Curing critical links in oscillator networks as power flow models

Abstract

Modern societies crucially depend on the robust supply with electric energy so that blackouts of power grids can have far reaching consequences. Typically, large scale blackouts take place after a cascade of failures: the failure of a single infrastructure component, such as a critical transmission line, results in several subsequent failures that spread across large parts of the network. Improving the robustness of a network to prevent such secondary failures is thus key for assuring a reliable power supply. In this article we analyze the nonlocal rerouting of power flows after transmission line failures for a simplified AC power grid model and compare different strategies to improve network robustness. We identify critical links in the grid and compute alternative pathways to quantify the grid's redundant capacity and to find bottlenecks along the pathways. Different strategies are developed and tested to increase transmission capacities to restore stability with respect to transmission line failures. We show that local and nonlocal strategies typically perform alike: one can equally well cure critical links by providing backup capacities locally or by extending the capacities of bottleneck links at remote locations. OPEN ACCESS RECEIVED

Stability and control of power grids with diluted network topology

“…If we denote the eigenvalues of the matrix M by µ, i.e., |µI − M| = 0, then we have to solve quadratic equations of the type λ 2 + λα − σµ = 0 in order to determine the eigenvalues of the matrix G defined in eq. (14). The eigenvalues are given by λ = −α ± α 2 + 4µσ 2 (16) and depending on the properties of M the following holds:…”

“…Recently the model has been used to investigate the self-synchronization emerging in disordered arrays of underdamped Josephson junctions 4 as well as to show the emergence of explosive synchronization 5 in a network of rotators whenever the natural frequency is chosen to be proportional to the node degree. Nowadays the Kuramoto model with inertia is a standard mathematical model used to study the dynamical behavior of power generators and consumers [6][7][8][9][10][11][12][13][14] since it captures the essential dynamical features of a power grid on coarse scales, but is still simple enough to allow for a comprehensive understanding of the fundamental properties of power grid dynamics.…”

On structural and dynamical factors determining the integrated basin instability of power-grid nodes

“…If finding the critical lines to prevent the power outage is the main purpose of the DC approximation, it is possible to set more sophisticated strategies to improve power grids' performance with this more realistic AC approximation. Rohden et al 37 compared the strategies to heal the damaged power grid and Tchawou et al 41 suggested a control strategy to maintain the synchronization. Li et al 38 and Tchuisseu et al 42 tried to improve power grids' stability by optimization and dynamic demand control, respectively.…”

Bridging between load-flow and Kuramoto-like power grid models: A flexible approach to integrating electrical storage units

“…It is derived from the original Kuramoto model, which describes the phase dynamics of coupled oscillators, in particular the phase transition from incoherence to self-organized synchronization 9,10 . Kuramoto-like models have been used to address various issues of power system dynamics and topology-stability interplay [11][12][13][14][15][16][17][18] . In a previous work 6 , it was shown how the turbulent-like character of wind feed-in, in particular its intermittency, is directly transferred into frequency and voltage fluctuations.…”