Design of Two-Degree-of-Freedom PID Controllers Optimized by Bee Algorithm for Frequency Control in Renewable Energy Systems

Sarawoot Boonkirdram, Sitthisak Audomsi, Worawat Sa-Ngiamvibool and Wassana Kasemsin ()
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Sarawoot Boonkirdram: Program of Electrical and Electronic, Faculty of Industrial Technology, Sakon Nakhon Rajabhat University, Sakon Nakhon 47000, Thailand
Sitthisak Audomsi: Faculty of Engineering, Mahasarakham University, Maha Sarakham 44150, Thailand
Worawat Sa-Ngiamvibool: Faculty of Engineering, Mahasarakham University, Maha Sarakham 44150, Thailand
Wassana Kasemsin: Program of Electrical and Electronic, Faculty of Industrial Technology, Sakon Nakhon Rajabhat University, Sakon Nakhon 47000, Thailand

Energies, 2025, vol. 18, issue 18, 1-18

Abstract: The increasing incorporation of renewable energy sources, such as photovoltaic and wind power, results in considerable variability and uncertainty within modern power systems, thereby complicating load frequency control. Conventional controllers, including PI and PID, often fail to provide sufficient performance in dynamic conditions. This study introduces a Two-Degree-of-Freedom PID (2DOF-PID) controller optimized through the Bee Algorithm (BA) for Load Frequency Control (LFC) in a two-area interconnected power system that includes renewable energy sources. The BA is employed to enhance controller parameters according to two objective functions: the Integral of Time-weighted Absolute Error (ITAE) and the Integral of Time-weighted Squared Error (ITSE). Simulation studies utilizing MATLAB/Simulink are conducted to evaluate the comparative effectiveness of PI, PID, and 2DOF-PID controllers. The results demonstrate that the 2DOF-PID controller consistently outperforms conventional PI and PID controllers in terms of frequency stability. The ITAE optimization of the 2DOF-PID results in a reduction in the ITAE index by more than 95% compared to PI and PID controllers, a decrease in settling time by approximately 40–60%, and a near elimination of overshoot and undershoot. Through ITSE optimization, the 2DOF-PID achieves an error reduction exceeding 90% and ensures smooth convergence with minimal oscillations. The PID controller has slightly improved effectiveness in minimizing tie-line power deviation, whereas the 2DOF-PID demonstrates greater resilience and damping capability in frequency regulation across both regions. The findings confirm that the Bee Algorithm-tuned 2DOF-PID controller serves as a robust and effective approach for frequency management in systems primarily reliant on renewable energy sources. Future research should incorporate multi-objective optimization algorithms that concurrently address frequency and tie-line power variations, thereby providing a more equitable control framework for practical Automatic Generation Control (AGC) operations.

Keywords: bee algorithm; load frequency control; PID controller; renewable energy systems; 2DOF-PID controller (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2025
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