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.
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http://dx.doi.org/10.1063/5.0180204 | DOI Listing |
Phys Rev Lett
August 2024
Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
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.
View Article and Find Full Text PDFChaos
January 2024
School of Electronics and Information Engineering, Guangxi Normal University, Guilin, Guangxi 541004, China.
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.
View Article and Find Full Text PDFChaos
November 2022
Department of Nonlinear Dynamics, Institute of Applied Physics of RAS, 46 Ulyanov Str., 603950 Nizhny Novgorod, Russia.
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.
View Article and Find Full Text PDFNature
October 2019
Department of Physics and Astronomy, Northwestern University, Evanston, IL, USA.
Microfluidic systems are now being designed with precision as miniaturized fluid manipulation devices that can execute increasingly complex tasks. However, their operation often requires numerous external control devices owing to the typically linear nature of microscale flows, which has hampered the development of integrated control mechanisms. Here we address this difficulty by designing microfluidic networks that exhibit a nonlinear relation between the applied pressure and the flow rate, which can be harnessed to switch the direction of internal flows solely by manipulating the input and/or output pressures.
View Article and Find Full Text PDFPLoS One
September 2017
School of Traffic and Transportation Engineering, Central South University, Changsha, Hunan, P.R. China.
An effective evaluation of transportation network efficiency could offer guidance for the optimal control of urban traffic. Based on the introduction and related mathematical analysis of three quantitative evaluation methods for transportation network efficiency, this paper compares the information measured by them, including network structure, traffic demand, travel choice behavior and other factors which affect network efficiency. Accordingly, the applicability of various evaluation methods is discussed.
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