Doubly-Fed Induction Generator (DFIG) Wind Turbine (WT) is rather sensitive to power system faults and requires specific power converter protection, namely a crowbar. When the crowbar is triggered, the rotor is short circuited over the crowbar impedance, the rotor-side converter (RSC) is incapacitated and therefore the DFIG operates as a squirrel-cage induction generator (SCIG) that tends to drain large amount of reactive power from the grid during fault, potentially causing a voltage drop. Therefore, in order to enhance the transient stability and damping of the electro-mechanical oscillations of a grid-connected DFIG wind farm, in this paper we propose the use of DFIG based Low-voltage Ride Through (LVRT) scheme including crowbar, RSC, GSC (Grid-side converter) and PSS (Power System Stabilizers)

The paper is concerned with the Bose-Einstein condensate described by the attractive Gross-Pitaevskii equation in R 2 , where the external potential is unbounded from below. We show that when the interaction strength increases to a critical value, the Gross-Pitaevskii minimizer collapses to one singular point and we analyze the details of the collapse exactly up to the leading order.

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We study the large-time behavior of bounded from below solutions of parabolic viscous Hamilton-Jacobi Equations in the whole space R N in the case of superquadratic Hamiltonians. Existence and uniqueness of such solutions are shown in a very general framework, namely when the source term and the initial data are only bounded from below with an arbitrary growth at infinity. Our main result is that these solutions have an ergodic behavior when t → +∞, i.e., they behave like λ * t + φ(x) where λ * is the maximal ergodic constant and φ is a solution of the associated ergodic problem. The main originality of this result comes from the generality of the data: in particular, the initial data may have a completely different growth at infinity from those of the solution of the ergodic problem.

We consider a Bose-Einstein condensate in a 2D dilute Bose gas, with an external potential and an interaction potential containing both of the shortrange attractive self-interaction and the long-range self-gravitating effect. We prove the existence of minimizers and analyze their behavior when the strength of the attractive interaction converges to a critical value. The universal blow-up profile is the unique optimizer of a Gagliardo-Nirenberg interpolation inequality.MSC: 35Q40; 46N50.