Application of Robust PCA with a structured outlier matrix to topology estimation in power grids

Abstract

Robust PCA is a widely used technique for Principal Component Analysis when the data is corrupted by outliers. The goal of the present short note is to report on the performance results of a simple modification of the method of Netrapali et al. for estimating Low Rank + Sparse models where the sparse matrix has the structure of a tree. We demonstrate the efficiency of the approach on the problem of estimating the topology in power grid networks.

Real-time fault detection in PV systems under MPPT using PMU and high-frequency multi-sensor data through online PCA-KDE-based multivariate KL divergence

“…9(f) shows the successful detection of fault F6 using the proposed algorithm through both fault indicators 𝐷 1 (𝑡) and 𝐷 7 (𝑡) obtained through Eq. (25)(26)(27)(28)(29)(30). Notice first that these indicators are very accurate as they have negligible values (<< 0.05) during normal operating conditions compared to the 𝐼 index, 𝐷 1 (𝑡) and 𝐷 7 (𝑡) remain clearly under their respective control limits 𝐶𝐿 𝐷1 and 𝐶𝐿 𝐷7 (Eq.…”

“…PCA plays a major role in solar engineering for various applications such as the analysis of big time-series data such as the satellite-derived irradiance data and string-level measurements from a utility-scale PV system. PCA is also used in PV systems for power forecasting and monitoring [29,30]. Despite its paramount advantages in handling big data and reducing computational complexity, PCA theory relies on three heavy assumptions: (a1) multivariate Gaussian distribution of data, (a2) stationarity of the process assuming a fixed operating point of a system, and (a3) linear correlations assuming a linear time-invariant system.…”

Exploration of grid energy efficiency influencing factors by applying principal component analysis approach

“…Through PCA analysis, we can not only identify the main factors affecting the energy efficiency of the grid but also quantify the degree of influence of these factors, and these findings are important for the design, operation, and maintenance of the grid [11][12]. Through this method, we can more systematically and accurately identify and analyze the factors affecting the energy efficiency of power grids and provide theoretical support for the optimization and upgrading of power grids [13][14].…”

Prediction of China’s Energy Consumption Based on Robust Principal Component Analysis and PSO-LSSVM Optimized by the Tabu Search Algorithm

“…Luong et al [17] considered a new method named online robust principal component analysis (RPCA) for time-varying decomposition problems and proposed a compressive online RPCA algorithm that can combine various information about decomposed vectors via an n − l 1 minimization method. Chretien et al [18] proposed a robust principal component analysis (RPCA) method to build the Low Rank + Sparse models when the used data is corrupted by outliers and applied it to estimate the topology in power grid networks. Sadeghian et al [19] thought that traditional robust principal component analysis (RPCA) algorithms only focused on output outliers, however, both input and output data can make mistakes in developing soft sensors.…”