng orders Fg. D.5 Frequency response of an ellptcal flter Fg. D.6 Block dagram of the overall system Fg. D.7 Block dagram for processng measured data Fg. D.8 Feld current and voltage sgnals ndcatng the presence of nose v

10 Table of Fgures (contnued) Fg. D.9 Feld current sgnal replotted on expanded ordnate axs to show low frequency behavor Fg. D.1 Frequency response n feld current and voltage plots ndcatng the presence of nose and bad data Fg. D.11 Tme doman plots for the movng average fltered feld quanttes Fg. D.12 Flter performance comparson for dfferent cutoff frequences Fg. D.13 Feld quanttes after 5-pont movng average followed by fourth-order ellptc flterng at 2 Hz cut-off and 2 Hz stop band frequences Fg. D.14 Frequency response of feld current and voltage after flterng wth a movng average flter and ellptc flter Fg. D.15 Fltered feld quanttes usng eghth-order ellptc flter at 12 Hz cut-off and 1 Hz stop band frequences... 8 Fg. D.16 Tme doman plots for phase A current and voltage Fg. D.17 Frequency response of phase A current and voltage Fg. D.18 Tme doman plots for the d-axs voltage and current Fg. D.19 Frequency response n feld current and voltage plots ndcatng the presence of nose and bad data Fg. D.2 Tme doman plots for the d-axs quanttes (transformed phase quantty) after 5 pont movng average flter Fg. D.21 Transformed phase quanttes after 5-pont movng average followed by fourth-order ellptc flterng at 2 Hz cut-off and 2 Hz stop band frequences Fg. E.1 Block dagram of the generator, the data measurement usng a dgtal fault recorder (DFR), and the data processng system Fg. E.2 Schematc showng strategy for phase and feld flterng Fg. E.3 Zero-phase flterng system Fg. E.4 Magntude of d-axs voltage from Park s transformaton wthout flterng Fg. E.5 Pre-fltered phase data showng flter specfcatons and magntudes of the estmates Fg. E.6 Post-fltered phase data showng flter specfcatons and magntudes of the estmates... 1 Fg. F.1 A brushless exctaton system Fg. F.2 Brushless excter-generator Fg. F.3 Type AC1A-alternator-rectfer exctaton system Fg. F.4 Smulnk model of brushless excter Fg. F.5 Rectfer regulaton functon Fg. F.6 Termnal voltage v

11 Table of Fgures (contnued) Fg. F.7 Feld voltage Fg. F.8 Termnal voltage error Fg. F.9 Feld voltage error v

12 Table of Tables Table 1.1 Unversty research staff... 7 Table 1.2 Report appendces... 8 Table 2.1 Synchronous generator parameters: 483 MVA machne used n both synthetc and actual on-ste tests Table 3.3 Multple smultaneous parameter estmaton for generator FC5HP (case study R-NC-3-11) Table 3.4 Calculaton of unsaturated parameters for generator FC5HP (case study R-NC-3-11) Table 3.5 Multple smultaneous parameter estmaton for generator FC5HP (case study R-NC-3-12) Table 3.6 Calculaton of unsaturated parameters for generator FC5HP (case study R-NC-3-12) Table 3.7 Parameter estmaton results for Redhawk gas turbnes 1 and Table 3.8 Calculaton of standard parameters from the estmated derved parameters Table 3.9 Comparson of estmated standard parameters to manufacturer standard parameters (case study R-NC-1-1) Table 5.1 Comments from the power engneerng ndustry... 5 Table 5.2 Prncpal sources of dfferences between estmated and manufacturer parameters Table D.1 Comparson of the performance characterstcs of three IIR flter types consdered for the project Table D.2 Results before and after flterng the data sets Table E.1 Park s transformaton output frequency for postve sequence nputs Table E.2 Park s transformaton output frequency for negatve sequence nputs Table E.3 Magntude of transformed quanttes for dfferent unbalanced cases Table E.4 Results wth pre and post flterng of data set FC Table F.1 Measurable sgnals - synchronous machne nstrumentaton Table F.2 Estmaton results after flterng nput data Table F.3 Test example usng Chnese machne data x

13 1 Modelng of Synchronous Generators 1.1 Background and Motvaton Synchronous generators are the manstay of electrc power generaton n the World. These machnes were nvented n the late 18s and further refned n the early 19s. There s a huge lterature of synchronous generators pror to 193, but the man ntal advance n synchronous machne analyss was the development of Park s model. The orgnal paper by Park s [1]. Dscusson of the model and classcal references of the feld appear n [2-9]. Park s model was not the only synchronous machne model: Jackson and Wnchester [1] developed drect and quadrature axs equvalent crcuts for round rotor synchronous generators. Durng the same perod, Canay [11] focused on developng equvalent crcuts for feld and damper wndngs to estmate generator parameters. A sgnfcant contrbuton was made by Yu and Moussa n 1971 [12] who reported a systematc procedure that can be mplemented to determne the parameters of the equvalent crcuts of synchronous generators. A further alternatve s to appeal to the fnte element approach n whch the magnetc crcuts n a synchronous machne are modeled at the mcroscopc level, and a translaton s made to the mesoscopc level. It suffces to say that n all but the most unusual cases, the Park model s used. And ths model has survved the test of tme. If modfcatons and refnements are made on the Park model, the usual approach s to add wndngs to the model. Ths procedure entals the addton of R crcuts that are magnetcally coupled to the classcal model. By ths procedure, second order effects can be captured by relatvely mnor addtons to the classcal model. Models are needed for most engneerng applcatons n any area. Applcatons of synchronous generators and ther steady state and dynamc responses are no dfferent. It s standard practce n power engneerng to utlze Park s model of a synchronous generator for all engneerng applcatons. As examples, the followng are typcal applcaton areas: Standard steady state operatons analyss, ncludng calculaton of voltage regulaton, response to excter sgnals Post-mortem analyses of falures and msoperaton Identfcaton of ncpent falures of electrcal wndngs n the machne Response analyss to dsturbances, both large and small Desgn of excters, power system stablzers, and other controls. However, modelng of synchronous machnes always entals calculaton or measurement of model parameters. In Park s model, there are at least three resstances and three nductances that need to be known. If machne damper wndngs are to be ncluded n the model (essental for most transent analyses), at least two more resstances and two more 1

14 nductances must be known. Oftentmes, the model has n the order of ten R- parameters that must be known. Some of these parameters are readly correlated to actual resstances or nductances but some are not. Standardzed tests have been developed to establsh these parameters, and references [13-14] document these tests. One ssue n these tests s that most standard tests requre that the machne under test be taken off-lne. The operaton of modern power systems, and the judcous use of large synchronous machnes often suggest that takng a machne down for testng s clearly undesrable. Therefore, there s strong motvaton for on-lne methods to establsh machne parameters. Ths report contans the detals of an on-lne procedure to accurately determne synchronous generator parameters usng Park s model, and usng a technology smlar to state estmaton. The state estmaton utlzed s actually parameter estmaton, and the method s based on a mathematcal tool known as the method of least squares. References [15-19] contan a full descrpton of that technology. 1.2 Off ne Alternatves for Obtanng Synchronous Machne Model Off-lne methods, however, are nether practcal nor accurate n most cases. Decommtng a generator for parameter measurng s not economcal for a utlty especally f the specfc generator s a base unt. Furthermore, under dfferent loadng condtons certan generator parameters may vary slghtly and therefore off-lne methods may not be accurate enough for certan applcatons. Fnally, the effect of saturaton of generator nductances cannot be accounted for n off-lne studes. Saturaton s a crtcal concept n generator operaton; n order to consder t n the estmaton process, one has to account for the operatng level of the generator at the partcular estmaton nterval [2]-[22]. Contrary to off-lne methods, on-lne methods to dentfy machne parameters are very attractve to utltes because of ther mnmal nterference n the normal operaton of the generator. Ideally, generator parameters may be calculated under dfferent operatng condtons, both n steady state and transent operaton. In 1977 ee and Tan [22] proposed an algorthm to determne the parameters of a salent pole generator from data obtaned durng a sudden short crcut. In 1981, Dandeno [23] used on-lne frequency response measurements from two large turbo generators to dentfy machne parameters; durng the same perod, Nshwak [24] used the extended Kalman flter to dentfy dynamc stablty constants for small dsturbances under steady state operatng condtons. In 1982 Bollnger [25] proposed a technque to estmate system parameters by utlzng wde bandwdth nose sgnals n an exctaton sgnal whch acts as a dsturbance to the system. 1.3 Project Objectves The man objectve of ths research work s to develop a method to dentfy synchronous generator parameters from on-lne measurements. It s also desred to develop a graphc user nterface (GUI) applcaton whch wll be user frendly and self gudng so as to facltate prompt estmaton of the desred parameters. In ths way, possble fault condtons can be detected and remedy acton can be undertaken. Moreover, t s necessary to develop an algorthm that wll enable bad measurement detecton and rejecton so as to 2

