Pressurized Water Reactor Core Maneuvering Utilizing Optimal Control Theory

Abstract

The computational capability of automatically determining the optimal control strategies for pressurized water reactor core maneuvering, in terms of an operating strategy generator (OSG), has been developed. The OSG was developed for use with an on-line, three-dimensional core simulator and applies optimal control theory. To reduce computer run time, the optimization engine employs a one-dimensional axial core model. A method has been developed for generating a consistent one-dimensional axial core model from the three-dimensional on-line core simulator based on the consistent collapse methodology. From the one-dimensional, model-based, optimal control strategy, the associated axial offset versus time is obtained. These axial offsets are subsequently used in the three-dimensional simulator to determine with enhanced accuracy the associated control rod insertions and boration/dilution operations versus time.Various operational objectives are defined as the performance index to be minimized. The axial flux difference limit constraint and the maximum boration/dilution limit constraint are treated as penalty functions added to the performance index. The control rod insertion/withdraw limit constraint is treated as a hard constraint on the control variable. The optimality condition is obtained by applying Pontryagin’s maximum principle for constrained optimization. The resulting nonlinear, two-point boundary-value problem is solved via an iterative approach based on the first-order gradient method.Several sample OSG maneuvering problems have been studied to assess the robustness and efficiency of the optimization search and nonlinear iterations. The algorithm exhibited excellent control of the axial power distribution during maneuvering. For the cases of minimizing the boron system duty during maneuvering, the optimal strategies produced reduced volumes of primary water generated by dilution and boration operations of 12% for beginning-of-cycle cases and 10% for end-of-cycle cases over the volumes generated using heuristic rules.