A barrel theory-based optimization of stochastic PV-DG integration in radial distribution networks under load and solar uncertainties

The increasing penetration of photovoltaic distributed generation (PV-DG) in Radial Distribution Systems (RDSs) plays a vital role in achieving sustainable energy transition objectives; however, the inherent uncertainty associated with solar irradiance and load demand poses significant challenges to optimal planning and operation. This paper presents a stochastic optimization framework for PV-DG allocation in RDSs using the Barrel Theory-Based Optimizer (BTO). Uncertainties in solar irradiance and load demand are explicitly modeled using appropriate probability density functions and efficiently represented through a higher-order Point Estimate Method (PEM), which captures the essential statistical characteristics with a limited number of representative scenarios. The proposed framework simultaneously optimizes the location and capacity of PV-DG units to minimize real power losses and enhance voltage profile performance while ensuring system operational constraints are satisfied. The effectiveness of the proposed approach is validated on the 85-bus and the IEEE 118-bus RDSs, where the BTO exhibits superior convergence characteristics and enhanced solution robustness when compared with several benchmark optimization techniques, including the well-established Differential Evolution Algorithm (DEA), the recent Crocodile Ambush Optimization (CAO, 2025), and the Schrödinger Optimizer Algorithm (SOA, 2025). For the 85-bus RDS, the impact of integrating different numbers of PV units is systematically investigated. Simulation results confirm that the proposed BTO-based stochastic planning strategy significantly improves energy efficiency, voltage regulation, and loss reduction, thereby enhancing the overall sustainability of the RDS. For the 85-node RDS, the BTO achieves a noticeable reduction in average real power losses, outperforming DEA, CAO, and SOA by 2.55%, 4.10%, and 6.74%, respectively, when three PV units are installed. Additionally, for the case of four PV units, the proposed BTO yields even greater improvements, with loss reductions of 5.12%, 7.50%, and 14.12%, respectively, compared with the same benchmark algorithms. Furthermore, for five PV units, the BTO achieves much greater reduction, outperforming DEA, CAO, and SOA by 13.05%, 6.45%, and 32.31%, respectively, when three PV units are installed.