Analysis of voltage control systems exhibiting Hopf bifurcation

Rajagopalan, C.; Sauer, Peter W.; Pai, M.A.

doi:10.1109/cdc.1989.70129

Cited by 40 publications

(8 citation statements)

References 5 publications

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“…The Hopf bifurcation for the constant power case has been studied and is subcritical [28]. This means that, as the loading is increased towards the bifurcation point, there is an unstable limit cycle which bounds the region of attraction of the stable system.…”

Section: I1mentioning

confidence: 99%

Structural stability in power systems-effect of load models

Pai

Sauer

Lesieutre

et al. 1995

IEEE Trans. Power Syst.

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In this paper a new notion of power system stability, is introduced, namely structural stability, and its significance in the context of load modeling is examined. It is shown that beyond certain values of load indices in the case of static models and beyond certain value of the dynamic component in the load such as induction motors, the system may become structurally unstable. The immediate application of these results is in the voltage stability problems.

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Section: I1mentioning

confidence: 99%

Structural stability in power systems-effect of load models

Pai

Sauer

Lesieutre

et al. 1995

IEEE Trans. Power Syst.

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“…Application of normal form theory to power system examples is given by Vittal et al (1992Vittal et al ( , pp. 2553 and examples of the application of centre-manifold theory to power systems are given by Rajgopalan et al (1989), Chiang et al (1989) and Ajjarapu & Lee (1992).…”

Section: Xs = (8)mentioning

confidence: 99%

Parallel processing in dynamic simulation of power systems

Bose

1993

Sadhana

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The dynamic behaviour of a large interconnected electric power system is characterized by a simultaneous set of nonlinear algebraic and ordinary differential equations. The solution is obtained by numerical methods and the simulation of the transient behaviour for a few seconds after a fault is the standard analytical procedure used in planning and operational studies of the system. The need for on-line simulation in near real time for more efficient operation has encouraged the search for faster solution methods and the use of parallel computers for this purpose has attracted the attention of many researchers. The success of paraUelization depends on three factors: the problem structure, the computer architecture, and the algorithm that takes maximum advantage of both. In this problem, the generator equations are only coupled through the electrical network providing some parallelization in (variable) space, and a solution is needed at each time step leading to some parallelization in time (waveform relaxation). However, since the problem formulation is not completely decoupled, parallel algorithms can only be developed by trading off any relaxation with a degradation in convergence. The fastest sequential algorithm used today is the combination of implicit trapezoidal integration with a dishonest Newton solution. The Newton algorithm is not parallel at all but has the fastest convergence while a Gauss-Jacobi algorithm is completely parallel but converges very slowly. A relaxation of the Newton algorithm appears to be a good compromise. As for the parallel hardware, the coupling seems to require significant communication between processors thus favouring a data-sharing architecture over a messagepassing hypercube. Special architectures to match the problem structure have also been an area of investigation. This paper elaborates on the above issues and assesses the present state-of-the-art.

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“…Lossy transmission lines can prevent the existence of a Lyapunov function (Narasimhamurthi 1984;Chiang 1989). T h e addition of exciter systems and load dynamics to the swing equations, however, is probably l~he primary cause of the existence of local dynamic phenomena such as the Hopf bifurcation (Abed & Varaiya 1984;Rajagopalan et al 1989) Load characteristics are known to have a significant effect on system dynamics. Classical load models such as the constant PQ, constant impedance, and constant current models are not appropriate to capture voltage dynamics.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation and chaos in power systems

Tan

Varghese

Varaiya

et al. 1993

Sadhana

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A detailed example of a power system model with load dynamics is studied by investigating qualitative changes or bifurcations in its behaviour as a reactive power demand at one load bus is increased. In addition to the saddle-node bifurcation often associated with voltage collapse, we find other bifurcation phenomena which include Hopf bifurcation, cyclic fold bifurcation, period doubling bifurcation, and the emergence of chaos. The presence of these dynamic bifurcations motivates a re-examination of the role of saddle-node bifurcations in the voltage collapse phenomenon. In fact, simulation results suggest that voltage collapse may take place before the reactive power demand is increased to the system steady-state operating limit where a saddle-node bifurcation is detected. We also consider the role that the algebraic constraints imposed by some load models may play in the global analysis of the attractors of the system. Implications for power system operations are drawn.

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Analysis of voltage control systems exhibiting Hopf bifurcation

Cited by 40 publications

References 5 publications

Structural stability in power systems-effect of load models

Structural stability in power systems-effect of load models

Parallel processing in dynamic simulation of power systems

Bifurcation and chaos in power systems

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