15 ncrease the relablty of the results. Another objectve of ths research work s to develop the saturaton model of the nductances of a synchronous machne. A number of nductances n the synchronous machne model experence sgnfcant change n ther values dependng on the operatng condton of the machne. The effect of saturaton s modeled and ncorporated t n the GUI so as to obtan accurate estmates that reflect the true status of the machne at every operatng pont. Secondary objectves of the research nclude: Development of an observer for damper currents Calculaton of the error characterstcs of the estmaton Development of an ndex of confdence Calculaton of a range of values for each estmated parameter Study of whch machne parameters can be estmated, and whch can not Evaluaton of alternatve GUI features. Fg. 1.1 shows the actvtes related to a synchronous generator, ther relaton to the graphc user nterface, and the estmaton method utlzed n ths research work. 1.4 Techncal Documentaton of the Project Ths project was executed over three years at three unverstes and wth the cooperatve efforts of over eleven researchers ncludng ndustry lasons and contrbutors. The man unversty contrbutons were made at Arzona State Unversty (the lead unversty); Iowa State Unversty; and Texas A & M Unversty. One of the authors of the report was afflated wth Iowa State Unversty durng the executon of ths work but has snce left that poston for a poston at Arzona State Unversty. 3

16 SYNCHRONOUS GENERATOR OPERATION oadng schedule Synchronzaton and stablzaton Mantenance and parameter trackng Relablty Coordnaton area requrements Generator hstory Preventve mantenance Forced outage analyss Parameter trackng va GUI Modelng and EMTP studes Examnaton of tracked parameters through GUI GRAPHIC USER INTERFACE Damper current observer Saturaton model a pror system knowledge Park's transformaton model GUI features Estmator Fg. 1.1 Synchronous generator operaton and graphc user nterface mplementaton 4

17 Approxmately 15 techncal reports, theses and papers were prepared for the project, and these fully document the project. These are: S. U. Borkar, K. E. Holbert, Dgtal Flterng of Synchronous Generator Measurements for Parameter Estmaton, Proceedngs of the Seventh IASTED Internatonal Conference on Power and Energy Systems, Clearwater, F, Nov. 28-Dec. 1, 24, pp Ths s reprnted n part n Appendx E. S. U. Borkar, K. E. Holbert, Dgtal Flterng and Bad Data Rejecton for Synchronous Generator Parameter Estmaton, Proceedngs of the Thrty-ffth Annual North Amercan Power Symposum (NAPS 23), Rolla, MO, October 2-21, 23, pp Ths s reprnted n part n Appendx D. E. Kyrakdes, Innovatve Concepts For On-ne Synchronous Generator Parameter Estmaton, PhD. Thess, Arzona State Unversty, Tempe AZ, December, 23. The man results appear n Chapters 1 5 of ths report. S. U. Borkar, Desgn of a Dgtal Flter for Synchronous Generator Parameter Estmaton, M. S. E. E. Thess, Arzona State Unversty, Tempe, AZ, August 24 E. Kyrakdes, G. T. Heydt, and V. Vttal, On-lne estmaton of synchronous generator parameters usng an observer for damper currents and a graphcal user nterface, IEEE Transactons on Energy Converson, Aug. 23, to be publshed. E. Kyrakdes, G. T. Heydt, An observer for the estmaton of synchronous generator damper currents use n parameter dentfcaton, IEEE Transactons on Energy Converson, Vol. 18, March 22, pp N. ogc, E. Kyrakdes, G. T. Heydt, p state estmators for power systems, Journal of Electrc Power Components and Systems, v. 33, No. 7, July 25. E. Kyrakdes, G. Heydt, Estmaton of Synchronous Generator Parameters Usng an Observer for Damper Currents and a Graphcal User Interface, J. Electrc Power Systems Research, No. 69, v. 24, pp. 7-16, February 24. Elas Kyrakdes, Gerald T. Heydt, Vjay Vttal, On-ne parameter estmaton of round rotor synchronous generators ncludng magnetc saturaton, Accepted for publcaton, 24, IEEE Transactons on Power Systems. E. Kyrakdes, G. Heydt, An observer for the estmaton of synchronous generator damper currents for use n parameter dentfcaton, IEEE Power Engneerng etters, IEEE Transactons on Energy Converson, v. 18, No. 1, ITCNE4, pp , 23. E. Kyrakdes, G. T. Heydt, A graphcal user nterface for synchronous machne parameter dentfcaton, 21 North Amercan Power Symposum, October, 21, College Staton, TX, pp E. Kyrakdes, G. T. Heydt, Synchronous machne parameter estmaton usng a vsual platform, Proceedngs of the IEEE Power Engneerng Socety Summer Meetng, 21, v. 3, pp N. ogć, E. Kyrakdes, G. T. Heydt, p state estmators for power systems, Proceedngs of the North Amercan Power Symposum, October , Tempe AZ, pp

18 M. Bakroun, A. İnan, G. T. Heydt, A comparson of p state estmators for power engneerng applcatons, Proceedngs of the North Amercan Power Symposum, October , Tempe AZ, pp E. Kyrakdes, G. Heydt, Damper wndng representaton and magnetc saturaton n synchronous generator modelng, Proceedngs of the 23 North Amercan Power Symposum, pp , Rolla MO, October, Research Staff Table 1.1 shows the research staff on the project and ther man roles. 1.6 A Gude to the Appendces Ths report contans sx appendces. The appendces manly contan techncal detals to the man body of the report. Ther content s ndcated n Table 1.2. The specal topc of brushless excters (.e., feld current suppled to the machne electromagnetcally) s dscussed n Appendx F. 1.7 Analyss and Modelng of Synchronous Generators The classc Westnghouse Transmsson and Dstrbuton Handbook provdes nformaton for the constructon and operaton of synchronous machnes [26]. Another useful handbook n the feld of electrcal machnery s the Electrc Motor Repar by Rosenberg [27]. It s a handbook for the practcally mnded concentratng on the wndng, repar, and troubleshootng of a large number of AC and DC motors and controllers. Power System Stablty and Control by Kundur [2] and Power System Control and Stablty by Anderson and Fouad [21] provde an extensve and detaled analyss of synchronous machnes, n both theory and modelng. They dedcate three chapters on ths topc and, among others, they cover the dq transformaton, the per unt representaton, equvalent crcuts, and analyss n both steady state and transent operaton. Saadat n Power System Analyss [28] concentrates on the transent analyss of the synchronous generator and on balanced and unbalanced faults. Saadat offers coverage on the Park s transformaton and on dervng the generator equaton n the rotor frame of reference. Anderson, Agrawal, and Van Ness [29] provde an extensve analyss of synchronous machnes. They dedcate a chapter on synchronous machne modelng and provde an extensve analyss of the drect and quadrature axs equatons. They also examne thoroughly Park s transformaton, whle n one of ther chapters they concentrate on parameter computaton, measured data from feld tests, and sample test results. Very useful sources of nformaton are the books Electrc Machnery [3] and Analyss of Electrc Machnery [31]. Both books contan the theory of synchronous machnes and analyss of steady state operaton. In addton, [31] offers nterestng detals on operatonal mpedances and tme constants, lnearzed equatons, and a chapter on the asynchronous and unbalanced operaton of synchronous machnes. 6

19 Table 1.1 Unversty research staff Staff member Insttuton where work was Man project role done Sandeep Borkar Arzona State Unversty Researched nstrumentaton sgnal flterng Wnter Gu Arzona State Unversty Investgated brushless excter applcatons Gerald T. Heydt Arzona State Unversty Prncpal nvestgator Keth E. Holbert Arzona State Unversty Researched nstrumentaton sgnal flterng Garng Huang Texas A&M Unversty Investgated brushless excter applcatons George Karady Arzona State Unversty Investgated brushless excter applcatons Elas Kyrakdes* Arzona State Unversty Man researcher and developer of the computer mplementaton K. Men Texas A&M Unversty Investgated brushless excter applcatons Vjay Vttal ** Iowa State Unversty Investgated saturaton, report preparaton *Dr. Kyrakdes s presently wth the Unversty of Cyprus, Ncosa, Cyprus. ** Dr. Vttal s presently wth Arzona State Unversty. 7

20 Table 1.2 Report appendces Appendx Subject area Content Man subject matter reprnted from ths reference A Modelng Modelng of the damper [69] currents usng a devce known as an observer B Bad data Elmnaton of bad measurement [69] data va preproc- essng C Modelng Modelng magnetc satura- [67], [69] D E F Data acquston, measurement flterng Measurement flterng Brushless exctaton ton Desgn of specfc numercal flters (e.g., Butterworth, Chebyshev) for synchronous machne nstrumentaton Mantanng phase relatonshps among AC voltages and currents n measurements durng nose flterng; harmoncs n measurements [68] [71] An attempt was made to modfy the parameter estmaton algorthm for brushless machnes. No data were avalable for ths type of machne for cases of known model of the brushless excter. Some progress was made, but the concepts were not ntegrated nto the algorthm developed. 1.8 Estmaton of Parameters of Synchronous Generators Keyhan, who has conducted research on parameter estmaton usng a number of dfferent technques, has offered extensve lterature on ths topc. One of the methods used by Keyhan was the estmaton of parameters from Standstll Frequency Response (SSFR) test data [31], [32]. In ths approach, curve fttng technques are used to derve the transfer functons of the drect axs and quadrature axs usng the avalable test data. The parameters of the model are then calculated from nonlnear equatons, whch relate the machne parameters and the tme constants correspondng to the transfer functons [32]. However, nose-corrupted data cause multple parameter sets to be estmated. To obtan a unque set of parameters, Keyhan used a maxmum lkelhood estmaton (M) technque [31]. The results ndcate that a unque and relatvely accurate parameter set s estmated even though the data are corrupted wth nose. 8

