Design of type-2 fuzzy fractional-order proportional-integral-derivative controller and multi-objective parameter optimization under load reduction condition of the pumped storage unit

Abstract

Pumped storage unit (PSU) is an effective regulation tool of the smart power grid system. The inherent “S” characteristics caused by the reversible design of the pump-turbine will make the PSU run into a state of instability, resulting in severe hydraulic fluctuation, unit speed, and frequency oscillation. PSU load reduction is an operation condition often encountered in the process of peak load regulation and frequency regulation. The operation stability of this condition is very important to the safety of the power station and power grid. Firstly, a mathematical model suitable for the numerical calculation of all working conditions transition process in the power generation direction of pumped storage unit regulating system (PSURS) is established. Further, the load reduction condition under typical water heads is selected. Through numerical calculation and analysis, it is found that when the PSU operates in the low water head-small load area and encounters load reduction to no-load, the PSURS is easy to fall into an unstable state. Therefore, an interval type-2 fuzzy fractional-order proportional-integral-derivative (PID) controller is proposed for the load reduction condition of the PSU under low water head and small load operation. And a multi-objective joint optimization strategy is proposed for tuning controller parameters. The experimental results show that the interval type-2 fuzzy fractional-order PID controller after parameters optimization has better control performance than traditional controllers. Compared with the PID control method, the double objective optimal result index is reduced by 0.025 and 47.98 respectively, the rotational speed regulation time of the PSU is reduced by 20.27 s, the maximum water hammer pressure is reduced by 9.2 m. The novel method effectively solves the instability problem of PSU under low water head load reduction conditions.