A Correlation Analysis Method for Power Systems Based on Random Matrix Theory

• Published in: IEEE transactions on smart grid 2017-07, Vol.8 (4), p.1811-1820
• Main Authors: Xinyi Xu, Xing He, Qian Ai, Qiu, Robert Caiming
• Format: Article
• Language: English
• Subjects: augmented matrix; Big data; big data analytics; Buses (vehicles); Complexity; Correlation; Correlation analysis; Covariance matrices; Eigenvalues and eigenfunctions; Line spectra; linear eigenvalue statistics; Mathematical analysis; Mathematical models; Matrices (mathematics); Matrix methods; Matrix theory; Power system stability; power systems; random matrix theory; Real time; Robustness (mathematics)
• ISSN: 1949-3053; 1949-3061
• DOI: 10.1109/TSG.2015.2508506

The operating status of power systems is influenced by growing varieties of factors, resulting from the developing sizes and complexity of power systems. In this situation, the model-based methods need to be revisited. A data-driven method, as the novel alternative on the other hand, is proposed in this paper. It reveals the correlations between the factors and the system status through statistical properties of data. An augmented matrix as the data source is the key trick for this method and is formulated by two parts: (1) status data as the basic part; and (2) factor data as the augmented part. The random matrix theory is applied as the mathematical framework. The linear eigenvalue statistics, such as the mean spectral radius, are defined to study data correlations through large random matrices. Compared with model-based methods, the proposed method is inspired by a pure statistical approach without a prior knowledge of operation and interaction mechanism models for power systems and factors. In general, this method is direct in analysis, robust against bad data, universal to various factors, and applicable for real-time analysis. A case study based on the standard IEEE 118-bus system validates the proposed method.