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

TL;DR

This paper introduces a data-driven correlation analysis method for power systems using random matrix theory, enabling real-time, model-free insights into system factors and status with robustness to data issues.

Contribution

It proposes a novel statistical approach based on random matrix theory and augmented data matrices for analyzing power system correlations without prior models.

Findings

Effective in real-time analysis of power systems.

Robust against bad or incomplete data.

Validated on IEEE 118-bus system.

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.