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

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.