Multicycle Adaptive Simulation of Boiling Water Reactor Core Simulators

Abstract

Adaptive simulation (AS) is an algorithm utilizing a regularized least squares methodology to correct for the discrepancy between core simulators predictions and actual plant measurements. This is an inverse problem that will adjust the cross sections input to a core simulator within their range of uncertainty to obtain better agreement with the plant measurements. The cross section adjustments are constrained to their range of uncertainty using the covariance matrix of the few-group cross sections and in imposing the regularization on the least squares solution. This few-group covariance matrix is obtained using the covariance matrix of the multi-group cross sections and the corresponding lattice physics sensitivity matrix. To perform the adaption, one must also have the sensitivity matrix of the core simulator. Constructing the sensitivity matrix of both the lattice physics code and core simulator would be a daunting task using the traditional brute-force method of computing a forward solve for a perturbation of every input. To avoid this, a singular value decomposition (SVD) is used to construct a low rank approximation of the covariance matrices, thus drastically reducing the number of required forward solves.

Until now, AS has been used on a single depletion cycle to correct for discrepancies resulting from errors introduced by incorrect cross sections only. Adapting to a single depletion cycle means that the cross sections of cycle m were adjusted so that the core simulator better predicts the actual measurements of cycle m (and future cycles if the algorithm is robust). This, however, does not account for the reloaded burnt fuel number density errors at the beginning-of-cycle (BOC) m. By definition a burnt assembly has been used and depleted in a previous cycle. If adaption changes the cross sections of that burnt assembly in cycle m, those cross sections should have also been changed in any cycle preceding m which would have resulted in different BOC m number densities. This means that the number densities obtained using the original cross sections are not consistent with the newly adapted cross sections.

Hence, the number densities input to a core simulator are not the actual values in the reactor's fuel assemblies for the burnt fuel. This discrepancy in isotopics is another component to the discrepancy between the core simulator and actual observables. This means that the adaption algorithm is adjusting cross sections to account for number density errors.

It is the goal of this research to 1) remove these inconsistencies between the adapted cross sections and the burnt fuel BOC n number densities, and 2) ensure that adjusting cross sections to make up for number density errors does not corrupt the adaption. To do this, we assume that to best predict cycle n (by correcting both cross sections and BOC number densities of cycle n), one must adapt cycles m through n-1 simultaneously, where cycle m is the cycle in which the oldest assembly in cycle n is a fresh assembly. After adaption, the cross sections must be used to deplete from cycle m to n. This will remove the number density errors in two ways: 1) burnup healing, and 2) beginning the depletion of fresh assemblies in cycles m through n-1 with the correct cross sections. To ensure the cross sections adjustments are not overcompensating for the number density errors, we restrain their adjustment to stay near one standard deviation of their a prior values.