Stochastic-Metaheuristic Model for Multi-Criteria Allocation of Wind Energy Resources in Distribution Network Using Improved Equilibrium Optimization Algorithm

In this paper, a stochastic-meta-heuristic model (SMM) for multi-criteria allocation of wind turbines (WT) in a distribution network is performed for minimizing the power losses, enhancing voltage profile and stability, and enhancing network reliability defined as energy not-supplied cost (ENSC) incorporating uncertainty of resource production and network demand. The proposed methodology has been implemented using the SMM, considering the uncertainty modeling of WT generation with Weibull probability distribution function (PDF) and load demand based on the normal PDF and using a new meta-heuristic method named the improved equilibrium optimization algorithm (IEOA). The traditional equilibrium optimization algorithm (EOA) is modeled by the simple dynamic equilibrium of the mass with proper composition in a control volume in which the nonlinear inertia weight reduction strategy is applied to improve the global search capability of the algorithm and prevent premature convergence. First, the problem is implemented without considering the uncertainty as a deterministic meta-heuristic model (DMM), and then the SMM is implemented considering the uncertainties. The results of DMM reveal the better capability of the IEOA method in achieving the lowest losses and the better voltage profile and stability and the higher level of the reliability in comparison with conventional EOA, particle swarm optimization (PSO), manta ray foraging optimization (MRFO) and spotted hyena optimization (SHO). The results show that in the DMM solving using the IEOA, traditional EOA, PSO, MRFO, and SHO, the ENSC is reduced from $3223.5 for the base network to $632.05, $636.90, $638.14, $635.67, and $636.18, respectively, and the losses decreased from 202.68 kW to 79.54 kW, 80.32 kW, 80.60 kW, 80.05 kW and 80.22 kW, respectively, while the network minimum voltage increased from 0.91308 p.u to 0.9588 p.u, 0.9585 p.u, 0.9584 p.u, 0.9586 p.u, and 0.9586 p.u, respectively, and the VSI improved from 26.28 p.u to 30.05 p.u, 30.03 p.u, 30.03 p.u, 30.04 p.u and 30.04 p.u; respectively. The results of the SMM showed that incorporating uncertainties increases the losses, weakens the voltage profile and stability and also reduces the network reliability. Compared to the DMM, the SMM-based problem is robust to prediction errors caused by uncertainties. Therefore, SMM based on existing uncertainties can lead to correct decision-making in the conditions of inherent-probabilistic changes in resource generation and load demand by the network operator