Advanced and flexible genetic algorithms for BWR fuel loading pattern optimization

This work proposes advances in the implementation of a flexible genetic algorithm (GA) for fuel loading pattern optimization for Boiling Water Reactors (BWRs). In order to avoid specific implementations of genetic operators and to obtain a more flexible treatment, a binary representation of the solution was implemented; this representation had to take into account that a little change in the genotype must correspond to a little change in the phenotype. An identifier number is assigned to each assembly by means of a Gray Code of 7 bits and the solution (the loading pattern) is represented by a binary chain of 777 bits of length. Another important contribution is the use of a Fitness Function which includes a Heuristic Function and an Objective Function. The Heuristic Function which is defined to give flexibility on the application of a set of positioning rules based on knowledge, and the Objective Function that contains all the parameters which qualify the neutronic and thermal hydraulic performances of each loading pattern. Experimental results illustrating the effectiveness and flexibility of this optimization algorithm are presented and discussed.     

BWR fuel cycle optimization using neural networks

In nuclear fuel management activities for BWRs, four combinatorial optimization problems are solved: fuel lattice design, axial fuel bundle design, fuel reload design and control rod patterns design. Traditionally, these problems have been solved in separated ways due to their complexity and the required computational resources. In the specialized literature there are some attempts to solve fuel reloads and control rod patterns design or fuel lattice and axial fuel bundle design in a coupled way. In this paper, the system OCONN to solve all of these problems in a coupled way is shown. This system is based on an artificial recurrent neural network to find the best combination of partial solutions to each problem, in order to maximize a global objective function. The new system works with a fuel lattices’ stock, a fuel reloads’ stock and a control rod patterns’ stock, previously obtained with different heuristic techniques. The system was tested to design an equilibrium cycle with a cycle length of 18 months. Results show that the new system is able to find good combinations. Cycle length is reached and safety parameters are fulfilled.     

Multiobjective fuel management optimization for self-fuel-providing LMFBR using genetic algorithms

One of the conceptual options under consideration for the future of nuclear power is the long-term development without fuel reprocessing. This concept is based on a reactor that requires no plutonium reprocessing for itself, and provides high efficiency of natural uranium utilization, so called Self-Fuel-Providing LMFBR (SFPR). Several design considerations were previously given to this reactor type which, however, suffer from some problems connected with insufficient power flattening, large reactivity swings during burnup cycles, and peak fuel burnup being significantly higher than recent technology experience, which is about 18% for U-10 wt%Zr metallic fuel to be considered. Yet, the mentioned core parameters demonstrate high sensitivity to the fuel management strategy selected for the reactor. Therefore, the aim of this study is to develop a practical tool for the improvement of the core characteristics by fuel management optimization, which is based on advanced optimization techniques such as Genetic Algorithms (GA). The calculation results obtained by a simplified reactor model can serve as estimates of achievable values for mentioned core parameters, which are necessary to make decisions at the preliminary optimization stage.     

BWR fuel reloads design using a Tabu search technique

We have developed a system to design optimized boiling water reactor fuel reloads. This system is based on the Tabu Search technique along with the heuristic rules of Control Cell Core and Low Leakage. These heuristic rules are a common practice in fuel management to maximize fuel assembly utilization and minimize core vessel damage, respectively. The system uses the 3-D simulator code CM-PRESTO and it has as objective function to maximize the cycle length while satisfying the operational thermal limits and cold shutdown constraints. In the system tabu search ideas such as random dynamic tabu tenure, and frequency-based memory are used. To test this system an optimized boiling water reactor cycle was designed and compared against an actual operating cycle. Numerical experiments show an improved energy cycle compared with the loading patterns generated by engineer expertise and genetic algorithms.     

BWR in-core fuel management optimization using parallel simulated annealing in FORMOSA-B

The process of finding optimized fuel reload patterns for boiling water reactors is complicated by a number of factors including the large number of fuel assemblies involved, the three-dimensional neutronic and thermal-hydraulic variations, and the interplay of coolant flow rate with control rod programming. The FORMOSA-B code was developed to provide an automated method for finding fuel loading patterns, control rod programs and coolant flow rate schedules to minimize certain quantitative metrics of core performance while satisfying given operational constraints. One drawback of this code has been the long runtimes required for a complete cycle optimization on a desktop workstation (oftentimes several days or more). To address this shortcoming, a parallel simulated annealing algorithm has been added to the FORMOSA-B code, so that the runtimes may be greatly reduced by using a multiprocessor computer cluster. Tests of the algorithm on a sample problem indicate that it is capable of parallel efficiencies exceeding 80% when using four processors.     

