Scaling of transmission capacities in coarse-grained renewable electricity networks

Abstract

Network models of large-scale electricity systems feature only a limited spatial resolution, either due to lack of data or in order to reduce the complexity of the problem with respect to numerical calculations. In such cases, both the network topology, the load and the generation patterns below a given spatial scale are aggregated into representative nodes. This coarse-graining affects power flows and thus the resulting transmission needs of the system. We derive analytical scaling laws for measures of network transmission capacity and cost in coarse-grained renewable electricity networks. For the cost measure only a very weak scaling with the spatial resolution of the system is found. The analytical results are shown to describe the scaling of the transmission infrastructure measures for a simplified, but data-driven and spatially detailed model of the European electricity system with a high share of fluctuating renewable generation.

Multistability and variations in basin of attraction in power-grid systems

“…These two transition points are indicated by red vertical lines in figure 5(g), which are consistent with the more slowly decaying tail of the local peak in B. The evolution of the instantaneous frequency of each node for K ä [12,19]. They exhibit limit cycle behavior and do not converge to the synchronized state except for the cases of K=13 and K=14.…”

“…Even a small failure at a single transmission line can cause a massive cascade resulting in a large-scale blackout, which has motivated a number of recent studies focusing on the stability of power grids [1,2,3,4,5]. Some studies estimated structural stability arXiv:1807.09420v1 [nlin.CD] 25 Jul 2018 of power grids in response to the amount of transmission load when the electricity flows from power plants to substations [5,6,7,8,9,10,11,12,13], while others focused on the dynamical synchronization stability of power-grid nodes in response to the disturbance in their phase or frequency [14,15,16,17,18,19,20,21]. The synchronization stability refers to the ability to recover synchronization of power-grid nodes after the nodes get perturbed.…”

“…The blue (top right) and mint (bottom right) nodes are the consumers.In all cases, an external perturbation is applied to the red producer node such that ω red = 16.2, while the frequencies of all other nodes remain 0. (b) The evolution of the instantaneous frequency of each node for K ∈[12,19]. They exhibit limit cycle behavior and do not converge to the synchronized state except for the cases of K = 13 and K = 14.…”

Tracing carbon dioxide emissions in the European electricity markets

“…A clear suggestion about which of these two perspectives, direct vs. aggregated coupling, should be selected for the analysis of a specific system mostly depends on the grid structure and the spatial scale of the analysis. In this context, further understanding of the influence of the spatial scale in the network representation on the flow tracing results is needed [20].…”

Principal flow patterns across renewable electricity networks

“…(11) if both the distribution of the eigenvalues of Σ p and of T are heterogeneous, such that the distribution of the product of their ordered sequences dis- plays an even higher degree of heterogeneity. This condition of a heterogeneous distribution of the eigenvalues of Σ p is expressed by the comparatively small number of principal injection components, whereas for the eigenvalues of T it follows from the network topology which can to first order be approximated as a two-dimensional lattice [21]. Figure 7 shows for the detailed network representation with N = 1024 nodes the partial sums over the eigenvalues K k=1 λ f k depending on K, and the upper and lower bound derived from the majorisation in eqs.…”