21 Keyhan n [33] offers an evaluaton of the performance of the M method usng case studes and SSFR data from tests on a 722 MVA generator. It s shown that the M method gves estmates wth very small error, whle the nose has no notceable effect on the estmator. The M algorthm and SSFR data were also used n [32] to estmate parameters of a three phase salent pole 5 kva synchronous machne. The equvalent crcut models were developed and onlne dynamc responses were performed to valdate the dentfed models. Tsa, Keyhan, Demcko, and Farmer used small-dsturbance responses and the M estmaton technque to dentfy an onlne synchronous generator model [35]. The frst step was to dentfy the machne lnear model parameters. Consequently, the saturaton models of the machne were dentfed usng the estmated mutual nductances under a wde range of operatng condtons. It was shown that when the MMF saturaton model was used, the smulated responses of the developed model matched closely wth the measured responses. Another method used by Keyhan was the dentfcaton of synchronous machne lnear parameters from standstll step voltage nput data [36]. The procedure nvolves applyng a step voltage as an nput and estmaton of the parameters of the tme constant and equvalent crcut models. The ntal values of the parameters to be estmated are extracted from the operatonal nductances whch are derved from the measured tme doman data. Tsa, Keyhan, Demcko, and Seln presented a new approach to develop a model of the saturated synchronous generator usng artfcal neural networks (ANN) [37]. ANN are possble to be traned after beng arranged n a certan pattern. The pattern used n ths network s a feed-forward network and the learnng scheme s of the error backpropagaton form. Moreover, the tranng pattern was based on onlne small dsturbance responses and the M algorthm. The mportant concluson of ths paper s the fact that the developed ANN saturaton model s capable of predctng the machne nonlnear changes whch were not used n the tranng process. Etelberg n [38] uses a lnearly formulated least squares problem to obtan approxmate parameter values. Consequently, a numercal search method s used to solve the nonlnear problem of magntude and phase fttng. Boje [39] proposes tme doman measurements for determnng selected parameters of synchronous machnes. These are proposed as an alternatve to standstll frequency doman tests, snce as the authors argue, the proposed method uses smpler equpment and model parameters are obtaned drectly n parametrc form. However, as wth tradtonal SSFR testng, ths method does not model the machne at normal operatng condtons. Karayaka, Keyhan, Agrawal, Seln, and Heydt n [4]-[42] concentrated on large synchronous utlty generators to develop a procedure of parameter estmaton from onlne measurements. In [4] a one-machne nfnte bus system s smulated n the abc frame of reference usng parameters provded by the manufacturer. The armature crcut pa- 9

22 rameters are hence calculated usng the recursve maxmum lkelhood (RM) estmaton technque. Based on these estmates, the feld wndng and some damper parameters are estmated usng an Output Error Estmaton (OEM) technque. It s found that even wth hghly corrupted data the estmated and actual parameters are n good agreement. In [41] the authors present a method to estmate machne parameters usng synthetc data as prevously, but also real tme operatng data from a utlty generator. Ths study showed that nose-corrupted data could be handled up to a certan pont. Below a certan sgnal-tonose rato (SNR), estmaton of machne parameters was not possble. The estmaton of machne parameters usng data obtaned onlne showed that there was a reasonable agreement between estmated and actual curves. The above methods were repeated by the authors usng Artfcal Neural Networks [42]. The data used to tran the ANN were taken from real tme operatng data and the developed models were valdated wth measurements not used n the tranng of ANN and wth large dsturbance responses. It was shown that ANN models could correctly nterpolate between patterns not used n tranng. Rco, Heydt, Keyhan, Agrawal, and Seln attempted to estmate machne parameters usng orthogonal seres expansons such as Fourer, Walsh, and Hartley seres [43], [44]. In [43] the authors propose the use of the Hartley seres for fttng operatng data such as voltage and current measurements and the use of lnear state estmaton to dentfy the coeffcents of the seres. In ths way, the machne parameters can be dentfed. At the same tme, ths method s tested for nose corrupton n the measurements. The authors show that the error n the estmaton s below 1% even for SNR of 5:1. In [44] the authors expand ther prevous study to nclude Walsh and Fourer seres n machne parameter estmaton. A matrx of coeffcents common to all orthogonal seres expansons s used. The results show that the estmated parameters are n good agreement wth the actual parameters. Also, ths method takes nto account the dependence of the parameters wth respect to the operatng pont. More nformaton on orthogonal seres expansons for varous power system components such as synchronous generators and transmsson lnes can be found n [45]. Fnally, Kyrakdes and Heydt n [46] and [47] offer an algorthm for the estmaton of synchronous generator parameters from measurements that are taken at the machne termnals whle the generator serves ts load. Ths report s an extenson of the dea presented n the papers. 1.9 Estmaton Technques Estmaton technques such as state estmaton, least squares, and maxmum lkelhood are used n engneerng applcatons nterchangeably. For the purposes of ths research the mathematcal model s desred to be transformed n a form realzable by a state estmaton algorthm. State estmaton s a process durng whch a number of unknown system state varables or parameters are assgned a value based on measurements from that system [48]. 1

23 Schweppe [49]-[5] was one of the frst to propose and develop the dea of state estmaton for the montorng of power systems. Wood and Wollenberg dedcate a chapter of ther book on state estmaton [5]. They offer nsght to maxmum lkelhood concepts and derve the least squares equatons used n state estmaton. An ntroducton on advanced topcs on state estmaton and a lot of examples on AC network state estmaton are offered. Advanced topcs nclude bad data detecton, estmaton of quanttes not beng measured, network observablty, and pseudo-measurements. 1.1 Nose Flterng Generatng statons are notorous for ther poor electromagnetc nterference (EMI) envronment. Ths s a consequence of the hgh currents whch produce hgh magnetc felds, and the hgh voltages whch may produce electrostatc couplng as well as partal dscharges. These usual test condtons, as well as general envronmental ssues that result n measurement error, are the bass for a specalzed nterest n nose flterng. There are some fortunate ssues n that many power system nose ssues relate to the 6 Hz supply, or to ntegral harmoncs (e.g., ffth harmonc = 3 Hz). In between the data acquston and the estmator mplementaton there are a number of other processes that need to be performed to prepare the data n a form that can be used by the estmator. One of the most fundamental processes s the flterng of the measured data for the removal of nconsstent measurements and nose. Varous flters have been developed and mplemented for the purposes of nose flterng. The flters consdered for ths work are dgtal dscrete flters. Representatve types of dgtal flters are the Butterworth, Chebyshev, Bessel, and movng average flters [51]-[53]. A flter almost always ntroduces a phase shft to the fltered sgnal. Ths phase shft s not desred, snce the varous frequency components of the sgnal are phase shfted by a dfferent amount. Therefore, a zero phase shft flter s desred to be mplemented so that there s no phase dfference between the orgnal and fltered sgnals. Informaton on zero phase shft flters can be found n [59], [54]-[56]. Zero phase dgtal flters effectvely flter the sgnal n both the forward and the reverse drectons. The resultng sequence has zero phase dstorton and twce the flter order. In all measurement technologes, there are the possbltes of bad measurements or mssng measurements. Bad data detecton and rejecton algorthms have been consdered and mplemented to remove outlers from the measurements. Such outlers appear n the form of spkes n the data sets and are nconsstent measurements. References [57]-[59] propose new methods for the mplementaton of bad data detecton and rejecton algorthms n power system state estmaton problems. The ssues of mssng data (e.g., a datum nadvertently dropped from a clocked measurement) are dscussed by Heydt n [6]. 11

24 1.11 Magnetc Saturaton Saturaton s a phenomenon n whch a functonal or physcal relatonshp y = f(x) experences a condton n whch for suffcently large x, the values of y no longer change sgnfcantly. Ths occurs n magnetc crcuts when a large number of the magnetc domans algn, and the applcaton of a magnetc feld no longer produces sgnfcant ncrease n magnetc ntensty. Saturaton of the generator magnetc crcuts s an mportant concept n ths research work. The effect of saturaton has been the subject of many scentfc papers and s stll a subject of actve research due to the mportance of the change of the generator parameters wth operatng condtons and the dffculty for modelng saturaton accurately. Reference [61] dentfes saturaton representaton as the most mportant factor n the mprovement of synchronous machne models. Saturaton and dfferent methods to model t are consdered n IEEE standards such as [5], as well as a number of research artcles and books [11], [2]-[22], [62], [63]. Fg. 1.2 shows a sample saturaton curve for a synchronous generator. It has been stated that the modelng of magnetc saturaton s one of the most dffcult engneerng problems n exstence. In [22], [62] the authors propose two quadratc saturaton functons to represent saturaton and they ft the proposed functons wth measured data from two generators. Ths s performed usng the method of fnte element analyss. Reference [64] compares two methods of saturaton representaton by examnng results of calculatons and avalable test data for a specfc synchronous generator. Saturaton n both the drect and quadrature axes s consdered. Authors n [65] descrbe a maxmum lkelhood estmaton algorthm to dentfy saturated nductances of a synchronous machne. The saturaton was modeled from operatng data that were generated from small voltage exctaton dsturbances. An alternatve method to model saturaton by usng a lnearzed generator model and stochastc approxmaton to solve for the parameters of the model s presented n [63]. The authors n [66] present a saturaton representaton by usng a fnte element numercal analyss technque. However, the method does not apply to all operatng condtons. 12

