A novel mixed Rayleigh distribution model using PID based search algorithm for wind energy applications

Accurate modeling of wind speed distributions is a critical prerequisite for reliable wind energy assessment, system optimization, and long-term performance prediction. Conventional probability distribution functions exhibit notable deviations between the observed and estimated wind speed frequency distributions, indicating their limited capability in capturing the actual variability of wind regimes. To address this gap, this study introduces, for the first time in the wind energy domain, the application of a Mixed Rayleigh distribution in combination with a PID-based metaheuristic optimization algorithm (PSA) for parameter estimation. The proposed approach was tested at three measurement stations: Karaburun, Mersinkoy, and Gelibolu, using extensive wind speed datasets. Comparative analyses were conducted between PSA based Rayleigh, Mixed Rayleigh, and Weibull models, alongside conventional Moment and Maximum Likelihood methods. The proposed model achieved the lowest Sum Square Error (SSE) (0.0016) and Root Mean Square Error (RMSE) (0.0091) in Karaburun, the lowest SSE (0.0014) and RMSE (0.0075) in Gelibolu, and consistently high determination coefficients (R 2 ≈ 0.9999) across all regions. Additionally, the model yielded the lowest Mean Absolute Percentage Error (MAPE) based on Wind Power Density (WPD) (4.11 %) in Mersinköy and relatively low MAPE values based on Average Wind Speed (3.74 % and 3.26 %) in Karaburun and Mersinköy, respectively. In particular, the Mixed Rayleigh model demonstrated superior flexibility, resulting in improved fitting accuracy and reduced estimation errors. Overall, the findings highlight the methodological novelty and practical potential of combining hybrid distribution functions with advanced optimization algorithms.