The introduction of microgrids in distribution networks based on power electronics facilitates the use of renewable energy resources, distributed generation (DG) and storage systems while improving the quality of electric power and reducing losses thus increasing the performance and reliability of the electrical system. The hierarchical control structure, which consists of primary, secondary, and tertiary levels for microgrids that mimic the behavior of the mains grid, is reviewed. The main objective of this article is to give a description of state of the art for distributed power generation systems (DPGS) based on renewable energy and explore the power converters connected in parallel to the grid which are distinguished by their contribution to the formation of the grid voltage and frequency and are accordingly classified in three classes. This analysis is extended focusing mainly on the three classes of configurations: grid-forming, grid-feeding, and grid-supporting. The article ends up with an overview and a discussion of the control structures and strategies to control distribution power generation system (DPGS) units connected to the network.