Navigating the complexity of photovoltaic system integration: an optimal solution for power loss minimization and voltage profile enhancement considering uncertainties and harmonic distortion management

This manuscript investigates the optimal placement and sizing of Photovoltaic (PV) systems within electrical distribution networks. The problem is formulated as a multiobjective optimization, seeking to simultaneously minimize power losses and enhance voltage profiles while accounting for uncertainties in PV power output, variations in consumer load demand, and the impact of PV inverter-induced harmonic current injection on power quality. The optimal solution is obtained via a Mixed-Integer NonLinear Programming (MINLP) approach, leveraging the Basic Open-source Nonlinear Mixed-Integer programming (BONMIN) solver embedded within the General Algebraic Modeling Systems (GAMS) platform. The performance of the proposed BONMIN-based methodology is evaluated through two case studies. In the first case, the BONMIN solver is employed for the optimal allocation and sizing of 1, 2, and 3 PVs in the IEEE 33-bus test system. The obtained optimal solutions are compared with those from popular metaheuristic algorithms-Particle Swarm Optimization (PSO), Gray Wolf Optimizer (GWO), Gravitational Search Algorithm (GSA), and Bat Algorithm (BAT), in terms of both objective function minimization and numerical efficiency. The results in the first case showed that 3 optimally placed PVs contributed to a 26.46% loss reduction and 38.18% voltage deviation reduction. The results demonstrate the superiority of the proposed approach, which achieves better optimal solutions with enhanced computational performance relative to metaheuristic alternatives. In the second case, the BONMIN solver is applied to the optimal PV integration problem in the real-world "Bijela" distribution network in Montenegro, where the results show that the optimal placement of 3 PVs contributes to a 22.49% loss reduction and a 28.14% voltage deviation reduction. Furthermore, the findings in the second case confirm the applicability of the BONMIN solver for optimal PV integration in realistic distribution network environments. Additionally, the simulation results indicated minimal negative impacts of optimally allocated and sized PVs on the power quality of the distribution network for both test systems.