Bifurcations of grid-following rectifiers and routes to voltage instability in weak AC grids

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Journal / PublicationIEEE Transactions on Power Systems
Online published31 May 2022
Publication statusOnline published - 31 May 2022


As indispensable components in modern power systems, grid-following rectifiers would interact with the grid. Such interaction may lead to unexpected collapse of the ac bus voltage. In this paper, three routes to voltage instability are identified, namely, (i) supercritical Hopf bifurcation and successive saddle-node bifurcation of periodic orbits; (ii) subcritical Hopf bifurcation; and (iii) departure from a stable basin of attraction. It is also found that the rectifier-based system may undergo a Bautin bifurcation, which changes a Hopf bifurcation from supercritical to subcritical, or vice versa. The current loop of rectifiers has been found to play a crucial role in these bifurcation behaviors. Considering the inevitable and immediate voltage breakdown after the onset of a subcritical Hopf bifurcation, it is recommended to increase the bandwidth of the current loop to trigger the Bautin bifurcation, so that only supercritical Hopf bifurcation may occur. Furthermore, the original high-order and nonlinear model can be simplified to a reduced order system by focusing on the center manifold. Based on the reduced system, the occurrence mode of Hopf bifurcation can be confirmed by inspecting the first Lyapunov coefficient. Finally, relevant bifurcation diagrams are derived, providing practical design guidelines to avoid an eventual system collapse.

Research Area(s)

  • Bautin bifurcation, Bifurcation, center manifold, grid-following rectifier, Inverters, Phase locked loops, Power system dynamics, Power system stability, saddlenode bifurcation of periodic orbits, Stability analysis, supercritical and subcritical Hopf bifurcations, Voltage control, Voltage instability