Wind energy is particularly significant in the power system today since it is a cheap and clean power source. The unpredictability of wind speed leads to uncertainty in devolved power which increases the difficulty in wind energy system operation. This paper presents a stochastic optimal power flow (SCOPF) for obtaining the best scheduled power from wind farms while lowering total operational costs. A novel metaheuristics method called Aquila Optimizer (AO) is used to address the SCOPF problem due to its highly nonconvex and nonlinear nature. Wind speed is represented by the Weibull probability distribution function (PDF), which is used to anticipate the cost of wind-generated power from a wind farm based on scheduled power. Weibull parameters that provide the best match to wind data are estimated using the AO approach. The suggested wind generation cost model includes the opportunity costs of wind power underestimation and overestimation. Three IEEE systems (30, 57, and 118) are utilized to solve optimal power flow (OPF) using the AO method to prove the accuracy of this method, and results are compared with other metaheuristic methods. With six scenarios for the penalty and reverse cost coefficients, SCOPF is applied to a modified IEEE-30 bus system with two wind farms to obtain the optimal scheduled power from the two wind farms which reduces total operation cost.

This paper applies two reliable and efficient evolutionary-based methods named Shuffled Frog Leaping Algorithm (SFLA) and Grey Wolf Optimizer (GWO) to solve Optimal Power Flow (OPF) problem. OPF is one of the essential functions of electrical power generation control and operation. It aims to estimate the optimal settings of real generator output power, bus voltage, reactive power compensation devices, and transformer tap setting. The objective function of OPF is to minimize total production cost while maintaining the power system operation within its security limit constrains. SFLA and GWO are meta-heuristic evolutionary-based methods. SFLA mimics the frogs' behavior while searching for food. GWO mimics the grey wolfs behavior while hunting for prey. These methods are simulated and tested on the standard IEEE 30-bus and 57-bus test systems. Moreover, the performances of the applied algorithms are analyzed and compared with each other as well as with other existing optimization techniques. The obtained results show the strengths of the two applied methods and the superiority of them in comparison to the other methods.

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The growing usage of renewable energy sources, such as solar and wind energy, has increased the electrical system’s unpredictability. The stochastic behavior of these sources must be considered to obtain significantly more accurate conclusions in the analysis of power systems. To depict renewable energy systems, the three-component mixture distribution (TCMD) is introduced in this study. The mixture distribution (MD) is created by combining the Weibull and Gamma distributions. The results show that TCMD is better than original distributions in simulating wind speed and solar irradiance by reducing the error between real data and the distribution curve. Additionally, this study examines the optimal power flow (OPF) in electrical networks using the two stochastic models of solar and wind energy. The parameters of the probability distribution function (PDF) are optimized using the Mayfly algorithm (MA), which also solves single- and multi-objective OPF issues. Then, to prove the accuracy of the MA method in solving the OPF problem, single- and multi-objective OPF is applied on a standard IEEE-30 bus system to minimize fuel cost, power loss, thermal unit emissions, and voltage security index (VSI), and results are compared with other metaheuristic methods. The outcomes show that the MA technique is dependable and effective in overseeing this challenging problem. Additionally, the suggested OPF MA-based is studied in the OPF problem while accounting for the uncertainty in the models of the wind and solar systems and taking the emissions, VSI, power loss, and fuel cost into consideration in the objective function. The significance of the work lies in the application of a unique optimization technique to a hybrid electrical system using TCMD stochastic model using actual wind and solar data. The proposed MA method could be valuable to system operators as a decision-making aid when dealing with hybrid power systems.