25 Fg. 1.2 Sample saturaton curve for a synchronous generator 1.12 Organzaton of the Report The report s organzed nto 5 chapters and 5 appendces. Chapter one s ntroductory and leads the reader to addtonal references as well as further reports of ths work. The man theory s shown n Chapter 2. Chapter 3 relates to the mplementaton and testng of the computer code. Examples are shown. Chapter 4 gves the detals of a graphc user nterface n an object orented (menu drven) mplementaton. Chapter 5 contans conclusons, recommendatons, and nput receved from ndustry for the project. The appendces cover: A. Modelng of the damper currents usng a devce known as an observer B Elmnaton of bad measurement data va preprocessng C. Modelng magnetc saturaton 13

26 D. Desgn of specfc numercal flters (e.g., Butterworth, Chebyshev) for synchronous machne nstrumentaton E. Mantanng phase relatonshps among AC voltages and currents n measurements durng nose flterng; harmoncs n measurements F. Brushless excters. 14

27 2 Modelng of Synchronous Machnes 2.1 Introducton In ths chapter, Park s model s explaned. References to reports gvng added detal are also gven. The man enhancements to Park s model are descrbed n the context of obtanng a method to dentfy synchronous machne parameters 2.2 Park s Model of a Synchronous Generator In order to formulate the state estmaton equatons for a synchronous generator, t s necessary to employ a mathematcal model whch represents the synchronous generator n the condtons under study. The model used n ths research work conssts of three stator wndngs, one feld wndng and three damper wndngs as shown n Fg Magnetc couplng s a functon of the rotor poston and therefore, the flux lnkng each wndng s also a functon of the rotor poston. The nstantaneous termnal voltage of any wndng takes the form, v r λ& = (2.1) where r s the wndng resstance, s the current and λ s the flux lnkage. It should be noted that n ths notaton t s assumed that the drecton of postve stator currents s out of the termnals, snce the synchronous machne under consderaton s a generator. In (2.1) the voltage s expressed n terms of both currents and flux lnkages. Ths s not desrable and therefore one of the two varables has to be replaced. The flux lnkage varables can be substtuted by approprate expressons that relate them to generator currents va machne nductances. Ths substtuton wll result n dfferental equatons wth tme-varyng coeffcents. It s convenent to refer all quanttes to a rotor frame of reference through Park s transformaton, P = cosθ sn θ 1 2 cos( θ 2π ) 3 sn( θ 2π ) cos( θ 2π ) 3. sn( θ 2π ) 3 15

28 r F a v F F F r D r a v D = D D aa bb r b b b v a r Q r n cc v b v Q = Q r G Q n v n r c c c v c v G = G G n Fg. 2.1 Schematc dagram of a synchronous machne The angle θ s gven by [12], θ = ωr t δ π 2 where ω R s the rated (synchronous) angular frequency n rad/s and δ s the synchronous torque angle n electrcal radans. The transformed currents are, where the current vectors are defned as, dq = d q dq = P abc a and abc = b. c Smlarly, the transformed voltages and flux lnkages are, v dq = Pv abc λ = Pλ and dq abc. 16

29 17 Equaton (2.1) n ts expanded form becomes, = n n n Q G D F c b a Q G D F c b a Q G D F c b a Q G D F c b a v v v λ λ λ λ λ λ λ r r r r r r r v v v v v v v & & & & & & & (2.2) Equaton (2.2) s transformed nto a dq frame of reference through a Park s transformaton. The system of equatons s converted nto ts per unt form and the followng relatons are used to smplfy the model, D AD D F AD F d AD d l l l = = = Q AD Q G AD G q AD q l l l = = = AQ Y Q G AD X D F M km km M km km = = = = = = The resultng synchronous generator model that s used for the parameter estmaton s thus gven by,

30 18 = Q G D F q d Q AQ AQ AQ AQ G AQ AQ D AD AD AD AD F AD AD AQ AQ q AQ AD AD d AD n B Q G D F q d Q G D F AD AD d AD AQ AQ q AQ n Q G D F q d ω r r r r ω ω r ω ω ω ω r r r v v v v v v v & & & & & & & l l l l l l l l 3 1 ) ( ) ( 3 (2.3) where all quanttes are n per unt except whch s n rad/s and tme whch appears n the dervatve terms n seconds. ω B All parameters n the coeffcent matrces n (2.3) are constant. Furthermore, snce the rotor speed s nearly constant f small tme perods are studed, (2.3) can be consdered as a lnear tme nvarant dfferental equaton. 2.3 Development of an Observer for the Damper Wndng Currents Usually, avalable data for synchronous generators are the stator phase currents and voltages at the termnals of the machne, and the feld voltage and current. In order to formulate the parameter estmaton problem, t s necessary to have measurements for the damper currents D, G, and Q. Snce t s not possble to measure the damper currents drectly usng physcal nstruments, even n the case that the damper wndngs are not fcttous, t s necessary to estmate the damper currents by means of an observer pror to the mplementaton of the state estmator for the generator parameters. The general concept of an observer s as follows: certan states of a physcal system may be dffcult to measure or calculate. These unobserved states may nonetheless be needed to calculate an estmate of the machne parameters. An observer s a dynamc system that s constructed so that the unobserved states may be estmated. The observer s adaptve: parameters of the observer are adjusted methodcally so that the output of the machne smulaton agrees wth the actual measured machne output. Fg. 2.2 shows the concept of an observer. For the constructon of the observer, the last three equatons of the synchronous generator model n (2.3) can be rearranged so as to obtan expressons for the damper wndng currents. The three equatons are gven by,

31 1 1 1 v D = = rd D AD d AD F ( AD l D ) D ω ω ω B B v G = = rg G AQ q ( AQ l G ) G AQ Q ω ω ω v Q = = rq Q AQ q AQ G ( AQ l Q ) Q ω ω ω B B B B B B B (2.4) (2.5) (2.6) where for the purposes of the development of the observer the current dervatves are replaced by the forward dfference formula, ( t t) ( t) ( t). t (2.7) INPUTS PHYSICA SYSTEM OUTPUTS STATES THAT ARE MEASURED OR CACUATED STATES STATES THAT ARE NEITHER MEASURED NOR CACUATED OBSERVER - METHODICA ADJUSTMENT OF OBSERVER PARAMETERS TO FORCE OUTPUT TO AGREE WITH PANT Fg. 2.2 Concept of an observer for a dynamc system Solvng (2.4) for D, an expresson can be obtaned n terms of known measurements and the value of D at the prevous step. rdωb t AD t ( n 1) = (1 ) D ( n) ( d ( n) F ( n)) l l D AD D AD D (2.8) 19

32 The quadrature axs damper wndng currents G and Q can be obtaned by the smultaneous soluton of (2.5) and (2.6) and are gven by, Q G ( AQ l ( n 1) = 1 k ( AQ l ( n 1) = 1 k Q G ) r AQ ) r AQ G Q ωb t AQ rq ω G ( n) k AQ AQ t AQl G ( AQ l G ) k AQ ωb t Q B t Q ( n) 1 q ( n) AQ rg ωb t ( n) G ( n) k AQ AQl G t q ( n), k AQ (2.9) (2.1) where k AQ = l l. 2 ( AQ Q )( AQ G ) AQ Equatons ( ) enable the calculaton of the damper currents. All parameters can be accurately calculated usng manufacturer s data, whle the tme varyng quanttes are avalable measurements. The only ambguty n the observer equatons s the value of D (), G (), and Q (). These are needed to ntate the observaton process. Nevertheless, the ntal condtons can be assumed to be zero wthout loss of accuracy as wll be shown n the two case studes n the next secton. 2.4 Case Studes Usng a Damper Wndng Currents Observer The foregong concept of parameter estmaton was tested n two ways: n smulated models; and utlzng actual generator measurements and manufacturer s data. The smulaton approach s consdered frst. A synchronous generator was smulated usng the Electromagnetc Transents Program (EMTP) both n the steady state and n transent mode. EMTP s sutable for testng the estmaton algorthm because data from the smulaton are free of nose, and one has access to all machne parameters and sgnals. Furthermore, EMTP provdes the smulated damper currents n the drect and quadrature axes. Therefore, a means of testng the observer s provded. The machne under consderaton s a cross-compound generator located n the southwest U.S.A. The generator contans a hgh pressure unt rated at 483 MVA and a low pressure unt rated at 426 MVA. Table 2.1 shows the parameters for the hgh pressure generator as calculated by manufacturer s data. These parameters are used n the EMTP program to obtan the requred measurements. Ths example s chosen because subsequently, a real-lfe example of the same machne, wth measurements taken by a dgtal fault recorder (DFR) wll be used. At ths pont t suffces to state that the measurements re- 2

