Adaptive Parameter Estimation of Power System Dynamic Model Using Modal Information

A novel method for estimating parameters of a dynamic system model is presented using estimates of dynamic system modes (frequency and damping) obtained from wide area measurement systems (WAMS). The parameter estimation scheme is based on weighted least squares (WLS) method that utilizes sensitivities of the measured modal frequencies and damping to the parameters. The paper concentrates on estimating the values of generator inertias but the proposed methodology is general and can be used to identify other generator parameters such as damping coefficients. The methodology has been tested using a wide range of accuracy in the measured modes of oscillations. The results suggest that the methodology is capable of estimating accurately inertias and replicating the dynamic behavior of the power system. It has been shown that the damping measurements do not influence estimation of generator inertia. The method has overcome the problem of observability, when there were fewer measurements than the parameters to be estimated, by including the assumed values of parameters as pseudo-measurements.

[1]  A.H.M.A. Rahim,et al.  Dynamic equivalent of external power system and its parameter estimation through artificial neural networks , 2002 .

[2]  F. Schweppe,et al.  Selective Modal Analysis with Applications to Electric Power Systems, PART I: Heuristic Introduction , 1982, IEEE Transactions on Power Apparatus and Systems.

[3]  J. F. Hauer,et al.  Making Prony analysis more accurate using multiple signals , 1999 .

[4]  Ning Zhou,et al.  Initial results in power system identification from injected probing signals using a subspace method , 2006, IEEE Transactions on Power Systems.

[5]  J.M. Ramfirez,et al.  A technique to reduce power systems electromechanical models , 2004, IEEE Transactions on Energy Conversion.

[6]  Adel El Shahat,et al.  Permanent magnet synchronous motor dynamic modeling with genetic algorithm performance improvement , 2010 .

[7]  C. Y. Chung,et al.  A Combined TSA-SPA Algorithm for Computing Most Sensitive Eigenvalues in Large-Scale Power Systems , 2013, IEEE Transactions on Power Systems.

[8]  D.J. Trudnowski,et al.  Use of least mean squares (LMS) adaptive filtering technique for estimating low-frequency electromechanical modes in power systems , 2004, IEEE Power Engineering Society General Meeting, 2004..

[9]  G. J. Rogers,et al.  A fundamental study of inter-area oscillations in power systems , 1991 .

[10]  Vaithianathan Venkatasubramanian,et al.  Electromechanical Mode Estimation Using Recursive Adaptive Stochastic Subspace Identification , 2014, IEEE Transactions on Power Systems.

[11]  A. M. Gole,et al.  Dynamic system equivalents: A survey of available techniques , 2009, 2009 IEEE Power & Energy Society General Meeting.

[12]  J. W. Pierre,et al.  Use of ARMA Block Processing for Estimating Stationary Low-Frequency Electromechanical Modes of Power Systems , 2002, IEEE Power Engineering Review.

[13]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[14]  Tarun Khanna,et al.  Foundations of neural networks , 1990 .

[15]  A.R. Messina,et al.  Identification of instantaneous attributes of torsional shaft signals using the Hilbert transform , 2004, IEEE Transactions on Power Systems.

[16]  Ovidiu Ivanov,et al.  REI equivalent design for electric power systems with genetic algorithms , 2008 .

[17]  P. Kundur,et al.  Dynamic reduction of large power systems for stability studies , 1997 .

[18]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[19]  David M. Skapura,et al.  Neural networks - algorithms, applications, and programming techniques , 1991, Computation and neural systems series.

[20]  J. F. Hauer,et al.  Application of Prony analysis to the determination of modal content and equivalent models for measured power system response , 1991 .

[21]  G. J. Rogers,et al.  Slow coherency based network partitioning including load buses , 1993 .

[22]  R. Podmore,et al.  Dynamic Aggregation of Generating Unit Models , 1978, IEEE Transactions on Power Apparatus and Systems.

[23]  S. Hahn.  Hilbert Transforms in Signal Processing , 1996 .

