Bogdanov-Takens bifurcation points and Sil'nikov homoclinicity in a simple power-system model of voltage collapse

Budd, C. J.; Wilson, Jon

doi:10.1109/tcsi.2002.1001947

Cited by 21 publications

(18 citation statements)

References 36 publications

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“…It is reported in [8] that when reactive load Q 1 varies to 2.98975, chaotic attractor will emerge and when Q 1 varies to 2.9898258, voltage collapse will be triggered by the boundary crisis of chaotic attractor. Chaotic oscillation is an important precursor for voltage collapse and has been identified as one of dynamical mechanisms for voltage collapse [8][9][10][11]. Therefore, this paper studies chaos suppression problem for threebus power system.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Chiang et al [7] were the first to observe chaotic behavior in this power system model over a range of loading conditions. Since then, chaotic oscillation has been recognized by a number of researchers as one of mechanisms for voltage collapse [8][9][10][11]. In recent years, suppressing chaos in three-bus power system has attracted the attention from researchers in both the power system and control community.…”

Section: Introductionmentioning

confidence: 99%

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Fixed-time dynamic surface high-order sliding mode control for chaotic oscillation in power system

Liu

et al. 2016

Nonlinear Dyn

126

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In this paper, a fixed-time dynamic surface high-order sliding mode control approach is presented for chaos suppression and voltage stabilization in three-bus power system via design of current source converter-based static synchronous compensator controller. The proposed control strategy constructs two high-order sliding mode surfaces to achieve control objective. By combining backstepping idea with dynamic surface control (DSC) technique, highorder sliding mode controller is designed and the inherent problem of "explosion of complexity" in backstepping design is avoided. Further, a new stability concept is introduced into DSC design to achieve semiglobal uniform ultimate boundedness of the signals in high-order sliding mode system within finite time independent of initial condition. In addition, stability analysis is provided to show that the proposed control scheme can achieve semi-globally fixed-timely uniformly ultimately bounded stabilization. Finally, simulation results are given to demonstrate the effectiveness of the proposed control scheme and the superior performance over conventional DSC.

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Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fixed-time dynamic surface high-order sliding mode control for chaotic oscillation in power system

Liu

et al. 2016

Nonlinear Dyn

126

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“…2). This model is suitable for analyzing structural characteristics and is used in a lot of studies [I], [2], [4], [5], [6], [14], [15].…”

Section: Three Bus Modelmentioning

confidence: 99%

“…These effects are of interest in order to understand power system incidents and their control, respectively. Contrary to [2] bifurcation parameters are not only the load demands. Influences due to other load parameters are considered as well as load demand changings.…”

mentioning

confidence: 96%

Bifurcation analysis of power system load characteristics with continuation methods

Fette¹,

Winzenick²

2005

Mathematical and Computer Modelling of Dynamical Systems

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Power systems are capable of exhibiting complex dynamics. Sometimes critical ones are. e.g. nonlinear incidents like collapse and swing phenomena. Many efTorts are made by researchers and operators in order to prevent and dominate these undesirable effects. Il is well known that parameter variations have influences on the system behavior and its stabilily. Sometimes they can cause incidents like the ones mentioned above. Because of former studies (e.g. in the field of catastrophe theory) it is also known that very often only a few parameters dominate the system behavior. An identitication of these main parameters is desirable in order to get more information about the underlying mechanisms. On this basis an improvement or developement of adequate strategies in order to prevent critical system slates is possible.Limit induced problems due to parameter variations as well as effects of generator controls on the system have been investigated in several papers. This paper neglects the limit induced problems and considers influences of different load characteristics on the system behavior. Therefore, an appropriate load model is needed. It is desirable that the chosen model represents the physical behavior as well as influences of individual parameter.The presented analysis uses continuation methods and the concepts of bifurcation theory. Therewith an investigation due to parameter of interest is possible and furthermore properties of the solution points can be investigated and classified, too. Moreover, appropriate network models are needed. An often-used, three-node power system mode! is chosen here. It represents the main system behavior and the physical dependencies in principle. Additionally it is clearly arranged and easy to handle. This paper presents two major results. At first bifurcation-studies are made. These studies regard especially load parameter variations. In contrast to other solutions these results are transformed into so-called power diagrams. It is possible to use this well known representation to derive or adapt control schemes. Secondly, the usage of flexible AC transmission devices (FACTS) is analyzed m order to avoid critical bifurcations. Although this was studied in several papers before, this work analyzes again the influences of different load characteristics. As a result, one gets information about possible limits. In special cases gain -intervals of the used FACTS -device can be determined within the system is independent of load parameter variation.

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“…Nonlinear phenomena in power systems like voltage collapse or interarea oscillations have been investigated by many researchers (Ajjarapu et al, 1992;Budd et al, 2002;Chiang et al, 1990;Chiang et al, 1993;Dobson et al, 1989;Seydel, 2001). Understanding these phenomena is crucial because they can cause critical situations up to blackouts.…”

Section: Introductionmentioning

confidence: 99%

Control of Power Systems With Facts Devices Considering Different Load Characteristics

Winzenick

Fette²,

Horn

2005

IFAC Proceedings Volumes

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Power systems form one of the largest and most complex technical systems. Changes of load parameters may lead to so called bifurcations, resulting in nonlinear phenomena like voltage collapse or interarea oscillations. Special software tools are able to simulate these systems and to identify bifurcations. This paper presents a systematic approach to determine gain factors of Flexible AC Transmission Devices (FACTS) considering changes of load parameters. This approach is applied to two different power system models.

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Bogdanov-Takens bifurcation points and Sil'nikov homoclinicity in a simple power-system model of voltage collapse

Cited by 21 publications

References 36 publications

Fixed-time dynamic surface high-order sliding mode control for chaotic oscillation in power system

Fixed-time dynamic surface high-order sliding mode control for chaotic oscillation in power system

Bifurcation analysis of power system load characteristics with continuation methods

Control of Power Systems With Facts Devices Considering Different Load Characteristics

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