Static Equivalent of Distribution Grids With High Penetration of PV Systems

High penetrations of photovoltaic (PV) systems within load pockets in distribution grids have changed pure consumers to prosumers. This can cause technical challenges in distribution and transmission grids, such as overvoltage and reverse power flow. Embedding voltage support schemes into PVs, such as standard ${\cos \phi (P)}$ characteristic proposed by the German grid codes, may cause more changes in the steady-state behavior of distribution grids and, in turn, the transmission side. Accordingly, it is important to properly model active distribution grids to analyze the system impacts of these changes to plan and operate future smart power grids. However, due to the high dimension of distribution grids, considering a detailed distribution grid to study the transmission side or a fraction of the distribution grid is either cumbersome or impractical. Therefore, it is required to develop a reasonable equivalent that can fairly capture the dominant behavior of the distribution grids. The aim of this paper is to use gray-box modeling concepts to develop a static equivalent of distribution grids comprising a large number of PV systems embedded with voltage support schemes. In the proposed model, the PV systems are aggregated as a separate entity, and not as a negative load, which is traditionally done. The results demonstrate the superior quality of the proposed model compared with the model with PV systems as the negative load.