Optimal Power Flow with Stochastic Renewable Energy Using Three Mixture Component Distribution Functions

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.