###### Abstract  
In an effort to reduce greenhouse gas emissions, experts are looking to substitute fossil fuel energy with renewable energy for environmentally sustainable and emission free societies. This paper presents the hybridization of particle swarm optimization (PSO) with grey wolf optimization (GWO), namely a hybrid PSO-GWO algorithm for the solution of optimal power flow (OPF) problems integrated with stochastic solar photovoltaics (SPV) and wind turbines (WT) to enhance global search capabilities towards an optimal solution. A solution approach is used in which SPV and WT output powers are estimated using lognormal and Weibull probability distribution functions respectively, after simulation of 8000 Monte Carlo scenarios. The control variables include the forecast real power generation of SPV and WT, real power of thermal generators except slack-bus, and voltages of all voltage generation buses. The total generation cost of the system is considered the main objective function to be optimized, including the penalty and reserve cost for underestimation and overestimation of SPV and WT, respectively. The proposed solution approach for OPF problems is verified on the modified IEEE 30 bus test system. The performance and robustness of the proposed hybrid PSO-GWO algorithm in solving the OPF problem is assessed by comparing the results with five other metaheuristic optimization algorithms for the same test system, under the same control variables and system constraints. Simulation results confirm that the hybrid PSO-GWO algorithm performs well compared to other algorithms and shows that it can be an efficient choice for the solution of OPF problems. renewable energy sources; optimal power flow; solar photovoltaic power; wind power; hybrid PSO-GWO +
Footnote †: journal: Applied Sciences  
integrating enormous storage systems into the transmission network that will also help to reduces fluctuations in the network [4]. Energy storage devices, such as those that are lithium and sodium based [5; 6], can be integrated along with conventional thermal and RES. Lithium-ion batteries have gained a lot of significance due to their high energy density, long life span and low self-discharge property, which can be added in the future expansion of microgrids [7]. OPF solutions provide the best operating values of control parameters, which are generators of real power and voltages, to reduce the total generation cost of the system [8]. Optimizing the generation cost system constraints, which are power flow balance, bus voltages, line capacity, and generator capability, is to be satisfied. OPF solutions must incorporate the uncertainties of these RES, which makes OPF a more complex and nonlinear problem. For OPF problem formulation and solutions, many optimization algorithms and techniques have been developed and used in the past couple of years. These methods can be classified into classical methods, evolutionary based methods, and advanced metaheuristic algorithm-based methods. The classical method consists of linear programming [9], quadratic programming [10], non-linear programming [11], interior point method [12], and dynamic programming etc. For large scale problems, these classical methods are inadequate due to their complex and extensive calculation and their high dependency on initial guess values. Evolutionary based algorithms copy the evolutionary idea of generating next generations from the parentages by mating to obtain the optimal solution. One of the most popular evolutionary based algorithms is the Genetic Algorithm, which has been used to solve OPF as mentioned in [PERSON] et al. [13], [PERSON] et al. [14], and [PERSON] et al. [15]. Another algorithm is the Differential Evolution (DE), that falls under this category and has been successfully implemented for constraint handling while optimizing the different objectives of OPF [16]. To overcome the discrepancies of the classical and evolutionary based methods, various metaheuristic algorithms have been effectively utilized for OPF solutions.