Linear Eigenvalue Statistics: An Indicator Ensemble Design for Situation Awareness of Power Systems

Power systems are developing very fast nowadays, both in size and in complexity; this trend is challenging the situation awareness (SA) with classical indicators, which are always deterministic and highly relying on the mechanism models. This paper proposes an indicator ensemble of linear eigenvalue statistics (LESs) as an alternative; besides, the random matrix model (RMM) is introduced as a connection with the physical systems. Thus, related to the ensemble, a data-driven methodology of SA is presented; moreover, we develop 3D powermap as a visualization. The LES ensemble and according methodology conduct SA with a pure statistical procedure, requiring no knowledge of system topologies, unit operation/control models, causal relationship, etc. This mode has numerous advantages, such as sensitive, universal and fast, and flexible and compatible; especially, its robustness against bad data is highlighted.

[1]  Christopher L. DeMarco,et al.  SVD-Based Voltage Stability Assessment From Phasor Measurement Unit Data , 2016, IEEE Transactions on Power Systems.

[2]  Santiago Grijalva,et al.  Prosumer-based smart grid architecture enables a flat, sustainable electricity industry , 2011, ISGT 2011.

[3]  Qian Ai,et al.  A Big Data Architecture Design for Smart Grids Based on Random Matrix Theory , 2015, IEEE Transactions on Smart Grid.

[4]  Dan Feldman,et al.  Turning big data into tiny data: Constant-size coresets for k-means, PCA and projective clustering , 2013, SODA.

[5]  Qian Ai,et al.  A Correlation Analysis Method for Power Systems Based on Random Matrix Theory , 2015, IEEE Transactions on Smart Grid.

[6]  Le Xie,et al.  Dimensionality Reduction of Synchrophasor Data for Early Event Detection: Linearized Analysis , 2014, IEEE Transactions on Power Systems.

[7]  Yong Jing,et al.  Power Disturbance Data Analytics –New Application of Power Quality Monitoring Data , 2013 .

[8]  A.G. Phadke,et al.  The Wide World of Wide-area Measurement , 2008, IEEE Power and Energy Magazine.

[9]  Robert C. Qiu,et al.  Cognitive Networked Sensing and Big Data , 2013 .

[10]  Mariya Shcherbina,et al.  Central Limit Theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices , 2011, 1101.3249.

[11]  Z. Bai,et al.  CLT for linear spectral statistics of large dimensional sample covariance matrices with dependent data , 2017, Statistical Papers.

[12]  E. Wigner.  On the Distribution of the Roots of Certain Symmetric Matrices , 1958 .

[13]  Qian Ai,et al.  An Unsupervised Learning Method for Early Event Detection in Smart Grid with Big Data , 2015, ArXiv.

[14]  Mica R. Endsley,et al.  Designing for Situation Awareness : An Approach to User-Centered Design , 2003 .

[15]  O. Zeitouni,et al.  A CLT for a band matrix model , 2004, math/0412040.

[16]  Jianfeng Yao,et al.  Fluctuations for linear spectral statistics of large random covariance matrices , 2013, 2014 22nd European Signal Processing Conference (EUSIPCO).

[17]  R. Handel.  Probability in High Dimension , 2014 .

[18]  Math Bollen,et al.  Understanding Power Quality Problems , 1999 .

[19]  Vahid Madani,et al.  Wide-Area Monitoring, Protection, and Control of Future Electric Power Networks , 2011, Proceedings of the IEEE.

[20]  Y. Thomas Hou,et al.  Cognitive radio communications and networks: principles and practice , 2012 .

[21]  L. Pastur.  On the spectrum of random matrices , 1972 .

[22]  Ameet Talwalkar,et al.  Foundations of Machine Learning , 2012, Adaptive computation and machine learning.

[23]  Mohammad Shahidehpour,et al.  The IEEE Reliability Test System-1996. A report prepared by the Reliability Test System Task Force of the Application of Probability Methods Subcommittee , 1999 .

[24]  Vahid Madani,et al.  The Situation Room: Control Center Analytics for Enhanced Situational Awareness , 2012, IEEE Power and Energy Magazine.

[25]  Mario Kieburg,et al.  Weak commutation relations and eigenvalue statistics for products of rectangular random matrices. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  V. Marčenko,et al.  DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES , 1967 .

[27]  Robert C. Qiu,et al.  Massive MIMO as a Big Data System: Random Matrix Models and Testbed , 2015, IEEE Access.

[28]  Z. Bai,et al.  Large Sample Covariance Matrices and High-Dimensional Data Analysis , 2015 .

[29]  F. W. Nutter,et al.  Improving the accuracy and precision of disease assessments : selection of methods and use of computer-aided training programs , 1995 .

[30]  Richard A. Davis,et al.  Introduction to time series and forecasting , 1998 .

[31]  Qi-Man Shao,et al.  Universality of sample covariance matrices: CLT of the smoothed empirical spectral distribution , 2011, 1111.5420.

[32]  L. Pastur,et al.  CENTRAL LIMIT THEOREM FOR LINEAR EIGENVALUE STATISTICS OF RANDOM MATRICES WITH INDEPENDENT ENTRIES , 2008, 0809.4698.

[33]  M.A. El-Sharkawi,et al.  Support vector machines for transient stability analysis of large-scale power systems , 2004, IEEE Transactions on Power Systems.

[34]  Thomas J. Overbye,et al.  Voltage contours for power system visualization , 2000 .

[35]  Ofer Zeitouni,et al.  The single ring theorem , 2009, 0909.2214.