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

Abstract

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 modelbased methods need 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; it is formulated by two parts: 1) status data as the basic part, and 2) factor data as the augmented part. The random matrix theory (RMT) is applied as the mathematical framework. The linear eigenvalue statistics (LESs), such as the mean spectral radius (MSR), 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.

Invisible Units Detection and Estimation Based on Random Matrix Theory

“…Suppose that active power values P for each node stay around their initial points with fluctuations given as Eq. (13). From 14:00 to 17:00, some fraud events on Node 6 and Node 14 cause a reduction of 0.005 MW (8.33% of P 6 , 4.17% of P 14 ), as shown in Fig.…”

“…Reference [12] proposes an approach for anomaly detection and causal impact analysis using a two-layer dynamic optimal synchrophasor measurement devices selection algorithm. Our previous work [1,13,14], based on RMT, outlines a datadriven framework of big data analytics for power systems. Our RMT-based framework, via spectrum analysis, studies the statistical information which is unique in high-dimensional space.…”

Spatiotemporal Big Data Analysis for Smart Grids Based on Random Matrix Theory

“…On the other hand, as a novel alternative, the lately advanced data driven estimators [38,39,52,53] can assess stability without knowledge of the power network parameters or topology. However, these estimators are based on the analysis of individual window-truncated PMU data.…”

“…This is not true to principal components-we really do not know the rank of the covariance matrix. Thus, the RMT approach is robust against those challenges in classical data-driven methods, such as error accumulations and spurious correlations [53]. • For the statistical indicator, a theoretical or empirical value can be obtained in advance.…”

“…The key for correlation analysis is the concatenated matrix A i , which consist of two part-the basic matrix B and a certain factor matrix C i , i.e., A i = [B; C i ]. For more details, see our previous work [53]. The LES of each A i is computed in parallel, and Fig.…”