arXiv subjects

Martin Rohden

Publications and source records attributed to Martin Rohden.

9 recordsLinked to original sources

arXiv2019

Competitive percolation strategies for network recovery

Restoring operation of critical infrastructure systems after catastrophic events is an important issue, inspiring work in multiple fields, including network science, civil engineering, and operations research. We consider the problem of finding the optimal order of repairing elements in power grids and similar infrastructure. Most existing methods either only consider system network structure, potentially ignoring important features, or incorporate component level details leading to complex optimization problems with limited scalability. We aim to narrow the gap between the two approaches. Analyzing realistic recovery strategies, we identify over- and undersupply penalties of commodities as primary contributions to reconstruction cost, and we demonstrate traditional network science methods, which maximize the largest connected component, are cost inefficient. We propose a novel competitive percolation recovery model accounting for node demand and supply, and network structure. Our model well approximates realistic recovery strategies, suppressing growth of the largest connected component through a process analogous to explosive percolation. Using synthetic power grids, we investigate the effect of network characteristics on recovery process efficiency. We learn that high structural redundancy enables reduced total cost and faster recovery, however, requires more information at each recovery step. We also confirm that decentralized supply in networks generally benefits recovery efforts.

nlin.AO↗

arXiv2019

Cascading failures in scale-free interdependent networks

Large cascades are a common occurrence in many natural and engineered complex systems. In this paper we explore the propagation of cascades across networks using realistic network topologies, such as heterogeneous degree distributions, as well as intra- and interlayer degree correlations. We find that three properties, scale-free degree distribution, internal network assortativity, and cross-network hub-to-hub connections, are all necessary components to significantly reduce the size of large cascades in the Bak-Tang-Wiesenfeld sandpile model. We demonstrate that correlations present in the structure of the multilayer network influence the dynamical cascading process and can prevent failures from spreading across connected layers. These findings highlight the importance of internal and cross-network topology in optimizing stability and robustness of interconnected systems.

nlin.AO↗

arXiv2017

Self-Organization of Dragon Kings

The mechanisms underlying cascading failures are often modeled via the paradigm of self-organized criticality. Here we introduce a simple model where nodes self-organize to be either weak or strong to failure which captures the trade-off between degradation and reinforcement of nodes inherent in many network systems. If strong nodes cannot fail, this leads to power law distributions of failure sizes with so-called "Black Swan" rare events. In contrast, if strong nodes fail once a sufficient fraction of their neighbors fail, this leads to "Dragon Kings", which are massive failures caused by mechanisms distinct from smaller failures. In our model, we find that once an initial failure size is above a critical value, the Dragon King mechanism kicks in, leading to piggybacking system-wide failures. We demonstrate that the size of the initial failed weak cluster predicts the likelihood of a Dragon King event with high accuracy and we develop a simple control strategy which also reveals that a random upgrade can inadvertently make the system more vulnerable. The Dragon Kings observed are self-organized, existing throughout the parameter regime.

physics.soc-ph↗

arXiv2017

Escape Routes, Weak Links, and Desynchronization in Fluctuation-driven Networks

Shifting our electricity generation from fossil fuel to renewable energy sources introduces large fluctuations to the power system. Here, we demonstrate how increased fluctuations, reduced damping and reduced intertia may undermine the dynamical robustness of power grid networks. Focusing on fundamental noise models, we derive analytic insights into which factors limit the dynamic robustness and how fluctuations may induce a system escape from an operating state. Moreover, we identify weak links in the grid that make it particularly vulnerable to fluctuations. These results thereby not only contribute to a theoretical understanding of how fluctuations act on distributed network dynamics, they may also help designing future renewable energy systems to be more robust.

nlin.AO↗

arXiv2016

Network susceptibilities: theory and applications

We introduce the concept of network susceptibilities quantifying the response of the collective dy- namics of a network to small parameter changes. We distinguish two types of susceptibilities: vertex susceptibilities and edge susceptibilities, measuring the responses due to changes in the properties of units and their interactions, respectively. We derive explicit forms of network susceptibilities for oscillator networks close to steady states and offer example applications for Kuramoto-type phase- oscillator models, power grid models and generic flow models. Focusing on the role of the network topology implies that these ideas can be easily generalized to other types of networks, in particular those characterizing flow, transport, or spreading phenomena. The concept of network susceptibil- ities is broadly applicable and may straightforwardly be transferred to all settings where networks responses of the collective dynamics to topological changes are essential.

