Quasi-stationarity of electric power grid dynamics based on a spatially embedded Kuramoto model

Abstract

Abstract-A novel and simple network model that is capable to reproduce quasi-stationary behavior and propagation phenomena in electric power grid dynamics is introduced. A new Kuramoto approximation to distributed generator dynamics is obtained from combining a continuous spatial interaction function with a discrete lattice model representing generator positions and network structure over a continuous spatial domain. At hand of model properties and a numerical study quasi-stationarity of electric power grid dynamics results, being related to non-vanishing fluctuation and oscillations in stationary state.

Synchronization in complex networks of phase oscillators: A survey

“…Notice that, with the exception of the inertial terms M iθi and the possibly non-unit coefficients D i , the power network dynamics (8)-(10) are a perfect electrical analog of the coupled oscillator model (1) with ω i ∈ {−P l,i , P m,i , P d,i }. Thus, it is not surprising that scientists from different disciplines recently advocated coupled oscillator approaches to analyze synchronization in power networks (Tanaka et al, 1997;Subbarao et al, 2001;Hill and Chen, 2006;Filatrella et al, 2008;Buzna et al, 2009;Fioriti et al, 2009;Simpson-Porco et al, 2013;Dörfler and Bullo, 2012b;Rohden et al, 2012;Dörfler et al, 2013;Mangesius et al, 2012;Motter et al, 2013;Ainsworth and Grijalva, 2013). The theoretical tools presented in this article establish how frequency synchronization in power networks depend on the nodal parameters (P l,i , P m,i , P d,i ) as well as the interconnecting electrical network with weights a ij .…”

“…The continuum-limit model has enjoyed a considerable amount of attention by the physics and dynamics communities. Related controltheoretical applications of the continuum-limit model are estimation of gait cycles (Tilton et al, 2012), spatial power grid modeling and analysis (Mangesius et al, 2012), and game theoretic approaches (Yin et al, 2012).…”

On the synchronization of spatially coupled oscillators

“…Interestingly, analogous considerations regard also the study of the electric power grid dynamics where, again, the Kuramoto model proves to be an agile and useful model tool. In particular, [11] describes a spatially embedded Kuramoto dynamics that involves a constant delay proportional to the spatial distance between the oscillators, phase shifts caused by transmission delays and a coupling function that decreases with the distance. More in general, the basic idea that the distances among the agents affect the synchronization dynamics can be find also in [9], where it is considered the behavior of a lattice of oscillators that interact with a power-law coupling strength.…”

Distributed Widely Linear Kalman Filtering for Frequency Estimation in Power Networks

“…Currently used frequency estimation techniques include: i) Fourier transform approaches [4]- [7], ii) gradient decent and least squares adaptive estimation [8], and iii) state space methods and Kalman filters [9]- [12]. However, these are typically designed for single-phase systems and often assume balanced operating conditions (equal voltage amplitudes and equally spaced phases) and are therefore inadequate for the demands of modern three-phase and dynamically optimised power systems.…”