A. R. Messina

Nonlinear, non-stationary analysis of interarea oscillations via Hilbert spectral analysis

Hilbert spectral analysis (HSA) is used to characterize the time evolution of non-stationary power system oscillations following large perturbations. Using an analytical procedure based on the Hilbert-Huang Technique (HHT), data from transient stability simulations are decomposed into a finite number of time-varying oscillating components that can be associated with different time scales. Hilbert analysis is then utilized to characterize the time evolution of critical components giving rise to the observed oscillations. The objectives of this study are to obtain information of a quantitative nature on nonlinear processes in power system oscillatory phenomena and assess the applicability of the developed procedures to track the evolving dynamics of critical system modes. A six-area, 377-machine power system is analyzed to examine the onset of nonlinear, non-stationary behavior. Examples of the developed procedures to detect and quantify the strength of nonlinear interaction in power system behavior and to estimate the distribution of the non-stationarity are provided

Interpretation and Visualization of Wide-Area PMU Measurements Using Hilbert Analysis

Characterization of the dynamic phenomena that arise when the system is subjected to a perturbation is important in real-time power system monitoring and analysis. This paper discusses the use of Hilbert spectral analysis to visualize and characterize nonlinear oscillations from synchronized wide-area measurements. The method has the potential to be applied for real-time, wide-area monitoring and analysis. As an illustrative example, synchronized phasor measurements of a real event in northern Mexico are used to examine the potential usefulness of nonlinear time series analysis techniques to characterize the time evolution of nonlinear, nonstationary oscillations and to determine the nature and propagation of the system disturbance. The proposed approach is also compared with Prony analysis

A Refined Hilbert–Huang Transform With Applications to Interarea Oscillation Monitoring

This paper focuses on the refinement of standard Hilbert-Huang transform (HHT) technique to accurately characterize time varying, multicomponents interarea oscillations. Several improved masking techniques for empirical mode decomposition (EMD) and a local Hilbert transformer are proposed and a number of issues regarding their use and interpretation are identified. Simulated response data from a complex power system model are used to assess the efficacy of the proposed techniques for capturing the temporal evolution of critical system modes. It is shown that the combination of the proposed methods result in superior frequency and temporal resolution than other approaches for analyzing complicated nonstationary oscillations.

Extraction of Dynamic Patterns From Wide-Area Measurements Using Empirical Orthogonal Functions

An approach based on the empirical mode decomposition (EMD) technique and proper orthogonal decomposition is proposed to examine dynamic trends and phase relationships between key system signals from measured data. Drawing on the EMD approach, and the method of snapshots, a technique based on the notion of proper orthogonal modes, is used to express an ensemble of measured data as a linear combination of basis functions or modes. This approach improves the ability of the EMD technique to capture abrupt changes in the observed data. Analytical criteria to describe the energy relationships in the observed oscillations are derived and a physical interpretation of the system modes is suggested. It is shown that in addition to providing estimates of time dependent mode shapes, the analysis also provides a method to identify the modes with the most energy embedded in the underlying signals. The method is applied to conduct post-mortem analysis of measured data of a real event in northern Mexico and to transient stability data

Inclusion of higher order terms for small-signal (modal) analysis: committee report-task force on assessing the need to include higher order terms for small-signal (modal) analysis

This paper summarizes the work done by the Task Force on Assessing the Need to Include Higher Order Terms for Small-Signal (Modal) Analysis. This Task Force was created by the Power System Dynamic Performance Committee to investigate the need to include higher order terms for small signal (modal) analysis. The focus of the work reported here is on establishing and documenting the practical significance of these terms in stability analysis using the method of Normal Forms. Special emphasis was placed on determining and describing conditions when higher order terms need to be included to accurately describe modal interactions. Test cases were developed on a standard test system to demonstrate the application of appropriate indices to detect the occurrence of nonlinear interaction and hence the need for higher order terms in stability analyzes. The use of the higher order terms in the site selection for a damping controller is also documented.