[24]  Raj Mittra,et al.  Problems and Solutions Associated with Prony's Method for Processing Transient Data , 1978, IEEE Transactions on Electromagnetic Compatibility.

[25]  Z. Lubosny,et al.  Dynamic Equivalencing of Distribution Network with High Penetration of Distributed Generation , 2006, Proceedings of the 41st International Universities Power Engineering Conference.

[26]  T. Sarkar,et al.  Using the matrix pencil method to estimate the parameters of a sum of complex exponentials , 1995 .

[27]  N. D. Rao,et al.  Artificial neural networks and their applications to power systems—a bibliographical survey , 1993 .

[28]  Jovica V. Milanovic,et al.  Development of equivalent dynamic model of distribution network using clustering procedure , 2011 .

[29]  G.T. Heydt,et al.  A Comparative Assessment of Two Techniques for Modal Identification From Power System Measurements , 2008, IEEE Transactions on Power Systems.

[30]  Tianshu Bi,et al.  WAMS Implementation in China and the Challenges for Bulk Power System Protection , 2007, 2007 IEEE Power Engineering Society General Meeting.

[31]  J. Quintero,et al.  Oscillation monitoring system based on wide area synchrophasors in power systems , 2007, 2007 iREP Symposium - Bulk Power System Dynamics and Control - VII. Revitalizing Operational Reliability.

[32]  N. Martins,et al.  Efficient online estimation of electromechanical modes in large power systems , 2013, 2013 IEEE 4th Latin American Symposium on Circuits and Systems (LASCAS).

[33]  Y. Hua,et al.  Generalized pencil-of-function method for extracting poles of an EM system from its transient response , 1989 .

[34]  A.R. Messina,et al.  Interpretation and Visualization of Wide-Area PMU Measurements Using Hilbert Analysis , 2006, IEEE Transactions on Power Systems.

[35]  Luis M. Fernández,et al.  Dynamic models of wind farms with fixed speed wind turbines , 2006 .

[36]  J.W. Pierre,et al.  Bootstrap-based confidence interval estimates for electromechanical modes from multiple output analysis of measured ambient data , 2005, IEEE Transactions on Power Systems.

[37]  Jovica V. Milanovic,et al.  Validation of Equivalent Dynamic Model of Active Distribution Network Cell , 2013, IEEE Transactions on Power Systems.

[38]  A. R. Messina,et al.  Nonlinear, non-stationary analysis of interarea oscillations via Hilbert spectral analysis , 2006, IEEE Transactions on Power Systems.

[39]  N. Zhou,et al.  A Bootstrap Method for Statistical Power System Mode Estimation and Probing Signal Selection , 2006, 2006 IEEE PES Power Systems Conference and Exposition.

[40]  Yoh-Han Pao,et al.  Adaptive pattern recognition and neural networks , 1989 .

[41]  Innocent Kamwa,et al.  A minimal realization approach to reduced-order modelling and modal analysis for power system response signals , 1993 .

[42]  Joe H. Chow,et al.  A Measurement-Based Framework for Dynamic Equivalencing of Large Power Systems Using Wide-Area Phasor Measurements , 2011, IEEE Transactions on Smart Grid.

[43]  E. M. Gulachenski,et al.  Electromechanical Equivalent for Use in Power System Stability Studies , 1971 .

[44]  D.J. Trudnowski,et al.  Fixed-speed wind-generator and wind-park modeling for transient stability studies , 2004, IEEE Transactions on Power Systems.

[45]  Fred C. Schweppe,et al.  Uncertain dynamic systems , 1973 .

[46]  C. E. Grund,et al.  Comparison of Prony and eigenanalysis for power system control design , 1993 .

[47]  G. Verghese,et al.  Selective Modal Analysis With Applications to Electric Power Systems, Part II: The Dynamic Stability Problem , 1982, IEEE Transactions on Power Apparatus and Systems.

[48]  Andrew J. Poggio,et al.  Evaluation of a Processing Technique for Transient Data , 1978, IEEE Transactions on Electromagnetic Compatibility.

[49]  Dorothea Heiss-Czedik,et al.  An Introduction to Genetic Algorithms. , 1997, Artificial Life.

