Understanding Braess’ Paradox in power grids

Robust design of bicycle infrastructure networks

Promoting active mobility like cycling relies on the availability of well-connected, high-quality bicycle networks. However, expanding these networks over an extended planning horizon presents one of the most complex challenges in transport science. This complexity arises from the intricate interactions between infrastructure availability and usage, such as network spillover effects and mode choice substitutions. In this paper, we approach the problem from two perspectives: direct optimization methods, which generate near-optimal solutions using operations research techniques, and conceptual heuristics, which offer intuitive and scalable algorithms grounded in network science. Specifically, we compare direct welfare optimization with an inverse network percolation approach to planning cycle superhighway extensions in Copenhagen. Interestingly, while the more complex optimization models yield better overall welfare results, the improvements over simpler methods are small. More importantly, we demonstrate that the increased complexity of planning approaches generally makes them more vulnerable to input uncertainty, reflecting the bias-variance tradeoff. This issue is particularly relevant in the context of long-term planning, where conditions change during the implementation of the planned infrastructure expansions. Therefore, while planning bicycle infrastructure is important and renders exceptionally high benefit-cost ratios, considerations of robustness and ease of implementation may justify the use of more straightforward network-based methods.

Introduction to Focus Issue: Chimera states: From theory and experiments to technology and living systems

One of the pillars of modern science is the concept of symmetries. Spontaneously breaking such symmetries gives rise to non-trivial states, which can explain a variety of phenomena around us. Chimera states, characterized by the coexistence of localized synchronized and unsynchronized dynamics, are a novel example. This Focus Issue covers recent developments in the study of chimera states, from both theoretical and experimental points of view, including an emphasis on prospective practical realization for application in technology and living systems.

Braess's Paradox Analog in Physical Networks of Optimal Exploration

In stochastic exploration of geometrically embedded graphs, intuition suggests that providing a shortcut between a pair of nodes reduces the mean first passage time of the entire graph. Counterintuitively, we find a Braess's paradox analog. For regular diffusion, shortcuts can worsen the overall search efficiency of the network, although they bridge topologically distant nodes. We propose an optimization scheme under which each edge adapts its conductivity to minimize the graph's search time. The optimization reveals a relationship between the structure and diffusion exponent and a crossover from dense to sparse graphs as the exponent increases.

Management of resilient urban integrated energy system: State-of-the-art and future directions

The urban integrated energy system (UIES) is the fundamental infrastructure supporting the operation of resilient cities. The resilience of UIES plays a critical role in effectively responding to extreme events. We provide a comprehensive review on the management of resilient UIES. Firstly, we examine the existing studies on the resilience of UIES through quantitative and qualitative methodologies. Secondly, it points out that the coupling characteristics of UIES have a dual impact on resilience. The definition of UIES resilience can be understood from three perspectives, namely partial resilience versus total resilience, physical resilience versus digital resilience, and current resilience versus future resilience. Thirdly, this review summarizes the strategies for improving the resilience of UIES across three distinct stages, namely before, during, and after extreme events. The resilience of UIES can be enhanced by effective measures to prediction, adaptation, and assessment. Finally, the challenges faced by management of resilient UIES are presented and discussed, in terms of mitigating compound risks, modeling complex systems, addressing data collection and quality issue, and collaborating within multi stakeholders.

Resilience of transportation infrastructure networks to road failures

Anthropogenic climate change drives extreme weather events, leading to significant consequences for both society and the environment. This includes damage to road infrastructure, causing disruptions in transportation, obstructing access to emergency services, and hindering humanitarian organizations after natural disasters. In this study, we develop a novel method for analyzing the impacts of natural hazards on transportation networks rooted in the gravity model of travel, offering a fresh perspective to assess the repercussions of natural hazards on transportation network stability. Applying this approach to the Ahr valley flood of 2021, we discovered that the destruction of bridges and roads caused major bottlenecks, affecting areas considerably distant from the flood's epicenter. Furthermore, the flood-induced damage to the infrastructure also increased the response time of emergency vehicles, severely impeding the accessibility of emergency services. Our findings highlight the need for targeted road repair and reinforcement, with a focus on maintaining traffic flow for emergency responses. This research provides a new perspective that can aid in prioritizing transportation network resilience measures to reduce the economic and social costs of future extreme weather events.

