A steady-state analysis of distribution networks by diffusion-limited-aggregation and multifractal geometry

Global energy transformation, urban growth and the increasing share of electricity in energy consumption stimulate the development of electrical distribution systems. In most cases, the structure of distribution networks has been the result of progressive decisions limited by technical, socio-economic and spatial constraints. These decisions are taken with the help of dedicated tools that fail in grasping in a simple way the connections between the structural choices and the achieved performances. To improve planning process, a new approach is proposed which is based on multifractality to connect the distribution system’s network structure and steady-state properties. The structure of distribution grids is modeled by coupling a Diffusion-Limited-Aggregation approach and a binomial multiplicative process. The multifractal spectrum of the synthesized grids is calculated from a power flow and shows how the structural parameters are linked to the steady-state values (voltages and losses). The results are compared to realistic test cases. The article finally concludes on the interest of multifractality to grade distribution grids and the advantages of fractal architectures for future power networks.