Berlin 2015 – wissenschaftliches Programm
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AKE: Arbeitskreis Energie
AKE 15: Energy Systems (joint session DY/ AKE /SOE)
AKE 15.5: Vortrag
Donnerstag, 19. März 2015, 10:30–10:45, BH-N 243
Large-deviation study of the maximum-disturbance stability of power grids — •Alexander K. Hartmann1, Timo Dewenter1, Wiebke Heins2, and Benjamin Werther2 — 1Institut of Physics, University of Oldenburg — 2Institut for Electrical Energy Technology, Technical University of Clausthal
We study numerically the distribution of “maximum-disturbance” stability of power grids. The model is based on networks of oscillators. Here, we consider different ensembles of random networks, like standard Erdös-Renyi and two dimensional spacial networks. To access the distribution down to very small probabilities, we use specific large deviation techniques [1]. The stability is given by a conservative estimation of an asymptotic stability boundary, which is well known in stability theory [2,3]. The starting point is the matrix A defined by JTA+AJ =E, J being the Jacobean Matrix. By calculating the maximum disturbance of x, which results in the quadratic form V=xT A x=є(x) not being a Lyapunov-function of the system any longer, the boundaries for the stability can be found.
For comparsion, for the given networks also simple stability measures beased on shortest paths [4], on the eigenvalues of the Jacobi matrix and on a linearized power-flow model [5] are obtained.
[1] A.K. Hartmann, Eur. Phys. J. B 84, 627-634 (2011)
[2] R. Unbehauen, Systemtheorie (Vol. 2), Oldenbourg, Munich (1998)
[3] E.J. Davison and E.M. Kurak, Automatica 7, 627-636 (1971)
[4] A.K. Hartmann, Eur. Phys. J. B 87, 114 (2014)
[5] T. Dewenter and A.K. Hartmann, preprint arXiv:1411.5233 (2014)