[50]  Ni Jingmin,et al.  Estimating the electromechanical oscillation characteristics of power system based on measured ambient data utilizing stochastic subspace method , 2011, 2011 IEEE Power and Energy Society General Meeting.

[51]  M. Crow,et al.  The matrix pencil for power system modal extraction , 2005, IEEE Transactions on Power Systems.

[52]  K. N. Stanton,et al.  Coherency based dynamic equivalents for transient stability studies , 1974 .

[53]  F. L. Pagola,et al.  Developments in selective modal analysis of small-signal stability in electric power systems , 1990, Autom..

[54]  Randall J. Allemang,et al.  THE MODAL ASSURANCE CRITERION–TWENTY YEARS OF USE AND ABUSE , 2003 .

[55]  A. Bakirtzis,et al.  Optimal Power Flow by Enhanced Genetic Algorithm , 2002, IEEE Power Engineering Review.

[56]  Ning Zhou,et al.  Robust RLS Methods for Online Estimation of Power System Electromechanical Modes , 2007, IEEE Transactions on Power Systems.

[57]  G. G. Karady,et al.  Comparison of various power system electromechanical mode estimators , 2011, 2011 IEEE Trondheim PowerTech.

[58]  I. Erlich,et al.  Identification of dynamic equivalents for distribution power networks using recurrent ANNs , 2004, IEEE PES Power Systems Conference and Exposition, 2004..

[59]  Joe H. Chow,et al.  Time-Scale Modeling of Dynamic Networks with Applications to Power Systems , 1983 .

[60]  John W. Pierre,et al.  Estimating electromechanical modes and mode shapes using the multichannel ARMAX model , 2013, IEEE Transactions on Power Systems.

[61]  J. MacQueen.  Some methods for classification and analysis of multivariate observations , 1967 .

[62]  O. Ruhle,et al.  Industrial approaches for dynamic equivalents of large power systems , 2002, 2002 IEEE Power Engineering Society Winter Meeting. Conference Proceedings (Cat. No.02CH37309).

[63]  Y. H. Ku,et al.  Electric Power System Dynamics , 1983 .

[64]  M. A. Poller.  Doubly-fed induction machine models for stability assessment of wind farms , 2003, 2003 IEEE Bologna Power Tech Conference Proceedings,.

[65]  Zhenyu Huang,et al.  Generator dynamic model validation and parameter calibration using phasor measurements at the point of connection , 2014, IEEE Transactions on Power Systems.

[66]  John Pierre,et al.  A recursive maximum likelihood estimator for the online estimation of electromechanical modes with error bounds , 2013, 2013 IEEE Power & Energy Society General Meeting.

[67]  Philip D. Wasserman,et al.  Neural computing - theory and practice , 1989 .

[68]  J. F. Hauer,et al.  Identifying linear reduced-order models for systems with arbitrary initial conditions using Prony signal analysis , 1992 .

[69]  Begnaud Francis Hildebrand,et al.  Introduction to numerical analysis: 2nd edition , 1987 .

[70]  J. F. Hauer,et al.  Advances in the Identification of Transfer Function Models using Prony Analysis , 1993, 1993 American Control Conference.

[71]  D.H. Wilson.  Continuous damping measurement for power system analysis , 2005, 2005 IEEE Russia Power Tech.

[72]  Joe H. Chow,et al.  Performance comparison of three identification methods for the analysis of electromechanical oscillations , 1999 .

[73]  Douglas H. Wilson,et al.  Dynamic model verification using a continuous modal parameter estimator , 2003, 2003 IEEE Bologna Power Tech Conference Proceedings,.

[74]  D. J. Trudnowski,et al.  Overview of algorithms for estimating swing modes from measured responses , 2009, 2009 IEEE Power & Energy Society General Meeting.

[75]  A.R. Messina,et al.  Extraction of Dynamic Patterns From Wide-Area Measurements Using Empirical Orthogonal Functions , 2007, IEEE Transactions on Power Systems.

