Characteristics Analysis and Fuzzy Fractional-Order PID Parameter Optimization for Primary Frequency Modulation of a Pumped Storage Unit Based on a Multi-Objective Gravitational Search Algorithm

Compared with conventional hydropower units, the pumped storage unit has the characteristics of diverse working conditions and frequent switching. Therefore, the stability and regulation quality of the primary frequency modulation transition process of the regulating system is very important. Due to the “S” characteristics of the pumped storage unit (PSU), the pumped storage unit regulating system has a strong nonlinearity, and the conventional proportional-integral-derivative (PID) controller cannot provide high-quality control under low water head conditions. In this paper, the nonlinear PSU model with an elastic water hammer effect is studied, and the fuzzy fractional-order PID (FFOPID) controller is designed to improve the stability of the system. The membership function and the control parameters of the fractional-order PID are optimized based on the multi-objective gravitational search algorithm (MOGSA). The experimental results show that the optimized design of the FFOPID controller has better control quality than the traditional PID controller, the fractional-order PID (FOPID) controller, and the fuzzy PID controller (FPID) when the system is disturbed by the rotating speed under low water head.