Stability Theory for Differential/Algebraic Systems with Application to Power Systems

Hill, David; Mareels, Iven

doi:10.1007/978-1-4612-4484-4_42

Cited by 71 publications

(118 citation statements)

References 3 publications

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“…The stability of these types of systems is thoroughly discussed in [34]. The main idea is that if can be guaranteed to be nonsingular along system trajectories of interest, the behavior of (6) along the given trajectories is primarily determined by the local reduction where comes from applying the Implicit Function Theorem to the algebraic constraints on the trajectories of interest.…”

Section: A Saddle-node Bifurcationsmentioning

confidence: 99%

Calculating optimal system parameters to maximize the distance to saddle-node bifurcations

Cañizares

1998

IEEE Trans. Circuits Syst. I

105

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This paper presents a new methodology to calculate parameters of a nonlinear system, so that its distance to a saddlenode bifurcation is maximized with respect to the particular parameters that drive the system to bifurcation. The technique is thoroughly justified, specifying the conditions when it can be applied and the numeric mechanisms to obtain the desired solutions. A comparison is also carried out between the proposed method and a known methodology to determine closest saddlenode bifurcations in a particular power system model, showing that the new technique is a generalization of the previous method. Finally, applications to power systems are discussed, particularly regarding the design of some FACTS devices, and a simple generator-line-load example is studied to illustrate the use of the proposed technique to determine the optimal shunt and/or series compensation to maximize distances to voltage collapse. The effect of the optimal compensation on the stability of the sample system is also analyzed.

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Section: A Saddle-node Bifurcationsmentioning

confidence: 99%

Calculating optimal system parameters to maximize the distance to saddle-node bifurcations

Cañizares

1998

IEEE Trans. Circuits Syst. I

105

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“…We define the set D ∈ R nα × R 2mα × R 2 where the solutions of the DAE are unique and well defined [10]:…”

Section: Power System Modelingmentioning

confidence: 99%

Application of frequential properties of power systems to robustness analysis

Giusto

2010

Proceedings of the 2010 American Control Conference

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This paper studies the application of certain frequency domain properties of a class of power systems to the robustness analysis. The small signal models of a significant class of power systems-namely, systems without resistive losses nor excitation control-was recently shown to meet passivitylike, convex conditions in the frequency domain. A classical benchmark is considered and it is shown that the presence of excitation control and resistive elements does not completely destroy the above-mentioned property, which remains valid in the frequency band associated to the electromechanical modes. The example includes a detailed robustness analysis showing the importance of the a priori knowledge of the frequential properties of these models in the frequency band of interest.

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“…We need to define the set D ∈ R N × R 2m × R 2me where the solutions of the DAE are unique and well defined [3]: D {(x, y, z)|g(x, y, z) = 0 and ∇ y g(x, y, z)is nonsingular}.…”

Section: F Power System Modelmentioning

confidence: 99%

On some frequency domain properties of small signal models of a class of power systems

Giusto

2007

2007 46th IEEE Conference on Decision and Control

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This paper studies frequency domain properties of linear models of a class of power system, characterized by synchronous generators with constant excitation and the absence of resistive loads and leaky lines. A Port-Controlled Hamiltonian (PCH) representation is given for each component of the network. The corresponding linear model around the equilibrium point is shown to meet a convex condition in the frequency domain, able to be exploited in the stability analysis of interconnected systems. The application of this property to a classical two-areas example shows that it can be computationally exploited even in the case of non-idealized models.

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Stability Theory for Differential/Algebraic Systems with Application to Power Systems

Cited by 71 publications

References 3 publications

Calculating optimal system parameters to maximize the distance to saddle-node bifurcations

Calculating optimal system parameters to maximize the distance to saddle-node bifurcations

Application of frequential properties of power systems to robustness analysis

On some frequency domain properties of small signal models of a class of power systems

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