Multiobjective Optimization of a Fractional-Order PID Controller for Pumped Turbine Governing System Using an Improved NSGA-III Algorithm under Multiworking Conditions

In order to make the pump turbine governing system (PTGS) adaptable to the change of working conditions and suppress the frequency oscillation caused by the “S” characteristic area running at middle or low working water heads, the traditional single-objective optimization for fractional-order PID (FOPID) controller under single working conditions is extended to a multiobjective framework in this study. To establish the multiobjective FOPID controller optimization (MO-FOPID) problem under multiworking conditions, the integral of the time multiplied absolute error (ITAE) index of PTGS running at low and high working water heads is adopted as objective functions. An improved nondominated sorting genetic algorithm III based on Latin hypercube sampling and chaos theory (LCNSGA-III) is proposed to solve the optimization problem. The Latin hypercube sampling is adopted to generate well-distributed initial population and take full of the feasible domain while the chaos theory is introduced to enhance the global search and local exploration ability of the NSGA-III algorithm. The experimental results on eight test functions and a real-world PTGS have shown that the proposed multiobjective framework can improve the Pumped storage units’ adaptability to changeable working conditions and the proposed LCNSGA-III algorithm is able to solve the MO-FOPID problem effectively