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This paper presents a new data-driven methodology for power system coherency identification of generator and non-generator buses. This methodology is exclusively based on intrinsic statistical properties extracted directly from observations, without any prior assumption of the probability distribution function (PDF) for the data. The main advances of this proposal are: (i) gathering of statistical information from the data itself despite scenarios where the PDF may change (different inverter-based load and generation scenarios, load levels of the system, and changes in topology); and (ii) assignment of buses into coherent areas without any tuning of parameters, nor manually labeling of huge amounts of training data. This new method, called typicality-based data analysis (TDA), is applied to the correlation metric of the distance between dynamic responses of buses, either voltage angles or frequencies. Simulated signals from a benchmark power system with cases considering the presence of non-synchronous generation and islanding conditions, and real data associated with generation trips in the U.S. Eastern Interconnection are used to corroborate the methodology effectiveness. [ABSTRACT FROM AUTHOR]

The paper proposes a new approach for the recovery of missing data from phasor measurement units (PMUs). The approach is based on the application of tensor decomposition to PMU data organized as three-dimensional tensors with respect to time, location and type of variables. The organization of the PMU data is in the form of a bus-oriented data structure and a branch-oriented data structure. Two versions of the approach are introduced. The first version uses polyadic tensor decomposition and the second version uses Tucker tensor decomposition. Several case studies are conducted validating the proposed approaches including measured PMU data in the New York transmission system. Comparison with existing approaches is performed to demonstrate the improvement in missing data recovery accuracy achieved by the new approach. [ABSTRACT FROM AUTHOR]

To enhance reliability and observability, power systems in North America have installed a significant number of Phasor Measurement Units (PMUs) to monitor dynamic behaviors. For real-time applications, the PMU data are streamed via the Internet from the substations to the phasor data concentrators, in the control centers. The transmission of the PMU data however, is not always reliable and can be subjected to quality issues and losses due to latency and equipment malfunctions. In this paper, a temporal version of the OnLine Algorithm for PMU data processing (OLAP) is proposed to recover the missing data. The algorithm is geared toward prolonged data outages and especially signals exhibiting significant temporal patterns. The method is connected to adaptive filtering and a necessary stability criterion for the algorithm is derived.The method is compared against several low rank and streaming data recovery methods to evaluate its effectiveness. [ABSTRACT FROM AUTHOR]

This paper presents a new framework to improve the quality of streaming synchrophasor measurements with the existence of missing data and bad data. The method exploits the low-rank property of the Hankel structure to identify and correct bad data, as well as to estimate and fill in the missing data. The method is advantageous compared to existing methods in the literature that only estimate missing data by leveraging the low-rank property of the synchrophasor data observation matrix. The proposed algorithm can efficiently differentiate event data from bad data, even in the existence of simultaneous and consecutive bad data. The algorithm has been verified through numerical experiments on recorded synchrophasor datasets. [ABSTRACT FROM AUTHOR]

This paper proposes a data-driven real-time event identification method based on the measurements of Phasor Measurement Units (PMUs). The central idea is to characterize an event by the low-dimensional subspace spanned by the dominant singular vectors of a data matrix that contains spatial–temporal blocks of PMU data. The subspace representation is robust to system initial conditions and characterizes the system dynamics. A dictionary of subspaces that correspond to different events are established offline, and an event is identified online with the most similar event in the dictionary through subspace comparison. The compact subspace representation reduces the dictionary size and the computational time of the event identification method. Numerical experiments on both simulated events in an IEEE 68-bus power system and the recorded data in New England validate the proposed method. [ABSTRACT FROM AUTHOR]

