Advancing Distribution System Planning: Exact MINLP Methods for Optimal PV and Reactive Device Deployment

The planning of unbalanced three-phase distribution networks increasingly requires the coordinated integration of distributed energy resources, such as photovoltaic (PV) generators and static compensators (D-STATCOMs), to enhance system performance and reduce costs. This planning task is inherently challenging, as it leads to a mixed-integer nonlinear optimization problem driven by nonconvex voltage–current–power relationships, phase unbalances, and the temporal variability of demand and solar irradiance. This work proposes an exact Mixed-Integer Nonlinear Programming (MINLP) framework for the joint siting and sizing of PV units and D-STATCOM devices, with an objective function based on the minimization of the equivalent annual cost of energy purchases and investments. The methodology is applied to 25- and 37-bus unbalanced test systems and benchmarked against four state-of-the-art metaheuristic algorithms. The results show that the exact MINLP consistently attains the global optimum, yielding reductions in equivalent annual cost of USD 392,855 (14.36%) and USD 436,361 (14.90%) for the respective test systems, whereas the metaheuristics provide near-optimal but slightly dispersed solutions. These findings highlight the potential of exact optimization as a robust and economically sound tool for long-term distribution network planning, combining technical reliability with guaranteed global optimality.