Pengzhi Gao

Missing Data Recovery by Exploiting Low-Dimensionality in Power System Synchrophasor Measurements

This paper presents a new framework of recovering missing synchrophasor measurements (erasures). Leveraging the approximate low-rank property of phasor measurement unit (PMU) data, we connect the problem of recovering PMU data erasures with recent advances in low-rank matrix completion methods. Since the existing analysis for matrix completion methods assumes an independent-erasure model that does not capture the correlations in PMU erasures, we propose two models to characterize the temporal and the channel correlations in PMU erasures and provide theoretical guarantees of a matrix completion method in recovering correlated erasures in both models. We also propose an online algorithm that can fill in the missing PMU measurements for real-time applications. Numerical experiments on actual PMU data are conducted to verify the effectiveness of the proposed methods.

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

With the installation of many new multi-channel phasor measurement units (PMUs), utilities and power grid operators are collecting an unprecedented amount of high-sampling 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.

Modeless reconstruction of missing synchrophasor measurements

This paper presents a new framework of reconstructing missing synchrophasor measurements (erasures) without the modeling of power system dynamics. Leveraging the approximate low-rank property of phasor measurement unit (PMU) data, we connect the problem of reconstructing PMU data erasures with the recent advance in low-rank matrix completion methods. Erasures can be reconstructed through existing computationally-efficient algorithms such as singular value thresholding (SVT) and information cascading matrix completion (ICMC). Numerical experiments on actual PMU data are conducted to verify the effectiveness of the proposed method. Since existing analysis for matrix completion methods assumes an independent-erasure model that does not capture the correlation among PMU data erasures, we propose two models to characterize temporal correlation and channel correlation in PMU data erasures. We provide theoretical guarantees of the ICMC algorithm in reconstructing correlated erasures in both models.

Identification of Successive “Unobservable” Cyber Data Attacks in Power Systems Through Matrix Decomposition

This paper presents a new framework of identifying a series of cyber data attacks on power system synchrophasor measurements. We focus on detecting “unobservable” cyber data attacks that cannot be detected by any existing method that purely relies on measurements received at one time instant. Leveraging the approximate low-rank property of phasor measurement unit (PMU) data, we formulate the identification problem of successive unobservable cyber attacks as a matrix decomposition problem of a low-rank matrix plus a transformed column-sparse matrix. We propose a convex-optimization-based method and provide its theoretical guarantee in the data identification. Numerical experiments on actual PMU data from the Central New York power system and synthetic data are conducted to verify the effectiveness of the proposed method.

Identification of “unobservable” cyber data attacks on power grids

This paper presents a new framework of identifying cyber data attacks on synchrophasor measurements. We focus on detecting “unobservable” cyber data attacks that cannot be detected by any existing detection method that purely relies on measurements received at one time instant. Leveraging the approximate low-rank property of phasor measurement unit (PMU) data, we formulate the unobservable cyber attack identification problem as a matrix decomposition problem where the observed data matrix is the sum of a low-rank matrix plus a linear projection of a column-sparse matrix. We propose a convex-optimization-based decomposition method and provide its theoretical guarantee in the attack identification. Numerical experiments on actual PMU data and synthetic data are conducted to verify the effectiveness of the proposed method.

Low-rank matrix recovery from quantized and erroneous measurements: Accuracy-preserved data privatization in power grids

This paper recovers data from quantized and partially corrupted measurements. The data recovery is achieved through solving a constrained maximum likelihood estimation problem that exploits the low-rank property of the actual measurements. The recovery error is proven to be order optimal and decays in the same order as that of the state-of-the-art method when no corruption exists. The data accuracy is thus maintained while the data privacy is enhanced. A new application of this method for data privacy in power systems is discussed. Experiments on synthetic data and real synchrophasor data in power systems demonstrate the effectiveness of our method.

Missing Data Recovery for High-Dimensional Signals With Nonlinear Low-Dimensional Structures

Motivated by missing data recovery in power system monitoring, we study the problem of recovering missing entries of high-dimensional signals that exhibit low-dimensional nonlinear structures. We propose a novel model, termed as “union and sums of subspaces,” to characterize practical nonlinear datasets. In this model, each data point belongs to either one of a few low-dimensional subspaces or the sum of a subset of subspaces. We propose convex-optimization-based methods to recover missing entries under this model. We theoretically analyze the recovery guarantee of our proposed methods with both noiseless and noisy measurements. Numerical experiments on synthetic data and simulated power system data are conducted to verify the effectiveness of the proposed methods.