Early Anomaly Detection for Power Systems Based on Kullback-Leibler Divergence Using Factor Model Analysis

Qing Feng; Ghadir Radman; Xuebin Li

doi:doi:10.11648/j.epes.20211004.12

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Early Anomaly Detection for Power Systems Based on Kullback-Leibler Divergence Using Factor Model Analysis

Qing Feng, Ghadir Radman, Xuebin Li

Published in American Journal of Electrical Power and Energy Systems (Volume 10, Issue 4)

Received: 3 August 2021 Accepted: 21 August 2021 Published: 30 August 2021

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Abstract

Real-time anomaly detection is a critical monitoring task for power systems. Most studies of power network detection fail to identify small fault signals or disturbances that might lead to damages or system-wide blackout. This work presents a methodology for analyzing high-dimensional PMU data and detecting early events for large-scale power systems in a non-Gaussian noise environment. Also, spatio-temporal correlations of PMU data are explored and determined by the factor model for anomaly detection. Based on random matrix theory, the factor model monitors the variation of spatio-temporal correlations in PMU data and estimates the number of dynamic factors. Kullback-Leibler Divergence is employed to measure the deviation between two spectral distributions: the empirical spectral distribution of the covariance matrix of residuals from online monitoring data and its theoretical spectral distribution determined by the factor model. Using IEEE 57-bus, IEEE 118-bus, and Polish 2383-bus systems, three different case studies demonstrate that the proposed method is more effective in identifying early-stage anomalies in high-dimensional PMU data collected from large-scale power networks. Performance evaluations validate that this method is sensitive and robust to small fault signals compared with other statistical approaches. The proposed method is a data-driven approach that doesn’t require any prior knowledge of the topology of power networks.

Published in	American Journal of Electrical Power and Energy Systems (Volume 10, Issue 4)
DOI	10.11648/j.epes.20211004.12
Page(s)	60-73
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Anomaly Detection, Spatio-Temporal Correlation, Kullback-Leibler Divergence (KLD), Factor Model

