An analysis of truncated fractal growths in the stability boundaries of three-node swing equations

Varghese, Needhu; Thorp, James S.

doi:10.1109/31.1829

Cited by 27 publications

(19 citation statements)

References 9 publications

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“…Order is where the system is stable (i.e., in equilibrium). This is referred to as a basin of stability, or simply a basin [82]. The basin is not a permanent place or state.…”

Section: Basins Of Stabilitymentioning

confidence: 99%

Systems Theory

Hester

Adams

2014

Systemic Thinking

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Systems theory is a term that has been used inconsistently in a variety of disciplines. Further, few of these disciplines provide any type of formal definition for the term. As such, it is often subject to misunderstanding when used between disciplines. We believe that systems theory provides the foundation for improved understanding when dealing with systems and their attendant problems and messes. Before exposing you to a formal definition for systems theory, we will present a classification and high-level view of the major streams of thought that have addressed systems theory (i.e., the historical roots of systems theory). This will be followed by our definition of systems theory and the axioms and supporting propositions (i.e., systems principles) that we feel apply to all systems. Finally, we'll present a linkage of the principles of systems theory to the systemic thinking perspectives.

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“…Order is where the system is stable (i.e., in equilibrium). This is referred to as a basin of stability, or simply a basin [82]. The basin is not a permanent place or state.…”

Section: Basins Of Stabilitymentioning

confidence: 99%

Systems Theory

Hester

Adams

2014

Systemic Thinking

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“…Analysis of the equations, which especially deals with statespace dynamics far from equilibria, is hence needed for understanding the swing instability: see e.g. [5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Decomposition of energy function and hierarchical diagnosis of power grid swing instabilities

Kojima

Susuki

Tsumura

et al. 2016

NOLTA

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This paper considers an electric power grid with multiple synchronous machines exhibiting coupled swing dynamics and aims at developing a hierarchical diagnosis of loss of transient stability of the machines, which we term as swing instabilities. We introduce a standard energy function for the power grid and decompose it into individual energy functions of a collective system of the grid, of the motions relative to the collective system, and of the infinite bus. This decomposition enables us to extract distinctive behaviors embedded in the swing instabilities in terms of energy. We numerically apply the individual energy functions in the proposed decomposition to analysis of swing instabilities in the IEEE New England 39-bus test system. We then propose a hierarchical diagnosis of the swing instabilities based on the decomposition and discuss its validity by approximating the individual energy functions along solutions representing the grid's instabilities.

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“…Analysis of the swing equations, which especially deals with global structures of phase space far from equilibria, is hence needed for prevention of loss of transient stability (see e.g. Kopell and Washburn 1982;Abed and Varaiya 1984;Salam et al 1984;Varghese and Thorp 1988;Ueda et al 1992).…”

Section: Introductionmentioning

confidence: 99%

Coherent Swing Instability of Power Grids

2011

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We interpret and explain a phenomenon in short-term swing dynamics of multi-machine power grids that we term the Coherent Swing Instability (CSI). This is an undesirable and emergent phenomenon of synchronous machines in a power grid, in which most of the machines in a sub-grid coherently lose synchronism with the rest of the grid after being subjected to a finite disturbance. We develop a minimal mathematical model of CSI for synchronous machines that are strongly coupled in a loop transmission network and weakly connected to the infinite bus. This model provides a dynamical origin of CSI: it is related to the escape from a potential well, or, more precisely, to exit across a separatrix in the dynamical system for the amplitude of the weak nonlinear mode that governs the collective motion of the machines. The linear oscillations between strongly coupled machines then act as perturbations on the nonlinear mode. Thus we reveal how the three different mode oscillations-local plant, inter-machine, and inter-area modes-interact to destabilize a power grid. Furthermore, we present a phenomenon of short-term swing dynamics in the New England (NE) 39-bus test system, which is a well-known benchmark model for power grid sta- bility studies. Using a partial linearization of the nonlinear swing equations and the proper orthonormal decomposition, we show that CSI occurs in the NE test system, because it is a dynamical system with a nonlinear mode that is weak relative to the linear oscillatory modes.

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An analysis of truncated fractal growths in the stability boundaries of three-node swing equations

Cited by 27 publications

References 9 publications

Systems Theory

Systems Theory

Decomposition of energy function and hierarchical diagnosis of power grid swing instabilities

Coherent Swing Instability of Power Grids

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