Singularity-Induced Bifurcations in Electrical Power Systems

Marszałek, Wiesław; Trzaska, Z.

doi:10.1109/tpwrs.2004.841244

Cited by 76 publications

(43 citation statements)

References 22 publications

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“…In this paper we extend some of the results presented in [1]. In particular, we present further studies of the singularly perturbed power systems, their SIB, singular Hopf bifurcations and interactions between them.…”

Section: Introductionsupporting

confidence: 55%

“…Either first or second order matrix pencils can be used depending on an individual preference (see Appendices 1.1 and 1.2 for more details). A second order matrix pencil would normally be preferred for power systems as it may directly lead to double SIB points [1,21].…”

Section: Daes As Models Of Power Systemsmentioning

confidence: 99%

“…In an effort to better understand dynamical properties of power systems, their stability features and the impact of various parameters, the DAEs approach seems to be very important as was shown in a number of recent papers (see for example [1][2][3][4][5][6][7][8][9][10]). …”

Section: Introductionmentioning

confidence: 99%

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Singular Hopf Bifurcations in DAE Models of Power Systems

Marszałek¹,

Trzaska²

2011

EPE

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We investigate an important relationship that exists between the Hopf bifurcation in the singularly perturbed nonlinear power systems and the singularity induced bifurcations (SIBs) in the corresponding differenttial-algebraic equations (DAEs). In a generic case, the SIB phenomenon in a system of DAEs signals Hopf bifurcation in the singularly perturbed systems of ODEs. The analysis is based on the linear matrix pencil theory and polynomials with parameter dependent coefficients. A few numerical examples are included.

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Section: Introductionsupporting

confidence: 55%

Section: Daes As Models Of Power Systemsmentioning

confidence: 99%

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Singular Hopf Bifurcations in DAE Models of Power Systems

Marszałek¹,

Trzaska²

2011

EPE

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“…In recent years, several research works have discussed about the boundaries of voltage stability feasible region [3,5,[24][25][26]. In References [3,26,27], HB point is considered as the boundary of dynamic voltage stability, which is also adopted in this paper.…”

Section: The Problem Descriptionmentioning

confidence: 99%

Dynamic voltage stability prediction of power systems by a new feature selection technique and probabilistic neural network

Amjady

Velayati

2010

Euro. Trans. Electr. Power

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SUMMARYWith continued increase in the electrical energy demand and tendency towards maximizing economic benefits in power transmission system, especially in the liberalized electricity markets, real-time voltage security analysis has become a growing concern in electric power utilities. However, static analysis methods, such as power flow based methods, have difficulty in evaluating voltage stability and some voltage stability feasible region boundaries may not be correctly analyzed by these methods due to the use of simple models for the system components. On the other hand, dynamic modeling and evaluation of voltage stability are complex, expensive, and time consuming. In this paper, a new feature selection technique combined with a probabilistic neural network (PNN) is proposed for this purpose. A major difference of our paper with the previous research works in the area is that this paper proposes voltage stability prediction, while the previous works usually focus on the voltage stability evaluation. The proposed dynamic voltage stability prediction method is examined on the IEEE 14-bus and New England 39-bus test systems and the effectiveness of the proposed method is demonstrated. Also, the effect of different load models, branch contingencies, and generator contingencies is evaluated. Another advantage of the proposed prediction method is that it can be used for varied topologies and configurations of the power system.

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“…In parametrized problems, a stability change phenomenon due to the divergence of an eigenvalue was first analyzed by Venkatasubramanian [49,50] and later addressed by several authors [4,5,6,42,43,52]. This arises in different application fields [3,24,44,51]; related problems are discussed in [8,23,53]. The change of stability occurs when an equilibrium branch intersects a singular manifold, and this results in the divergence of one (or more) eigenvalue(s) through infinity.…”

Section: Introductionmentioning

confidence: 99%

Stability Loss in Quasilinear DAEs by Divergence of a Pencil Eigenvalue

Riaza¹

2010

SIAM J. Math. Anal.

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Abstract. The divergence through infinity of certain eigenvalues of a linearized differentialalgebraic equation (DAE) may result in a stability change along an equilibrium branch. This behavior cannot be exhibited by explicit ODEs, and its analysis in index one contexts has been so far unduly restricted to semiexplicit systems. By means of a geometric reduction framework we extend the characterization of this phenomenon to quasilinear DAEs, which comprise semiexplicit problems as a particular case. Our approach clarifies the nature of the singularities which are responsible for the stability change and also accommodates rank deficiencies in the leading system matrix. We show how to address this problem in a matrix pencil setting, an issue which leads to certain results of independent interest involving the geometric index of a quasilinear DAE and the Kronecker index of its linearization. The results are shown to be of interest in electrical circuit theory, since the differential-algebraic network models actually used in circuit simulation are not in semiexplicit but in quasilinear form.

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Singularity-Induced Bifurcations in Electrical Power Systems

Cited by 76 publications

References 22 publications

Singular Hopf Bifurcations in DAE Models of Power Systems

Singular Hopf Bifurcations in DAE Models of Power Systems

Dynamic voltage stability prediction of power systems by a new feature selection technique and probabilistic neural network

Stability Loss in Quasilinear DAEs by Divergence of a Pencil Eigenvalue

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