Coexistence of four different attractors in a fundamental power system model

Venkatasubramanian, V.; Ji, Weijun

doi:10.1109/81.751316

Cited by 74 publications

(25 citation statements)

References 11 publications

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“…The switching function of sliding mode control is defined as σ = k 1 e 1 + e 2 = k 1 e 1 +ė 1 + c 1 e 1 (10) and the parameters k 1 , c 1 are positive. Obviously, if the switching function σ = 0, then e 1 = e 2 = 0 andV ≤ 0.…”

Section: Adaptive Backstepping Sliding Mode Controlmentioning

confidence: 99%

“…This phenomenon, called multistability, has been observed in many fields of science. [7][8][9] Venkatasubramanian and Ji 10 reported four attractors coexisted phenomena in a power system, but no detail report on bifurcation and Lyapunov with changing parameters of system was given. Ma and Min 11 also investigated the coexistence of periodic orbits and chaos in a delayed power system.…”

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: Adaptive Backstepping Sliding Mode Controlmentioning

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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“…Nonlinear behavior and chaotic oscillations occurring in electrical systems have been extensively studied in recent years . Many electrical systems, such as permanent magnet synchronous motors , permanent magnet synchronous generators , induction motors , brushless dc motors , smart grids , and power system models show nonlinear and chaotic behaviors. The study of chaotic oscillations in power system models dates back to the 1990s when Venkatasubramanian and Wang et al .…”

Section: Introductionmentioning

confidence: 99%

Bifurcation, Chaos and its Control in A Fractional Order Power System Model with Uncertainties

Rajagopal¹,

Karthikeyan²,

Duraisamy³

et al. 2018

Asian Journal of Control

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The paper investigates the complex nonlinear behavior of a fractional order four dimension power system (FOFDPS). The discrete mathematical model of the FOFDPS is derived and presented. The equilibrium points along with the Eigen values of commensurate and incommensurate FOFDPS are presented. The existence of chaotic oscillations are supported by a positive Lyapunov exponent. Bifurcation plots are derived for both parameters and fractional orders to show the impact of the same on the dynamic behavior of FOFDPS. Having shown the existence of such complex behaviors in the FOFDPS, we present an adaptive fractional order sliding mode control (FOASMC) to suppress the chaotic oscillations. Numerical results are presented to support the theoretical results.

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“…Additionally, it was proved that after the subcritical Hopf bifurcations the excitation control with a voltage control device could induce sustained oscillations and the hard-limit can induce a stable limit cycle and further chaotic motions via a sequence of period-doubling bifurcations [26, 27]. Researchers even found the rare phenomenon of the coexistence of four different attractors including a stable equilibrium point, a stable limit cycle and two strange attractors [28]. A forth-order time-delayed model of power system was studied and coexisting phenomenon was discovered extensively [29].…”

Section: Introductionmentioning

confidence: 99%

Dynamics and Collapse in a Power System Model with Voltage Variation: The Damping Effect

Sun

Yuan

et al. 2016

PLoS ONE

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Complex nonlinear phenomena are investigated in a basic power system model of the single-machine-infinite-bus (SMIB) with a synchronous generator modeled by a classical third-order differential equation including both angle dynamics and voltage dynamics, the so-called flux decay equation. In contrast, for the second-order differential equation considering the angle dynamics only, it is the classical swing equation. Similarities and differences of the dynamics generated between the third-order model and the second-order one are studied. We mainly find that, for positive damping, these two models show quite similar behavior, namely, stable fixed point, stable limit cycle, and their coexistence for different parameters. However, for negative damping, the second-order system can only collapse, whereas for the third-order model, more complicated behavior may happen, such as stable fixed point, limit cycle, quasi-periodicity, and chaos. Interesting partial collapse phenomena for angle instability only and not for voltage instability are also found here, including collapse from quasi-periodicity and from chaos etc. These findings not only provide a basic physical picture for power system dynamics in the third-order model incorporating voltage dynamics, but also enable us a deeper understanding of the complex dynamical behavior and even leading to a design of oscillation damping in electric power systems.

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Coexistence of four different attractors in a fundamental power system model

Cited by 74 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

Bifurcation, Chaos and its Control in A Fractional Order Power System Model with Uncertainties

Dynamics and Collapse in a Power System Model with Voltage Variation: The Damping Effect

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