In the last two decades, electricity grids have faced many challenges that they were not designed to handle. These include integrating weather-dependent renewables, distributed generators, storage units and other advanced components, as well as taking into account active demand. These challenges, together with the ageing of infrastructures, make it more difficult to deliver cost-effective, reliable power. To overcome these issues requires creating new network architectures. The research project Fractal Grid proposes fractality as a core concept to model, analyze and design smart grids in their evolution up to 2030 and beyond. This paper presents the project, its methodological approach and the first results.