Modeling and Simulation for Bifurcations of SSR in Large Wind Farms

Majdi M. Alomari, Mohammad Sabati, Mohammad S. Widyan, Nafesah I. Alshdaifat


Bifurcations of subsynchronous resonance (SSR) is applied to the induction generator (IG) based wind farms connected to series compensated lines. The developed first system of the IEEE second benchmark model of subsynchronous resonance is considered. The system studied can be mathematically modeled as a set of first order nonlinear ordinary differential equations with a compensation factor as a bifurcation parameter. Therefore, bifurcation theory can be applied to the nonlinear dynamical systems. The impress of both torsional interaction and induction generator effect are considered. Bifurcations of SSR are studied for a wide range of series compensation levels in the cases of various sizes of wind farms and various wind farm power outputs. The results show that Hopf bifurcations may occur in large wind farms based on double-cage IGs at high level of series compensation. When the size of wind farm increases, the Hopf bifurcation point initially shifts to the left at a less value of compensation then shifts to the right at a larger value of compensation with a supercritical Hopf bifurcation remains in all cases. This resulted in only quantitative changes in Hopf bifurcation for the case of variation in wind farm size. On the other hand, when the power output of a large wind farm increases the Hopf bifurcation point shifts a little to the left at a slightly less value of compensation. On the contrary, the type of Hopf bifurcation changes from subcritical to supercritical. Therefore, the impact of the variation in the wind farm size on bifurcation is only of a quantitative change, while the impact of variation in the power output is mainly a qualitative change.

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Hopf Bifurcation; Subsynchronous Resonance; Wind Turbine; Induction Generator.

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