References

[1]	Anderson, D., Zhao, C., Hauser, C., Venkatasubramanian, V., Bakken, D., & Bose, A. (2012). Real-time simulation for smart grid control and communications design. IEEE Power Energy Mag., 10 (1), 49-57.
[2]	Kim, D. I., Chun, T. Y., Yoon, S. H., Lee, G., & Shin, Y. J. (2015). Wavelet-based event detection method using PMU data. IEEE Transactions on Smart grid, 8 (3), 1154-1162.
[3]	Rafferty, M., Liu, X., Laverty, D. M., & McLoone, S. (2016). Real-time multiple event detection and classification using moving window PCA. IEEE Transactions on Smart Grid, 7 (5), 2537-2548.
[4]	Ge, Y., Flueck, A. J., Kim, D. K., Ahn, J. B., Lee, J. D., & Kwon, D. Y. (2015). Power system real-time event detection and associated data archival reduction based on synchrophasors. IEEE Transactions on Smart Grid, 6 (4), 2088-2097.
[5]	Lim, J. M., & DeMarco, C. L. (2015). SVD-based voltage stability assessment from phasor measurement unit data. IEEE Transactions on Power Systems, 31 (4), 2557-2565.
[6]	Wang, B., Fang, B., Wang, Y., Liu, H., & Liu, Y. (2016). Power system transient stability assessment based on big data and the core vector machine. IEEE Transactions on Smart Grid, 7 (5), 2561-2570.
[7]	Zhou, D. Q., Annakkage, U. D., & Rajapakse, A. D. (2010). Online monitoring of voltage stability margin using an artificial neural network. IEEE Transactions on Power Systems, 25 (3), 1566-1574.
[8]	Khaledian, E., Pandey, S., Kundu, P., & Srivastava, A. K. (2020). Real-Time Synchrophasor Data Anomaly Detection and Classification Using Isolation Forest, KMeans, and LoOP. IEEE Transactions on Smart Grid, 12 (3), 2378-2388.
[9]	Shen, L., Du, H., Liu, S., Chen, S., Qiao, L., Liu, S.,... & Li, J. (2020). Real time outlier monitoring for power transformer fault diagnosis based on isolated forest. In IOP Conference Series: Materials Science and Engineering (Vol. 715, No. 1, p. 012033). IOP Publishing.
[10]	Tan, Y., Hu, C., Zhang, K., Zheng, K., Davis, E. A., & Park, J. S. (2020). LSTM-Based Anomaly Detection for Non-Linear Dynamical System. IEEE Access, 8, 103301-103308.
[11]	Malhotra, P., Vig, L., Shroff, G., & Agarwal, P. (2015, April). Long short term memory networks for anomaly detection in time series. In Proceedings (Vol. 89, pp. 89-94).
[12]	Shi, X., Qiu, R., Mi, T., He, X., & Zhu, Y. (2019). Adversarial feature learning of online monitoring data for operational risk assessment in distribution networks. IEEE Transactions on Power Systems, 35 (2), 975-985.
[13]	Zhang, L., Wang, G., & Giannakis, G. B. (2019). Real-time power system state estimation and forecasting via deep unrolled neural networks. IEEE Transactions on Signal Processing, 67 (15), 4069-4077.
[14]	Qiu, R. C., & Antonik, P. (2017). Smart grid using big data analytics: a random matrix theory approach. John Wiley & Sons.
[15]	Qiu, R., Chu, L., He, X., Ling, Z., & Liu, H. (2018). Spatiotemporal Big Data Analysis for Smart Grids Based on Random Matrix Theory. Transportation and Power Grid in Smart Cities: Communication Networks and Services, 591-633.
[16]	Ma, D., Hu, X., Zhang, H., Sun, Q., & Xie, X. (2019). A hierarchical event detection method based on spectral theory of multidimensional matrix for power system. IEEE Transactions on Systems, Man, and Cybernetics: Systems.
[17]	Zhou, W., Sheng, J., Luo, H., Li, W., & He, X. (2018). Detection and localization of submodule open-circuit failures for modular multilevel converters with single ring theorem. IEEE Transactions on Power Electronics, 34 (4), 3729-3739.
[18]	He, X., Qiu, R. C., Ai, Q., Chu, L., Xu, X., & Ling, Z. (2016). Designing for situation awareness of future power grids: An indicator system based on linear eigenvalue statistics of large random matrices. IEEE Access, 4, 3557-3568.
[19]	Xu, X., He, X., Ai, Q., & Qiu, R. C. (2015). A correlation analysis method for power systems based on random matrix theory. IEEE Transactions on smart grid, 8 (4), 1811-1820.
