DS0201 - Exploration de concepts en rupture

Fractal Grids - Towards the future smart grids – FractalGrid

Fractal Grid - Fractal electrical grids

FractalGrid is about the use of fractality as a core concept to analyze, understand, design and operate the future Smart Grids.

Understanding and optimizing electrical networks

For many years, the energy provider was far and strongly centralized. The ecological transition has moved it into the territories, the regions, the cities, the neighborhoods and closest to individuals. A recent example of this shift is the concept of local energy community. This trend towards local energy will be efficient, safe and will last only if we study carefully the different components involved in the planning and operation of the system. The electrical grid is a key part in an energy system. It mutualises electrical energy to distribute it throughout the territory. Fractal grid introduces new multi-scale tools and concepts for the analysis, planning and operation of electrical grids.

In Fractal Grid, the network is studied through different scales, starting from the distribution at household level all the way to the transport grid. Our fractal analysis of distribution networks in rural, suburbian and urban areas of the Jura, Haute- Saône and Isere departments showed particular scaling laws. We carried out a similar analysis of the built areas and road networks and found similarities in the development of these different objects on a territory. We concluded that the values of the fractal dimensions for these different regions depend on their history (recent or old areas) and their main function (residential, commercial or industrial).
The electrical grid should provide energy to all users with the most reliability. We identified vulnerable lines and actions to repair failures. Multi-scale methods from graph theory allowed us to introduce a new mathematical representation of the network and give practical predictions. We also showed how defects can be identified by monitoring a few nodes of the network.
Finally, the flexibility available to bring services to the system on both local (reduction of congestions) and global (balance production-consumption)levels was modeled using an original multi-scale approach.

The first important results concern the methods. Their definition and application to electrical grids are a first at international level. Perhaps, a most important result is a proposition to reconfigure the electrical grid of Grenoble into a fractal grid. This architecture allows both to serve the territory on its whole and for clusters to emerge. On these clusters very local energy exchanges will be possible, for example between users from the same neighborhood having both photovoltaic panels and storage facilities (electric car batteries).

Fractal architecture and multi-scale management strategies certainly enable the connection of dispersed local resources (renewable energy sources or storage element). They provide an hierarchical way of operating both together, local energy clusters and the global electrical system. The advantages of fractal architectures were not formally demonstrated in the project but Fractal Grid has produced the tools to demonstrate in a near future what brings fractality to future smart grids.

The more fundamental results have been published in journals or international conferences. For a larger dissemination, we organized a day conference « Faire énergie territoire » for academics, institutional managers and industrialists (https://eco-fractal.sciencesconf.org/).

8 international journals, 4 communications, 2 PhD report and 1 PhD award were obtained by the project members.

FractalGrid is about the use of fractality as a core concept to analyze, understand, design and operate the future smart grids. Development of new analysis tools and design concepts based on fractal geometry will be proposed to better achieve the control of highly distributed loads and generators in power systems and to improve the resilience “by design” of the future grid.

The project aims to analyze the multiscale organization of smart grids and propose a new architecture paradigm for the smart grids based on fractality. We will show how smart grids structure impact performances and how the self-similar topology can benefit to the electrical system, from consumers to utilities. Links between the spatial organization of the built-up spaces and the optimal topology of the grid will be done.

A simulation framework for the coordinated management of a fractal power system will be also developed considering the different spatial and temporal scales associated to the power grids, meteorological system and energy market. The last system cannot be anymore ignored because of their high impact on the todays' operation of the electrical system.

Project coordination

Nicolas Retière (Laboratoire de Génie Electrique de Grenoble)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.


ARMINES PERSEE ARMINES Centre Procédés, Energies Renouvelables, Systèmes énergétiques de Mines ParisTech
LMI - INSA Rouen Laboratoire de Mathématiques de l'INSA de Rouen
ThéMA - UFC Théoriser et Modéliser pour Aménager
G2Elab - UJF Laboratoire de Génie Electrique de Grenoble

Help of the ANR 498,189 euros
Beginning and duration of the scientific project: January 2016 - 42 Months

Useful links

Explorez notre base de projets financés



ANR makes available its datasets on funded projects, click here to find more.

Sign up for the latest news:
Subscribe to our newsletter