nlin.AO↗

arXiv2016

Cascading Failures in AC Electricity Grids

Sudden failure of a single transmission element in a power grid can induce a domino effect of cascading failures, which can lead to the isolation of a large number of consumers or even to the failure of the entire grid. Here we present results of the simulation of cascading failures in power grids, using an alternating current (AC) model. We first apply this model to a regular square grid topology. For a random placement of consumers and generators on the grid, the probability to find more than a certain number of unsupplied consumers decays as a power law and obeys a scaling law with respect to system size. Varying the transmitted power threshold above which a transmission line fails does not seem to change the power law exponent $q \approx 1.6$. Furthermore, we study the influence of the placement of generators and consumers on the number of affected consumers and demonstrate that large clusters of generators and consumers are especially vulnerable to cascading failures. As a real-world topology we consider the German high-voltage transmission grid. Applying the dynamic AC model and considering a random placement of consumers, we find that the probability to disconnect more than a certain number of consumers depends strongly on the threshold. For large thresholds the decay is clearly exponential, while for small ones the decay is slow, indicating a power law decay.

nlin.AO↗

arXiv2015

Curing critical links in oscillator networks as power grid models

Modern societies crucially depend on the robust supply with electric energy. Blackouts of power grids can thus have far reaching consequences. During a blackout, often the failure of a single infrastructure, such as a critical transmission line, results in several subsequent failures that spread across large parts of the network. Preventing such large-scale outages is thus key for assuring a reliable power supply. Here we present a non-local curing strategy for oscillatory power grid networks based on the global collective redistribution of loads. We first identify critical links and compute residual capacities on alternative paths on the remaining network from the original flows. For each critical link, we upgrade lines that constitute bottlenecks on such paths. We demonstrate the viability of this strategy for random ensembles of network topologies as well as topologies derived from real transmission grids and compare the nonlocal strategy against local back-ups of critical links. These strategies are independent of the detailed grid dynamics and combined may serve as an effective guideline to reduce outages in power grid networks by intentionally strengthen optimally selected links.

nlin.AO↗

arXiv2015

Critical links and nonlocal rerouting in complex supply networks

Link failures repeatedly induce large-scale outages in power grids and other supply networks. Yet, it is still not well understood, which links are particularly prone to inducing such outages. Here we analyze how the nature and location of each link impact the network's capability to maintain stable supply. We propose two criteria to identify critical links on the basis of the topology and the load distribution of the network prior to link failure. They are determined via a link's redundant capacity and a renormalized linear response theory we derive. These criteria outperform critical link prediction based on local measures such as loads. The results not only further our understanding of the physics of supply networks in general. As both criteria are available before any outage from the state of normal operation, they may also help real-time monitoring of grid operation, employing counter-measures and support network planning and design.

physics.soc-ph↗

arXiv2013

Impact of network topology on synchrony of oscillatory power grids

Replacing conventional power sources by renewable sources in current power grids drastically alters their structure and functionality. The resulting grid will be far more decentralized with an distinctly different topology. Here we analyze the impact of grid topologies on spontaneous synchronization, considering regular, random and small-world topologies and focusing on the influence of decentralization. We employ the classic model of power grids modeling consumers and sources as second order oscillators. We first analyze the global dynamics of the simplest non-trivial (two-node) network that exhibit a synchronous (normal operation) state, a limit cycle (power outage) and coexistence of both. Second, we estimate stability thresholds for the collective dynamics of small network motifs, in particular star-like networks and regular grid motifs. For larger networks we numerically investigate decentralization scenarios finding that decentralization itself may support power grids in reaching stable synchrony for lower lines transmission capacities. Decentralization may thus be beneficial for power grids, regardless of their special resulting topology. Regular grids exhibit a specific transition behavior not found for random or small-world grids.

nlin.AO↗