A modified equilibrium void distribution model applicable to subchannel-scale vapor–liquid cross flow model for conventional square and tight lattice BWR fuel bundles

As a part of the advanced subchannel code development project sponsored by Ministry of Economy, Trade and Industry, Japan, this paper describes improvement of the equilibrium void distribution model that is a main part of the vapor–liquid cross flow model.The three-component cross flow (TCCF) model is defined as the present framework that separates contributions of diversion, turbulent mixing and void drift. The Lahey's void settling model is introduced to express the latter two components. Based on the high-resolution air–water database and other published data of steam-water tests, general trends of vapor–liquid cross flow processes are examined. It can be assumed that subchannel void distributions are dominated by the three major effects, i.e. the fluid dynamic effect, the geometrical effect and the narrow gap effect.The equilibrium void distribution model is modified to include the above-mentioned three effects. Three characteristic parameters are assigned for each of the three effects and they are identified experimentally as functions of the void fraction. Multi-dimensional lattice geometries are incorporated based on the two-dimensional flow network model. The network equation is constructed by mapping the equilibrium void balance problem into the force-deflection problem. The resultant models are verified based on equilibrium void distribution data obtained by Sadatomi and Kawahara.     

AXIAL: a system for boiling water reactor fuel assembly axial optimization using genetic algorithms

A system named AXIAL is developed based on the genetic algorithms (GA) optimization method, using the 3D steady state simulator code Core-Master-PRESTO (CM-PRESTO) to evaluate the objective function. The feasibility of this methodology is investigated for a typical boiling water reactor (BWR) fuel assembly (FA). The axial location of different fuel compositions is found in order to minimize the FA mean enrichment needed to obtain the cycle length under the safety constraints. Thermal limits are evaluated at the end of cycle using the Haling calculation; the hot excess reactivity and the shutdown margin at the beginning of cycle are also evaluated. The implemented objective function is very flexible and complete, incorporating all the thermal and reactivity limits imposed during fuel design analysis; furthermore, additional constraints can be easily introduced in order to obtain an improved solution. The results show a small improvement in the FA average enrichment obtained with the system related to the reference case that has been studied. The results show that the system converge to an optimal solution, it is observed that the mean fuel enrichment decreases while all the constraints are satisfied. A comparison was also performed using one-point and two-points crossover operator and the results of a sensitivity study for different mutation percentage are also showed.     

Super-cell model for predicting local power distribution in BWR type fuel assemblies and its experimental validation

A super-cell model is described for the prediction of the local power distribution in BWR type fuel assemblies. The model is validated against the measured power distribution in nine fuel-loading patterns reported in the literature. Overall agreement is observed to be quite satisfactory. Local Peaking Factor (LPF) is predicted within a maximum uncertainity of 3.7%. The maximum root-mean-square error among the nine fuel loading patterns is observed to be 2.3%.     

Estimation of distribution algorithms for nuclear reactor fuel management optimisation

In this paper, estimation of distribution algorithms (EDAs) are used to solve nuclear reactor fuel management optimisation (NRFMO) problems. Similar to typical population based optimisation algorithms, e.g. genetic algorithms (GAs), EDAs maintain a population of solutions and evolve them during the optimisation process. Unlike GAs, new solutions are suggested by sampling the distribution estimated from all the solutions evaluated so far. We have developed new algorithms based on the EDAs approach, which are applied to maximize the effective multiplication factor (K_eff) of the CONSORT research reactor of Imperial College London. In the new algorithms, a new ‘elite-guided’ strategy and the ‘stand-alone’ K_eff with fuel coupling is used as heuristic information to improve the optimisation. A detailed comparison study between the EDAs and GAs with previously published crossover operators is presented. A trained three-layer feed-forward artificial neural network (ANN) was used as a fast approximate model to replace the three-dimensional finite element reactor simulation code EVENT in predicting the K_eff. Results from the numerical experiments have shown that the EDAs used provide accurate, efficient and robust algorithms for the test case studied here. This encourages further investigation of the performance of EDAs on more realistic problems.     

