Selective Modal Analysis with Applications to Electric Power Systems, Part II: The Dynamic Stability Problem

Verghese,; Pérez-Arriaga, Ignacio J.; Schweppe,

doi:10.1109/mper.1982.5519462

Cited by 32 publications

(88 citation statements)

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“…It isn't clear at the outset that these two senses should lead to identical formulas for participation factors. However, the precise definitions in [9], [5], [10] for these two senses of participation factors did indeed result in identical mathematical expressions. The same conclusion is found to apply in the present paper, under assumptions valid for a large class of problems.…”

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confidence: 89%

“…Since its introduction by Verghese, Pérez-Arriaga and Schweppe [9], [5], [10], Selective Modal Analysis (SMA) has become a popular tool for system analysis, order reduction and actuator placement. In particular, this tool is extensively used in the electric power systems area [4].…”

Section: Introductionmentioning

confidence: 99%

“…The initial condition is modeled as an uncertain quantity, which can be viewed either in a set-valued or a probabilistic setting. If the initial condition uncertainty obeys a symmetry condition, the new definitions are found to reduce to the original definition of [9], [5], [10]. Since the initial condition is viewed as uncertain, the definitions model its effect on the level of mode-state interaction in an average sense.…”

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confidence: 99%

“…Fowllowing Verghese, Pérez-Arriaga and Schweppe [9], [5], [10], participation factors are considered in two basic senses. In the first sense, a participation factor measures the relative contribution of a mode to a state.…”

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confidence: 99%

“…It should be noted that there have been other interpretations of participation factors since the original work of [9], [5], [10]. For example, participation factors are often viewed as sensitivities of eigenvalues to changes in the diagonal entries of the state dynamics matrix (see, e.g., [8]).…”

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On participation factors for linear systems

Abed

Lindsay

Hashlamoun³

2000

Automatica

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ISR develops, applies and teaches advanced methodologies of design and analysis toAbstract Participation factors are nondimensional scalars that measure the interaction between the modes and the state variables of a linear system. Since their introduction by Verghese, Pérez-Arriaga and Schweppe, participation factors have been used for analysis, order reduction and controller design in a variety of fields. In this paper, participation factors are revisited, resulting in new definitions. The aim of these definitions is to achieve a conceptual framework that doesn't hinge on any particular choice of initial condition. The initial condition is modeled as an uncertain quantity, which can be viewed either in a set-valued or a probabilistic setting. If the initial condition uncertainty obeys a symmetry condition, the new definitions are found to reduce to the original definition of participation factors.

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mentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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On participation factors for linear systems

Abed

Lindsay

Hashlamoun³

2000

Automatica

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Developing feedback model for power system dynamic sensitivity analysis

Hill

et al. 2017

Int Trans Electr Energ Syst

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Summary Since sensitivity analysis provides information on changes of the system dynamics with respect to changes of system parameters, it has been long recognized as an important tool for power system small‐signal stability analysis and controller designs. Sensitivity analysis is now much more important due to all the anticipated changes of future power systems, so more efficient and feasible methods are needed. The current sensitivity analysis methods are either simulation based or eigenvalue based. The eigenvalues and/or the time domain trajectories of the investigated system are solved for scenarios both before and after the parameter changes to evaluate the impacts of these changes on the system dynamics. However, both methods are actually numerically based, so often insufficient in fully revealing system physical characteristics. This paper analyzes the drawbacks of the available methods for analyzing the dynamic impacts of parameter changes in a power system and then develops a feedback‐based model for sensitivity analysis. The model is easier to identify the dynamic interactions of components; meanwhile, it also offers a new perspective on sensitivity analysis from the frequency domain. Case studies of increasing complexity demonstrate fully that the application of the proposed method reveals new insights on power system dynamics that conventional methods could not do.

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Spectral analysis for uncertainty quantification

Lee

2020

Numerical Linear Algebra App

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During the past few decades, uncertainty quantification (UQ) techniques have been developed and applied to many applications. The majority of these techniques have been applied directly to specifically defined problems, that is, problems described by a mathematical operator and a specific source term, both which may be endowed with uncertainty. In this article, we take an alternative approach: applying UQ techniques to probe the operator. The goal is to extract intrinsic structures of the problem, particularly operator structures that reveal the propagation of uncertainty which a UQ analysis of a specific problem may not accurately extract. There are many practical reasons for this. For example, the operator often contains more aspects of uncertainty than the forcing term, and the operator is often computationally expensive to form and hence, wasteful to use only for determining the solution of a sample instantiation. The anticipation is that the detailed information can lead to more accurate and efficient UQ analysis of the general problem. In this article, we consider only linear problems since we want to explore the potential benefits of this approach without the added complexities introduced by nonlinearities. This linearity assumption allows us to explore structures exposed by the spectrum of the operator. We explore sensitivity of the eigenvectors to determine a relationship between the spatial and uncertainty parameter dimensions, and then construct an adaptive parameter procedure based on this relationship. We also explore the propagation of uncertainties in multicomponent systems, like in multiphysics applications, by examining the coupling in the smooth-frequency eigenvectors; and explore componentized UQ processing based on the eigenvalues/vectors of the state-equation operator in goal-oriented multiple-input/multiple-output systems. Analysis and numerical examples demonstrating the applicability of the methods are presented. K E Y W O R D Sgoal-oriented problems, participation factors, sensitivity analysis, spectral analysis, uncertainty quantification INTRODUCTIONUncertainty quantification (UQ) involves the development, analysis, and application of mathematical and statistical methods to assess the reliability and predictability of models that have uncertainties. Until recent decades,

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Selective Modal Analysis with Applications to Electric Power Systems, Part II: The Dynamic Stability Problem

Cited by 32 publications

References 0 publications

On participation factors for linear systems

On participation factors for linear systems

Developing feedback model for power system dynamic sensitivity analysis

Spectral analysis for uncertainty quantification

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