Data will become a strategic resource and even prime driving force for future grid. Essentially, rather than massive data themselves, we are much more interested in the potential contained in the data. In other words, how to mine the value from the 4Vs data (data with features of volume, variety, velocity, and veracity) within tolerant resources (time, hardware, human, etc.) is the key challenge. This chapter studies the methodology of applying big data analytics to power grids. First, the definition of big data and random matrix theories (RMTs), as well as related system mapping framework and data processing methods are introduced as foundations. Especially, some mathematical contents, such as random matrix models (RMMs), probability in high dimension, and linear eigenvalue statistics (LES), are discussed in detail. Then, a series of functions related to situation awareness (SA) of power grids, including early event detection (EED), fault diagnosis and location, correlation analysis, high-dimensional indicator system and its visualization (i.e., auxiliary 3D power-map), are developed as concrete applications. In this way, a typical data-driven methodology, mainly based on RMT, is proposed to cognize power grids. Three main procedures are essential: (1) big data model-to build the RMMs with raw data; (2) big data analysis-to conduct high-dimensional analyses to construct the indicator system via statistical transformations; and (3) engineering interpretation-to visualize and interpret the statistical results to human beings. This methodology is a more precise and natural way to gain insight into the large-scale interconnected systems. Furthermore, the indicator system will build a new epistemology to reveal the physical systems; it will open a new ear for the SA.

Chapter Contents:

• 13.1 Background for conduct SA in power grid with big data analytics
• 13.1.1 Smart grid-an essential big data system with 4Vs data
• 13.1.2 Smart grid and its stability, control, and SA
• 13.1.3 Approach to SA-big data analytics and unsupervised learning mechanism
• 13.1.4 RMM and probability in high dimension
• 13.2 Three general principles related to big data analytics
• 13.2.1 Concentration
• 13.2.2 Suprema
• 13.2.3 Universality
• 13.3 Fundamentals of random matrices
• 13.3.1 Types of matrices
• 13.3.2 Central limiting theorem
• 13.3.3 Limit results of GUE and LUE
• 13.3.4 Asymptotic expansion for the Stieltjes transform of GUE
• 13.3.5 The rate of convergence for spectra of GUE and LUE
• 13.4 From power grid to RMM
• 13.5 LES and related research
• 13.5.1 Definition of LES
• 13.5.2 Law of Large Numbers
• 13.5.3 CLTs of LES
• 13.5.4 CLT for covariance matrices
• 13.5.5 LES for Ring law
• 13.5.6 LES for covariance matrices
• 13.6 Data preprocessing-data fusion
• 13.6.1 Augmented matrix method for power systems
• 13.6.2 Another kind of data fusion
• 13.7 A new methodology and epistemology for power systems
• 13.7.1 The evolution of power systems and group-work mode
• 13.7.2 The methodology of SA for smart grids
• 13.7.3 Novel indicator system and its advantages
• 13.8 Case studies
• 13.8.1 Case 1: anomaly detection and statistical indicators designing using simulated 118-bus system
• 13.8.2 Case 2: correlation analysis for single factor using simulated 118-bus system
• 13.8.3 Case 3: advantages of LES and visualization using 3D power-map
• 13.8.4 Case 4: SA using real data
• Bibliography

Inspec keywords: Big Data; power system interconnection; fault location; matrix algebra; eigenvalues and eigenfunctions; power grids; correlation methods

Other keywords: RMM; linear eigenvalue statistics; random matrix models; RMT; fault location; random matrix theory; EED; 4V data; power grid; Big data analysis; situation awareness; early event detection; data driven methodology; correlation analysis; fault diagnosis; data processing methods; LES

Subjects: Power system measurement and metering; Algebra; Power engineering computing; Data handling techniques; Power system management, operation and economics; Algebra; Signal processing and detection; Power system protection