Integration of Distributed Energy Resources in Unbalanced Networks Using a Generalized Normal Distribution Optimizer - Laura Sofía Avellaneda-Gómez; Brandon Cortés-Caicedo; Oscar Danilo Montoya; Jesús M. López-Lezama (Computation)
This article proposes an optimization methodology to address the joint placement as well as the capacity design of PV units and D-STATCOMs within unbalanced three-phase distribution systems. The proposed model adopts a mixed-integer nonlinear programming structure using complex-valued variables, with the objective of minimizing the total annual cost—including investment, maintenance, and energy purchases. A leader–followeroptimization framework is adopted, where the leader stage utilizes the Generalized Normal Distribution Optimization (GNDO) algorithm to generate candidate solutions, while the follower stage conducts power flow calculations through successive approximation to assess the objective value. The proposed approach is tested on 25- and 37-node feeders and benchmarked against three widely used metaheuristic algorithms: the Chu and Beasley Genetic Algorithm, Particle Swarm Optimization, and Vortex Search Algorithm. The results indicate that the proposed strategy consistently achieves highly cost-efficient outcomes. For the 25-node system, the cost is reduced from USD 2,715,619.98 to USD 2,221,831.66 (18.18%), and for the 37-node system, from USD 2,927,715.61 to USD 2,385,465.29 (18.52%). GNDO also surpassed the alternative algorithms in terms of solution precision, robustness, and statistical dispersion across 100 runs. All numerical simulations were executed using MATLAB R2024a. These findings confirm the scalability and reliability of the proposed method, positioning it as an effective tool for planning distributed energy integration in practical unbalanced networks.