33 qured are the three phase stator voltages and currents, and the DC feld voltage and current. The measurements are assumed to be error free for the smulaton tests. In the frst case study, the machne s operatng nearly n steady state. The damper wndng currents are observed accordng to the observer equatons (2.8)-(2.1) wth the ntal condtons assumed to be zero. All estmated damper currents match the smulated damper currents and are equal to zero to fve decmal places, as expected from a synchronous generator that operates n steady state. The error between the estmated and smulated currents can be calculated usng the formula, smulated observed % error = 2 1, smulated 2 Table 2.1 Synchronous generator parameters: 483 MVA machne used n both synthetc and actual on-ste tests Parameter Value (p.u.) Parameter name R.46 Stator phase resstance d 1.8 Equvalent drect axs reactance q 1.72 Equvalent quadrature axs reactance M F Stator to feld mutual nductance M D Stator to damper D mutual nductance M X 1.64 Rotor mutual nductance n the d axs crcut r F 9.722x1-4 Equvalent feld resstance r D.125 Equvalent resstance of damper wndng D F Feld wndng self nductance D Self nductance of damper wndng D M G Stator to damper G mutual nductance M Q Stator to damper Q mutual nductance M Y 1.56 Rotor mutual nductance n the q axs crcut r G.171 Equvalent resstance of damper wndng G r Q.1632 Equvalent resstance of damper wndng Q G Self nductance of damper wndng G Q Self nductance of damper wndng Q.15 Equvalent zero sequence nductance r n 1 Equvalent neutral resstance n 1 Equvalent neutral nductance 21

34 where. 2 denotes the 2-norm (square root of the sum of the squares of all the elements). The errors n the three damper wndng currents D, G, and Q for the steady state data case are.16%,.28% and.14% respectvely. In the second smulated case study, transent data were consdered. A permanent lne to lne fault was appled at.25 seconds between phases b and c. The observed damper currents as compared to the EMTP smulated damper currents for each axs can be seen n Fgs. 2.3, 2.4, and 2.5. As can be seen from the graphs, the estmated damper currents match the smulated damper currents. The percent errors between the smulated and estmated damper currents can be calculated n the same way as n the steady state case. The errors n the three damper wndng currents D, G and Q for the transent data case are.3%,.63% and.16% respectvely. Snce the dfference between the smulated and estmated sgnals s not dscernble n Fgs. 2.3, 2.4, and 2.5, a porton of Q as shown n Fg. 2.5 was magnfed to vsualze the dfference between the two sgnals. Ths dfference s shown n Fg Fg. 2.3 Smulated and estmated damper current D usng transent data 22

35 Fg. 2.4 Smulated and estmated damper current G usng transent data Fg. 2.5 Smulated and estmated damper current Q usng transent data 23

36 Fg. 2.6 Magnfcaton of porton of Q to demonstrate the dfference between the smulated and observed sgnals 2.5 Confguraton of the State Estmator State estmaton s a process durng whch a number of unknown system state varables or parameters are assgned a value based on measurements from that system. Typcally, the number of measurements (or number of equatons) s much greater than the parameters to be estmated. In ths case the system s overdetermned and the soluton s found n a least squares sense. That s, the sum of the squares of the dfferences between the estmated and the measured parameters s mnmzed. Snce the last three equatons of (2.9) have been used for the development of the observer, the remanng four equatons of (2.9) are rearranged nto the form Hx = z to obtan the estmated parameters by xˆ = H z, where H s the pseudonverse of H. Matrx H (the process matrx) s of dmenson m n and contans the coeffcents of the unknowns, whch are ether obtaned by drect measurements of current and voltages, or va the observer n the case of the damper currents, or va calculaton n the case of the dervatves. The formula for the dervatves s the forward dfference formula (2.11). The vector z has dmenson m and t contans known parameters, or measurements or a combnaton of the two. Fg. 2.7 llustrates n block dagram form the dea of the observer, the data manpulaton and the parameter estmaton algorthm. For example, f parameters AD, AQ and r F are to be estmated, (2.9) can be rearranged n the form Hx = z to obtan, 24

37 25 = Q G D F q d Q G D F q d F q d n B Q G D F q d d q n F AQ AD F B D F d B Q G q D F d Q G q B D F d v v v v v v v ω r ω ω r r r r ω ω ω ω ω ) ( ) ( ) ( ) ( ) ( & & & & & & & l l l l l In ths way, the three unknown parameters and ther coeffcents are solated on the left hand sde, and all elements of the rght hand sde are known. Moreover, the rght hand sde reduces to a vector and therefore the system takes the fnal form. z Hx = The lnear system Hx = z represents multple tme steps. Each measurement results n an equaton of the form Hx = z. At each subsequent tme step, the new data are augmented to the exstng H matrx and z vector to create an overdetermned system. Unknown plant (Approxmate model known) Observer Parameter dentfcaton algorthm V I a pror system knowledge ˆ ˆ ˆ,, D G Q Estmated parameters - Î e Fg. 2.7 Block dagram for observer mplementaton and parameter dentfcaton algorthm

38 2.6 Bad Data Detecton, Rejecton and Flterng Real data have errors resultng manly from meter and communcaton errors, ncomplete meterng, or naccuracy of meterng equpment. Therefore, pror to any estmaton t s necessary to perform bad data detecton and rejecton, and flterng of the nose. In the feld crcut, the man frequency components of nterest are at or near DC. On the other hand, n the stator measurements t s possble to perform flterng n the AC measurements (5-6 Hz range), or n the dq transformed sgnals (at or near DC). In the synchronous machne parameter estmaton applcaton, t was found that the stator measurements are most effectvely fltered after the dq transformaton. Fg. 2.8 shows the flterng and bad data detecton/rejecton confguraton. After the transformaton of the abc voltages and currents nto dq sgnals through Park s transformaton, a flter s appled to remove outlers from the measurements. Such outlers appear n the form of spkes, n the tme doman plot of each sgnal. They are caused by meterng errors and can be safely removed wthout rskng naccuraces n the estmaton process. If a spke n any one sgnal s detected, then the whole measurement at that tme s removed from the data set. Measured sgnals from DFR Fltered sgnals for nput to the estmator abc stator sgnals V ab, V bc, V ca I a, I b, I c dq transformaton Bad data rejecton/ detecton Flterng Feld sgnals V F, I F Bad data rejecton/ detecton Flterng Fg. 2.8 Flterng and bad data detecton/rejecton confguraton A second flter was mplemented for the removal of random nose. Frequency doman plots of the measured sgnals ndcate the exstence of nose n a wde range of frequences from the man frequency component up to the Nyqust frequency. Ths nose s detrmental to the estmaton process, especally n the calculaton of dervatves. A small random nose content n consecutve measurements s amplfed when dvded by the tme step between the measurements ( t s n the order of.1 ms). A Butterworth flter s used to mplement the flterng. Butterworth flters are characterzed by a magntude response 26

39 that s maxmally flat n the passband and s characterzed by monotoncty n the passband and stopband regons. To compensate for the shallower rolloff characterstc of a Butterworth flter, the data are fltered successvely by passng them through the same flter untl the frequency components that are due to nose are mnmzed. Flter characterstcs are chosen dependng on the locaton and on the sze of the nosy frequency components, but n general, the flters for all the sgnals have a cutoff frequency of approxmately 1 Hz and a stopband frequency of 1 Hz wth a stopband attenuaton of about 6-8 db. Fg. 2.9 depcts the drect axs voltage component n the tme doman as calculated from measurements obtaned at the generator termnals, whle Fg. 2.1 shows the fltered sgnal after applyng a spke flter and multple Butterworth flters. Fg. 2.9 Unfltered drect axs voltage n the tme doman 27

40 Fg. 2.1 Fltered drect axs voltage n the tme doman 2.7 Magnetc Saturaton In order to represent saturaton n stablty studes several assumptons are made. The reason for ths s that a rgorous treatment of synchronous machne performance ncludng saturaton s a futle exercse. Hence, one typcally looks for a practcal method for dealng wth saturaton effects based on sem-heurstc reasonng, carefully chosen approxmatons, smplcty of model structure, data avalablty, and accuracy of results. The elementary approaches to ncludng saturaton are documented n [3. In ths approach several smplfyng assumptons are made n determnng saturaton. The effects of saturaton are represented as, = K AD = K AQ sd sq ADu AQu where ADu and AQu are unsaturated values of AD and AQ. The saturaton factors K sd and K sq dentfy the degrees of saturaton n the drect and quadrature axs, respectvely. The saturaton factors are less than 1. The d-axs saturaton s determned from the open crcut characterstc. Typcally the saturaton curve s dvded nto three segments, whch are defned by threshold values of the flux lnkage λ. Sutable approxmatons for the behavor of λ are made based on the operatng segment and thus, approprated expressons for K sd are derved. It s commonly assumed that for salent pole machnes, snce the path for the q-axs flux s largely n ar, AQ does not vary sgnfcantly wth saturaton of the ron porton of the path. Hence, typcally the saturaton factor K sq s assumed to be equal to 1. for all loadng condtons. 28

