Hard limit induced oscillations

Jiang, Xun; Schättler, Heinz; Zaborszky, J.; Venkatasubramanian, V.

doi:10.1109/iscas.1995.521472

Cited by 10 publications

(7 citation statements)

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“…Small disturbance stability assessment cannot predict the effects of such limits. It has been shown previously [5], [6] that stable limit cycles may be induced by state limits. Furthermore, these limit-induced limit cycles can coexist with other stable and unstable attractors, for values of K A both above and below K * A .…”

Section: Introductionmentioning

confidence: 89%

Limit-induced stable limit cycles in power systems

Reddy

Hiskens

2005

2005 IEEE Russia Power Tech

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Abstract-Heavily loaded power systems are susceptible to Hopf bifurcations, and consequent oscillatory instability. The onset of instability can be predicted by small disturbance (eigenvalue) analysis, but the ensuring behaviour may depend strongly on nonlinearities within the system. In particular, physical limits place bounds on the divergent behaviour of states. This paper explores the situation where generator field-voltage limits capture behaviour, giving rise to a stable (though non-smooth) limit cycle. It is shown that shooting methods can be adapted to solve for such non-smooth limit-induced limit cycles. By continuing branches of limit-induced and smooth limit cycles, the paper established the co-existence of equilibria, smooth and non-smooth limit cycles. Furthermore, it is shown that when branches of limit-induced and smooth limit cycles merge, the limit cycles are annihilated at a grazing bifurcation.

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Section: Introductionmentioning

confidence: 89%

Limit-induced stable limit cycles in power systems

Reddy

Hiskens

2005

2005 IEEE Russia Power Tech

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“…Given any initial condition (x 0 1 ; x 0 2 ) 2 I 2 , in positive time, i.e., for t 0, there exists a unique solution starting from (x 0 1 ; x 0 2 ) which satisfies (1)- (2); however, in negative time, neither existence nor uniqueness of solutions can be guaranteed [2], [3]. In other words, it can be proved that the dynamics (1)- (2) admits a positive semiflow but not a flow in general [2].…”

Section: Problem Formulationmentioning

confidence: 99%

Stability analysis of continuous time planar systems with state saturation nonlinearity

Mantri

Saberi²,

Venkatasubramanian³

1998

IEEE Trans. Circuits Syst. I

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“…Note that when the matrix A is a not a Hurwitz matrix, it can indeed be proved that there exist state saturation related stable limit cycles as well as more complicated limit sets such as homoclinic orbits for the nonlinear dynamics 6 [3]. However, the proposition above proves a very useful result that the planar nonlinear system 6 contains no limit cycles (stable or unstable) whenever the matrix A is a Hurwitz matrix.…”

Section: Problem Formulationmentioning

confidence: 90%

“…Given any initial condition (x which satisfies (1)- (2); however, in negative time, neither existence nor uniqueness of solutions can be guaranteed [2], [3]. In other words, it can be proved that the dynamics (1)- (2) admits a positive semiflow but not a flow in general [2].…”

Section: Problem Formulationmentioning

confidence: 99%

“…The effects of saturation nonlinearities or system hardlimits are always significant in modeling physical systems and need to be considered for a better analysis. The qualitative behavior of large nonlinear systems subject to state saturation (under the name of state limits) was investigated in [2] and [3] motivated by the phenomena in power system models. In this brief, we have adopted the model developed in [2] for the case of a continuous time planar linear system subject to hard-limits on its states.…”

Section: Introductionmentioning

confidence: 99%

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