Estimation of Amplitude, Phase and Unbalance Parameters in Three-phase Systems: Analytical Solutions, Efficient Implementation and Performance Analysis

This paper focuses on the estimation of the instantaneous amplitude, phase, and unbalance parameters in three-phase power systems. Due to the particular structure of three-phase systems, we demonstrate that the maximum-likelihood estimates (MLEs) of the unknown parameters have simple closed-form expressions and can be easily implemented without matrix algebra libraries. We also derive and analyze the Cramer-Rao Bounds (CRBs) for the considered estimation problem. The performance of the proposed approach is evaluated using synthetic signals compliant with the IEEE Standard C37.118. Simulation results show that the proposed estimators outperform other techniques and reach the CRB under certain conditions.

[1]  W. Marsden.  I and J , 2012 .

[2]  Petre Stoica,et al.  MUSIC, maximum likelihood, and Cramer-Rao bound , 1989, IEEE Transactions on Acoustics, Speech, and Signal Processing.

[3]  Jing Huang,et al.  State Estimation in Electric Power Grids: Meeting New Challenges Presented by the Requirements of the Future Grid , 2012, IEEE Signal Processing Magazine.

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

[5]  S. Kay.  Fundamentals of statistical signal processing: estimation theory , 1993 .

[6]  A.K. Pradhan,et al.  Power system frequency estimation using least mean square technique , 2005, IEEE Transactions on Power Delivery.

[7]  David Bonacci,et al.  On-Line Monitoring of Mechanical Faults in Variable-Speed Induction Motor Drives Using the Wigner Distribution , 2008, IEEE Transactions on Industrial Electronics.

[8]  Petre Stoica,et al.  The Gaussian Data Assumption Leads to the Largest Cramér-Rao Bound [Lecture Notes] , 2011, IEEE Signal Processing Magazine.

[9]  Nicolas Le Bihan,et al.  The ℍ-analytic signal , 2008, 2008 16th European Signal Processing Conference.

[10]  Edward J. Coyle,et al.  Observing the Power Grid: Working Toward a More Intelligent, Efficient, and Reliable Smart Grid with Increasing User Visibility , 2012, IEEE Signal Processing Magazine.

[11]  Geert M. P. van Kempen,et al.  Mean and variance of ratio estimators used in fluorescence ratio imaging. , 2000 .

[12]  Alexis Kwasinski,et al.  Signal Processing in the Electrification of Vehicular Transportation: Techniques for Electric and Plug-In Hybrid Electric Vehicles on the Smart Grid , 2012, IEEE Signal Processing Magazine.

[13]  Danilo P. Mandic,et al.  Adaptive Frequency Estimation in Smart Grid Applications: Exploiting Noncircularity and Widely Linear Adaptive Estimators , 2012, IEEE Signal Processing Magazine.

[14]  M. Blodt,et al.  Distinguishing Load Torque Oscillations and Eccentricity Faults in Induction Motors Using Stator Current Wigner Distributions , 2006, IEEE Transactions on Industry Applications.

[15]  Vincent Choqueuse,et al.  Diagnosis of Three-Phase Electrical Machines Using Multidimensional Demodulation Techniques , 2012, IEEE Transactions on Industrial Electronics.

[16]  Bjorn Ottersten,et al.  Exact and Large Sample ML Techniques for Parameter Estimation and Detection in Array Processing , 1993 .

[17]  B. Banerjee,et al.  Assessment of Voltage Unbalance , 2001, IEEE Power Engineering Review.

[18]  Danilo P. Mandic,et al.  Widely Linear Adaptive Frequency Estimation of Unbalanced Three-Phase Power Systems , 2012, IEEE Transactions on Instrumentation and Measurement.

[19]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[20]  Joachim Kopp.  EFFICIENT NUMERICAL DIAGONALIZATION OF HERMITIAN 3 × 3 MATRICES , 2006 .

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

[22]  B. Hofmann-Wellenhof,et al.  Introduction to spectral analysis , 1986 .

[23]  T. Tayjasanant,et al.  A resistance sign-based method for voltage sag source detection , 2005, IEEE Transactions on Power Delivery.

[24]  Jr. S. Marple,et al.  Computing the discrete-time 'analytic' signal via FFT , 1999, Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136).

[25]  G. Marsaglia.  Ratios of Normal Variables , 2006 .

[26]  Danilo P. Mandic,et al.  Augmented MVDR Spectrum-Based Frequency Estimation for Unbalanced Power Systems , 2013, IEEE Transactions on Instrumentation and Measurement.

[27]  Bernard C. Picinbono,et al.  On instantaneous amplitude and phase of signals , 1997, IEEE Trans. Signal Process..

[28]  Philippe Forster,et al.  Unconditional Maximum Likelihood Performance at Finite Number of Samples and High Signal-to-Noise Ratio , 2007, IEEE Transactions on Signal Processing.

[29]  L.I. Eguiluz,et al.  Three-phase adaptive frequency measurement based on Clarke's transformation , 2006, IEEE Transactions on Power Delivery.

[30]  A. E. Emanuel,et al.  IEEE Std 1459–2010. IEEE Standard Definitions for the Measurement of Electric Power Quantities under Sinusoidal, Nonsinusoidal, Balanced or Unbalanced Conditions , 2010 .

[31]  P. Djurić,et al.  Frequency tracking in power networks in the presence of harmonics , 1993 .

[32]  P. Larzabal,et al.  On the High-SNR Conditional Maximum-Likelihood Estimator Full Statistical Characterization , 2006, IEEE Transactions on Signal Processing.

[33]  Adel Belouchrani,et al.  Fault Diagnosis in Industrial Induction Machines Through Discrete Wavelet Transform , 2011, IEEE Transactions on Industrial Electronics.

[34]  M. Viberg,et al.  Two decades of array signal processing research: the parametric approach , 1996, IEEE Signal Process. Mag..

[35]  Petre Stoica,et al.  Performance study of conditional and unconditional direction-of-arrival estimation , 1990, IEEE Trans. Acoust. Speech Signal Process..

[36]  Mohamed El Hachemi Benbouzid.  A review of induction motors signature analysis as a medium for faults detection , 2000, IEEE Trans. Ind. Electron..

[37]  David Vakman,et al.  On the analytic signal, the Teager-Kaiser energy algorithm, and other methods for defining amplitude and frequency , 1996, IEEE Trans. Signal Process..

[38]  Garry Tamlyn,et al.  Music , 1993 .