Stochastic modeling for eind energy and multi-objective optimal power flow by novel meta-heuristic method

Amr Khaled Khamees, Almoataz Y. Abdelaziz, Makram Roshdy Eskaros, Hassan Haes Alhelou, Mahmoud Abdallah Attia

Research output: Contribution to journalArticleResearchpeer-review

16 Citations (Scopus)


Wind energy is considered one of the most important alternative energy sources for generating electricity. But 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 and robustness 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 robustness 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.

Original languageEnglish
Pages (from-to)158353-158366
Number of pages14
JournalIEEE Access
Publication statusPublished - 2021
Externally publishedYes


  • Aquila optimizer
  • Mayfly algorithm
  • Multi-objective optimization
  • Optimal power flow
  • Stochastic optimal power flow
  • Weibull distribution
  • Wind energy

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