Present status of reactor physics in the United States and Japan-III. 2. Nuclear Fuel Management Optimization Capabilities

Nuclear fuel management is a very difficult design optimization problem in that decisions ranging from the microscopic level, e.g., pin enrichment, to the macroscopic level, e.g., core flow rate, and spanning time horizons of several reload cycles are strongly coupled. Added to these attributes are the highly constrained design, disjointed decision space, multimodal objective function, mixed integer type decision variables, highly nonlinear objective and constraint functions, and computationally demanding evaluation of the objective and constraint functions. Not surprisingly, after years of research on nuclear fuel management optimization, only limited progress has been made. The traditional approach to partially overcome these difficulties involves constraining the search space via heuristic rules, decomposing the problem into sub-optimization problems, and utilizing simplified core physics models. These approaches have sometimes proven effective, but to claim that the design decisions are global optimum decisions would not be appropriate. Given the increasingly tight constraints and design complexities of nuclear cores, and stronger desire to reduce generating costs, the nuclear fuel management design optimization problem has grown more challenging and important with the passage of time. In this paper, we summarize our research on this design optimization problem. A suite of computer codes that aid in making nuclear fuel management decisions has been developed. From Table I, it is obvious that decomposition of the global optimization problem into suboptimum problems has been employed. All of these computer codes utilize stochastic optimization techniques to search the decision space for determining the family of near-optimum decisions in the sub-optimization problem being solved. A stochastic optimization approach has been selected since it is well suited to address the problems' attributes noted earlier. The drawback of employing a stochastic optimization approach is that many histories, i.e., combinations of decision variables, must be evaluated, which implies that many core physics calculations are required to determine the family of near-optimum decisions. To reduce computer execution time, highly efficient, core physics models with only the fidelity required for the assigned task are utilized. Ideally, one would like to utilize the same core physics models for all nuclear problems for consistency and ease of usage, which may someday occur with increases in computational power and advances in computational reactor physics. In considering core physics models, a unique aspect for nuclear fuel management optimization applications is that many repetitive calculations need to be completed during the optimization search. This implies that considerable overhead can be tolerated to reduce the computational time per history since the overhead will be amortized over many histories. This feature can imply the employment of different solution approaches than normally utilized. How various suboptimum problems integrate in an attempt to address the global optimization problem is now explained. The out-of-core optimization OCEON-P code has a number of decision variables, but the only decision that carries-forward in the reload design process is the cycling scheme, i.e., batch sizes in each cycle of the planning horizon. Note that OCEON-P is the only optimization code within the suite that truly does multicycle optimization and so can meaningfully evaluate and minimize levelized fuel cycle cost. The FORMOSA-L code optimizes the lattice, normally constrained to follow a specified reactivity versus burnup. This constraint provides the linkage to the core-wide analysis but is problematic to obtain. There currently does not exist within the suite of codes one that addresses the suboptimum problem of bundle design, which other researchers have addressed to a limited extent. With our current capabilities, a number of different bundle designs are developed by the designer from the lattice designs. These bundle designs are then provide d to the in-core optimization code, either FORMOSA-P (Ref. 4) or FORMOSA-B (Ref. 5). Since the fresh fuel inventory can be over-specified in either of these codes, it can now select from the available bundle designs the preferred designs to utilize. Since FORMOSA-P and FORMOSA-B both complete only single cycle optimization, multicycle effects must be treated in an ad hoc manner. This is done by imposing upper and lower batch power share limits, including discharge burnup maximization as an objective function, and automating a multicycle restart capability. As we look into the future, nearer-term activities underway include reducing the computational time and relaxing the control rod programming heuristic rules of FORMOSA-B, developing a robust multi-objective optimization capability for FORMOSA-P and FORMOSA-B, enhancing the fidelity of the core simulators utilized in OCEON-P, and loosely linking OCEON-P and FORMOSA-P. The longer-term activity, which we can think of as the grand challenge of nuclear fuel management optimization, will be the integration of the sub-optimization problems into a global optimization problem that involves the simultaneous selection of all decision variables so selected to optimize performance over multiple cycles. (authors)