Selective Modal Analysis with Applications to Electric Power Systems, Part I: Heuristic Introduction

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

doi:10.1109/mper.1982.5519461

Cited by 107 publications

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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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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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confidence: 89%

Section: Introductionmentioning

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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“…Most of the remaining research traces back to eigenvalue elasticity theory originally proposed by Perez-Arriaga (1981) and introduced to the system dynamics field by Nathan Forrester (1983). The method calls for the computation of eigenvalues and then explores how the eigenvalues change as link gains change, that is, link gain elasticities.…”

Section: Literature Reviewmentioning

confidence: 99%

Behavior modes, pathways and overall trajectories: eigenvector and eigenvalue analysis of dynamic systems

Gonçalves

2009

System Dynamics Review

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One of the most fundamental principles in system dynamics is the premise that the structure of the system will generate its behavior. Such a philosophical position has fostered the development of a number of formal methods aimed at understanding the causes of model behavior. Behavior, to most in the field of system dynamics, is commonly interpreted as modes of behavior (e.g., exponential growth, exponential decay, and oscillation) because of their direct association with the feedback loops (e.g., reinforcing, balancing, and balancing with delays, respectively) that generate them. Hence, traditional research on formal model analysis has emphasized which loops cause a particular "mode" of behavior, with eigenvalues representing the most important link between structure and behavior. The main contribution of this work arises from a choice to focus our analysis on the overall trajectory of a state variable, instead of only a specific behavior mode. Since the overall behavior trajectory of state variable x i (t) is determined by a linear combination of the product of eigenvector components (r ji ) and behavior modes ( e λ j t ) generated by eigenvalues (λ j ), contributions from both eigenvalues and eigenvectors are important. By studying how the overall trajectory changes due to changes in link (or loop) gains, we observe that the derivatives of eigenvectors are more closely associated with the short-term transient impact of those changes, whereas derivatives of eigenvalues are associated with the long-term impact. Since we care deeply about both the short-and the long-term impact of those changes, there is value in looking at the contributions from both eigenvalues and eigenvectors.

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Studies of SMES power oscillation for measurement of natural frequency of power systems

2001

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It is important to power system designers and operators to understand the conditions of a power system while it is in operation. As a means of understanding power system conditions, a new method using Superconducting Magnetic Energy Storage (SMES) has been proposed. This method is a new usage of SMES. Since SMES is a controllable power source with quick response, it can impart power disturbances with arbitrary patterns to power systems. The transient response resulting from the SMES power disturbance is analyzed by FFT. From the peak of the power spectrum, the natural frequency of the power system is determined. In the conventional method for diagnosis of the power system by SMES, the power disturbance is a continuous sinusoidal oscillation. In this paper, we propose to use the one‐period sinusoidal wave as the power disturbance. This method is superior because the data for analysis come almost entirely from free oscillation and the periodicity of the disturbance does not appear in the analyzed power spectrum. In this paper, we show that the natural frequency of power systems can be measured by use of the proposed one‐period sinusoidal SMES oscillation. © 2001 Scripta Technica, Electr Eng Jpn, 134(4): 43–49, 2001

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Selective Modal Analysis with Applications to Electric Power Systems, Part I: Heuristic Introduction

Cited by 107 publications

References 0 publications

On participation factors for linear systems

On participation factors for linear systems

Behavior modes, pathways and overall trajectories: eigenvector and eigenvalue analysis of dynamic systems

Studies of SMES power oscillation for measurement of natural frequency of power systems

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