Bifurcation points and loadability limits as solutions of constrained optimization problems

Vournas, Costas; Karystianos, M.; Maratos, N.G.

doi:10.1109/pess.2000.868821

Cited by 36 publications

(17 citation statements)

References 18 publications

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“…Previous works have formally shown that optimization methods can be used to compute SNBs in power system models and that these methods are basically equivalent to more "classical" computational approaches [10]. Also, some issues associated with the application of OPF-DMs to the computation of LIBs are discussed in [18], and the structure of the loadability surface is studied in [19] using similar optimization methods. In [20], fold bifurcations are also studied based on an optimization model.…”

Section: Introductionmentioning

confidence: 99%

Equivalency of Continuation and Optimization Methods to Determine Saddle-Node and Limit-Induced Bifurcations in Power Systems

Avalos

Cañizares

Milano

et al. 2009

IEEE Trans. Circuits Syst. I

132

109

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This paper presents a comprehensive and detailed study of an optimization-based approach to identify and analyze saddle-node bifurcations (SNBs) and limit-induced bifurcations (LIBs) of a power system model, which are known to be directly associated with voltage stability problems in these systems. Theoretical studies are presented, formally demonstrating that solution points obtained from an optimization model, which is based on complementarity constraints used to properly represent generators' voltage controls, correspond to either SNB or LIB points of this model. These studies are accomplished by proving that optimality conditions of these solution points yield the transversality conditions of the corresponding bifurcation points. A simple but realistic test system is used to numerically illustrate the theoretical discussions. Index Terms-Limit-induced bifurcations (LIBs), maximum loadability, optimization methods, saddle-node bifurcations (SNBs), transversality conditions, voltage stability (VS).

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Section: Introductionmentioning

confidence: 99%

Equivalency of Continuation and Optimization Methods to Determine Saddle-Node and Limit-Induced Bifurcations in Power Systems

Avalos

Cañizares

Milano

et al. 2009

IEEE Trans. Circuits Syst. I

132

109

View full text Add to dashboard Cite

show abstract

“…This problem can be solved by various methods such as continuation methods [19,20], optimization methods [21], direct methods [22] and quasi-steady state (QSS) simulations [23,24]. …”

Section: Stability Limitsmentioning

confidence: 99%

Approximating the parameter-space stability boundary considering post-contingency corrective controls

Perninge

2015

Electric Power Systems Research

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“…. , n s }, f a,i (x) = f b,i (x) = 0, is referred to as a breaking point [8] due to the shape that the PV-curve takes at such points, or a constraint switching point [9]. At such points the limit of the control variable, in this case E f , is reached and the set of active constraints change.…”

Section: Loadability Limitsmentioning

confidence: 99%

“…In [8] an equality and inequality constrained optimization problem for the power system loadability limit is formulated. In this article it is also demonstrated that the normal vector to the loadability surface is linked to the Lagrange multipliers of a penalty function formulation of this optimization problem.…”

Section: Introductionmentioning

confidence: 99%

Using a fixed point method to compute the parameter space distance to the surface of constant critical energy

Perninge

Eriksson

2012

2012 11th International Conference on Environment and Electrical Engineering

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Power system voltage security assessment is generally applied by considering the steady-state stability surface. However, as seen in the literature, random perturbations can drive the system away from stable operation, long before the steady-state stability surface is reached.In this article we include the value of the critical energy for the transient energy function, as a stability criterion when defining the stability boundary surface in parameter space. We show how the closest point on the surface of constant critical energy can be computed.The main contribution of this article is that it serves as a first step to include dynamic voltage collapse issues in the analysis of bulk power transfer security.

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Bifurcation points and loadability limits as solutions of constrained optimization problems

Cited by 36 publications

References 18 publications

Equivalency of Continuation and Optimization Methods to Determine Saddle-Node and Limit-Induced Bifurcations in Power Systems

Equivalency of Continuation and Optimization Methods to Determine Saddle-Node and Limit-Induced Bifurcations in Power Systems

Approximating the parameter-space stability boundary considering post-contingency corrective controls

Using a fixed point method to compute the parameter space distance to the surface of constant critical energy

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