Multi-temporal optimal power flow for assessing the renewable generation hosting capacity of an active distribution system

The detailed modeling of distribution grids is expected to be critical to understand the current functionality limits and necessary retrofits to satisfy integration of massive amounts of distributed generation, energy storage devices and the electric consumption demand of the future. Due to the highly dimensional non-convex characteristics of the power flow equations, convex relaxations have been used to ensure an efficient calculation time. However, these relaxations have been proven to be inexact during periods of high RES injection. In this paper additional linear constraints were introduced in the power flow formulation to guaranty an exact relaxation. This convex relaxation is then applied within a multi-temporal algorithm in order to evaluate the benefits of storage grid integration. The case study of a French medium voltage feeder is studied to evaluate the maximum capacity of the grid to host RES sources and the advantages of storage systems in reducing curtailment of RES.