The Design of Reload Cores Using Optimal Control Theory

Abstract

A formal approach for the optimization of the final design of reload cores has been devised and verified. The method is based on applying the calculus of variations (Pontryagin's principle) to the normal flux and depletion system equations. The resulting set of coupled system, Euler-Lagrange (E-L), and optimality equations are solved iteratively. This is done by assuming a loading pattern for the old fuel, first solving the system equations, and then the E-L equations. The pattern is then modified by using the optimality (or Pontryagin) condition, and the process is repeated until no further improvements can be made. A computer program, OPMUV, implementing these procedures has been written and verified. The code can handle two-dimensional, quarter-core symmetric configurations with up to 241 assemblies and 4 nodes per assembly with modified one-group theory. It also has the capability of optimizing over the entire depletion cycle as well as just at the beginning of cycle (BOC). The results show that the procedure does work. In all cases tried, the method led to a reduction in nodal peaks of 1 to 3% over the final designer-obtained loading pattern within a couple of iterations. These savings carry over to comparable reductions in pin peaksmore » when the optimized patterns are used in four-group, fine-mesh calculations. Since the changes on each iteration are limited to ensure convergence, the method is thus well suited for the final fine tuning of the normally obtained patterns to gain an extra few percent in power flattening.« less