A multi-objective improved horse herd optimizer based on convex lens imaging for stochastic optimization of wind energy resources in distribution networks considering reliability and uncertainty

In this study, stochastic multi-objective allocation of wind turbines (WTs) in radial distribution networks is performed using a new multi-objective improved horse herd optimizer (MOIHHO) and an unscented transformation (UT) method for modeling the uncertainties of WTs power and network load. The objective function aims to minimize power loss, improve reliability, and reduce the costs associated with wind turbines (WTs), presenting these goals as a three-dimensional function. The Multi-Objective Improved Horse Herd Optimizer (MOIHHO) is derived from an enhanced version of the traditional horse herd optimizer. This enhancement utilizes mirror imaging based on convex lens principles to address issues of premature convergence. Additionally, the decision-making process is designed to identify the final fuzzy solution among the non-dominant solutions within the Pareto front set. The simulation results are presented with and without considering uncertainty in two scenarios of deterministic and stochastic WT allocation on 33- and 69-bus distribution networks and different objectives are compared. Also, the effect of incorporating uncertainties are evaluated on power loss and reliability using the MOIHHO. Moreover, the superiority of the MOIHHO is investigated in achieving better objective function value compared with conventional MOHHO, multi-objective particle swarm optimization (MOSPO), multi-objective gray wolf optimizer (MOGWO), and multi-objective gazelle optimization algorithm (MOGOA). The obtained results demonstrated that considering the UT-based stochastic scenario, the power losses cost is increased, and the reliability is weakened for 33- and 69-bus networks in comparison with the deterministic scenario.