A Comparative Assessment of Two Techniques for Modal Identification From Power System Measurements

Power system oscillatory behavior can be analyzed in terms of modes, expressed as exponentially modulated sinusoids, exhibited in signals measured on the system. These signals are driven by the behavior of a large, nonlinear, time-variant system. In this paper, two modal identification methods are examined comparatively: Prony analysis and a method based on the Hilbert transform. Considerable structural differences exist between the two methods. Prony analysis yields modes which are directly expressed as exponentially modulated sinusoids, whereas the Hilbert method provides a more general solution. Synthetic and measured signals are used in the comparison. Some general conclusions are drawn from the analysis of several signals, including two sets of measured field data.

Nonstationary Approaches to Trend Identification and Denoising of Measured Power System Oscillations

This paper discusses the application of nonstationary time-frequency analysis techniques to identify nonlinear trends and filtering frequency components of the dynamics of large, interconnected power systems. Two different analytical approaches to examine nonstationary features are investigated. The first method is based on selective empirical mode decomposition (EMD) of the measured data. The second is based on wavelet shrinkage analysis. Experience with the application of these techniques to quantify and extract nonlinear trends and time-varying behavior is discussed and a physical interpretation of the proposed algorithms is provided. The practical application of these techniques is tested on time-synchronized phasor measurements collected by phasor measurement units (PMUs). Numerical simulations computed using time-energy nonstationary methods are critically compared with conventional approaches.

Assessment of nonlinear interaction between nonlinearly coupled modes using higher order spectra

Higher order spectral analysis techniques are used to identify nonlinear interaction involving the electromechanical modes of oscillation in complex power systems. First, the presence and extent of nonlinear interactions between frequency components in oscillatory processes following large perturbations are identified using bispectrum and bicoherence analysis methods. Then, the strength and distribution of nonlinear couplings between frequency components is investigated using the phase relationships between spectral components. A case study with a 377-generator model of the Mexican interconnected system is used to illustrate nonlinear aspects arising from the nonlinear interaction of the different low-frequency inter-area modes. The results of the numerical simulations show that low-frequency modes may interact nonlinearly producing intermodulation components at the sum and/or difference frequency of the fundamental modes of oscillation. Such an identification can be used as a benchmark for validation of nonlinear analysis methods, and to reduce the burden associated with these methods.

Co-ordinated application of FACTS devices to enhance steady-state voltage stability

This paper examines the co-ordinated application of flexible ac transmission system (FACTS) technologies to extend system voltage stability margins. A systematic analysis and design method, based on the singular value/eigenvalue decomposition analysis of the load-flow Jacobian and the study of the controllability characteristics of an equivalent state model is used to study the voltage instability phenomenon as well as to assess the potential for small-signal voltage stability improvement by means of FACTS compensation. The method is of particular interest for the preliminary design of new system devices and the study of interactions among existing controllers. Results obtained using a practical system representative of the Central American interconnected network are presented, illustrating the application of FACTS technologies to extend voltage stability limit. q 2003 Elsevier Science Ltd. All rights reserved.

Assessing placement of controllers and nonlinear behavior using normal form analysis

Normal form (NF) theory is used to characterize and quantify nonlinear modal interaction near critical equilibria. This study focuses on the analysis of second-order modal interaction and the study of nonlinear aspects of system behavior which are of interest to the design and location of system controllers. A systematic approach to deriving second-order NF representations in the neighborhood of equilibrium points is presented. On the basis of this model, nonlinear interaction measures are then obtained to assess the extent and distribution of nonlinearity in the system. Analytical criteria are developed to predict the existence of nonlinear modal interactions that significantly affect system dynamic performance. To demonstrate the effect of nonlinear interaction, a case study of locating controllers to damp electromechanical oscillations is developed. Examples of application of the developed approaches on a two-area four-machine test system are presented to determine the strength of nonlinear interactions in the system response, and estimating its effects on system dynamic performance and control design.