41 In the case of round rotor machnes, magnetc saturaton should be accounted for n both axes. In general the saturaton factor K sq can be determned from the no-load saturaton characterstc of the q-axs. However, q-axs saturaton data are typcally not avalable. As a result one normally makes the assumpton that K sq s equal to K sd. Ths essentally assumes that the reluctance of the magnetc path s homogeneous around the perphery of the rotor. An approach to mproved saturaton modelng usng q-axs saturaton characterstcs derved from fnte-element analyss s shown n [7] and dscussed n [69]. Kundur [2] shows a method to calculate the saturaton functon. In the parameter estmaton method shown n the present paper, AD and AQ (as well as other parameters) are estmated for a gven set of operatng data. Estmaton of parameters usng data from an actual synchronous generator operatng at dfferent load levels, ndcates that nductances AD and AQ are the nductances that are most affected by saturaton and these quanttes vary consderably. 2.8 Brushless excters Many modern synchronous generators utlze brushless exctaton. In ths confguraton, the feld current s delvered to the rotor by nducton. The AC n the feld wndng s then rectfed on the rotor. There are no slp rngs or brushes n ths confguraton. Unfortunately, n the brushless confguraton, there s no possblty of the drect measurement of the DC feld current. And the nature of the waveshape and controls depends heavly on the type of excter crcut used. In many cases, the exact excter model s unknown and / or propretary. Power system small sgnal, transent, and dynamc stablty studes are only as accurate as the underlyng models used n the computer analyss. The valdty of the results of these studes depends heavly on the accuracy of the model parameters of the system components. In practce, the parameters commonly used n stablty studes are manufacturer specfed values, or typcal values. These typcal values may be grossly naccurate, as varous parameters may drft over tme or wth operatng condton. Thus, t s desrable to develop methods for estmatng component parameters. Accurate models of exctaton systems are essental to transent smulaton, whch s a key part n power system plannng and operaton. Transent smulaton s also used to analyze, explan and prevent the outage of the power system. One of the popular software packages s ETMSP (Extended Transent/Md Term Stablty Program) by EPRI. In order to obtan a relable transent smulaton, t s necessary to have accurate models and parameters of exctaton systems, synchronous machnes and other control systems such as a speed-governor system. Whle parameter estmaton of synchronous machnes has been well documented, parameter estmaton of exctaton systems has only begun to receve thorough attenton. The objectve of ths study s to establsh a procedure to perform parameter estmaton of 29

42 an AC1A type exctaton system usng least squares method. The detals are shown n Appendx F. Unfortunately, very lmted success was obtaned n the brushless excter case, and t s not known whether machne parameters may be calculated by the methods gven n ths report for the brushless case. 3

43 3 Estmaton of Machne Parameters and Testng of the Algorthm 3.1 Descrpton of a Testng Regmen The parameter estmaton algorthm was tested usng real data collected from the termnals of a commtted synchronous generator. The machne under consderaton s the cross-compound generator descrbed n Secton 3.2. Measurements were collected usng a dgtal fault recorder (DFR). The data were collected at steady state operaton, whle the machne served ts load. The samplng frequency was 1 khz and eght sgnals were measured: stator lne currents and voltages (I a, I b, I c, V ab, V bc, V ca ), and feld current and voltage (I F, V F ). Sample results are shown n Secton Descrpton of Tests Implementaton of any proposed algorthm usng actual measurements s the ultmate test for ts vablty and applcablty to the system under study. After the successful testng of the parameter estmaton algorthm usng both synthetc and EMTP data as demonstrated n [69], t s necessary to test the estmator usng data obtaned from synchronous generators and observe whether the proposed method agrees to the practcal results. Synchronous generator measurements for the purpose of ths research work are obtaned through a dgtal fault recorder (DFR). A DFR s effectvely a data acquston system that s used to montor the performance of generaton and transmsson equpment, and therefore s connected permanently to utlty generators. DFRs are typcally used by the majorty of the utltes to montor the operaton of generators. For ths partcular estmaton methodology, the measurements are obtaned at the termnals of commtted synchronous generators (the unts serve ther typcal loads). Dfferent operatng levels are consdered to examne the accuracy of the proposed method wth varyng degrees of exctaton and dfferent saturaton levels. The measurements are stored n a data fle that can be read by the estmator. The data fles are typcally of the COMTRADE data fle format, whch s an approved IEEE data format for storage of measurements. The data can ether be n ASCII format or bnary format. In between the data acquston and the estmator mplementaton there are a number of other processes that need to be performed to prepare the data n a form that can be used by the estmator. Fg. 3.1 shows a flowchart of the procedure followed to perform the parameter estmaton. The measurements obtaned for the stator voltages are sometmes lne to lne measurements, and therefore t may be necessary to transform these sgnals nto phase quanttes. Further, the power angle δ needs to be calculated n order to perform the Park's transformaton as explaned n Chapter 2 and Appendces D - E. The above transformatons and the procedure s llustrated n Fg

44 3.3 Results of Parameter Estmaton from Actual Measurements In contrast to the smulated data set, an examnaton of the actual data sets obtaned from the synchronous generator termnals and used for the parameter estmaton descrbed n ths secton, ndcates that the generators operate wthn the saturaton regon. Therefore, the estmator algorthm needs to adjust the parameters for saturaton as explaned n Chapter 2. The parameters obtaned from the estmator reflect the true state of the system ncludng saturaton. START Obtan stator (abc) measurements and feld measurements Obtan MVA and kv base and known parameters Flter hgh frequency nose n feld voltage and current Calculate actve and reactve power and power factor at each pont Convert lne-lne voltages to phase voltages Calculate the power angle δ Reject outlers n stator measurements Flter hgh frequency nose n stator measurements Convert all measurements to per unt quanttes Calculate dervatves of currents Implement observer for damper wndng currents Estmate generator parameters Perform Park's transformaton to convert abc to dq END Fg. 3.1 Algorthm for estmator mplementaton for actual measurements 32

45 Table 3.1 depcts the estmated parameters n each of the three proposed models usng actual measurements from generator FC5HP (case study R-NC-1-1). All parameters are ndvdually estmated assumng that all other parameters are known. In the case of model 2.2x, AD and AQ are the only parameters affected by saturaton snce all other nductances have been expressed n terms of these mutual nductances. In the case of models 2.1 and 2.2 a number of parameters s affected by saturaton and these parameters are adjusted pror to the estmaton procedure f they are not desred to be estmated. Therefore, Table 3.1 depcts the saturated values of the parameters (where applcable). Table 3.1 Estmated parameters for the three proposed models for generator FC5HP (case study R-NC-1-1) Parameter (p.u.) Model 2.1 Model 2.2 Model 2.2x d N/A q N/A F N/A km F N/A AD N/A N/A AQ N/A N/A R r F 8.386x x x1-4 As mentoned above, the estmated nductances of Table 3.1 potentally reflect the true state of the system ncludng the effect of saturaton. Snce the exact values of the parameters at every operatng pont are not known, t s not possble to derve any defnte conclusons about the accuracy of the estmated parameters. Therefore, t s desred to nullfy the effect of saturaton by applyng the nverse of the approprate saturaton factor to each of the saturated nductances. Ths wll offer estmates of the unsaturated nductances and a comparson to the manufacturer values may be obtaned. However, the manufacturer values of the parameters have been calculated by off-lne tests and testng methods that may not necessarly reflect the operatng pont under consderaton. Moreover, manufacturer values are typcally desgn values for a seres of manufactured generators, and consequently dfferences between desgned and actual parameter values do exst. Therefore, the percent dfference between the estmated parameters and the manufacturer parameters cannot be classfed as a percent error as n the case of the smulated measurements. The dfference between the estmates and ther nomnal values s re- 33

46 ferred to as a percent devaton. The percent devaton cannot be used as a verfcaton or rejecton of the proposed method, but t can offer an nsght as to whether the estmates obtaned are reasonable or not. In general, t s more mportant to have consstency n the estmated parameters between varous data sets from the same generator, than to have results wth varyng degrees of accuracy. Table 3.2 depcts the percent devaton of the estmated parameters from the manufacturer suggested values for the parameters, after the effect of saturaton has been nullfed to obtan an estmate of the unsaturated values of the nductances. All three models are consdered to enable comparson of the estmaton method between all the canddate models. Table 3.2 Calculaton of unsaturated parameters from the estmated parameters of generator FC5HP (case study R-NC-1-1) Parameter Manufacturer value (p.u.) Model 2.1 Model 2.2 Model 2.2x Estmated parameter (p.u.) % Devaton Estmated parameter (p.u.) % Devaton Estmated parameter (p.u.) % Devaton d N/A N/A q N/A N/A F N/A N/A km F N/A N/A AD 1.64 N/A N/A N/A N/A AQ 1.56 N/A N/A N/A N/A R r F 8.454x x x x1-4.8 Table 3.2 shows that the results obtaned from all three models are smlar. Results from models 2.2 and 2.2x are slghtly mproved due to the more accurate modelng of the quadrature axs. A dscusson for some of the results from the three models s approprate at ths pont. The feld resstance s estmated wth a devaton of.8% n all three models. Estmaton of the feld resstance s a crtcal aspect of the overall estmaton procedure snce one of the motvatons for ths research work s the trackng of the change n 34

