- Physical Review Journals
All JournalsPhysics Magazine

PRX Energy

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Power Grid Network Growth Model Based on Rural-Urban Differentiation

Emile Emery*, Sébastien Aumaître, and Hervé Bercegol

  • *Contact author: emile.emery@etik.com
PDF

PRX Energy 4, 033014 – Published 9 September, 2025

DOI: https://doi.org/10.1103/kysp-hgxt

Abstract

The development of clean energy solutions requires an extension of electrical grids in size and power. Network evolution modeling is crucial for revealing critical insights into transmission grid growth dynamics. This study proposes an efficient analytical framework based on spatial network physics to enhance previous models and deliver better predictions. Utilizing the French transmission grid as a case study, our methodology demonstrates its aptitude to estimate energy invested and consumed, as well as topological and spatial characteristics. This new approach balances computational efficiency with predictive accuracy, making it particularly valuable for building datasets for research and contributing to well-informed infrastructure development forecast science.

View figure in article

Physics Subject Headings (PhySH)

Popular Summary

The worldwide shift toward low-carbon energy sources requires substantial modifications to standard energy systems. Though often underestimated, the evolution of electrical network design is vital for a successful energy transition. Here, using the French transmission grid as a case study, the authors built a network model that considers territorial inhomogeneities. This tunable model gives realistic predictions for the future structural changes to power grids. The model is a forecasting tool to estimate network characteristics as well as the associated energy invested and consumed. This framework can be used to estimate the order of magnitude of the energy cost of a network structure and to build datasets for research, and it can be expanded to implement distribution layer and/or country interconnections.

Article Text

Supplemental Material

References (44)

