###### Abstract  
The OPF problem has significant importance in a power system's operation, planning, economic scheduling, and security. Today's electricity grid is rapidly evolving, with increased penetration of renewable power sources (RPSs). Conventional optimal power flow (OPF) has non-linear constraints that make it a highly non-linear, non-convex optimization problem. This complex problem escalates further with the integration of renewable energy resource (RES), which are generally intermittent in nature. This study suggests a new and effective improved optimizer via a TFWO algorithm (turbulent flow of water-based optimization), namely the ITFWO algorithm, to solve non-linear and non-convex OPF problems in energy networks with integrated solar photovoltaic (PV) and wind turbine (WT) units (being environmentally friendly and clean in nature). OPF in the energy networks is an optimization problem proposed to discover the optimal settings of an energy network. The OPF modeling contains the forecasted electric energy of WT and PV by considering the voltage value at PV and WT buses as decision parameters. Forecasting the active energy of PV and WT units has been founded on the real-time measurements of solar irradiance and wind speed. Eight scenarios are analyzed on the IEEE 30-bus test system in order to determine a cost-effective schedule for thermal power plants with different objectives that reflect fuel cost minimization, voltage profile improvement, emission gases, power loss reduction, and fuel cost minimization with consideration of the valve point effect of generation units. In addition, a carbon tax is considered in the goal function in the examined cases in order to investigate its effect on generator scheduling. A comparison of the simulation results with other recently published algorithms for solving OPF problems is made to illustrate the effectiveness and validity of the proposed ITFWO algorithm. Simulation results show that the improved turbulent flow of water-based optimization algorithm provides an effective and robust high-quality solution of the various optimal power-flow problems. Moreover, results obtained using the proposed ITFWO algorithm are either better than, or comparable to, those obtained using other techniques reported in the literature. The utility of solar and wind energy in scheduling problems has been proposed in this work.  
power systems operation; metaheuristic algorithm; renewable energy resources; optimization; greenhouse gas emissions +
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into modern energy networks has generated novel types of problems for managing and operating the energy network [4; 5]. Optimizing the various OPF problems has become more intricate with the enormous incorporation of RPSs that constrain volatile dynamics for the energy network due to their uncertainty [6; 7].  
Conventional search approaches, such as quadratic programming (QP) [8], and nonlinear programming (NLP) [9; 10; 11] presented great convergence trends in optimizing the objective functions of the different OPF problems; however, these methods apply theoretical hypotheses not suitable for real-world problems, as they have non-smooth and non-differentiable objective functions [12; 13; 14]. In addition, the preceding methods sometimes fail to show the main trends of the objective function as a convex OPF function [12]. Therefore, metaheuristics have been applied to dominate the above-mentioned weaknesses [12; 15].