OPTIMAL CONTROL THEORY FOR XENON SPATIAL OSCILLATIONS IN LOAD FOLLOW OF A NUCLEAR REACTOR

A simple core control model has been developed for the control of xenon spatial oscillations in load-following operations of a current design commercial nuclear pressurized water reactor. The model has been formulated as a linear - quadratic - tracking problem in the context of modern optimal control theory and the resulting two-point boundary value problem (TPBVP) has been solved directly by the techniques of initial value methods.;The part-length control rod bank and the coolant inlet temperature are included in the control variables besides the full-length control rod bank and the boron concentration. The optimal control strategy which will closely follow the desired power distribution in space and time without too much control effort is sought via modern optimal control theory.;The singularly perturbed two-point boundary value problem which results from applying modern optimal control theory to the stiff dynamic system containing a small parameter exhibits prompt jump phenomena at both initial and final times. Singular perturbation theory is utilized to show that the solution of the reduced problem (similarly known as the prompt jump approximation in reactor kinetics) becomes the limiting solution of the original full problem as the small parameter approaches zero. The approximation by the reduced solution has the desirable feature of becoming more effective and accurate with increasing stiffness.;An optimal control program OPTCON has been developed to solve the reduced two-point boundary value problem directly by utilizing an available efficient two-point boundary value problem solver called SUPORT. Numerical studies have been performed for 3-6-3 daily load-following operations between 100% and 80% of rated power. Numerical experience shows that the computational effort required by SUPORT is minor compared to other peripheral calculations such as the steady state solution and matrix operations. Each case studied shows that the optimal solution closely follows the desired load demand and maintains the desired power distribution with a small control effort. Several numerical results are included to indicate the control model performance. The part-length control rod bank warrants more careful study for evaluation of its control effect. The inlet temperature is found to be an important control variable, which suggests that the steam generator dynamics be included in a more extended reactor control model.;The system of state equations is composed of the one-group diffusion equation with temperature and xenon feedbacks, the I-Xe dynamics equations, an energy balance relation for the core, and an equation of state for the coolant. The system is linearized around a steady state which is an eigensolution of the reactor static equation with explicit nonlinear terms of xenon and temperature feedbacks. The nonlinear eigenvalue problem is shown to have a unique positive solution under certain conditions by using bifurcation theory and solved by an iteration scheme based on monotone operators. The resulting linearized equation which belongs to a class of distributed parameter systems is then converted to a lumped parameter system by a modal expansion method.