A Stochastic Multi-Objective Framework for Wind DG Allocation and Dynamic Reconfiguration: Minimizing Losses and Enhancing Reliability with an Improved Grey Wolf Optimizer

The integration of wind-based DG introduces significant variability and uncertainty into the operation of distribution networks, which complicates the planning and decision-making process. This paper presents a dual-objective stochastic optimization framework for the optimal allocation of wind DG, considering dynamic network reconfiguration across multiple loading conditions. Probabilistic modeling of wind speed is integrated using the Weibull distribution and the associated wind power uncertainty is discretized through a scenario-based point estimation method. Variability in load is accounted for by considering multiple loading levels, and the integrated uncertainty space is constructed as the Cartesian product of wind scenarios and load profiles. The optimization seeks to minimize the total energy losses together with the enhancement of reliability, quantified through the expected energy not supplied. For the solution of the complex, nonlinear, multi-objective problem, the Improved Multi-Objective Grey Wolf Optimizer (I-MGWO) is developed, including quasi-oppositional population seeding, adaptive stochastic coefficient strategy, and dynamic convex combination position update. Simulation results on the IEEE 33-bus system demonstrate that the proposed integrated strategy of simultaneous wind DG allocation and network reconfiguration gives synergistic improvements, yielding up to 55.7% reduction in energy losses, and a reduction of up to 61.4% in EENS over the base case. In both convergence speed and solution quality, I-MGWO consistently outperforms conventional algorithms and gives a robust and computationally efficient tool for distribution system planning under uncertainty.