Local Bifurcation Analysis of One Parameter in the Greitzer’s Model with a General Compressor Characteristic

Meskine, Naima; Kessal, Mohand; Seba, Djamila

doi:10.1007/s00009-021-01933-z

Cited by 2 publications

(2 citation statements)

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“…Regarding the bifurcation characteristics of the non‐smooth DFIG model containing dead zones and limits in the control link, the causes of switching‐type chaotic oscillations were analyzed, and non‐smooth bifurcation in the control system of a non‐smooth DFIG due to the limiting and dead zones was investigated to reveal the influence of the control system on the system stability from the perspective of non‐smooth bifurcation 10,11 . In contrast to non‐smooth bifurcation, the smooth Hopf bifurcation phenomenon has been widely demonstrated in power systems 12–14 . Regarding the type of Hopf bifurcation, a nonlinear time‐domain simulation method was used to determine the Hopf bifurcation category of a hydroelectric DC islanding system 15 .…”

Section: Introductionmentioning

confidence: 99%

“…10,11 In contrast to non-smooth bifurcation, the smooth Hopf bifurcation phenomenon has been widely demonstrated in power systems. [12][13][14] Regarding the type of Hopf bifurcation, a nonlinear time-domain simulation method was used to determine the Hopf bifurcation category of a hydroelectric DC islanding system. 15 The stable limit ring formed by the supercritical Hopf occurred in the Lorenz system theoretically using the first Lyapunov coefficient.…”

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confidence: 99%

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Equivalent dimensionality reduction method of doubly‐fed induction generator model and discrimination of Hopf bifurcation type

Chen

Wei

et al. 2023

Energy Science & Engineering

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The strong coupling, multivariate, and nonlinear characteristics of the mathematical model of a doubly-fed induction generator (DFIG) make it challenging to analyze the bifurcation category of the DFIG. Therefore, in this study, we developed a method for analyzing the DFIG model via topologically equivalent dimensionality reduction in the neighborhood of bifurcation values based on the central manifold theorem and realized the discrimination of the Hopf bifurcation type of the DFIG. We established a complex frequency domain model of the DFIG and then calculated the critical open-loop gain point using the root trajectory method to obtain the relationship between the critical open-loop gain point and Hopf bifurcation. Thereafter, we performed topological equivalence dimensionality reduction in the neighborhood of the DFIG bifurcation values based on the central manifold theorem. Subsequently, the Hopf bifurcation type of the system was determined using the stability index (first Lyapunov exponent) of the Hopf bifurcation. Finally, a nonlinear time-domain simulation was used to verify that the four and two-dimensional DFIGs generate a stable limit cycle by supercritical Hopf bifurcation under the tuning parameter. The results indicated that the proposed method was feasible and effective in the neighborhood of bifurcation values in the state parameter space of DFIG, which provides a theoretical basis for the control of Hopf bifurcation of the DFIG.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%