### Contribution and Paper Organization  
In 2021, [PERSON] et al. [65] introduced the TFWO algorithm, which is inspired by the formula of turbulent fluctuations in water flow in nature. The recent research has demonstrated that TFWO can be effectively used to find optimal solutions to a variety of optimization problems. For example, TFWOs were used for optimal reactive power distribution (ORPD) in [66]. The chaotic TFWO (CTFWO) was introduced in [67] as a means of reducing voltage deviation (VD) and real power loss. The TFWO model has been successfully used to solve problems related to unit commitment model integration with electric vehicles in [68]. An estimation of the correlation parameter of the Kriging method, enhancing the accuracy of the Kriging surrogate modeling (KSM) used to approximate the complex and implicit performance functions in [69]. To solve short-term hydrothermal scheduling, the authors of [70; 71] have proposed quasi-oppositional TFWO (QOTFWO). The cascading nature of hydro plants, valve-point loading (VPL), and multiple fuel sources have been assumed in their modeling. Through a comprehensive comparison of three robust performance and fast convergence algorithms, ref. [72] proved that the TFWO can optimize an isolated hybrid microgrid. The TFWO also have been applied for proportional integral derivative (PID) controller to ensure reliable operation of active foil bearings [73], and optimal allocation of shunt compensators in distribution systems [74]. Based on the results of [74], the TFWO algorithm was found to be effective in reducing power loss,enhancing the voltage profile, and determining the type, size, and location of the reactive power compensators (RPCs).  
In different patterns of partial shading, TFWO was shown to be capable of maximizing duty cycle of DC/DC converters to achieve global optimal power [75]. In [76], the performance of the TFWO was compared and validated against seven well-known algorithms. As a result of optimizing photovoltaic models, the TFWO were able to provide the minimum fuel cost and significant robust solutions to the ELD problem over all networks tested in [77; 78]. It was demonstrated in [77; 78] that the estimated power-voltage (P-V) and current-voltage (I-V) curves achieved by the TFWO were very close to the experimental data.  
It has been demonstrated in recent research that TFWO can be effective in solving real-world problems. It is worth noting that, due to its non-convex and non-linear nature, the OPF problems can be extremely challenging. The robustness and convergence speed of existing algorithms, such as turbulent water flow (TFWO), need to be improved in order to tackle such a complex problem. An innovative and successful improvement of the TFWO (ITFWO) approach is presented in this paper to address a variety of OPF problems encountered in hybrid power systems. To demonstrate the algorithm's ability to solve OPF problems, this paper compares the developed algorithm with existing state-of-the-art methods.  
This paper highlights the following points:  
* Enhancing the TFWO algorithm's convergence speed, exploration capabilities, and exploitation capabilities.
* The original TFWO algorithm has been improved by the addition of an enhanced operator to update the population, which increases the local search capability of the algorithm.
* The proposed improved algorithm is successfully applied to solve the non-convex and non-linear OPF problems considering different objective functions.
* The magnitude of the voltage at the WT and PV buses is considered a decision variable, while the forecasts of the WT and PV power generation are considered dependent variables.  
The paper has been arranged as follows. The modeling of OPF is characterized in Section 2. The optimization process of TFWO and ITFWO is characterized in Section 3. Section 4 illustrates the obtained optimal results. Finally, the conclusions of this paper are supplied in Section 5.