Oliver Kamps

Self-organized synchronization and voltage stability in networks of synchronous machines

The integration of renewable energy sources in the course of the energy transition is accompanied by grid decentralization and fluctuating power feed-in characteristics. This development raises novel challenges for power system stability and design. We investigate power system stability from the viewpoint of self-organized synchronization aspects. In this approach, the power grid is represented by a network of synchronous machines. We supplement the classical Kuramoto-like network model, which assumes constant voltages, with dynamical voltage equations, and thus obtain an extended model, that incorporates the coupled categories voltage stability and rotor angle synchronization. We compare disturbance scenarios in small systems simulated on the basis of both classical and extended model and we discuss resultant implications and possible applications to complex modern power grids.

Bridging from Eulerian to Lagrangian statistics in 3D hydro- and magnetohydrodynamic turbulent flows

We present measurements of conditional probability density functions (PDFs) that allow one to systematically bridge from Eulerian to Lagrangian statistics in fully developed 3D turbulence. The transition is investigated for hydro- as well as magnetohydrodynamic flows and comparisons are drawn. Significant differences in the transition PDFs are observed for these flows and traced back to the differing coherent structures. In particular, we address the problem of an increasing degree of intermittency going from Eulerian to Lagrangian coordinates by means of the conditional PDFs involved in this transformation. First simple models of these PDFs are investigated in order to distinguish different contributions to the degree of Lagrangian intermittency.

Exact relation between Eulerian and Lagrangian velocity increment statistics.

We present a formal connection between Lagrangian and Eulerian velocity increment distributions which is applicable to a wide range of turbulent systems ranging from turbulence in incompressible fluids to magnetohydrodynamic turbulence. For the case of the inverse cascade regime of two-dimensional turbulence we numerically estimate the transition probabilities involved in this connection. In this context we are able to directly identify the processes leading to strongly non-Gaussian statistics for the Lagrangian velocity increments.

Lagrangian investigation of two-dimensional decaying turbulence

We present a numerical investigation of two-dimensional decaying turbulence in the Lagrangian framework. Focusing on single particle statistics, we investigate Lagrangian trajectories in a freely evolving turbulent velocity field. The dynamical evolution of the tracer particles is strongly dominated by the emergence and evolution of coherent structures. For a statistical analysis we focus on the Lagrangian acceleration as a central quantity. For more geometrical aspects we investigate the curvature along the trajectories. We find strong signatures for the self-similar universal behavior.

Two-point vorticity statistics in the inverse cascade of two-dimensional turbulence

A statistical analysis of the two-point vorticity statistics in the inverse energy cascade of two-dimensional turbulence is presented in terms of probability density functions (PDFs). Evolution equations for the PDFs are derived in the framework of the Lundgren–Monin–Novikov hierarchy, and the unclosed terms are studied with the help of direct numerical simulations (DNS). Furthermore, the unclosed terms are evaluated in a Gaussian approximation and compared to the DNS results. It turns out that the statistical equations can be interpreted in terms of the dynamics of screened vortices. The two-point statistics is related to the dynamics of two point vortices with screened velocity field, where an effective relative motion of the two point vortices originating from the turbulent surroundings is identified to be a major characteristics of the dynamics underlying the inverse cascade.Fully developed turbulent flows are systems far from equilibrium giving rise to a transport of energy or enstrophy across scales. Up to now, no generally accepted theoretical description of this transport process has emerged although the phenomenological theory based on the works of Kolmogorov, Onsager, Heisenberg and their successors is quite successful in describing the gross features of turbulent fields (we refer to the monographs [1], [2]). Two-dimensional turbulent flows play a prominent role due to the existence of a direct as well as an inverse cascade, as has been emphasized in the seminal work of Kraichnan [3]. The coexistence of both cascades has been convincingly demonstrated by Boffetta and Musacchio [4]. Recently, a detailed analysis of the contour lines of zero vorticity has revealed interesting scaling behaviour pointing to the existence of nontrivial multi-point statistics of vorticity in the inverse cascade [5]. The inverse cascade is a central issue in classical nonequilibrium physics [6]. The present contribution is concerned with the twopoint statistics of vorticity in the inverse cascade. Starting from the hierarchy of evolution equations for multipoint probability distributions of vorticity, we shall perform a detailed examination of the partial differential equation defining the probability distribution of the vorticity increment relying on input from direct numerical simulation (DNS).

The footprint of atmospheric turbulence in power grid frequency measurements

Fluctuating wind energy makes a stable grid operation challenging. Due to the direct contact with atmospheric turbulence, intermittent short-term variations in the wind speed are converted to power fluctuations that cause transient imbalances in the grid. We investigate the impact of wind energy feed-in on short-term fluctuations in the frequency of the public power grid, which we have measured in our local distribution grid. By conditioning on wind power production data, provided by the ENTSO-E transparency platform, we demonstrate that wind energy feed-in has a measurable effect on frequency increment statistics for short time scales (< 1 sec) that are below the activation time of frequency control. Our results are in accordance with previous numerical studies of self-organized synchronization in power grids under intermittent perturbation and rise new challenges for a stable operation of future power grids fed by a high share of renewable generation.

Statistical Description of Turbulent Flows

In this article we review two different approaches to the statistical description of turbulent flows in terms of evolution equations for probability density functions (PDFs), namely a description of the turbulent cascade by a Fokker- Planck equation, as well as kinetic equations in terms of the theoretical framework of the Lundgren-Monin-Novikov hierarchy. In both cases conditional averages are the building blocks that allow to make a connection to experimental or numerical data. Professor Dr. Rudolf Friedrich made central contributions to both of these approaches, which we want to highlight here.

Lagrangian Acceleration Statistics in 2D and 3D Turbulence

In this paper we compare Lagrangian statistical quantities in the direct energy cascade of three-dimensional turbulence and the corresponding observables for the case of the inverse energy cascade in two dimensions. We focus on the acceleration of a tracer particle along its trajectory. Interpreting the acceleration as a stochastic process we show that for both systems the Markov time scale, which is an indicator for the length of the memory of a stochastic process, is in the order of magnitude of the Lagrangian integral time scale.

Long Time Memory of Lagrangian Acceleration Statistics in 2D and 3D Turbulence

In this paper we report on a comparison of Lagrangian acceleration statistics in the direct energy cascade of three-dimensional turbulence and the corresponding observables for the case of the inverse energy cascade in two dimensions. We focus on the time scales describing the memory of the acceleration statistics of a tracer particle. We show that for both systems the Markov time scale, which is an indicator for the length of the memory of a stochastic process, is in the order of magnitude of the Lagrangian integral time scale. We also show that the decorrelation time for the cross-correlation between the squared components of the acceleration is larger than the integral time scale.

Power Grids as Synergetic Systems

In this article we study power grids from the viewpoint of Synergetics. We show that the typical behavior of self-organizing systems like phase transitions and critical fluctuations can be observed in models for the dynamics of power grids . Therefore we numerically investigate a model, where the phase and voltage dynamics are represented by Kuramoto-like equations. For the topology of the grid we use real world data from the northern Europe high voltage transmission grid.