Efficient Integration of Photovoltaic Solar Generators in Monopolar DC Networks through a Convex Mixed-Integer Optimization Model

The problem regarding the optimal siting and sizing of photovoltaic (PV) generation units in electrical distribution networks with monopolar direct current (DC) operation technology was addressed in this research by proposing a two-stage convex optimization (TSCO) approach. In the first stage, the exact mixed-integer nonlinear programming (MINLP) formulation was relaxed via mixed-integer linear programming, defining the nodes where the PV generation units must be placed. In the second stage, the optimal power flow problem associated with PV sizing was solved by approximating the exact nonlinear component of the MINLP model into a second-order cone programming equivalent. The main contribution of this research is the use of two approximations to efficiently solve the studied problem, by taking advantage of convex optimization models. The numerical results in the monopolar DC version of the IEEE 33-bus grid demonstrate the effectiveness of the proposed approach when compared to multiple combinatorial optimization methods. Two evaluations were conducted, to confirm the efficiency of the proposed optimization model. The first evaluation considered the IEEE 33-bus grid without current limitations in all distribution branches, to later compare it to different metaheuristic approaches (discrete versions of the Chu and Beasley genetic algorithm, the vortex search algorithm, and the generalized normal distribution optimizer); the second simulation included the thermal current limits in the model's optimization. The numerical results showed that when the maximum point power tracking was not regarded as a decision-making criterion, the expected annual investment and operating costs exhibited better performances, i.e., additional reductions of about USD 100,000 in the simulation cases compared to the scenarios involving maximum power point tracking.