Design of a fractional-order PID controller for a pumped storage unit using a gravitational search algorithm based on the Cauchy and Gaussian mutation

A pumped storage unit (PSU) is more difficult to control compared to a conventional hydropower generation unit due to the frequent switching of working conditions and the S-shaped characteristics of pump turbine. The traditional proportional-integral-derivative (PID) controller typically cannot easily provide high quality control. To overcome these difficulties, a fractional-order PID (FOPID) controller is designed for a PSU in this study. Although the FOPID controller is more effective compared to the traditional PID controller, it is more complex to optimize the parameters of this controller for a pump turbine governing system (PTGS). Thus, a gravitational search algorithm combined with the Cauchy and Gaussian mutation, named as CGGSA, is proposed and used to optimize the FOPID controller parameters. The experimental results indicate that the CGGSA has shown excellent optimization ability compared with some popular meta-heuristics on benchmark functions. Results have also proved that the FOPID-CGGSA controller shows significant advantages over other PID-type controllers with different optimization strategies. Meanwhile the optimally designed controller has shown great potential to improve the control quality of PTGS under multiple water heads.