Improved Smoothed Functional Algorithms- Optimized PID Controller for Efficient Speed Regulation of Wind Turbines

The stochastic behaviour of wind speed and the turbulence that develops between turbines are common factors that induce stress in wind turbines. PID controllers are widely used as a speed control strategy to manage this wind turbulence optimally due to their simplicity and effectiveness in regulating rotor speed and system stability under fluctuating wind speed. However, existing PID speed control strategies often struggle to handle wind fluctuation, increasing interest in adopting improved optimization methods to fine-tune PID controller. This will enhance the wind turbine system response while preserving the robustness and simplicity of the PID controller. Meanwhile, existing traditional optimization methods for PID tuning require a substantial number of function evaluations (NFE), resulting in a high computational load. This study introduces a novel approach for PID controller tuning in wind turbine systems using single-agent optimization methods, specifically the memory smoothed functional algorithm (MSFA) and norm-limited smoothed functional algorithm (NL-SFA). Unlike conventional techniques, the proposed approach significantly reduces the NFE required per iteration, leading to enhanced computational efficiency and improved tuning precision. Moreover, the suggested MSFA and NL-SFA effectively addressed the instability inherent in the smoothed functional algorithm (SFA). The competency of the proposed MSFA-PID and NL-SFA-PID controllers for wind turbine systems was evaluated through simulation, covering statistical analysis, boxplots of integral absolute error (IAE), time-domain integral error-performance indices, transient response analysis, and robustness to parameter uncertainty. The result indicated that the proposed controllers are highly effective in producing better IAE even with less NFE compared to other existing multi-agent-based methods.