  1. IEA, Electricity grids and secure energy transitions, IEA, Paris, licence: Cc by 4.0 https://www.iea.org/reports/electricity-grids-and-secure-energy-transitions (2023).
  2. R. Albert and A.-L. Barabási, Statistical mechanics of complex networks, Rev. Mod. Phys. 74, 47 (2002).
  3. Giuliano Andrea Pagani and Marco Aiello, Power grid complex network evolutions for the smart grid, Physica A 396, 248 (2014).
  4. S. G. Aksoy, E. Purvine, E. Cotilla-Sanchez, and M. Halappanavar, A generative graph model for electrical infrastructure networks, J. Complex Netw. 7, 128 (2019).
  5. S. Roy, C. Asavathiratham, B. C. Lesieutre, and G. C. Verghese, Network models: Growth, dynamics, and failure, in Proceedings of the 34th Annual Hawaii International Conference on System Sciences (2001), pp. 728–737.
  6. M. Rosas-Casals, S. Valverde, and R. Sole, A simple spatiotemporal evolution model of a transmission power grid, IEEE Syst. J. 12, 3747 (2018).
  7. S. Mei, X. Zhang, and M. Cao, Power Grid Complexity (Springer, Berlin, Heidelberg, 2011).
  8. P. Schultz, J. Heitzig, and J. Kurths, A random growth model for power grids and other spatially embedded infrastructure networks, Eur. Phys. J. Spec. Top. 223, 2593 (2014).
  9. M. Irfan, A. B. M. Eldaly, R. Qureshi, M. Bilal, and M. S. Hanif, PowerX: A probabilistic graph model for complex smart grid networks, IEEE Access 12, 48725 (2024).
  10. E. Emery, H. Bercegol, N. Jonqueres, and S. Aumaître, Complex network analysis of transmission networks preparing for the energy transition: Application to the current French power grid, Eur. Phys. J. B 97, 201 (2024).
  11. G. A. Pagani and M. Aiello, The power grid as a complex network: A survey, Physica A 392, 2688 (2013).
  12. R. Espejo, S. Lumbreras, and A. Ramos, Analysis of transmission-power-grid topology and scalability, the European case study, Physica A 509, 383 (2018).
  13. D. S. Callaway, J. E. Hopcroft, J. M. Kleinberg, M. E. J. Newman, and S. H. Strogatz, Are randomly grown graphs really random? Phys. Rev. E 64, 041902 (2001).
  14. M. Barthélemy, Spatial Networks (Springer Nature, Cham, Switzerland, 2022).
  15. B. Hartmann, G. Ódor, I. Papp, K. Benedek, S. Deng, and J. Kelling, Dynamical heterogeneity and universality of power-grids, Sustain. Energy Grids Netw. 39, 101491 (2024).
  16. A. Cattaneo, A. Adukia, D. L. Brown, L. Christiaensen, D. K. Evans, A. Haakenstad, T. McMenomy, M. Partridge, S. Vaz, and D. J. Weiss, Economic and social development along the urban–rural continuum: New opportunities to inform policy, World Dev. 157, 105941 (2022).
  17. C. Kühnert, D. Helbing, and G. B. West, Scaling laws in urban supply networks, Physica A 363, 96 (2006).
  18. C. Clark, Urban population densities, J. R. Stat. Soc. 114, 490 (1951).
  19. H. Persoz, J.-C. Lemoine, P. Sapet, and G. Santucci, La Planification des réseaux électriques, Collection de la Direction des études et recherches d’électricité de France No. 50 (Eyrolles, Paris, 1984).
  20. See the Supplemental Material, which includes Refs. [10, 32, 34, 38, 41, 42, 43, 44], at http://link.aps.org/supplemental/10.1103/kysp-hgxt for additional information on the topology of the growth model and details of the energy cost estimates.
  21. A.-L. Barabási and R. Albert, Emergence of scaling in random networks, Science 286, 509 (1999).
  22. M. Bastian, S. Heymann, and M. Jacomy, gephi: An open source software for exploring and manipulating networks, in Proceedings of the International AAAI Conference on Web and Social Media (2009), Vol. 3, pp. 361–362.
  23. G. B. West, Scale (Penguin Press, New York, 2017).
  24. J.-F. Goux, Les fondements de la loi de densité urbaine de c. clark, Can. J. Reg. Sci. 23, 27 (1981).
  25. ENEDIS, Panorama énergétique des territoires urbains https://www.enedis.fr/presse/panorama-energetique-territoires-urbains (2023).
  26. F. Avram and D. Bertsimas, On central limit theorems in geometrical probability, Ann. Appl. Probab. 3, 1033 (1993).
  27. R. E. Miles, On the homogeneous planar Poisson point process, Math. Biosci. 6, 85 (1970).
  28. S. Kullback and R. A. Leibler, On information and sufficiency, Ann. Math. Stat. 22, 79 (1951).
  29. S. F. Muldoon, E. W. Bridgeford, and D. S. Bassett, Small-world propensity and weighted brain networks, Sci. Rep. 6, 22057 (2016).
  30. P. J. Menck, J. Heitzig, N. Marwan, and J. Kurths, How basin stability complements the linear-stability paradigm, Nat. Phys. 9, 89 (2013).
  31. RTE, Pertes sur le réseau public de transport https://www.services-rte.com/fr/visualisez-les-donnees-publiees-par-rte/pertes-sur-le-reseau-public-de-transport.html.
  32. R. S. Jorge, T. R. Hawkins, and E. G. Hertwich, Life cycle assessment of electricity transmission and distribution—part 1: Power lines and cables, Int. J. Life Cycle Assess. 17, 9 (2012).
  33. B. Schäfer, T. Pesch, D. Manik, J. Gollenstede, G. Lin, H.-P. Beck, D. Witthaut, and M. Timme, Understanding Braess’ paradox in power grids, Nat. Commun. 13, 5396 (2022).
  34. K. Schmietendorf, J. Peinke, R. Friedrich, and O. Kamps, Self-organized synchronization and voltage stability in networks of synchronous machines, Eur. Phys. J. Spec. Top. 223, 2577 (2014).
  35. W. Hua, L. Wang, X. Fang, and L. Luo, Urbanization and energy equity: An urban-rural gap perspective, Environ. Sci. Pollut. Res. 30, 46847 (2023).
  36. A. Rozhkov, M. Zellner, J. T. Murphy, and D. Massey, Identifying leverage points for sustainable transitions in urban – rural systems: Application of graph theory to participatory causal loop diagramming, Environ. Sci. Policy 164, 103996 (2025).
  37. https://zenodo.org/records/16743911
  38. ODRé, Open data réseaux energies https://opendata.reseaux-energies.fr/.
  39. Downloadable link for department data https://osm13.openstreetmap.fr/∼cquest/openfla/export/departements-20180101-shp.zip.
  40. Agence ore, consommation annuelle d’électricité et gaz par département et par secteur d’activité in https://opendata.agenceore.fr.
  41. D. Monfort, F. Laurent, H. L. Boulzec, G. Lefevbre, B. Rodriguez, S. Muller, C. François, B. Andrieu, O. Vidal, and J. Villeneuve, Projet surfer, inventaires des besoins en matière, energie, eau et sols des technologies de la transition energetique (2020), https://librairie.ademe.fr/energies/4654-surfer.html#product-features.
  42. P. Chapman, The energy costs of materials, Energy Policy 3, 47 (1975).
  43. K. Purchala, L. Meeus, D. Van Dommelen, and R. Belmans, in IEEE Power Engineering Society General Meeting, 2005 (San Francisco, CA, USA, IEEE, 2005), Vol. 1, pp. 454–459, iSSN: 1932-5517.
  44. J. D. McCalley, The Power Flow Equations, https://home.engineering.iastate.edu/jdm/ee458_2011/PowerFlowEquations.pdf.

Outline

Information

PRX Energy 4, 033014– Published 9 September, 2025
  • Received 11 February 2025
  • Revised 28 May 2025
  • Accepted 7 August 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation