Under low water head and no-load conditions

the pumped storage unit is apt to fall into the “S” feature area which can lead to wide range of unit frequency fluctuations and unstable operation. As traditional proportion-integration-differentiation (PID) control under low water head and no-load conditions is unable to appropriately adjust the frequency fluctuation problem

a fractional order PID (FOPID) regulation and control model is proposed for the pumped storage unit

where the pump turbine mathematical model is developed based on the complete characteristic curves by using logarithmic projection transformation

and the regulation parameters of FOPID are optimized by particle swarm optimization (PSO) algorithm. This paper is mainly concerned with the application of FOPID control for two simulated experiments

including unloaded start-up operation and unloaded frequency perturbation condition under low water. Simulation analysis demonstrates that FOPID control is capable of significantly improving the transition process of the frequency of pumped storage unit and guide vane opening. Meanwhile

the FOPID control will enhance the dynamic performance and stability of the pumped storage unit governing systems. This work is supported by National Natural Science Foundation of China (No. 51239004

No. 51479076).