ABSTRACT
In future power systems, electrical storage will be the key technology for balancing feed-in fluctuations. With increasing share of renewables and reduction of system inertia, the focus of research expands toward short-term grid dynamics and collective phenomena. Against this backdrop, Kuramoto-like power grids have been established as a sound mathematical modeling framework bridging between the simplified models from nonlinear dynamics and the more detailed models used in electrical engineering. However, they have a blind spot concerning grid components, which cannot be modeled by oscillator equations, and hence do not allow one to investigate storage-related issues from scratch. Our aim here is twofold: First, we remove this shortcoming by adopting a standard practice in electrical engineering and bring together Kuramoto-like and algebraic load-flow equations. This is a substantial extension of the current Kuramoto-like framework with arbitrary grid components. Second, we use this concept and demonstrate the implementation of a storage unit in a wind power application with realistic feed-in conditions. We show how to implement basic control strategies from electrical engineering, give insights into their potential with respect to frequency quality improvement, and point out their limitations by maximum capacity and finite-time response. With that, we provide a solid starting point for the integration of flexible storage units into Kuramoto-like grid models enabling to address current problems like smart storage control, optimal siting, and rough cost estimations.
ABSTRACT
We introduce a general procedure for directly ascertaining how many independent stochastic sources exist in a complex system modeled through a set of coupled Langevin equations of arbitrary dimension. The procedure is based on the computation of the eigenvalues and the corresponding eigenvectors of local diffusion matrices. We demonstrate our algorithm by applying it to two examples of systems showing Hopf bifurcation. We argue that computing the eigenvectors associated to the eigenvalues of the diffusion matrix at local mesh points in the phase space enables one to define vector fields of stochastic eigendirections. In particular, the eigenvector associated to the lowest eigenvalue defines the path of minimum stochastic forcing in phase space, and a transform to a new coordinate system aligned with the eigenvectors can increase the predictability of the system.
ABSTRACT
It is a big challenge in the analysis of experimental data to disentangle the unavoidable measurement noise from the intrinsic dynamical noise. Here we present a general operational method to extract measurement noise from stochastic time series even in the case when the amplitudes of measurement noise and uncontaminated signal are of the same order of magnitude. Our approach is based on a recently developed method for a nonparametric reconstruction of Langevin processes. Minimizing a proper non-negative function, the procedure is able to correctly extract strong measurement noise and to estimate drift and diffusion coefficients in the Langevin equation describing the evolution of the original uncorrupted signal. As input, the algorithm uses only the two first conditional moments extracted directly from the stochastic series and is therefore suitable for a broad panoply of different signals. To demonstrate the power of the method, we apply the algorithm to synthetic as well as climatological measurement data, namely, the daily North Atlantic Oscillation index, shedding light on the discussion of the nature of its underlying physical processes.
