Fuel loading and control rod patterns optimization in a BWR using tabu search

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Fuel loading and control rod pabu, Jtera1115olvcoupled way. This system involves three dierent optimization stages; in the rst one, a seed fuel loading using the Haling principle isdesigned. In the second stage, the corresponding control rod pattern for the previous fuel loading is obtained. Finally, in the last stage, anew fuel loading is created, starting from the previous fuel loading and using the corresponding set of optimized control rod patterns.loading (FL) design, which implies to place an inventory niques, such as neural networks, ant colonies, genetic algo-Spectral Shift operation can be favored if control rod posi-tions (CRP design) are such, as to produce a peaked axialpower distribution at the bottom of the core. However, it isimportant to keep in mind that CRP design depends on FLdesign. In other words, if we do not have a good FL design,then we will not obtain a good CRP design. Therefore, anNucleares, Km. 36.5 Carretera Mexico-Toluca, Ocoyoacac 52045, Estadode Mexico, Mexico. Tel.: +52 55 53297200; fax: +52 55 53297301.E-mail addresses: jacm@nuclear.inin.mx (A. Castillo), jjortiz@nuclear.inin.mx (J.J. Ortiz), jlmt@nuclear.inin.mx (J.L. Montes), mrpc@nuclear.inin.mx (R. Perusqua).1 Also PhD student at the Facultad de Ciencias of the UniversidadAutonoma del Estado de Mexico, Mexico.Annals of Nuclear Energy 3annals ofof fuel assemblies into the core, in order to maximize thecycle length, while thermal limits, hot excess reactivityand cold shutdown margin are satised. Other optimiza-tion stage is related to the reactivity control during theoperation cycle. The goal in this part of the cycle designis to predict the full power control rod pattern (CRP). Inthis stage, the control rod axial locations during the wholeoperation cycle are considered. To obtain these CRPs it isrithms, tabu search and fuzzy logic (Ortiz and Requena,2004, 2006, 2004; Castillo et al., 2004, 2005; Francoiset al., 2004), among others. In some cases, Halings princi-ple (Haling, 1964) has been used to obtain FL design. TheHalings principle guarantees a safe operation of the reac-tor but it does not maximize cycle length. It is possible tomaximize cycle length using an adequate operation strat-egy. A good option is operating the reactor by using Spec-tral Shift strategy (Specker et al., 1978), which permits tobreed ssile material and allows a longer cycle length.* Corresponding author. Address: Instituto Nacional de InvestigacionesFor each stage, a dierent objective function is considered. In order to obtain the decision parameters used in those functions, the CM-PRESTO 3D steady-state reactor core simulator was used. Second and third stages are repeated until an appropriate fuel loading and itscontrol rod pattern are obtained, or a stop criterion is achieved. In all stages, the tabu search optimization technique was used. The Qui-nalliBT system was tested and applied to a real BWR operation cycle. It was found that the value for ke obtained by QuinalliBT was0.0024 Dk/k greater than that of the reference cycle. 2007 Elsevier Ltd. All rights reserved.1. IntroductionThe operation cycle design for a boiling water reactor(BWR) has several optimization stages. One is the fuelnecessary to take into account several constraints, includ-ing some of those mentioned above.FL and CRP problems have been commonly solved inan independent way by using several optimization tech-using taAlejandro Castillo *, Juan Jose OrtizInstituto Nacional de Investigaciones Nucleares, Km. 36.5 CarreReceived 19 May 2006; received in revised formAvailable onlineAbstractThis paper presents the QuinalliBT system, a new approach to s0306-4549/$ - see front matter 2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.anucene.2006.12.006tterns optimization in a BWRsearchose Luis Montes 1, Raul PerusquaMexico-Toluca, Ocoyoacac 52750, Estado de Mexico, MexicoDecember 2006; accepted 18 December 2006February 2007e fuel loading and control rod patterns optimization problem in awww.elsevier.com/locate/anucene4 (2007) 207212NUCLEAR ENERGYAs it was mentioned above, these problems have beensolved in an independent way, being one of the main rea-uclesons that the search space is too large if the problem is con-sidered in a coupled way in which case, the total number ofparameters included in the whole process is increased. Onthe other hand, the computers in the past did not havethe capacity to make the necessary calculations in a reason-able time. With present computers this is not a problemanymore. So, the coupled problem has begun to be investi-gated recently. An approach for solving this new problemwas proposed in a paper by Kobayashi and Aiyoshi(2002), by using a method based on Genetic Algorithms.In order to optimize the FL-CRP design, an if-then heu-ristic rule was implemented. As it was mentioned at