Hard-limit induced chaos in a fundamental power system model

Ji, Weijun; Venkatasubramanian, V.

doi:10.1016/0142-0615(95)00066-6

Cited by 68 publications

(43 citation statements)

References 11 publications

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“…A single-machine-infinite bus system with the excitation limitation 3 is presented in Fig. 1, which consists of generators, transformer, load, circuit breaker, systematic tie line and the simplified excitation model.…”

Section: The Power System Modelmentioning

confidence: 99%

“…In 1993, the existence of chaos for a simple power system was first confirmed through the calculation of Lyapunov exponents and broad-band spectrum. 2 The nonlinear phenomena 3 were observed in a single-machine-infinite-bus power system with the excitation hard-limits, and the global bifurcations including period-doubling cascades which leaded to chaotic behavior were observed. Yu et.…”

Section: Introductionmentioning

confidence: 99%

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Bifurcations, chaos and adaptive backstepping sliding mode control of a power system with excitation limitation

et al. 2016

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The bifurcation and Lyapunov exponent for a single-machine-infinite bus system with excitation model are carried out by varying the mechanical power, generator damping factor and the exciter gain, from which periodic motions, chaos and the divergence of system are observed respectively. From given parameters and different initial conditions, the coexisting motions are developed in power system. The dynamic behaviors in power system may switch freely between the coexisting motions, which will bring huge security menace to protection operation. Especially, the angle divergences due to the break of stable chaotic oscillation are found which causes the instability of power system. Finally, a new adaptive backstepping sliding mode controller is designed which aims to eliminate the angle divergences and make the power system run in stable orbits. Numerical simulations are illustrated to verify the effectivity of the proposed method.

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Section: The Power System Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bifurcations, chaos and adaptive backstepping sliding mode control of a power system with excitation limitation

et al. 2016

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“…The studies of nonlinear dynamical systems have been carried out by utilizing computer simulations. How ever, they require long computational time [2]- [6]. For this reason, a chaos circuit is one of the most efficient tools for experimental observation of chaos.…”

Section: Introductionmentioning

confidence: 99%

“…Chaos is the most frequently encountered phe nomenon in the study of nonlinear dynamical systems such as biological neural networks [1], power systems [2], [3], and so on. For example, in medical field, chaos can be observed in brain pulse, R-R interval in electro cardiogram (ECG), and so on.…”

Section: Introductionmentioning

confidence: 99%

FPGA design of a digital circuit for estimating chaotic characteristics from approximated nonlinear functions

et al. 2002

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In this paper, an FPGA circuit for estimating chaotic characteristics of unknown nonlinear systems is proposed. From particular solutions corresponding to chaotic signals of the unknown system, the proposed circuit approximates nonlinear functions. The approximation of these nonlinear functions are performed by using supervised learning. From the approximated functions, chaotic characteristics of the unknown system are estimated.An understanding of the behavior of unknown nonlinear system will be provided by uti lizing the estimated chaotic characteristics.The proposed circuit is implemented onto an FPGA by using Verilog-HDL. This implementation confirmed that the proposed circuit can achieve high-speed operation and low-cost development.

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“…In this work we focus on the classical SMIB power system of Ref. [14], consisting on an SMIB with a wind-up-type hard limit which is introduced to constrain the control gains in the system voltage. It should be emphasized that while such an SMIB model can be of limited validity for studies of networks with a large number of generators, the dynamics of an SMIB provides valuable insights into what could be expected from the interaction between a single generator and the rest of the power system.…”

mentioning

confidence: 99%

Boundary crises, fractal basin boundaries, and electric power collapses

Marcos

Lopes

Viana

2003

Chaos, Solitons & Fractals

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Electric power systems are frequently nonlinear and, when faced with increasing power demands, may behave in unpredictable and rather irregular ways. We investigated the nonlinear dynamics of a single machine infinite bus power system model in order to study the appearance of coexistent periodic and chaotic attractors, characterizing multi-stable behavior. The corresponding basins of attraction present fractal boundaries, for which we have determined the uncertain fraction scaling in phase space. The bifurcation diagrams are studied with respect to variations of the mechanical power input and may lead to voltage collapse under certain circumstances, which we relate to a boundary crisis suffered by a chaotic attractor. Ó 2002 Published by Elsevier Science Ltd.Voltage collapse in electric power systems have caused blackouts around the world, with losses of billions of dollars and many side effects as damages in household appliances, increase of crime rates, and car crashes, just to name a few [1]. Although the exact mechanism of a voltage collapse is still a matter of investigation, it is known that in such events the voltage magnitudes at electric power systems decrease rapidly under a heavy load [2]. From a more fundamental point of view, the ubiquitous presence of bifurcations in the dynamic behavior of nonlinear electric power systems may be related to the occurrence of voltage collapses [3]. In this picture, a normal operation of the power system would correspond to a stable equilibrium state. When the production or transmission of electric energy is insufficient to supply an increasing power demand, an electric power system may lose its operational stability through a bifurcation, where the actual state becomes unstable and new stable states are created [4].The current literature on this subject assigns as possible causes of voltage collapse: (i) a saddle node bifurcation [5], where stable and unstable equilibria coalesce at the bifurcation point and disappear; (ii) a chaotic blue-sky bifurcation [6], where a chaotic attractor collides with an unstable equilibrium, also known as an interior crisis [7,8]. This chaotic attractor is achieved through a flip bifurcation cascade that begins with a limit cycle produced through a supercritical Hopf bifurcation, after which the former stable equilibrium becomes unstable. The connection between these description lies in the fact that the unstable equilibrium that collides with the chaotic attractor coalesces with the stable equilibrium that undergoes a Hopf bifurcation, through a saddle-node bifurcation [9].Besides voltage collapse, the existence of long-lived chaotic transients is also an issue of major safety concern in the operation of an electric power system. The latter commonly has protective relay devices, designed not to interfere with the transient voltage oscillations. Hence they do not play a stabilizing role, which could be actually necessary to avoid undesirable voltage transients, which may cause severe damage to expensive equipment such as rotor...

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Hard-limit induced chaos in a fundamental power system model

Cited by 68 publications

References 11 publications

Bifurcations, chaos and adaptive backstepping sliding mode control of a power system with excitation limitation

Bifurcations, chaos and adaptive backstepping sliding mode control of a power system with excitation limitation

FPGA design of a digital circuit for estimating chaotic characteristics from approximated nonlinear functions

Boundary crises, fractal basin boundaries, and electric power collapses

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