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.

Wind energy is considered one of the most important alternative energy sources for generating electricity. The stochastic nature of wind leads to use the distribution function to present the wind system. The two-parameter Weibull distribution is often used in the wind speed presentation. The two-parameter Weibull distribution has scale and shape parameters that are important in wind energy applications, thus selecting the optimum method for estimation them is important. The unpredictability in wind speed leads to uncertainty in devolved power which leads to difficult system operation. In this study, two novel artificial intelligence (AI) methods called Mayfly algorithm (MA) and Aquila Optimizer (AO) are used for calculating the Weibull distribution parameters. Results are compared with four classical numerical methods called the Maximum likelihood approach, Energy pattern factor method, Graphical method, and Empirical method. The two AI methods prove superiority for evaluating two-parameter of Weibull distribution as they give lower errors and higher correlation coefficients. Moreover, to prove the accuracy of the MA method in solving the optimal power flow (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 results prove the validity and accuracy of the MA method in solving the OPF problem. Then, single and multi-objective stochastic optimal power flow (SCOPF) is applied to modified IEEE-30 which contains two wind farms to minimize total generation cost, power loss, thermal unit emission, and VSI. The fuzzy-based Pareto front technique is utilized in multi-objective optimization (MOO) to obtain the best compromise point solution. The objective function of SCOPF considers reserve cost for overestimation and penalty cost for underestimation of wind energy. Finally, this paper studies the effect of changing Weibull parameters, penalty cost coefficient, and reverse cost coefficient in wind energy generation cost. The proposed MA method could be valuable to system operators as a decision-making aid when dealing with hybrid power systems.

The rising use of renewable energy sources, particularly those that are weather-dependent like wind and solar energy, has increased the uncertainty of supply in these power systems. In order to obtain considerably more accurate results in the analysis of power systems, such as in the planning and operation, it is necessary to tackle the stochastic nature of these sources. Operators require adequate techniques and procedures to mitigate the negative consequences of the stochastic behavior of renewable energy generators. Thus, this paper presents a modification of the original probability distribution functions (PDFs) where the original PDFs are insufficient for wind speed and solar irradiance modeling because they have a significant error between the real data frequency distribution and the estimated distribution curve. This modification is using a mixture of probability distributions, which can improve the fitting of data and reduce this error. The main aim of this paper is to model wind speed and solar irradiance behaviors using a two-component and a three-component mixture of PDFs generated from the integration of the original Weibull, Lognormal, Gamma, and Inverse-Gaussian PDFs. Three statistical errors are used to test the efficiency of the proposed original and mixture PDFs, which are the root mean square error (RMSE), the coefficient of correlation (R²), and the Chi-square error (X²). The results show that the mixture of PDFs gives better fitting criteria for wind speed and solar irradiance frequency distributions than the original PDFs. The parameters of the original and the mixture of PDFs are calculated using the innovative metaheuristic Mayfly algorithm (MA). The three-component mixture of PDFs lowered the RMSE by about 73% and was 17% more than the best original and the two-component mixture distributions.

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.

Over the past decades, the mathematical formulation of wind turbines (WTs) has been handled using different methodologies to model the probabilistic nature via different distribution functions. Many recently published articles have applied either the wind speed or the obtained active power from the WT on various probabilistic curves, such as Weibull, log-normal, and Gamma. In this work, the wind speed was modeled at five different locations in Egypt via a novel mixture probability distribution function (MPDF) that included four well-known distribution functions used to imitate the probabilistic nature of wind speed. Moreover, a decision-making multiple objective formulation was developed to optimally fit the MPDF with a minimum root mean square error (RMSE) and ensure reliable fitting by two other effective indices. Two methodologies, namely, equal and variable class widths, were investigated to model the density of wind speed and obtain a more realistic model for the tested wind speed profiles. The results showed the effectiveness of the proposed MPDF model as the RMSE was effectively minimized using multiobjective particle swarm optimization (MOPSO), showing nearly 10% improvement compared to the nondominated sorting genetic algorithm (NSGA-II).

This paper proposes a comprehensive mathematical optimization framework for techno-economic demand side management (DSM) in hybrid energy systems (HESs), with a focus on standalone configurations. The framework incorporates load growth projections and the probabilistic uncertainties of renewable energy sources to enhance planning robustness. To identify high-quality near-optimal solutions, several advanced metaheuristic algorithms were employed, including the Exponential Distribution Optimizer (EDO), Teaching-Learning-Based Optimization (TLBO), Circle Search Algorithm (CSA), and Wild Horse Optimizer (WHO). The results highlight substantial economic and environmental improvements, with battery integration yielding a 69.7% reduction in total system cost and an 84.3% decrease in emissions. Additionally, this study evaluated the influence of future load growth on fuel expenditure, offering realistic insights into the techno-economic viability of HES deployment.