theapproximation with greater scope is to consider the solu-tion of FL and CRP problems in a coupled manner.QuinalliBT derives its name from QUItze and toN-ALLI, two words of two ancient Mexican languages,and Busqueda Tabu (tabu search) in Spanish. The sys-tem solves both FL and CRP designs in a coupled way.In each stage a dierent multi-objective function is usedand then evaluated with CM-PRESTO (Scandpower,1993) 3D code. The tabu search (TS) heuristic techniqueis applied in the whole process. The QuinalliBT systemwas designed using FORTRAN-77 language in an Alphaworkstation with UNIX operation system.2. Problem descriptionFuel loading design problemmay be described as follows:for a given inventory of fuel assemblies, an arrangement ofthem inside the reactor core has to be found, in such a waythat some restrictions will be satised during cycle opera-tion. Among these restrictions can be mentioned, for exam-ple, that some fuel bundle allocation rules have to besatised, as well as thermal limits, hot excess reactivity andcold shutdownmargin; also energy extraction has to bemax-imized. The Halings principle has been one of the most usedtechniques for designing FL. With this operation strategy asafe operation of the reactor can be achieved without prob-lems. However, the obtained energy is far from being themaximum energy of the cycle.In CRP design, it is necessary to establish axial controlrod positions for each one of several burnup steps. Becausean adequate CRP design allows for axial power distribu-tion to be adjusted to a peak at the bottom of the core,CRP has an important contribution in achieving SpectralShift operation in the reactor. Another important consider-ation in this stage of the design is that reactor core has tobe critical, and also that thermal limits must be satisedthroughout the cycle. Although cycle length is stronglyaected by CRP throughout the cycle, its maximizationat this stage is not a goal. This task will be made later bymeans of fuel loading pattern optimization.208 A. Castillo et al. / Annals of Nbeginning of this paper, the Halings principle has beenused by many authors, for example, Kobayashi et al. Inthat paper the authors, pay special attention on the numberof fresh assemblies during the iteration process.In a BWR reactor with a total of 444 fuel assemblies and109 control rods, we can make the following deliberationsabout the search space size. In the rst case, if all fuelassemblies are dierent, then we have 444! possible solu-tions to FL design. In the control rods case, if we are con-sidering 25 axial nodes and 10 burnup steps, then we have((109)25)10 possible solutions to CRP design. We can seethat, both FL and CRP designs are combinatorial prob-lems. For this reason, a combinatorial technique can beused to solve these problems.If some heuristic rules and simplications are consid-ered, the number of possible solutions can be reduced con-siderably. Then, for the FL search space, it is possible toreduce it from 2.1 10984 to 7.3 1054 possible solutions,applying the following rules or simplications:1. Fuel load design with low leakage strategy.2. Eighth reactor core symmetry.3. Control cell core load strategy.On the other hand, for the CRP search space, it is alsofeasible to reduce the total possible solutions, from 5.683 101523 to 7.8 1069 (with 10 burnup steps), applying the fol-lowing heuristic rules or simplications:1. Eighth reactor core symmetry.2. Control cell core load strategy.3. The intermediate positions of control rods are for-bidden.In this work, we take advantage of previously designedsystems, which were developed to individually optimizeboth problems (Castillo et al., 2004, 2005). By using them,it was possible to develop a new system to optimize thecoupled FL-CRP problem. In the following section, thenew system is described in detail.3. QuinalliBT systemThe QuinalliBT system was developed in order to opti-mize FL and CRP design in a coupled way, in a BWRoperating cycle. The system has three stages, each oneusing a dierent multi-objective function. In the rst stage,an optimized FL is obtained using the Halings principle(Haling, 1964) while thermal limits, hot excess reactivityand cold shutdown margin are satised. When the Halingsprinciple is applied in order to design an operation strat-egy, power peaks within reactor core are minimized. How-ever, the obtained FL is not an optimized design from thepoint of view of maximum energy extracted from the fuel,therefore it is used as a seed FL. This seed FL is used inthe second stage to obtain a set of optimized CRP usingSpectral Shift strategy (Specker et al., 1978). In the lastar Energy 34 (2007) 207212stage, the CRP design attained in the second stage is usedto obtain a new FL design, instead of using the Halingsprinciple. Thus, second and third stages are repeated in aniterative process, until optimized FL and CRP designs areobtained, or a stop criterion is achieved. Fig. 1 shows