How dead ends undermine power grid stability

Abstract

The cheapest and thus widespread way to add new generators to a high-voltage power grid is by a simple tree-like connection scheme. However, it is not entirely clear how such locally cost-minimizing connection schemes affect overall system performance, in particular the stability against blackouts. Here we investigate how local patterns in the network topology influence a power grid's ability to withstand blackout-prone large perturbations. Employing basin stability, a nonlinear concept, we find in numerical simulations of artificially generated power grids that tree-like connection schemes-so-called dead ends and dead trees-strongly diminish stability. A case study of the Northern European power system confirms this result and demonstrates that the inverse is also true: repairing dead ends by addition of a few transmission lines substantially enhances stability. This may indicate a topological design principle for future power grids: avoid dead ends.

Building blocks of the basin stability of power grids

“…The basin stability gradually increases as K increases and reaches the maximum (unity) at large K [ Fig. 2(a)], which is the same as the infinite-bus-bar model (for a node of interest, taking all of the other nodes as the environment) transition of basin stability as a function of coupling strength [18].…”

“…Besides the node i, the other nodes j i have the initial phase θ j = 0 and angular velocity ω j = 0. We consider the system is synchronized and stable when the system converges with the numerical convergence criteria [18,20], namely, the time derivative of angular frequencyω < 5 × 10 −2 and the angular frequency ω < 5 × 10 −2 for all of the nodes.…”

“…The governing dynamics for the synchronous interaction between power-grid nodes is often described as the second-order Kuramoto-type model [12,[15][16][17][18][19]21]:…”

“…Following Refs. [16,18,19], we set the dissipation constant α = 0.1 for all of the nodes. The initial random perturbation is assigned for given node i as −100 ≤ ω i ≤ 100 and −π ≤ θ i < π.…”

“…Since calculating basin stability requires the Monte Carlo sampling of nonlinear systems, it is computationally expensive. Accordingly, it is suggested to use the connectiontopology-based identification method-namely, the topological characteristics such as dead-end, dead-tree, and detourto identify nodes with large or small basin stability values for computational tractability [17][18][19]. They exploit the correlation between basin stability and topological characteristics of nodes.…”