(untitled) (Statistics, Optimization & Information Computing, 2026)
This paper presents the application of the Newton-metaheuristic algorithm (NMA) for the integrated optimal placement and sizing of photovoltaic (PV) systems and distribution static compensators (D-STATCOMs) in medium-voltage distribution networks. The problem is formulated as a mixed-integer nonlinear programming (MINLP) model aimed at minimizing total annualized costs—including energy procurement, investment, and operation and maintenance—while satisfying power flow constraints, voltage limits, and device capacity bounds. To address the computational complexity, a master–slave hierarchical framework is proposed: the upper level employs the NMA to explore the discrete–continuous search space of installation locations and capacities, while the lower level employs a successive-approximation power flow solver to ensure technical feasibility. The performance of the proposed methodology is validated on standard 33-bus and 69-bus radial test systems and compared against established metaheuristics such as the Vortex Search Algorithm (VSA), Sine–Cosine Algorithm (SCA), and Atan-Sinc Optimization Algorithm (ASOA). Results demonstrate that the NMA achieves the lowest total costs: USD 2,290,259.24 and USD 2,395,022.55, respectively, corresponding to a reduction of approximately 35.55% compared to the benchmark case without distributed resources. Moreover, the NMA exhibits superior computational efficiency, with execution times 4.8–17.1% faster than those of the benchmark algorithms, underscoring its scalability and practical applicability for real-world distribution system planning. The proposed approach thus offers a robust, efficient, and economically effective tool for integrating renewable-based active power sources and reactive compensators in modern distribution grids.