Continuation of local bifurcations for power systemdifferential-algebraic equation stability model

Guo-yun, Cao; Hill, David J.; Ren, Hui

doi:10.1049/ip-gtd:20059018

Cited by 26 publications

(11 citation statements)

References 11 publications

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“…Many other researchers [2,5,11,12,14,15] have used constant power model in bifurcation and singularity analysis of DAE power system model. However, a more accurate load model that faithfully reflects the nonlinear dynamical behavior of the physical load components should be included in the DAE model in order to obtain more physically relevant results since load models have significant impact on voltage stability of power systems [22,23].…”

Section: Discussionmentioning

confidence: 99%

“…These stability problems include voltage stability and collapse [2][3][4][5], oscillatory instabilities [6,7] and local bifurcations of equilibria and associated stability problems such as small-signal stability [8][9][10][11][12][13][14][15]. This paper investigates the effect of the algebraic singularities on the dynamic of a classical power system with constant PQ load buses, which is modeled as semi-explicit index-1 DAEs of the form [2,9]: _ x ¼ fðx; y; bÞ 0 ¼ gðx; y; bÞ…”

Section: Introductionmentioning

confidence: 99%

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Effects of algebraic singularities on the voltage dynamics of differential‐algebraic power system model

Ayasun

2007

Int Trans Elec Energy Syst

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SUMMARYVoltage stability analysis of differential-algebraic equation (DAE) power system model is more complicated than for systems described by ordinary differential equations (ODEs). In addition to unstable equilibria, algebraic singularity plays a crucial role in assessing the voltage stability. This paper explores the algebraic structure and singularities of the DAE model to investigate its influence on the voltage stability. Singular points are identified at various load levels and are illustrated together with the equilibria using nose curves. Then, at a given load level, the constraint manifold is decomposed into the voltage casual regions and singular points connecting them. Timedomain simulations initiated in the vicinity of singular points are performed to determine how singular points affect system dynamics. It is shown that depending on the relative location of initial points with respect to singular points, trajectories of bus voltages may settle to an infeasible low voltage stable equilibrium point, which may cause a further disturbance in the system leading a voltage stability problem.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effects of algebraic singularities on the voltage dynamics of differential‐algebraic power system model

Ayasun

2007

Int Trans Elec Energy Syst

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“…Reference [5] obtains the SSSR boundary by calculating a series of points on the solution manifold of the augmented system directly along with a certain direction. The direct method constructs an augmented system, including the differential-algebraic equations (DAEs) to describe the dynamic characteristics of the power system and the algebraic equations to describe the HB.…”

Section: Introductionmentioning

confidence: 99%

Polynomial approximation of the small-signal stability region boundaries and its credible region in high-dimensional parameter space

Liu

et al. 2012

Int. Trans. Electr. Energ. Syst.

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SUMMARY This paper presents a polynomial approximation method to give an explicit expression for the boundaries of small‐signal stability region (SSSR) based on the implicit function approach. Different from most of the current methods, the proposed method solves the problem of SSSR boundary approximation directly in the high‐dimensional parameter spaces. To settle the problem of local validity due to the polynomial approximation, we further put forward an optimization formula to estimate the credible region of the approximation with a given accuracy. The correctness and effectiveness of the proposed methods are verified through the case studies on a rudimentary power system and the real Hainan power grid of China. Copyright © 2012 John Wiley & Sons, Ltd.

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“…Chiang applied it in power system load flow equations to analyze the steady-state voltage stability [8]- [9] then in DAE systems associated with power systems dynamics [10]. Its basic principle is that it tracks the equilibrium curve of power W. Gu systems point by point as the parameters vary, and then detects and locates the possible local bifurcations by using an interpolation method based on the critical eigenvalues of the related system Jacobian matrix [11]- [13]. Obviously, this method would need to calculate the critical eigenvalue of a large-scale matrix of power systems at each point on the boundary during the continuation, this would take a lot of computation [14].…”

Section: Introductionmentioning

confidence: 99%

Study on prediction-correction homotopy method of tracking Hopf bifurcation point

Liu

Wang

2010

IEEE PES T&D 2010

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A new method named prediction-correction homotopy method is proposed to calculate Hopf bifurcation points associated with the parameter dependent differential algebraic equations (DAE) which are used to model power systems dynamics. It uses the secant prediction method to track the Hopf bifurcation homotopy path. Compared with the tangent prediction method, the computation load is much less because it is not related to the matrix inversion computation. At the same time, the automatic step-size control strategy ensures the calculation accuracy and speed to effectively implement the stepby-step correction. Finally, it is proved that this algorithm can be used accurately and effectively through WSCC 3-machine 9-bus system and NewEngland 39-bus system.

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Continuation of local bifurcations for power systemdifferential-algebraic equation stability model

Cited by 26 publications

References 11 publications

Effects of algebraic singularities on the voltage dynamics of differential‐algebraic power system model

Effects of algebraic singularities on the voltage dynamics of differential‐algebraic power system model

Polynomial approximation of the small-signal stability region boundaries and its credible region in high-dimensional parameter space

Study on prediction-correction homotopy method of tracking Hopf bifurcation point

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