Modern power grids are increasingly relying on real-time data, such as those from phasor measurement units (PMUs), for their control and management operations. Due to its dependence on the Internet for data transfer, the grid is susceptible to a wide range of cyber-attacks. Among these, data manipulation attacks are of particular interest in the context of PMU data, due to their potential for causing widespread damage. In such attacks, the adversary changes the measurements in order to bias the estimate of system states. In this paper, we propose an effective and simple-to-implement mechanism for detecting such attacks. The proposed methodology is based on evaluating the equivalent impedances of transmission lines. Being independent of the conventional bad data detection scheme, it is also able to detect the so called “false data injection attacks.” Extensive simulation results using real PMU data have been provided in order to verify the accuracy of the proposed detector. [ABSTRACT FROM AUTHOR]

This paper studies the multichannel missing data recovery problem when the measurements are generated by a dynamical system. A new model, termed multichannel low-rank Hankel matrices, is proposed to characterize the intrinsic low-dimensional structures in multichannel time series. The data recovery problem is formulated as a nonconvex optimization problem, and two fast algorithms (AM-FIHT and RAM-FIHT), both with linear convergence rates, are developed to recover the missing points with provable performance guarantees. The required number of observations is significantly reduced, compared with conventional low-rank completion methods. Our methods are verified through numerical experiments on synthetic data and recorded synchrophasor data in power systems. [ABSTRACT FROM AUTHOR]

Data from phasor measurement units (PMUs) enable the efficient functioning of critical power applications supporting real-time monitoring, advanced protection, and dynamic control. Given the time-sensitive and critical nature of these measurements, PMU data are attractive targets for malicious attackers aiming to cause widespread grid damage. This paper addresses the problem of detecting a class of cyber threats called gray-hole attack, where the adversary drops PMU data packets as they traverse the network, resulting in loss of observability and subsequently, incorrect control decisions. This paper proposes an online mechanism for detecting gray-hole attacks in real-time. The proposed mechanism uses the timing information inherent in the PMU data for detecting packet drop attacks, and does not impose any overheads or require any support from the network infrastructure. Extensive simulation results are presented to verify the effectiveness and accuracy of the proposed detection mechanism under different network conditions. [ABSTRACT FROM AUTHOR]

This paper proposes a communication-reduced, cyber-resilient, and information-preserved data collection framework. Random noise and quantization are applied to the measurements before transmission to compress data and enhance data privacy. Leveraging the low-rank property of the data, we develop novel methods to recover the original data from quantized measurements even when partial measurements are corrupted. The data recovery is achieved through solving a constrained maximum likelihood estimation problem. The recovery error is proven to be order-wise optimal and decays in the same order as that of the state-of-the-art method when there is no corruption. The data accuracy is thus maintained while the data privacy is enhanced. A proximal algorithm with convergence guarantee is proposed to solve the nonconvex problem. The analyses are extended to situations when some measurements are lost, or when multiple copies of noisy, quantized measurements are sent for each data point. A new application of this framework 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

This paper applies a phasor-only state estimator (PSE) to a large power system consisting of two control regions, using synchrophasor data from 56 765/345/230 kV substations. Although the technique has been previously developed, this paper describes a topology processor to determine the redundant clusters of connected buses such that the PSE can be used in real time. This PSE allows corrections for phase biases, transformer taps, and current magnitude scaling. The ability to simultaneously solve the PSE for the two control regions is due to a PMU monitoring a tie-line between these two regions. The results show that with this method, the total vector errors of the measured voltage phasor data in these two control regions average to less than 0.5% under ambient conditions. The PSE also computes virtual phasor measurements on 70 buses that do not have PMUs, including large steam generator and wind-turbine generator substations. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

This paper aims to study the measurement and modeling methods for delays in wide-area closed-loop control systems (WACS). The delays are classified into communication delays and operational delays based on the information flow of WACS. For communication delays, an affine evaluation model is proposed based on previous studies, and this model is verified by the measured communication delays of the Guizhou Power Grid in Southwest China. For operational delays, a real-time digital simulator (RTDS) hardware-in-the-loop measurement method is developed, and the measured operational delays are obtained and analyzed. Finally, an estimation method for the closed-loop delay in actual WACS is proposed, in which the uplink and downlink communication delays are modeled as constants and the operational delay is modeled as a normal distribution. Consequently, the closed-loop delay follows a normal distribution with the calculated parameters by combining the communication delays and operational delay. The measurement results and analysis presented in this paper are important for the development and applications of WACS. [ABSTRACT FROM AUTHOR]