[76]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[77]  H. Ghasemi,et al.  Oscillatory stability limit prediction using stochastic subspace identification , 2006, IEEE Transactions on Power Systems.

[78]  Babu Narayanan,et al.  POWER SYSTEM STABILITY AND CONTROL , 2015 .

[79]  Song Guo,et al.  Synchronous machine inertia constants updating using Wide Area Measurements , 2012, 2012 3rd IEEE PES Innovative Smart Grid Technologies Europe (ISGT Europe).

[80]  Andrija T. Saric,et al.  Identification of nonparametric dynamic power system equivalents with artificial neural networks , 2003 .

[81]  L.-A. Dessaint,et al.  Dynamic equivalent modeling of large power systems using structure preservation technique , 2006, IEEE Transactions on Power Systems.

[82]  Hans Knudsen,et al.  An aggregate model of a grid-connected, large-scale, offshore wind farm for power stability investigations—importance of windmill mechanical system , 2002 .

[83]  J. M. Undrill,et al.  Construction of Power System lectromechanical Equivalents by Modal Analysis , 1971 .

[84]  E. Muljadi,et al.  Comparing Single and Multiple Turbine Representations in a Wind Farm Simulation: Preprint , 2006 .

[85]  J. F. Hauer,et al.  Initial results in Prony analysis of power system response signals , 1990 .

[86]  John E. Mottershead,et al.  Finite Element Model Updating in Structural Dynamics , 1995 .

[87]  V. Vittal,et al.  A Hybrid Dynamic Equivalent Using ANN-Based Boundary Matching Technique , 2012, IEEE Transactions on Power Systems.

[88]  J.W. Bialek,et al.  Identification based Dynamic Equivalencing , 2007, 2007 IEEE Lausanne Power Tech.

[89]  Graham Rogers,et al.  Power System Oscillations , 1999 .

[90]  Daniel J. Trudnowski,et al.  Initial results in electromechanical mode identification from ambient data , 1997 .

[91]  J. W. Pierre,et al.  A Recursive Maximum Likelihood Estimator for the Online Estimation of Electromechanical Modes With Error Bounds , 2013, IEEE Transactions on Power Systems.

[92]  Kip Morison,et al.  REVIEW OF ON-LINE DYNAMIC SECURITY ASSESSMENT TOOLS AND TECHNIQUES , 2007 .

[93]  S. Geeves.  A modal-coherency technique for deriving dynamic equivalents , 1988 .

[94]  Malcolm Irving,et al.  A genetic algorithm for generator scheduling in power systems , 1996 .

[95]  Barrie L Kokanos,et al.  Associate Hermite Expansion Small Signal Mode Estimation , 2010, IEEE Transactions on Power Systems.

[96]  Donald A. Pierre,et al.  General formulation of a Prony based method for simultaneous identification of transfer functions and initial conditions , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[97]  Innocent Kamwa,et al.  Low-order black-box models for control system design in large power systems , 1995 .

[98]  J. H. Chow,et al.  Computation of power system low-order models from time domain simulations using a Hankel matrix , 1997 .

[99]  W. Marsden.  I and J , 2012 .

[100]  Richard A. Smith,et al.  EXTERNAL NETWORK MODELING - RECENT PRACTICAL EXPERIENCE , 1994 .

[101]  F. B. Hildebrand,et al.  Introduction To Numerical Analysis , 1957 .

[102]  S.M. Kay,et al.  Spectrum analysis—A modern perspective , 1981, Proceedings of the IEEE.

[103]  Robin Podmore,et al.  Identification of Coherent Generators for Dynamic Equivalents , 1978, IEEE Transactions on Power Apparatus and Systems.

[104]  E. M. Gulachenski,et al.  Testing of the Modal Dynamic Equivalents Technique , 1978, IEEE Transactions on Power Apparatus and Systems.

[105]  W. Mittelstadt,et al.  Electromechanical Mode Online Estimation Using Regularized Robust RLS Methods , 2008, IEEE Transactions on Power Systems.

[106]  Janusz Bialek,et al.  Power System Dynamics: Stability and Control , 2008 .