In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

Series Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index

/pdf/differential-equations-and-dynamical-systems-3chsjx2k45.pdf

Differential Equations and Dynamical Systems

(1990). ENERGY FUNCTION ANALYSIS FOR POWER SYSTEM STABILITY. Electric Machines & Power Systems: Vol. 18, No. 2, pp. 209-210.

Energy function analysis for power system stability

The potential and effectiveness of the newly developed Pareto-based multiobjective evolutionary algorithms (MOEA) for solving a real-world power system multiobjective nonlinear optimization problem are comprehensively discussed and evaluated in this paper. Specifically, nondominated sorting genetic algorithm, niched Pareto genetic algorithm, and strength Pareto evolutionary algorithm (SPEA) have been developed and successfully applied to an environmental/economic electric power dispatch problem. A new procedure for quality measure is proposed in this paper in order to evaluate different techniques. A feasibility check procedure has been developed and superimposed on MOEA to restrict the search to the feasible region of the problem space. A hierarchical clustering algorithm is also imposed to provide the power system operator with a representative and manageable Pareto-optimal set. Moreover, an approach based on fuzzy set theory is developed to extract one of the Pareto-optimal solutions as the best compromise one. These multiobjective evolutionary algorithms have been individually examined and applied to the standard IEEE 30-bus six-generator test system. Several optimization runs have been carried out on different cases of problem complexity. The results of MOEA have been compared to those reported in the literature. The results confirm the potential and effectiveness of MOEA compared to the traditional multiobjective optimization techniques. In addition, the results demonstrate the superiority of the SPEA as a promising multiobjective evolutionary algorithm to solve different power system multiobjective optimization problems.

Multiobjective evolutionary algorithms for electric power dispatch problem

Turbulence, Coherent Structures, Dynamical Systems and SymmetryP. Holmes, J. L. Lumley, G. Berkooz, and C. W. Rowley, 2nd ed., Cambridge University Press, Cambridge, England, U.K., 2012, 386 pp., $90

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

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

Inter-area Oscillations in Power Systems

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.

/pdf/a-refined-hilbert-huang-transform-with-applications-to-3knfw7vq5a.pdf

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

A global multiscale method based on a dynamic mode decomposition (DMD) algorithm to characterize the global behavior of transient processes recorded using wide-area sensors is proposed. The method interprets global dynamic behavior in terms of both, spatial patterns or shapes and temporal patterns associated with dynamic modes containing essentially single-frequency components, from which the mode shapes, frequencies and growth and decay rates of the modes can be extracted simultaneously. These modes are then used to detect the coherent and dominant structures within the data. The technique is well suited for fast wide-area monitoring and assessment of global instability in the context of modern data fusion-based estimation techniques. Results of the application of the proposed method to large, high-dimensional data sets are encouraging.

A Dynamic Mode Decomposition Framework for Global Power System Oscillation Analysis

This book deals with the application of new techniques based on time-frequency system representations and statistical approaches to the study, characterization, and control of nonlinear and non-stationary inter-area oscillations in power systems. The main focus is on the study of nonlinear, time-varying wide-area oscillatory problems associated with critical system perturbations. Techniques that explicitly address and treat nonlinearity are given and efficient methods to generate time-varying system approximations from both measured and simulated data are discussed. The theoretical basis for these methods is described as well as application properties and performance. Analysis techniques discussed include parametric methods such as Prony analysis, Yule-Walker based methods, Least-Squares methods, Wavelets and Fourier-based methods, and non-parametric methods such as Periodogram averaging and the Hilbert-Huang transform, as well as higher order statistical approaches. Emphasis is placed on the modeling and control of complex time-varying behavior which has not been present in previous work. Through case studies of synthetic and real-life test systems, the authors explain how an understanding of temporal, nonlinear behavior can be incorporated in the analysis and design process of complex control systems. Examples include computer simulations and actual system measurements from power systems in North America, Australia, India and Mexico. Particular attention is given to the vital new ideas of dynamic security assessment in real-time implementations and the evaluation of spatio-temporal behavior in systems with embedded f Flexible ac Transmission Systems (FACTS). Future applications of these methodologies focusing on the implementation of smart wide-area monitoring, protection control systems based on methods of analysis of time series are also discussed.

Arturo Roman Messina

Papers

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

Inter-area Oscillations in Power Systems

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

A Dynamic Mode Decomposition Framework for Global Power System Oscillation Analysis

Inter-area Oscillations in Power Systems: A Nonlinear and Nonstationary Perspective