This paper discusses the design and usage of a Simulink-based phasor measurement unit (PMU) simulator package. The simulator and PMU data is available upon request from the first author. The motivation for developing the package is to provide a flexible environment for teaching phasor measurement and frequency estimation to advanced undergraduate and graduate students, and providing a knowledge base to students for research. This software allows for the exploration of the algorithms and phenomena involved in the phasor estimation process. The package is built on the Simulink platform and is able to process simulated signals as well as measured point-on-wave data. The popularity and relevance of the proposed package is evaluated using formal questioners. [ABSTRACT FROM PUBLISHER]

Validation and data quality improvement of phasor data through state estimation is the first step in ensuring that the synchrophasor data is useful for applications in monitoring, visualization, and control. This paper presents a phasor-measurement-based state estimator (PSE) for improving data consistency by identifying angle biases and current scaling errors in the phasor data using the augmented state vector approach. These errors can arise from issues with the Global Positioning Signal (GPS), timing circuits, instrument channels, and/or data channel scaling. The PSE is demonstrated using several sets of disturbance data from the Central New York Power System. The PSE can also provide estimates of line parameters and transformer tap ratios with sufficient measurement redundancy. Finally, the PSE allows the computation of interface power flows for disturbance and stability monitoring. [ABSTRACT FROM AUTHOR]

The use of synchrophasor data for observation and control is expected to enhance the operation and efficiency of the next generation of power systems. However, the specific characteristics of the data generated by synchrophasors makes them particularly vulnerable to cyber attacks. This paper presents a set of strategies to protect the anonymity of synchrophasor data against passive traffic analysis attacks. Considering the periodic nature of synchrophasor data, we propose defense mechanisms based on packet concatenation and random packet drops as a countermeasure against attacks that may use the timing as well as data volume information to compromise the network. In contrast to existing defenses against traffic analysis attacks, our scheme can be easily deployed using the current networking infrastructure as it is based on end-to-end principles and does not require any specialized routers. The proposed defense mechanisms are evaluated using both analysis and simulations. [ABSTRACT FROM PUBLISHER]

Wide-area analysis and control of large-scale electric power systems are highly dependent on the idea of aggregation. For example, one often hears power system operators mentioning how northern Washington oscillates against southern California in response to various disturbance events. The main question here is whether we can analytically construct dynamic electromechanical models for these conceptual, aggregated generators representing Washington and California, which in reality are some hypothetical combinations of thousands of actual generators. In this paper we address this problem, and present a concise overview of several new results on how to construct simplified interarea models of large power networks by using dynamic measurements available from phasor measurement units (PMUs) installed at specific points on the transmission line. Our examples of study are motivated by widely encountered power transfer paths in the Western Electricity Coordinating Council (WECC), namely, a two-area radial system representing the WA-MT flow, and a star-connected three-area system resembling the Pacific AC Intertie. [ABSTRACT FROM PUBLISHER]

With amplitude and phase information, time-synchronized measured phasor data of bus voltages and line currents can be used to calculate, without iterations, the voltage phasor on neighboring buses. In some phasor measurement units (PMUs), it has been observed that the voltage and current phasors exhibit phase biases, which can corrupt the conventional state estimator solution if it is augmented with such biased phasor data. This paper presents a new approach for synchronized phasor measurement-based state estimation, which can perform phasor angle bias correction given measurement redundancy. In this approach, polar coordinates are used as the state variables, because the magnitude and phase are largely independent measurements. The state estimation is formulated as an iterative least-squares problem, and its application to portions of the AEP high-voltage transmission system is illustrated. [ABSTRACT FROM AUTHOR]