47 the feld resstance to detect and prevent short crcuts n the feld wndng. The nomnal feld wndng resstance noted as the manufacturer value n Table 8.2 s an approxmate quantty snce the generator under consderaton has been rewound a number of tmes because of short crcuts n the feld wndng. Therefore, no defnte comparson can be performed between the estmated and the nomnal value. Nevertheless, the estmaton procedure gans consderable confdence from these results snce the devaton between the two values s very small. Values for d, q, and km F are estmated wthn a reasonable accuracy n both models 2.1 and 2.2, wth q beng estmated more accurately n model 2.2. The percent devatons for these parameters vary from.2 to 2.4%. In the case of the feld nductance F, the percent devaton attaned s n the order of 7.4%. Ths result s not consdered satsfactory, but smlarly to the case of the feld resstance, the nomnal value of F may not be accurate because of the rewndng of the feld wndng of ths partcular generator. In the case of model 2.2x, AQ s estmated wth a devaton of 2.% from ts nomnal value, whle AD s estmated wth a devaton of 5.9%. A porton of the devaton of AD can be attrbuted to the feld nductance F, snce n model 2.2x the feld nductance was expressed as F = AD lf, where l F s the leakage nductance of the feld wndng. Therefore, the estmated AD wll reflect any possble naccuracy of l F because of the rewndng of the feld wndng. Fnally, the results for the stator resstance n all three models show that currently the stator resstance cannot be estmated accurately. The amount of nose n the measurements and the representaton of saturaton are two of the reasons for the naccuracy n the stator resstance. A number of case studes were performed to observe how usng dfferent saturaton factors and varous flterng mechansms affect the stator resstance. For example, f no saturaton s modeled, then the estmated stator resstance was postve and much hgher than the manufacturer value of r. As saturaton factors of ncreasng values were ntroduced to adjust AD and AQ, the value of the stator resstance reduced and n some cases the estmated value was negatve as n the case of Table 3.2. The nablty to estmate r wthn a satsfactory degree of accuracy s not an obstacle to ths method of estmaton. Typcally, there s no nterest n estmatng r. The man parameters of nterest are d, q (or AD and AQ ), and r F. 3.4 Multple Parameter Estmaton Multple parameter estmaton from actual measurements s an mportant aspect of the estmator. In many cases (lke the one under consderaton n ths research work) t s possble that there s uncertanty n more than one parameter. Therefore t s mperatve that the feasblty of multple parameter estmaton s nvestgated. Ideally, t s desred that the percent devaton obtaned for each parameter s the same n both ndvdual parameter estmaton and multple parameter estmaton. Two case studes are performed. In the frst case study (R-NC-3-11), d, q, and r F are estmated smultaneously for models 2.1 and 2.2, whle AD, AQ, and r F are estmated smultaneously for model 2.2x. The estmated parameters are depcted n Table 3.3, 35

48 whle the unsaturated parameters calculated from the estmated parameters are depcted n Table 3.4. It can be observed that for all three models the estmated parameters and ther percent devatons are dentcal to the correspondng parameters n the ndvdual parameter estmaton of Table 3.1 and Table 3.2. Table 3.3 Multple smultaneous parameter estmaton for generator FC5HP (case study R-NC-3-11) Parameter (p.u.) Model 2.1 Model 2.2 Model 2.2x d N/A q N/A AD N/A N/A AQ N/A N/A r F 8.386x x x1-4 Parameter Table 3.4 Calculaton of unsaturated parameters for generator FC5HP (case study R-NC-3-11) Manufacturer value (p.u.) Model 2.1 Model 2.2 Model 2.2x Estmated parameter (p.u.) % Devaton Estmated parameter (p.u.) % Devaton Estmated parameter (p.u.) % Devaton d N/A N/A q N/A N/A AD 1.64 N/A N/A N/A N/A AQ 1.56 N/A N/A N/A N/A r F 8.454x x x x1-4.8 In the second case study (R-NC-3-12), d, q, and F are estmated smultaneously for models 2.1 and 2.2, whle AD, AQ, and F are estmated smultaneously for model 2.2x. The estmated parameters are depcted n Table 3.5, whle the unsaturated parameters cal- 36

49 culated from the estmated parameters are depcted n Table 3.6. As n the prevous case study, the estmated parameters and ther percent devatons are dentcal to the correspondng parameters n the ndvdual parameter estmaton of Table 3.1 and Table 3.2. Table 3.5 Multple smultaneous parameter estmaton for generator FC5HP (case study R-NC-3-12) Parameter Model 2.1 Model 2.2 Model 2.2x d N/A q N/A AD N/A N/A AQ N/A N/A F N/A The results of the multple smultaneous parameter estmaton case studes ndcate that more than one parameter can be estmated at the same tme. It was shown that there s no degradaton of the percent devaton of the estmated parameters from ther nomnal values. Therefore, the confdence for the use of the estmator to estmate multple parameters smultaneously s renforced. In case that the confdence n some of the synchronous generator parameters s lmted (for example, because of alteratons to the generator crcutry), multple parameter estmaton holds the key to a relable estmaton procedure. 3.5 Applcaton of the Algorthm to Dfferent Machnes and Operatng Ponts Sectons 3.2 and 3.3 dscussed the parameter estmaton procedure and some of the results obtaned usng measurements from generator FC5HP. It s necessary to perform parameter estmaton for dfferent generators and at dfferent operatng ponts to ensure that the method s applcable to other generators as well. Usng measurements from dfferent generators enables the examnaton of the accuracy of the proposed method, whle the estmaton at varous operatng ponts for each generator ensures that the results are consstent. 37

50 Parameter Table 3.6 Calculaton of unsaturated parameters for generator FC5HP (case study R-NC-3-12) Manufacturer value (p.u.) Model 2.1 Model 2.2 Model 2.2x Estmated parameter (p.u.) % Devaton Estmated parameter (p.u.) % Devaton Estmated parameter (p.u.) % Devaton d N/A N/A q N/A N/A AD 1.64 N/A N/A N/A N/A AQ 1.56 N/A N/A N/A N/A F N/A N/A The case studes descrbed n Sectons 3.2 and 3.3 and a number of other case studes that were performed, permt the extracton of some conclusons pertanng to the model used n the estmaton procedure. Clearly the estmates obtaned from models 2.2 and 2.2x are superor to the ones obtaned from model 2.1. Ths s due to the modelng of one extra damper wndng n the quadrature axs of the generator; ths wndng causes the model to be symmetrc wth regards to the drect and quadrature axes. Results from models 2.2 and 2.2x are smlar consderng that the estmates of AD and AQ contan the error from the feld wndng nductance F and other quanttes such as the mutual nductances between axes n the stator and the rotor (see [69] for a comparson of the two models. A clear advantage of model 2.2x s that t offers an easer way of representng the magnetc saturaton n a synchronous generator. Therefore, model 2.2x s the preferred model. The parameter estmaton results presented n ths secton and n Appendx F are obtaned through the utlzaton of model 2.2x. Table 3.7 shows the parameter estmaton results for ten data sets obtaned from two dentcally desgned unts at the Redhawk generatng staton of APS. Eght of the data sets are obtaned from GT1, whle two of the data sets are obtaned from GT2. Although the two unts may have some dfferences n ther parameters snce no two unts are exactly dentcal, the use of more data sets wll allow the extracton of useful results pertanng to the accuracy of the method when appled to dfferent generators and the representaton of saturaton. The two unts are gas turbne unts rated at MVA and 18 kv. Ther characterstcs are descrbed n Table

51 Table 3.7 Parameter estmaton results for Redhawk gas turbnes 1 and 2* Case study Unt # ˆ AD (p.u.) ˆ AQ (p.u.) rˆ F (p.u.) K sd F (A) P (MW) Q (MVAr) ˆ ADu (p.u.) ˆ AQu (p.u.) % devaton AD AQ R-NC-3-13 R-NC-3-14 R-NC-3-15 R-NC-3-16 R-NC-3-17 R-NC-3-18 R-NC-3-19 R-NC-3-2 R-NC-3-21 R-NC-3-22 GT x GT x GT x GT x GT x GT x GT x GT x GT x GT x Mean (µ) 7.41 x Standard devaton (σ) x * From the manufacturer data sheet: AD = p.u., AQ = p.u., whle r F s unavalable. 39

