A Low-Rank Matrix Approach for the Analysis of Large Amounts of Power System Synchrophasor Data

Abstract

With the installation of many new multi-channel phasor measurement units (PMUs), utilities and power grid operators are collecting an unprecedented amount of highsampling rate bus frequency, bus voltage phasor, and line current phasor data with accurate time stamps. The data owners are interested in efficient algorithms to process and extract as much information as possible from such data for real-time and off-line analysis. Traditional data analysis typically analyze one channel of PMU data at a time, and then combine the results from the individual analysis to arrive at some conclusions. In this paper, a spatial-temporal framework for efficient processing of blocks of PMU data is proposed. A key property of these PMU data matrices is that they are low rank. Using this property, various data management issues such as data compression, missing data recovery, data substitution detection, and disturbance triggering and location can be processing using singular-value based algorithms and convex programming. These functions are illustrated using some historical data from the Central New York power system.

Recovering missing data via matrix completion in electricity distribution systems

“…However, the results therein are based on the assumption that missing entries are not correlated, which is not always the case in practical scenarios. Within that setting, low rank minimization tools are proving useful in electricity grid settings [14], [15]. The case of correlated missing entries for phasor measurement units data is studied in [16].…”

False data injection attacks on phasor measurements that bypass low-rank decomposition

“…In fact, they are stronger than Theorem 1 since we did not find any case where the LD detector results in C * (LD) such that C * (LD) = 0 and supp C * (LD) ⊆ I. (To Side) 1, 3,4,8,9,12,13,14,15,18,19,21,22,27,31,32,35,36,45,47,48,50,51,56,61,65,66,67,68,69,73,78,79,91,92,94,111,112,113,115,116,117,118,119,120,123,124,125,127,131,132,134,140,145,146,160,166,168,174,…”

“…Note that the state can be estimated based on PMU measurements via a single weighted least squares (WLS) [33], unlike traditional SCADA-based SE which requires multiple iterations due to the nonlinearity of the measurement function [34]. One possible way to process PMU data is to collect over a block of time (e.g., 5 to 20 seconds) and then process them as a batch (see for example [35]). We adopt this approach and write the PMU measurements as a matrix where each row vector corresponds to PMU measurements at one time instant and each column vector consists of the measurements collected in the same channel over a period of times.…”

Sample Complexity of Power System State Estimation using Matrix Completion

“…The first inequality comes from (52), the second comes from (53), and the third comes from (50). for b ≥ 1, we have…”