Abstract
This paper proposes a robust WKNN-TLS-ESPRIT algorithm that takes into account the effect of the unavailability of phasor measurement unit (PMU) data for identifying the low-frequency oscillatory modes in power systems. The main contribution of the proposed work is to create an enhanced autocorrelation matrix using a weighted K nearest neighbours (WKNN)-based predictive model to deal with such issues. In the present work, a Bayesian approach is utilized to determine the empirical number of neighbourhood parameters. The improved autocorrelation matrix is then used by total least square estimation of signal parameters via rotational invariance technique (TLS-ESPRIT) algorithm to provide a robust estimate of the modes. Robustness of the proposed method over the other methods is validated with a simulated test signal with missing data through Monte Carlo simulations at different SNRs. The effectiveness of the proposed approach is further verified on real data derived from PMU located in Western Electricity Coordinating Council grid.
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Abbreviations
- \(\textit{J}\) :
-
Number of partitions of the sample space
- \(f_j \) :
-
Density function
- \(\pi _j\) :
-
Prior probabilities of \(\textit{J}\)
- \(\mathbf{p} \) :
-
Vector of conditional probabilities
- \(\zeta _k(\mathbf{p} )\) :
-
Prior distribution of \(\mathbf{p} \) in a neighbourhood around \(\mathbf{x} \)
- \(\textit{q}_k\) :
-
Number of variables in k neighbours from the \(j^\mathrm{th}\) partition
- S(j|k):
-
Bayesian strength function
- \(\gamma (k)\) :
-
Accuracy index
- k :
-
Number of nearest neighbours
- \(\mathbf{D} \) :
-
Data set
- \(x_o\) :
-
Incomplete case
- Dist :
-
Euclidean distance measure
- \(w_{ik}\) :
-
Weight assigned to \(k^\mathrm{th}\) neighbour
- y(n):
-
Real-time signal
- s(n):
-
Clean signal
- z(n):
-
White Gaussian noise
- \(\alpha _j\) :
-
Complex signal amplitude
- \(\beta _j\) :
-
Modal parameters
- \(d_j\) :
-
Attenuation factor \(\omega _j\) Frequency
- B :
-
Length of data vector
- \(\hat{\mathbf{R }}_{yy}\) :
-
Estimated correlation matrix
- \(\hat{\mathbf{D }}\) :
-
Estimated data set
- \({\textit{P}}\) :
-
Number of dominant eigenvalues
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Acknowledgements
This work was supported in part by a grant from World Bank for NPIU, India (TEQIP-III/CRS/1-5728870640).
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Rai, S. A robust WKNN-TLS-ESPRIT algorithm for identification of electromechanical oscillation modes utilizing WAMS. Sādhanā 45, 265 (2020). https://doi.org/10.1007/s12046-020-01502-2
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DOI: https://doi.org/10.1007/s12046-020-01502-2