Design of three-stage start-up optimal strategy based on fuzzy fractional-order proportion integration differentiation controller of pumped storage unit under low water head

Abstract

When the pumped storage unit (PSU) operates in the low water heads, it is easy to enter the ‘S’ characteristic area, which leads to the chaotic phenomenon of the hydraulic transient of the PSU and makes the adjustment and control of the PSU under the no-load start-up condition extremely difficult. In this paper, a strategy of integrating three-stage guide vane opening law and fuzzy fractional-order proportion integration differentiation (PID) controller is proposed for the low water head start-up condition of PSU. Firstly, based on the mathematical model of pumped storage unit regulation system (PSURS), the mapping relationship between water head, no-load guide vane opening, the frequency switch point of the controller, and the number of rotational speed fluctuations is analyzed. Then a three-stage start-up optimal strategy based on a fuzzy fractional-order PID controller is proposed. On this basis, the multi-objective optimization method of control parameters for the three-stage start-up strategy is proposed by introducing the rotational speed overshoot and integrated time and absolute error (ITAE) index. Furthermore, to achieve efficient tuning of the high-dimensional control parameters for the multi-objective optimization method, a multi-objective grey wolf algorithm is proposed by introducing quantum space theory. Finally, numerical experiments are carried out to compare the start-up transition process under the three-stage start-up optimal strategy and conventional standard mode. The results indicate that compared with the conventional method, the proposed method has significant advantages in improving the dynamic stability and control quality of the low water head start-up of the PSU. The fluctuation times of the rotational speed of the PSU optimized and regulated by the novel method is 0 times, the regulation time is reduced by 34 s at most compared with the conventional method, and the steady-state error is only 0.003.