Optimization of the power ascension path for a boiling water reactor using genetic algorithms

To ensure the core status can meet the requirements of thermal limits, stability and other constraints during the power ascension process of a nuclear power plant, operators usually gradually increase power based on onsite measurements and experience. To reduce the operator’s burden, this research develops a method to find an optimal power ascension path that can be followed by operators. The power ascension path is formulated as a multiobjective optimization problem with the following constraints: power ascension time, thermal limits, core stability and maximum rod line. A genetic algorithm is adopted to obtain the optimal power ascension path. The results show that using our approach full power can be achieved quickly, while maintaining reasonable margins of thermal limit and stability, in addition to satisfying maximum rod line criteria.     

Evaluation of applying axial variation of enrichment distribution method and radial variation of enrichment distribution in VVER/1000 reactor using a Hopfield neural network to optimize fuel management

In this present work the analysis technique was developed to find the optimum core configuration by applying neural network. This work investigates an appropriate way to solve the problem of optimizing fuel management in VVER/1000 reactor. To automate this procedure, a computer program has been developed.This program suggests an optimal core configuration which is determined to establish safety constraints. The suggested solution is based on the use of coupled programs, which one of them is the nuclear code, for making a database and modeling the core, and another one is Hopfield Neural Network Artificial (HNNA).The first stage of computational procedure consists of creating the cross section database and calculating neutronic parameters by using WIMSD4 and CITATION codes. The second one, consists of finding the optimum core loading pattern by applying the primary fuel assemblies of the VVER/1000 reactor core, using the HNNA method that based on minimizing power peaking factor (PPF) and maximizing the effective multiplication factor (keff). In the third second one, we apply a heuristic method to flat the flux core and decreasing the power peaking factor of the core. It consists of finding the best axial and radial variation of enrichment distribution to reach an optimum core loading pattern, by using HNNA and the cross section database.Finally, we compared obtained results of these methods to obtained results of the primary core, Suggested pattern of the Russian contractor.In total, the results show that applying the HNNA led us to the appropriate PPF and keff. Therefore, we achieved to a set of two basic parameters PPF and keff as effective factors on satisfying the safety constraints of VVER/1000 reactor core. It should be mentioned to say that the obtained results of HNNA suggested pattern is promising.Therefore, these methods ultimately eventuated to find the optimum configuration for VVER/1000 reactor core.     

Design of a gadolinia bearing mixed-oxide fuel assembly for pressurized water reactors

A study on neutronics design of a gadolinia (Gd₂O₃) bearing mixed-oxide (MOX) fuel assembly (MOX-UO₂ (Gd₂O₃) assembly) was performed for the purpose of suppressing the use of fresh lumped burnable poison rods (BPRs). The MOX-UO₂ (Gd₂O₃) assembly investigated consists of MOX and UO₂ (Gd₂O₃) fuel rods, which have already been verified through both fabrication and irradiation experiences. In all, 16 UO₂ (10 wt% Gd₂O₃) fuel rods are located at every corner and the peripheral region of the MOX-UO₂ (Gd₂O₃) assembly in order to reduce the power peaking of MOX fuel rods due to the thermal neutron inflow, and to reduce the reactivity penalty at the end of cycle (EOC). Since fresh BPRs are not expected to be inserted and UO₂ (Gd₂O₃) fuel rods are located at every corner of the assembly, the number of splits in plutonium (Pu) content can be only two, which is less than three splits required for a standard MOX assembly. Core characteristics of an equilibrium core loaded with MOX-UO₂ (Gd₂O₃) assemblies are evaluated and it is verified that adoption of the MOX-UO₂ (Gd₂O₃) assembly is effective to avoid the use of fresh BPRs with securing both the core safety and cycle length. The simplication of the splits in Pu content is also supposed to be beneficial, since it has the possibility of reduce MOX fuel fabrication costs.     