Predicting Braess's paradox of power grids using graph neural networks

As an increasing number of renewable energy generators are integrated into the electrical grid, the necessity to add new transmission lines to facilitate power transfer and ensure grid stability becomes paramount. However, the addition of new transmission lines to the existing grid topology can lead to the emergence of Braess's paradox or even trigger grid failures. Hence, predicting where to add transmission lines to guarantee stable grid operation is of utmost importance. In this context, we employ deep learning to address this challenge and propose a graph neural network-based method for predicting Braess's paradox in electrical grids, framing the problem of adding new transmission lines causing Braess's paradox as a graph classification task. Taking into consideration the topological and electrical attributes of the grid, we select node features such as degree, closeness centrality, and power values. This approach assists the model in better understanding the relationships between nodes, enhancing the model's representational capabilities. Furthermore, we apply layered adaptive weighting to the output of the graph isomorphism network to emphasize the significance of hierarchical information that has a greater impact on the output, thus improving the model's generalization across electrical grids of varying scales. Experimental results on the IEEE 39, IEEE 57, and IEEE 118 standard test systems demonstrate the efficiency of the proposed method, achieving prediction accuracies of 93.8%, 88.8%, and 88.1%, respectively. Model visualization and ablation studies further validate the effectiveness of this approach.

Toward dynamic stability assessment of power grid topologies using graph neural networks

To mitigate climate change, the share of renewable energies in power production needs to be increased. Renewables introduce new challenges to power grids regarding the dynamic stability due to decentralization, reduced inertia, and volatility in production. Since dynamic stability simulations are intractable and exceedingly expensive for large grids, graph neural networks (GNNs) are a promising method to reduce the computational effort of analyzing the dynamic stability of power grids. As a testbed for GNN models, we generate new, large datasets of dynamic stability of synthetic power grids and provide them as an open-source resource to the research community. We find that GNNs are surprisingly effective at predicting the highly non-linear targets from topological information only. For the first time, performance that is suitable for practical use cases is achieved. Furthermore, we demonstrate the ability of these models to accurately identify particular vulnerable nodes in power grids, so-called troublemakers. Last, we find that GNNs trained on small grids generate accurate predictions on a large synthetic model of the Texan power grid, which illustrates the potential for real-world applications.

Power-grid vulnerability and its relation with network structure

Interconnected systems with critical infrastructures can be affected by small failures that may trigger a large-scale cascade of failures, such as blackouts in power grids. Vulnerability indices provide quantitative measures of a network resilience to component failures, assessing the break of information or energy flow in a system. Here, we focus on a network vulnerability analysis, that is, indices based solely on the network structure and its static characteristics, which are reliably available for most complex networks. This work studies the structural connectivity of power grids, assessing the main centrality measures in network science to identify vulnerable components (transmission lines or edges) to attacks and failures. Specifically, we consider centrality measures that implicitly model the power flow distribution in power systems. This framework allow us to show that the efficiency of the power flow in a grid can be highly sensitive to attacks on specific (central) edges. Numerical results are presented for randomly generated power-grid models and established power-grid benchmarks, where we demonstrate that the system's energy efficiency is more vulnerable to attacks on edges that are central to the power flow distribution. We expect that the vulnerability indices investigated in our work can be used to guide the design of structurally resilient power grids.

A new scenario for Braess's paradox in power grids

We consider several topologies of power grids and analyze how the addition of transmission lines affects their dynamics. The main example we are dealing with is a power grid that has a tree-like three-element motif at the periphery. We establish conditions where the addition of a transmission line in the motif enhances its stability or induces Braess's paradox and reduces stability of the entire grid. By using bifurcation theory and nonlocal stability analysis, we show that two scenarios for Braess's paradox are realized in the grid. The first scenario is well described and is associated with the disappearance of the synchronous mode. The second scenario has not been previously described and is associated with the reduction of nonlocal stability of the synchronous mode due to the appearance of asynchronous modes. The necessary conditions for stable operation of the grid, under the addition of a line, are derived. It is proved that the new scenario for Braess's paradox is realized in the grids with more complex topologies even when several lines are added in their bulks.