[20]	Shi, X., Qiu, R., Ling, Z., Yang, F., Yang, H., & He, X. (2019). Spatio-temporal correlation analysis of online monitoring data for anomaly detection and location in distribution networks. IEEE Transactions on Smart Grid, 11 (2), 995-1006.
[21]	Chakhchoukh, Y., Vittal, V., & Heydt, G. T. (2013). PMU based state estimation by integrating correlation. IEEE Transactions on Power Systems, 29 (2), 617-626.
[22]	Yeo, J., & Papanicolaou, G. (2016). Random matrix approach to estimation of high-dimensional factor models. arXiv preprint arXiv: 1611.05571.
[23]	Kapetanios, G. (2010). A testing procedure for determining the number of factors in approximate factor models with large datasets. Journal of Business & Economic Statistics, 28 (3), 397-409.
[24]	Pelger, M. (2019). Large-dimensional factor modeling based on high-frequency observations. Journal of Econometrics, 208 (1), 23-42.
[25]	Lee, D., & Baldick, R. (2016). Load and wind power scenario generation through the generalized dynamic factor model. IEEE Transactions on power Systems, 32 (1), 400-410.
[26]	Bakdi, A., Bounoua, W., Mekhilef, S., & Halabi, L. M. (2019). Nonparametric Kullback-divergence-PCA for intelligent mismatch detection and power quality monitoring in grid-connected rooftop PV. Energy, 189, 116366.
[27]	Gupta, S., Waghmare, S., Kazi, F., Wagh, S., & Singh, N. (2016, March). Blackout risk analysis in smart grid WAMPAC system using KL divergence approach. In 2016 IEEE 6th International Conference on Power Systems (ICPS) (pp. 1-6). IEEE.
[28]	Chen, H., Jiang, B., & Lu, N. (2018). An improved incipient fault detection method based on Kullback-Leibler divergence. ISA transactions, 79, 127-136.
[29]	Harmouche, J., Delpha, C., & Diallo, D. (2014). Incipient fault detection and diagnosis based on Kullback–Leibler divergence using principal component analysis: Part I. Signal processing, 94, 278-287.
[30]	Harmouche, J., Delpha, C., & Diallo, D. (2015). Incipient fault detection and diagnosis based on Kullback–Leibler divergence using principal component analysis: Part II. Signal Processing, 109, 334-344.
[31]	Zhang, X., Delpha, C., & Diallo, D. (2020). Incipient fault detection and estimation based on Jensen–Shannon divergence in a data-driven approach. Signal Processing, 169, 107410.
[32]	De La Ree, J., Centeno, V., Thorp, J. S., & Phadke, A. G. (2010). Synchronized phasor measurement applications in power systems. IEEE Transactions on smart grid, 1 (1), 20-27.
[33]	Sarri, S., Zanni, L., Popovic, M., Le Boudec, J. Y., & Paolone, M. (2016). Performance assessment of linear state estimators using synchrophasor measurements. IEEE Transactions on Instrumentation and Measurement, 65 (3), 535-548.
[34]	Marchenko, V. A., & Pastur, L. A. (1967). Distribution of eigenvalues for some sets of random matrices. Matematicheskii Sbornik, 114 (4), 507-536.
[35]	Burda, Z., Jarosz, A., Nowak, M. A., & Snarska, M. (2010). A random matrix approach to VARMA processes. New Journal of Physics, 12 (7), 075036.
[36]	Ghanavati, G., Hines, P. D., & Lakoba, T. I. (2015). Identifying useful statistical indicators of proximity to instability in stochastic power systems. IEEE Transactions on Power Systems, 31 (2), 1360-1368.
[37]	Kullback, S., & Leibler, R. A. (1951). On information and sufficiency. The annals of mathematical statistics, 22 (1), 79-86.
[38]	Kullback, S. (1997). Information theory and statistics. Courier Corporation.
[39]	Fuglede, B., & Topsoe, F. (2004, June). Jensen-Shannon divergence and Hilbert space embedding. In International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings. (p. 31). IEEE.
[40]	Zimmerman, R. D., Murillo-Sánchez, C. E., & Thomas, R. J. (2010). MATPOWER: Steady-state operations, planning, and analysis tools for power systems research and education. IEEE Transactions on power systems, 26 (1), 12-19.
[41]	Marcelino, C. G., Almeida, P. E., Wanner, E. F., Baumann, M., Weil, M., Carvalho, L. M., & Miranda, V. (2018). Solving security constrained optimal power flow problems: a hybrid evolutionary approach. Applied Intelligence, 48 (10), 3672-3690.

