A Comparative Assessment of Two Techniques for Modal Identification From Power System Measurements

Power system oscillatory behavior can be analyzed in terms of modes, expressed as exponentially modulated sinusoids, exhibited in signals measured on the system. These signals are driven by the behavior of a large, nonlinear, time-variant system. In this paper, two modal identification methods are examined comparatively: Prony analysis and a method based on the Hilbert transform. Considerable structural differences exist between the two methods. Prony analysis yields modes which are directly expressed as exponentially modulated sinusoids, whereas the Hilbert method provides a more general solution. Synthetic and measured signals are used in the comparison. Some general conclusions are drawn from the analysis of several signals, including two sets of measured field data.

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

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

[3]  Boualem Boashash,et al.  Estimating and interpreting the instantaneous frequency of a signal. II. A/lgorithms and applications , 1992, Proc. IEEE.

[4]  Peter J. O'Shea,et al.  The use of sliding spectral windows for parameter estimation in power system disturbance monitoring , 2000 .

[5]  R. Ceravolo Use of instantaneous estimators for the evaluation of structural damping , 2004 .

[6]  E. Bedrosian A Product Theorem for Hilbert Transforms , 1963 .

[7]  G. Ledwich,et al.  Estimation of Modal Damping in Power Networks , 2007, IEEE Transactions on Power Systems.

[8]  K.-C. Lee,et al.  Analysis of transient stability swings in large interconnected power systems by Fourier transformation , 1988 .

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

[10]  P. Flandrin,et al.  Empirical Mode Decomposition , 2012 .

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

[12]  Gabriel Rilling,et al.  On empirical mode decomposition and its algorithms , 2003 .

[13]  G. D. Cain,et al.  Hilbert transform relations for products , 1973 .

[14]  George R. Cooper,et al.  Continuous and discrete signal and system analysis , 1984 .

[15]  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.

[16]  P. Kundur,et al.  Power system stability and control , 1994 .

[17]  V. Vittal,et al.  Characterization of nonlinear modal interaction using normal forms and Hilbert analysis , 2004, IEEE PES Power Systems Conference and Exposition, 2004..

[18]  A.R. Messina,et al.  Inclusion of higher order terms for small-signal (modal) analysis: committee report-task force on assessing the need to include higher order terms for small-signal (modal) analysis , 2005, IEEE Transactions on Power Systems.

[19]  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.

[20]  Vijay Vittal,et al.  Interpretation and Visualization of Wide-Area PMU Measurements Using Hilbert Analysis , 2006 .

[21]  R. Stephenson A and V , 1962, The British journal of ophthalmology.

[22]  D.J. Trudnowski,et al.  Use of ARMA block processing for estimating stationary low-frequency electromechanical modes of power systems , 2003, 2003 IEEE Power Engineering Society General Meeting (IEEE Cat. No.03CH37491).

[23]  J. F. Hauer,et al.  Keeping an eye on power system dynamics , 1997 .

[24]  Daniel J. Trudnowski,et al.  Use of ARMA block processing for estimating stationary low-frequency electromechanical modes of power systems , 2002 .

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

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

[27]  N. Senroy,et al.  An Improved Hilbert–Huang Method for Analysis of Time-Varying Waveforms in Power Quality , 2007, IEEE Transactions on Power Systems.

[28]  G. Trudel,et al.  Multi-loop power system stabilizers using wide-area synchronous phasor measurements , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

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

[30]  J. W. Brown,et al.  Complex Variables and Applications , 1985 .

[31]  Angel Moises Iglesias,et al.  Investigating Various Modal Analysis Extraction Techniques to Estimate Damping Ratio , 2000 .

[32]  Innocent Kamwa,et al.  Wide-area measurement based stabilizing control of large power systems-a decentralized/hierarchical approach , 2001 .

[33]  G. Ledwich,et al.  A Kalman Filtering Approach to Rapidly Detecting Modal Changes in Power Systems , 2007, IEEE Transactions on Power Systems.

[34]  Huibert Kwakernaak,et al.  Modern signals and systems , 1991 .