Load-following control of a nuclear reactor using optimized FOPID controller based on the two-point fractional neutron kinetics model considering reactivity feedback effects

Load-following control of a nuclear reactor core is very crucial. The main challenge in examining power distribution control of the reactor core is to perform axial power distribution control rather than handling radial power distribution. In this work, a new model consisting of fractional order derivatives and two nodes of the reactor core with reactivity feedbacks is presented named as the two-point fractional neutron point kinetics (TPFNPK) model. According to neutron diffusion phenomena, this modeling method has a better physical interpretation for a quick change of neutron flux in load-following operation mode. For load-following control, a fractional order PID controller is implemented. Optimization of the parameters of this controller (KP, KI, lambda, KD, and mu) is carried out utilizing a genetic algorithm (GA) which is an evolutionary algorithm. The objective is the minimization of the weighted sum of the integral of time-weighted absolute error (ITAE), and the overshoot or the undershoot (MP). The new reactor core model is simulated in a MATLAB/SIMULINK environment coupled with a genetic algorithm. Different load patterns (the assumed tracking signal) considering different values of the model parameter (alpha) are introduced to address the effectiveness of the implemented control method. The simulation result demonstrates that the optimized control methods (GA-PID and GA-FOPID) have satisfactory and suitable functionality during load pattern tracking for all selected values of the model parameter. However, the GA-FOPID controller has a relatively better performance compared to the GA-PID controller. In all cases, it has lower costs and faster convergence. In addition, core normalized axial offset (AO) is always maintained within a certain limit during load-following operation for all the cases. Furthermore, in all the cases, the normalized axial xenon oscillation index (AXOI) remains bounded during the power transient.