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APA Style

Qing Feng, Ghadir Radman, Xuebin Li. (2021). Early Anomaly Detection for Power Systems Based on Kullback-Leibler Divergence Using Factor Model Analysis. American Journal of Electrical Power and Energy Systems, 10(4), 60-73. https://doi.org/10.11648/j.epes.20211004.12

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ACS Style

Qing Feng; Ghadir Radman; Xuebin Li. Early Anomaly Detection for Power Systems Based on Kullback-Leibler Divergence Using Factor Model Analysis. Am. J. Electr. Power Energy Syst. 2021, 10(4), 60-73. doi: 10.11648/j.epes.20211004.12

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AMA Style

Qing Feng, Ghadir Radman, Xuebin Li. Early Anomaly Detection for Power Systems Based on Kullback-Leibler Divergence Using Factor Model Analysis. Am J Electr Power Energy Syst. 2021;10(4):60-73. doi: 10.11648/j.epes.20211004.12

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@article{10.11648/j.epes.20211004.12,
  author = {Qing Feng and Ghadir Radman and Xuebin Li},
  title = {Early Anomaly Detection for Power Systems Based on Kullback-Leibler Divergence Using Factor Model Analysis},
  journal = {American Journal of Electrical Power and Energy Systems},
  volume = {10},
  number = {4},
  pages = {60-73},
  doi = {10.11648/j.epes.20211004.12},
  url = {https://doi.org/10.11648/j.epes.20211004.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.epes.20211004.12},
  abstract = {Real-time anomaly detection is a critical monitoring task for power systems. Most studies of power network detection fail to identify small fault signals or disturbances that might lead to damages or system-wide blackout. This work presents a methodology for analyzing high-dimensional PMU data and detecting early events for large-scale power systems in a non-Gaussian noise environment. Also, spatio-temporal correlations of PMU data are explored and determined by the factor model for anomaly detection. Based on random matrix theory, the factor model monitors the variation of spatio-temporal correlations in PMU data and estimates the number of dynamic factors. Kullback-Leibler Divergence is employed to measure the deviation between two spectral distributions: the empirical spectral distribution of the covariance matrix of residuals from online monitoring data and its theoretical spectral distribution determined by the factor model. Using IEEE 57-bus, IEEE 118-bus, and Polish 2383-bus systems, three different case studies demonstrate that the proposed method is more effective in identifying early-stage anomalies in high-dimensional PMU data collected from large-scale power networks. Performance evaluations validate that this method is sensitive and robust to small fault signals compared with other statistical approaches. The proposed method is a data-driven approach that doesn’t require any prior knowledge of the topology of power networks.},
 year = {2021}
}

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TY  - JOUR
T1  - Early Anomaly Detection for Power Systems Based on Kullback-Leibler Divergence Using Factor Model Analysis
AU  - Qing Feng
AU  - Ghadir Radman
AU  - Xuebin Li
Y1  - 2021/08/30
PY  - 2021
N1  - https://doi.org/10.11648/j.epes.20211004.12
DO  - 10.11648/j.epes.20211004.12
T2  - American Journal of Electrical Power and Energy Systems
JF  - American Journal of Electrical Power and Energy Systems
JO  - American Journal of Electrical Power and Energy Systems
SP  - 60
EP  - 73
PB  - Science Publishing Group
SN  - 2326-9200
UR  - https://doi.org/10.11648/j.epes.20211004.12
AB  - Real-time anomaly detection is a critical monitoring task for power systems. Most studies of power network detection fail to identify small fault signals or disturbances that might lead to damages or system-wide blackout. This work presents a methodology for analyzing high-dimensional PMU data and detecting early events for large-scale power systems in a non-Gaussian noise environment. Also, spatio-temporal correlations of PMU data are explored and determined by the factor model for anomaly detection. Based on random matrix theory, the factor model monitors the variation of spatio-temporal correlations in PMU data and estimates the number of dynamic factors. Kullback-Leibler Divergence is employed to measure the deviation between two spectral distributions: the empirical spectral distribution of the covariance matrix of residuals from online monitoring data and its theoretical spectral distribution determined by the factor model. Using IEEE 57-bus, IEEE 118-bus, and Polish 2383-bus systems, three different case studies demonstrate that the proposed method is more effective in identifying early-stage anomalies in high-dimensional PMU data collected from large-scale power networks. Performance evaluations validate that this method is sensitive and robust to small fault signals compared with other statistical approaches. The proposed method is a data-driven approach that doesn’t require any prior knowledge of the topology of power networks.
VL  - 10
IS  - 4
ER  -

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Author Information

Qing Feng

Department of Electrical and Computer Engineering, Tennessee Technological University, Cookeville, USA
Ghadir Radman

Department of Electrical and Computer Engineering, Tennessee Technological University, Cookeville, USA
Xuebin Li

Department of Electrical and Computer Engineering, Tennessee Technological University, Cookeville, USA

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APA Style

Qing Feng, Ghadir Radman, Xuebin Li. (2021). Early Anomaly Detection for Power Systems Based on Kullback-Leibler Divergence Using Factor Model Analysis. American Journal of Electrical Power and Energy Systems, 10(4), 60-73. https://doi.org/10.11648/j.epes.20211004.12

