Designing for Situation Awareness of Future Power Grids: An Indicator System Based on Linear Eigenvalue Statistics of Large Random Matrices

Abstract

Future power grids are fundamentally different from current ones, both in size and in complexity; this trend imposes challenges for situation awareness (SA) based on classical indicators, which are usually model-based and deterministic. As an alternative, this paper proposes a statistical indicator system based on linear eigenvalue statistics (LESs) of large random matrices: 1) from a data modeling viewpoint, we build, starting from power flows equations, the random matrix models (RMMs) only using the real-time data flow in a statistical manner; 2) for a data analysis that is fully driven from RMMs, we put forward the high-dimensional indicators, called LESs that have some unique statistical features such as Gaussian properties; and 3) we develop a three-dimensional (3D) power-map to visualize the system, respectively, from a high-dimensional viewpoint and a low-dimensional one. Therefore, a statistical methodology of SA is employed; it conducts SA with a model-free and data-driven procedure, requiring no knowledge of system topologies, units operation/control models, causal relationship, etc. This methodology has numerous advantages, such as sensitivity, universality, speed, and flexibility. In particular, its robustness against bad data is highlighted, with potential advantages in cyber security. The theory of big data based stability for on-line operations may prove feasible along with this line of work, although this critical development will be reported elsewhere.

Invisible Units Detection and Estimation Based on Random Matrix Theory

“…ULPs can be further divided into three categories-random behavior, invisible behavior, and fraudulent behavior. Our previous work [1,14], based on RMT, has already studied the random behavior, and verified that the (independent) random behavior, e.g., white noises, has little impact on the value of LESs. This paper focuses on the left two-the invisible behavior and the fraudulent one.…”

“…RMT and the relevant arXiv:1710.10745v2 [stat.AP] 14 Aug 2019 operations, which perform well in uncertainty processing in high-dimensional space, are employed to conduct feature extraction from the massive temporal-spatial data. Linear eigenvalue statistic indicators (LESs), which are robust against data errors (e.g., data loss, data out-of-synchronization [14]) and insusceptible to random noises (e.g., white noises [1]), are employed as the features. Based on the statistical properties of LESs, a hypothesis testing is formulated to conduct change point (CP) detection for invisible units modeling.…”

“…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.…”

A New Approach of Exploiting Self-Adjoint Matrix Polynomials of Large Random Matrices for Anomaly Detection and Fault Location

“…This paper is built upon our previous work [4,[8][9][10] in the last several years. Motivated for machine learning from massive datasets, our line of research is based on the modern high-dimensional statistics where RMT is central to this paradigm.…”

“…To model the fast time scale stochastic variation in a load, we assume that P is a random matrix with Gaussian random variables as its entries, following [4,9].…”