A MILP Model for Simultaneous Optimal Placement, Sizing, and Operation of PV Distributed Generation and D-STATCOMs in Distribution Systems

The increasing penetration of photovoltaic distributed generation (PV-DG) and the growing demand for reactive power compensation in power distribution systems (PDS) require coordinated planning and operational strategies to improve system efficiency and stability. This paper presents a novel Mixed-Integer Linear Programming (MILP) model for the simultaneous optimal placement, sizing, and operation of both PV-DG units and Distribution Static Synchronous Compensators (D-STATCOMs) in radial PDS. The proposed model incorporates multi-period optimization, enabling the dynamic dispatch of active and reactive power from PV-DG units and D-STATCOMs based on hourly load profiles. In addition, it includes detailed modeling of network constraints, such as voltage limits, branch flow limits, and nodal power balance. The optimization problem is formulated in AMPL and solved using the CPLEX solver to ensure global optimality and computational efficiency. The model is validated on the IEEE 33-bus, 69-bus, and 136-bus test systems. The results show that the proposed coordinated planning and operation strategy achieves significant improvements, including reductions in active power losses of up to 68.63%, increases in voltage levels of up to 7.69%, and investment cost savings of up to 41.75%. The MILP-based model guarantees reproducibility and scalability, making it a robust and practical tool for modern distribution system planning.