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ACS Style

Qing Feng; Ghadir Radman; Xuebin Li. Early Anomaly Detection for Power Systems Based on Kullback-Leibler Divergence Using Factor Model Analysis. Am. J. Electr. Power Energy Syst. 2021, 10(4), 60-73. doi: 10.11648/j.epes.20211004.12

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AMA Style

Qing Feng, Ghadir Radman, Xuebin Li. Early Anomaly Detection for Power Systems Based on Kullback-Leibler Divergence Using Factor Model Analysis. Am J Electr Power Energy Syst. 2021;10(4):60-73. doi: 10.11648/j.epes.20211004.12

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@article{10.11648/j.epes.20211004.12,
  author = {Qing Feng and Ghadir Radman and Xuebin Li},
  title = {Early Anomaly Detection for Power Systems Based on Kullback-Leibler Divergence Using Factor Model Analysis},
  journal = {American Journal of Electrical Power and Energy Systems},
  volume = {10},
  number = {4},
  pages = {60-73},
  doi = {10.11648/j.epes.20211004.12},
  url = {https://doi.org/10.11648/j.epes.20211004.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.epes.20211004.12},
  abstract = {Real-time anomaly detection is a critical monitoring task for power systems. Most studies of power network detection fail to identify small fault signals or disturbances that might lead to damages or system-wide blackout. This work presents a methodology for analyzing high-dimensional PMU data and detecting early events for large-scale power systems in a non-Gaussian noise environment. Also, spatio-temporal correlations of PMU data are explored and determined by the factor model for anomaly detection. Based on random matrix theory, the factor model monitors the variation of spatio-temporal correlations in PMU data and estimates the number of dynamic factors. Kullback-Leibler Divergence is employed to measure the deviation between two spectral distributions: the empirical spectral distribution of the covariance matrix of residuals from online monitoring data and its theoretical spectral distribution determined by the factor model. Using IEEE 57-bus, IEEE 118-bus, and Polish 2383-bus systems, three different case studies demonstrate that the proposed method is more effective in identifying early-stage anomalies in high-dimensional PMU data collected from large-scale power networks. Performance evaluations validate that this method is sensitive and robust to small fault signals compared with other statistical approaches. The proposed method is a data-driven approach that doesn’t require any prior knowledge of the topology of power networks.},
 year = {2021}
}

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TY  - JOUR
T1  - Early Anomaly Detection for Power Systems Based on Kullback-Leibler Divergence Using Factor Model Analysis
AU  - Qing Feng
AU  - Ghadir Radman
AU  - Xuebin Li
Y1  - 2021/08/30
PY  - 2021
N1  - https://doi.org/10.11648/j.epes.20211004.12
DO  - 10.11648/j.epes.20211004.12
T2  - American Journal of Electrical Power and Energy Systems
JF  - American Journal of Electrical Power and Energy Systems
JO  - American Journal of Electrical Power and Energy Systems
SP  - 60
EP  - 73
PB  - Science Publishing Group
SN  - 2326-9200
UR  - https://doi.org/10.11648/j.epes.20211004.12
AB  - Real-time anomaly detection is a critical monitoring task for power systems. Most studies of power network detection fail to identify small fault signals or disturbances that might lead to damages or system-wide blackout. This work presents a methodology for analyzing high-dimensional PMU data and detecting early events for large-scale power systems in a non-Gaussian noise environment. Also, spatio-temporal correlations of PMU data are explored and determined by the factor model for anomaly detection. Based on random matrix theory, the factor model monitors the variation of spatio-temporal correlations in PMU data and estimates the number of dynamic factors. Kullback-Leibler Divergence is employed to measure the deviation between two spectral distributions: the empirical spectral distribution of the covariance matrix of residuals from online monitoring data and its theoretical spectral distribution determined by the factor model. Using IEEE 57-bus, IEEE 118-bus, and Polish 2383-bus systems, three different case studies demonstrate that the proposed method is more effective in identifying early-stage anomalies in high-dimensional PMU data collected from large-scale power networks. Performance evaluations validate that this method is sensitive and robust to small fault signals compared with other statistical approaches. The proposed method is a data-driven approach that doesn’t require any prior knowledge of the topology of power networks.
VL  - 10
IS  - 4
ER  -

Copy | Download