Optimal Selection and Integration of Batteries and Renewable Generators in DC Distribution Systems through a Mixed-Integer Convex Formulation

The problem concerning the optimal placement and sizing of renewable energy resources and battery energy storage systems in electrical DC distribution networks is addressed in this research by proposing a new mathematical formulation. The exact mixed-integer nonlinear programming (MINLP) model is transformed into a mixed-integer convex model using McCormick envelopes regarding the product between two positive variables. Convex theory allows ensuring that the global optimum is found due to the linear equivalent structure of the solution space and the quadratic structure of the objective function when all the binary variables are defined. Numerical results in the 21-bus system demonstrate the effectiveness and robustness of the proposed solution methodology when compared to the solution reached by solving the exact MINLP model. Numerical results showed that the simultaneous allocation of batteries and renewable energy resources allows for the best improvements in the daily operating costs, i.e., about 53.29% with respect to the benchmark case of the 21-bus grid, followed by the scenario where the renewable energy resources are reallocated while considering a fixed location for the batteries, with an improvement of 43.33%. In addition, the main result is that the difference between the exact modeling and the proposed formulation regarding the final objective function was less than 3.90% for all the simulation cases, which demonstrated the effectiveness of the proposed approach for operating distributed energy resources in monopolar DC networks