52 Three parameters were estmated from each data set: AD, AQ, and r F. The operatng pont of the generator for each data set s shown, as well as the feld current. The saturaton factor for the drect axs s calculated and shown n the table for each case study. It s assumed that the saturaton factor s the same n both the drect and quadrature axes. It s necessary to apply the saturaton factor (< 1.) to the estmated saturated nductances n order to obtan the unsaturated nductances. Ths wll allow comparson to the manufacturer data and enable the assessment of the estmaton method. Table 3.7 depcts the estmated unsaturated mutual nductances and ther devaton from the manufacturer suppled mutual nductances. It should be noted that the manufacturer nductances AD and AQ are p.u. and p.u. respectvely. It s of practcal nterest to examne the change of the two mutual nductances wth exctaton, usng both the estmated saturated values as well as the values corrected for saturaton to obtan the unsaturated values. Fg. 3.2 shows the change n the estmated drect axs mutual nductance AD wth the feld current. A lnear regresson model s ftted to observe the trend n the estmated nductance over ncreasng saturaton levels. As expected there s a decrease n the apparent value of the nductance as the generator s drven to hgher operatng ponts. Fg. 3.3 compares both the saturated and the unsaturated values of AD for all case studes. The stacked column graph shows the estmated parameters and the correcton for saturaton. An overall agreement between the unsaturated values s observed. The unsaturated values of AD have a mean of p.u. and a standard devaton of.225 p.u. All of the values of the unsaturated AD agree to one decmal place. The results of each case study for the quadrature axs mutual nductance AQ are summarzed n Fgs. 3.4 and 3.5. The estmated values of the quadrature axs mutual nductance at dfferent operatng ponts are shown n Fg The trend n the saturated value of the nductance s decreasng, although the decrease s not as evdent as n the case of AD. It should be noted that the varaton of AQ s slghtly hgher than that of AD snce the standard devaton among the unsaturated parameters s.375 p.u. The mean of the unsaturated parameters s A comparson between the unsaturated values of AQ at each operatng pont s offered n Fg. 3.5, where the saturated nductances are corrected for saturaton usng the approprate saturaton factors at each operatng pont. Wth the excepton of two data sets, the unsaturated values of the nductance agree to one decmal place. Reference [69] presents parameter estmaton results for two steam turbne generators located at the Redhawk generatng staton of APS. A number of case studes are performed and an analyss smlar to the analyss of ths secton s offered. 4

53 AD (p.u.) Feld current (A) Fg. 3.2 Change of AD wth operatng pont for Redhawk gas turbne generators 41

54 Note that the saturated nductances are smaller than the unsaturated values AD (p.u.) Feld current (A) Estmated AD AD corrected for saturaton Fg. 3.3 Saturated and unsaturated values of AD for Redhawk gas turbne generators AQ (p.u.) Feld current (A) Fg. 3.4 Change of AQ wth operatng pont for Redhawk gas turbne generators 42

55 AQ (p.u.) Feld current (A) Estmated AQ AQ corrected for saturaton Fg. 3.5 Saturated and unsaturated values of AQ for Redhawk gas turbne generators. 3.6 Utlzaton of the Parameter Formulas to Obtan Machne Parameters Typcally machne parameters obtaned from manufacturer data are as shown n [69]. These machne parameters are referred to as standard machne parameters and nclude the drect and quadrature axs reactances and ther transent and subtransent counterparts, as well as the transent and subtransent tme constants. However, the estmated parameters obtaned through the model developed are derved parameters from these standard machne parameters. Therefore, t s necessary to calculate the standard parameters from the estmated parameters obtaned through the developed algorthm. Table 3.8 summarzes the formulae that are needed to perform the converson from derved parameters to standard parameters. Table 3.9 compares estmated standard parameters to manufacturer standard parameters for case study R-NC-1-1 (generator FC5HP). The results of Table 3.9 show a good correlaton between the estmated standard parameters and the manufacturer standard parameters. The correcton for saturaton typcally mproves the estmates. Some of the parameters such as the transent and subtransent nductances are estmated wth errors less than.3%. The hghest error s observed for the drect axs transent open crcut tme constant and t s equal to 5.5%. 43

56 Table 3.8 Calculaton of standard parameters from the estmated derved parameters* Parameter name Parameter symbol Formula Equvalent drect axs reactance x l Transent drect axs reactance Subtransent drect axs reactance Equvalent quadrature axs reactance Transent quadrature axs reactance Subtransent quadrature axs reactance Drect axs transent open crcut tme constant Drect axs subtransent open crcut tme constant Quadrature axs transent open crcut tme constant Quadrature axs subtransent open crcut tme constant d x d x d x q x q x q τ d τ d τ q τ q l l d q l 1 ω r B F d AD AD 1 l G AD AQ q AQ 1 D 1 ω r *Note: Tme constants are n seconds. All other quanttes are n per unt. B Q AQ l d AD F 1 1 l l l D q AQ G 1 1 l AD l ω r [ l [ l D AQ B F G F 1 l ω r Q B G AD G 1 AQ l d 1 l l q F 1 l Q 1 1 l F 1 1 l G ] ] 44

57 Table 3.9 Comparson of estmated standard parameters to manufacturer standard parameters (case study R-NC-1-1)* Parameter Manufacturer Value at operatng Unsaturated % Devaton value pont value x d x d x d x q x q x q τ d τ d τ q q τ *Note: Tme constants are n seconds. All other quanttes are n per unt. Note that the saturated and X are less than the unsaturated values. 45

58 4 Graphc User Interface Implementaton Usng Vsual C 4.1 A Graphc User Interface A partcularly convenent way to estmate generator parameters n a practcal engneerng settng s through the use of a GUI. To be consstent wth other engneerng tools, the GUI mght be n the form of a Wndows applcaton. A GUI utlzng on-lne DFR data enables the practcng engneer and nterested utltes to estmate parameters of a synchronous machne wthout havng to decommt the unt. In order to facltate use of the estmaton procedure descrbed, an on-lne mplementaton was developed and tested n a lmted envronment. The GUI enables on-lne parameter estmaton for a gven synchronous machne based on measurements of the feld and stator voltages and currents. Such measurements are usually avalable. An applcaton of ths nature should be portable and able to be nstalled on any personal computer operatng under Wndows. User frendly nteracton s acheved by means of the dalogs and context-senstve help provded on request. In the subsequent secton, the GUI developed s descrbed n greater detal. The mplementaton s offered as an example of what mght be done to mplement the estmaton algorthm descrbed n ths report. 4.2 A Sample Input / Output Dalog And Estmator Confguraton It s useful to confgure the man wndow of a GUI to mplement the estmator descrbed above to offer a varety of optons on ts toolbar, lke any other Wndows program. To begn the process of estmatng machne parameters, the user must open the nput screen as shown n Fg Ths s acheved by selectng the opton Estmator on the toolbar of the man wndow, and then selectng the Set up Estmator opton. The user can set up the Estmator and calculate the parameters of the synchronous machne that s to be studed by followng the drectons on the nput screen. The name of the data fle s entered n the edt box as shown n Fg The fle can be of any data format type (for example.dat or.txt). If applcable, the user can select the IEEE COM- TRADE opton by clckng on the respectve rado button and the Estmator wll read the measurements as obtaned drectly from the measurng devce that s connected to the machne. 46

59 Fg. 4.1 Input wndow of the estmator The parameter estmaton method descrbed n ths report requres a base set of values of selected machne parameters. The user nputs the requred parameters as contaned n the manufacturer data sheet of the synchronous machne or default values avalable n the program can be used. Subsequent to basc data entry, the user selects varous optons pertanng to the estmaton process. It s possble to perform ether a least squares estmaton (2 mnmzaton) or a mnmzaton of absolute devatons usng the 1 norm. Further, the user may select the level of flterng that s desred. Of the two optons, the full flterng s preferred snce t wll mnmze the nose content n the measured sgnals. Fnally, the user s gven the opton to apply weghts to the measurements. Ths s partcularly useful f t s known that certan measurements are less relable than other measurements. Further documentaton on all the optons s provded through context-senstve help or through the buttons that are located on the nput wndow. The fnal step of the estmaton process s to select the parameters that are to be estmated. For the test GUI mplemented, the user has the opportunty to select up to fve parameters for estmaton. Ths selecton can be done by smply clckng on the check box correspondng to the parameter to be estmated as shown n Fg The resultng output wndow after estmaton can be seen n Fg On the left sde of the output wndow, the user can see the parameters selected prevously and ther estmated value n per unt. The rms error on the lower rght sde of the estmator s a measure of confdence on the estmated parameters and s gven by, 47

60 rms error = resdual # of measurements ( resdual) 2 T [ H ][ xˆ ] [ z] } {[ H ][ xˆ ] [ z]} = {, where xˆ s the vector of the estmated parameters. Fnally, a confdence level s ndcated and has three states: hgh, average or low. In ths fashon, the user can verfy whether the measurements used are relable or not. Fg. 4.2 Output wndow of the estmator 4.3 stng of the Code and Flow Charts A lstng of the Matlab code, and flow charts for the GUI program appear n appendces of reference [69]. 48