Using Hopfield neural network to optimize fuel rod loading patterns in VVER/1000 reactor by applying axial variation of enrichment distribution

Abstract The present work investigates an appropriate way to solve the problem of optimizing fuel management in a VVER/1000 reactor. To automate this procedure, a computer program has been developed. This program suggests an optimal core configuration which is determined according to established safety constraints. The suggested solution is based on the use of coupled programs, one of which is the nuclear code, for making a database and modeling the core, and another one is the Hopfield neural network. In addition to we applied axial variations of enrichment in fuel rods to flat the flux core as novel role. This computational procedure consists of three main steps. The first one consists of creating the cross section database and calculating neutronic parameters by using WIMSD4 and CITATION codes. The second one consists of finding the best axial variations distributions of enrichment to create a fuel rod pattern by using Hopfield neural network artificial (HNNA) and the cross section database. The third one consists of loading of the fuel rods by the suggested fuel rod patterns and finding the optimum core configuration by HNNA that based on minimizing power peaking factor (PPF, PPF = maximum power/average power) and maximizing the effective multiplication factor ( k eff , the ratio of the number of neutrons in two successive fission generations). The procedure uses the optimized parameters in order to find configurations in which k eff is maximized. The penalty function is applied to limit the value of local PPF in the neighborhood fuel assemblies. Therefore, in this paper, we proposed a new approach for the use of Hopfield neural network to guide the heuristic search, and applied axial variations distributions of enrichment as novel method to flat the neutron flux and for evaluating the obtained results pertaining to the first core. The results show that applying the HNNA led us to the appropriate PPF and k eff . Also, applying HNNA and axial variation of enrichment is promising to reach the flattening neutronic flux and guaranteeing safety condition in the reactor core. Therefore, we achieved to a set of two basic parameters PPF and k eff as effective factors on satisfying the safety constraints of VVER/1000 reactor core.

[1]  W. B. Terney,et al.  The Design of Reload Cores Using Optimal Control Theory , 1982 .

[2]  Ali Pazirandeh,et al.  Optimizing the fuel management in a VVER-1000 reactor using an artificial neural network , 2012 .

[3]  Roberto Schirru,et al.  PARALLEL EVOLUTIONARY METHODS APPLIED TO A PWR CORE RELOAD PATTERN OPTIMIZATION , 2006 .

[4]  Hiroshi Motoda,et al.  Optimization of Refueling Schedule for Light-Water Reactors , 1973 .

[5]  Alfred F. Rohach,et al.  Perturbation theory in nuclear fuel management optimization , 1982 .

[6]  Mahesan Niranjan,et al.  A theoretical investigation into the performance of the Hopfield model , 1990, IEEE Trans. Neural Networks.

[7]  G. Pawley,et al.  On the stability of the Travelling Salesman Problem algorithm of Hopfield and Tank , 2004, Biological Cybernetics.

[8]  Roberto Schirru,et al.  A nuclear reactor core fuel reload optimization using artificial ant colony connective networks , 2008 .

[9]  T. O. Sauar,et al.  APPLICATION OF LINEAR PROGRAMMING TO IN-CORE FUEL MANAGEMENT OPTIMIZATION IN LIGHT WATER REACTORS. , 1971 .

[10]  Tsutomu Hoshino,et al.  In-Core Fuel Management Optimization by Heuristic Learning Technique , 1972 .

[11]  Ali Pazirandeh,et al.  Effects of various spacer grid modeling on the neutronic parameters of the VVER-1000 reactor , 2011 .

[12]  Alan H. Robinson,et al.  Determination of optimum fuel loadings in pressurized water reactors using dynamic programming , 1973 .

[13]  Roberto Schirru,et al.  The Ant-Q algorithm applied to the nuclear reload problem , 2002 .

[14]  Roberto Schirru,et al.  Parameterless evolutionary algorithm applied to the nuclear reload problem , 2008 .

[15]  Stephen J. Chapman.  Fortran 90/95 for Scientists and Engineers , 1998 .

[16]  J. J. Hopfield,et al.  “Neural” computation of decisions in optimization problems , 1985, Biological Cybernetics.

[17]  M. Sadighi,et al.  Neutron flux flattening in PWRs using neural networks in fuel management , 2002 .

[18]  Gang Feng,et al.  Using Hopfield networks to solve traveling salesman problems based on stable state analysis technique , 2000, Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. IJCNN 2000. Neural Computing: New Challenges and Perspectives for the New Millennium.