Optimal Sizing and Placement of Droop-based Converters in DC Microgrids With ZIP Loads

Achieving satisfactory voltage regulation in dc microgrids with distributed generators while using those as efficiently as possible, does not only depend on implementing appropriate control laws but also on making smart decisions in the planning stage. For the droop-based decentralized control framework, the droop design depends on the generator's location, the grid topology, and the load distribution, especially when constant power loads are considered. In this paper, a mixed-integer linear programming methodology is proposed for simultaneously deciding the locations and the size of distributed generators in dc microgrids to achieve optimal current sharing. The problem formulation includes a detailed discussion on the linearization of the various non-linear terms and the integration of the power flow equations. In addition, a set of constraints is proposed to help estimate the least upper bound of the generator's rating depending on the number of available generators. Then, the proposed formulation is used to explore the optimal placement and sizing of droop-based generators as a function of how many are available, revealing preference patterns associated with the microgrid structure. The proposed optimal decisions are also validated with time-domain simulations demonstrating the feasibility of the solution.