Adaptive condition predictive-fuzzy PID optimal control of start-up process for pumped storage unit at low head area

In order to overcome the rotational speed oscillation under no-load start-up condition caused by the 'S' characteristic area of the pump-turbine and the difficulty in improving the dynamic process under low head area of pumped storage unit (PSU), this paper uses the model predictive control and fuzzy logic control theory to study the optimal control of PSU under no-load start-up condition at low head area. Firstly, the instantaneous linearized controlled autoregressive integrated moving average model (CARIMA) of PSU is proposed. This model contains the dynamic equations of the complex pipeline system and pump-turbine generator-motor that accurately describe the hydraulic and mechanical dynamic characteristics. Based on the CARIMA, a novel adaptive condition predictive-fuzzy PID (ACP-FPID) controller is designed. The controller contains the operating point prediction and the avoidance of critical curves of the 'S' characteristic area. Then, multi-objective optimization control method combined with bacterial foraging algorithm is utilized for the optimal parameters selection of controller, guide opening time and frequency switching point when the closed-loop controller is put into operation. Furthermore, numerical simulation tests under start-up condition in typically low head are conducted to demonstrate the feasibility and robustness of the ACP-FPID optimal control method. The results indicate that the proposed method can effectively avoid the deep running of the unit into the 'S' characteristic area compared with traditional ones. The approximate periodic oscillations times and overshoot index of rotational speed obtained by ACP-FPID are less than 1 and 2% respectively, which are much smaller than that values obtained by the traditional ones. Moreover, strong robustness of ACP-FPID is testified when PSU disturbed by mechanical factors.