Complex Couplings – A universal, adaptive and bilinear formulation of power grid dynamics
arxiv(2023)
摘要
The paper is now published in PRX Enegry. Please refer to the PRX version
from now on.
Anna Büttner and Frank Hellmann. "Complex Couplings-A Universal, Adaptive,
and Bilinear Formulation of Power Grid Dynamics."
The energy transition introduces new classes of dynamical actors into the
power grid. There is a growing need for so-called grid-forming inverters (GFIs)
that can contribute to dynamic grid stability as the share of synchronous
generators decreases. Understanding the collective behavior and stability of
future grids, featuring a heterogeneous mix of dynamics, remains an urgent and
challenging task. Two recent advances in describing such modern power grid
dynamics have made this problem more tractable: First, the normal form for
grid-forming actors provides a uniform, technology-neutral description of
plausible grid dynamics, including grid-forming inverters and synchronous
machines. Secondly, the notion of the complex frequency has been introduced to
effortlessly describe how the nodal dynamics influence the power flows in the
grid. The major contribution of this paper is to show how the normal form
approach and the complex frequency dynamics of power grids combine, and how
they relate naturally to adaptive dynamical networks and control affine
systems. Using normal form and complex frequency, we derive a remarkably
elementary and universal equation for the collective grid dynamics. Notably, we
obtain an elegant equation entirely in terms of a matrix of complex couplings,
in which the network topology does not explicitly appear. These complex
couplings give rise to new adaptive network formulations of future power grid
dynamics. We give a new formulation of the Kuramoto model with inertia as a
special case.
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