Mathematical modeling of a pressurizer in a pressurized water reactor for control design

A pressurizer is a key equipment to ensure the safe operation of a pressurized water reactor by maintaining the reactor coolant system pressure within allowed tolerances. In this paper, a nonequilibrium three-region pressurizer model for the pressurized water reactor was developed first base on the basic conservation laws of mass and energy for the steam and water in the pressurizer. Then the nonlinear model was linearized to introduce the transfer function models of the pressurizer during insurge and outsurge transients for the controller design of a small pressurized water reactor pressurizer. Based on the developed transfer function models, the closed-loop pressurizer pressure and water level control systems including conventional proportional-integral-derivative controllers were designed employing the control strategy that uses a spray valve and two electric heaters for pressure control and regulates the charging flow rate with the letdown flow rate keeping constant for water level control. Finally, a simulation platform for the small pressurized water reactor pressurizer was developed in MATLAB/Simulink with implementation of the proposed nonlinear and nonequilibrium three-region pressurizer model, a widely-used nonlinear and nonequilibrium three-region pressurizer model and the designed pressure and water level controllers. Two typical load change transients, including the 100% to 90% of full power step load decrease and load rejection from 100% to 25% of full power, were simulated based on the platform. Dynamic responses of the pressure and water level obtained using the two nonlinear pressurizer models were analyzed, and the controller performances were assessed. The analysis and assessment results have shown satisfactory control performance and good robustness of the designed controllers regardless of the pressurizer simulation model adopted, demonstrating the feasibility, effectiveness and accuracy of the developed nonlinear and transfer function models of the pressurizer for dynamic simulation and controller design.