New genetic algorithms (GA) to optimize PWR reactors: Part II: Simultaneous optimization of loading pattern and burnable poison placement for the TMI-1 reactor

doi:10.1016/j.anucene.2007.05.004

Annals of Nuclear Energy

Volume 35, Issue 1, January 2008, Pages 113-120

https://doi.org/10.1016/j.anucene.2007.05.004 Get rights and content

Abstract

In this paper, the GARCO–PSU (Genetic Algorithm Reactor Code Optimization–Pennsylvania State University) code simultaneously optimizes the core loading pattern (LP) and the burnable poison (BP) placement in a pressurized water reactor (PWR). The LP optimization and BP placement optimization are interconnected, but it is difficult to solve the combined problem due to its large size. Separating the problem into two sequential steps provides a practical way to solve the problem. However, the result of this method alone may not develop the real optimal solution. GARCO–PSU achieves solving the LP optimization and BP placement optimization simultaneously by developing an innovative genetic algorithm (GA). The classical representation of the genotype has been modified to incorporate in-core fuel management basic knowledge. GARCO has three modes; the first mode optimizes the LP only, the second mode optimizes the LP and BP placement in sequence. The third mode, which optimizes the LP and BP placement simultaneously, is described in this paper. GARCO, as stated in Part I, can be applied to all types of PWR core structures having different geometries with an unlimited number of fuel assembly (FA) types in the inventory.

Introduction

A typical 1/8 core sector of symmetry has about 10²⁶ and more possible loading patterns (LPs) (DeChaine, 1995). The burnable poison (BP) placement optimization in the fresh fuel assemblies (FAs) introduces another enormous number of possible arrangements. The combination requires eliminating a majority of these possibilities both during the genetic algorithm (GA) process and also before transferring the design to be analyzed by the accurate commercial reactor physics codes. Separating the problem as performed in Part I provides a practical way to solve the problem. However, the result of this method should be verified by performing the LP optimization and BP placement optimization simultaneously. For this reason, simultaneous optimization is developed in Mode 3 of GARCO so as to be efficient and to includes a unique methodology to solve this optimization problem for a given PWR core. Mode 3 utilizes some results from Part I to greatly accelerate the calculation. Mode 3 employs the same TMI-1 core and its FAs, the same selection operator, and other aspects of Part I as explained in this paper. However, the Mode 3 algorithm and gene structure are completely different so as to succeed in simultaneously optimizing the LPs and the BP placement. SIMULATE-3, which is an advanced two-group nodal diffusion code, is used to perform reactor physics calculations for the TMI-1 core Umbarger and DiGiovine (1992). SIMULATE-3 incorporates a CASMO-4 cross section library previously developed by Yilmaz (2005).

Section snippets

Problem definition

The simultaneous optimization is performed on the same TMI-1 core as in Part I. Gadolinium (Gd) is used as an integral BP in the TM-1 core and the reference BP configurations for the TM-1 fuel assembly are taken from Yilmaz’s PhD thesis as was done in Part I (Yilmaz, 2005). The goal is to simultaneously select an optimum LP and BP placement together to find automatically the longest cycle length while satisfying all safety constraints.

Genotype structure

A simple example of the genotype for performing the simultaneous optimization is shown in Fig. 1 wherein the columns represent FA types and the rows represent the location numbers. It is necessary to have two different genes in each location to identify the symmetry number and the BP type and they are identified in the white squares. This structure allows changing the LP and BP designs simultaneously. Each square represents a FA type for which the upper part shows the symmetry number of the

Application

The first step in the simultaneous optimization is to arrange the BP types according to their rank, i.e. magnitude of the EOC soluble boron. The effect of the BP types is observed on a reference LP (Yilmaz, 2005), which is the TMI-1 LP shown in Fig. 4. The fresh FAs are shown with gray colors and are also listed in Table 3 in Part I.

Fifty different BP designs were used in this study and they are shown in Table 4 in Part I. To observe the effect of the BP designs on the cycle length of the

Conclusion

GARCO is capable of solving the LP and BP Placement reload configuration simultaneously. A new type genotype is introduced as shown in Fig. 1 that optimizes the core designs via the GA algorithms . New mutation operators as well as a new type cross over operator are introduced to work with this genotype so as to greatly reduce the calculation times.

Two cases were examined.

Case 1: The initial LP population was created randomly.
Case 2: The initial LP population was created using the HPD method to

References (4)

Alim, F., 2006. Heuristic Rules Embedded Genetic Algorithm for in-Core Fuel Management Optimization. Ph.D. Thesis in...
DeChaine, M., 1995. Stochastic Fuel Management Optimization Using Genetic Algorithms and Heuristic Rules, Ph.D. Thesis...

There are more references available in the full text version of this article.

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