An assessment of the BWR fuel box-lattice-cell homogenization procedures with the Tarapur BWR incore and excore measurements

A code system has been developed to provide the incorefuel-management guidelines to the Tarapur BWR reactors. Constant checking of the design calculational methods is rendered possible by the steady flow of operating data from the Tarapur units over the last few cycles. The operating data include cold/hot criticals and detailed flux/power maps. Besides these, the burnups and isotopic composition of a few irradiated fuel pins obtained by mass-spectrometric analyses, are also available for validation of the BWR core and lattice-cell modelling.The calculated eigen values for different power levels and at different core average burnups are found to have a spread of less than 0.25% ΔK. Analyses of a number of TIP measurements show that the core power distribution can be predicted in a satisfactory manner for uncontrolled fuel bundles and non-peripheral fuel assemblies (<10%). For prediction of cold-criticals the void-history effects are found to be unimportant.The pin burnups and isotopic densities of important U and Pu isotopes relative to ²³⁸U have been compared with mass-spectrometric measurements. The pin-burnup profile comparison is found to be good for fuel pins, which are not near water gaps. Deviation histograms of various isotopes are presented in this paper. ²³⁵U is predicted within ± 3% (r.m.s.). The total Pu is overpredicted by 5–8%, while the quality of Pu is predicted within ± 1.0% (r.m.s.).     

Application of the response matrix method to BWR lattice analysis

A lattice calculation code RESPLA has been developed for light-water reactor lattices on the basis of the response matrix method treating the heterogeneity in pin cells. The spatial dependency of neutron flux distribution along each cell boundary is taken into account by dividing the cell boundary into several subsurfaces and the anisotropy of neutron angular distribution is considered up to the P₁ component by using a relation between the P₀ and P₁ components. The RESPLA code has been applied to BWR lattice calculations and the calculational results have been compared with those obtained by the S_n method and the collision probability method. It has been found that the present response matrix method has the same accuracy as the collision probability method with fine spatial meshes and the error caused by the use of coarse meshes is much smaller than that by the collision probability method. Furthermore, the required computing time is smaller by about a factor of five than that in the collision probability method.     

Critical heat flux function approximation using genetic algorithms

Function approximation is the problem of finding a system that best explains the relationship between input variables and an output variable. We propose two hybrid genetic algorithms (GAs) of parametric and nonparametric models for function approximation. The former GA is a genetic nonlinear Levenberg-Marquardt algorithm of parametric model. We designed the chromosomes in a way that geographically exploits the relationships between parameters. The latter one is another GA of nonparametric model that is combined with a feedforward neural network. The neuro-genetic hybrid here differs from others in that it evolves diverse input features instead of connection weights. We tested the two GAs with the problem of finding a better critical heat flux (CHF) function of nuclear fuel bundle which is directly related to the nuclear-reactor thermal margin and operation. The experimental result improved the existing CHF function originated from the KRB-1 CHF correlation at the Korea Atomic Energy Research Institute (KAERI) and achieved the correlation uncertainty reduction of 15.4% that would notably contribute to increasing the thermal margin of the nuclear power plants.     

Pressurized water reactor reloading optimization using genetic algorithms

The application of genetic algorithms (GAs) to pressurized water reactor (PWR) reloading pattern optimization is described. Standard bit-based genetic operators are used to optimize the arrangement of assemblies, burnable absorber, and burnt assembly orientations. The developed system has a modular structure. The GAs operators, reactor physics code, constraint conditions and objective function are all flexible. Test examples illustrating the effectiveness and flexibility of this system are presented and optimization results are discussed.     

Analysis of radiant heat transfer in a BWR fuel assembly

A computer code ‘CIDER’ was developed which analyzes radiant heat transfer in a BWR fuel rod bundle under loss of coolant conditions. In the code, (1) a channel box and fuel rods are considered to be gray bodies, (2) reflection and absorption of radiation beams in the atmosphere is neglected, (3) a fuel rod is approximated by a regular polygonal rod, and (4) radiant heat flux is calculated considering circumferential temperature distribution on each fuel rod surface, which is determined from radial and circumferential heat conduction calculations in a fuel rod. It was found that the conventional model with uniform cladding temperature overestimated heat flux about 30% in a typical situation, or correspondingly underestimated the temperature rises.