theowchart of the QuinalliBT system. In the following para-graphs, QuinalliBT system stages are described.As mentioned above, the Halings principle is used inrst stage in order to obtain an initial FL design. The mainidea is to maximize ke value at the end of the cycle, whilethermal limits, hot excess reactivity and cold shutdownmargin are satised. The objective function to be maxi-mized is the following:F obj keff w1 DLim1 w2 DLim2 w3 DLim3 w4 DLim4 w5 DLim5 w6 1whereke eective multiplication factor at end of the cycleDLim1 = MFLPDlim MFLPDobtainedDLim2 = MPGRlim MPGRobtainedA. Castillo et al. / Annals of NucleDLim3 = MFLCPRlim MFLCPRobtainedDLim4 = SDMobtained SDMlimDLim5 = HERlim HERobtainedMFLPD maximum fraction of linear power densityMPGR maximum power generation ratioMFLCPR maximum fraction of limiting critical powerratioSDM cold shutdown margin at the beginning of cycleHER hot excess reactivity at the beginning of cycleand w1, w2, w3, w4, w5, w6 are non-negative weighting fac-tors obtained from a statistical analysis. When restrictionsLimi (i = 1, . . . , 5) are satised, their respective wi are equalto zero. It can be seen that if all constraints are satised,then Eq. (1) works only to maximize eective multiplica-tion factor ke. Input Data stop YES Fuel Loading with Halings stop principle NO criterion was satisfied? Seed Fuel Loading Control Rod Fuel Loading Patterns using CRP Fig. 1. QuinalliBTs owchart.In the next stage, operation cycle is divided into ten bur-nup steps. In each one of these steps control rod positionsmust be xed, taking into account that the reactor must becritical, the axial power shape must match a target axialpower prole and that thermal limits must be satised.The objective function to minimize is the following:F X25i1P iobj P iact w1 jkeff kcritj w2 DLim1 w3 DLim2 w4 DLim3 w5 2wherePobj target axial power prolePact obtained axial power proleke obtained eective multiplication factorkcrit objective eective multiplication factorLim1 = MFLPDlim MFLPDobtainedLim2 = MPGRlim MPGRobtainedLim3 = MFLCPRlim MFLCPRobtainedand wi, i = 1, . . . , 5 are weighting factors. It is desirable tominimize the dierences between the target and the obtainedaxial power proles.When the constraints Limi (i = 1, . . . , 3)are satised, then its respective wi, i 2 {3, . . . , 5} is equal tozero. w2 is zero if jke kcritj < 0.00010. It can be seen thatif all of these constraints are satised, Eq. (2) works onlyto minimize the dierence between the axial power proles.In the last stage of the iterative process, the optimizedCRP design is used instead of Halings principle to obtaina new FL design. In this case, ke at the end of cycle is max-imized, while the thermal limits in each burnup step, thecold shutdown margin and the hot excess reactivity at thebeginning of cycle must be satised. The objective functionused in this stage is the following:F kEOR w1 Xn1i1jkieff kcritj w2 Xni1Limi1 w3Xni1Limi2 w4 Xni1Limi3 w5 Lim4 w6 Lim5 w73wheren number of burnup stepskEOR obtained eective multiplication factor at the endof cyclekieff obtained eective multiplication factor in eachburnup stepkcrit objective eective multiplication factorLimi1 = MFLPDi,lim MFLPDi,obtainedLimi2 = MPGRi,lim MPGRi,obtainedLimi3 = MFLCPRi,lim MFLCPRi,obtainedLim4 = SDMobtained SDMlimLim5 = HERlim HERobtainedi denotes one of the burnup steps in which cycle length isar Energy 34 (2007) 207212 209divided. In the samewaywi, i = 1, . . . , 7 areweighting factorswith the same considerations of those for Eqs. (1) and (2).the present study. This array is equal to zero at the begin-ning of the process and updated in the following way:FVEC(i, j) = FVEC(i, j) + 2, if (i, j) move was made.In order to nish the process, it is necessary to denesome stop criteria. The rst one is to stop the algorithmwhen a maximum number of iterations is achieved; the sec-ond one is to stop the process after k iterations, if the objec-tive function does not improve.uclear Energy 34 (2007) 207212As it was mentioned, the second and third stages per-form an iterative process until FL-CRP design is obtained,or a stop criterion is achieved.4. Tabu searchIn both FL and CRP design, the tabu search (TS) tech-nique was applied. Following is a brief description aboutthis technique. See reference Glover (1968) for more detailson these concepts.The TS technique is an iterative process used to obtaina solution that maximizes (or minimizes) an objectivefunction, in a set X of feasible solutions. The TS techniquestarts from a randomly chosen initial feasible solution.Then, space X is explored by moving in a neighborhoodfrom one solution to another. In this process, each feasiblesolution x has an associated set of neighbors, called theneighborhood of x, N(x) 2 X. If N(x) is very large, it ispossible to choose, at each iteration of the process, a sub-set SN(x) N(x) in which case, a search from the currentsolution x to the best one x* in SN(x), whether or notf(x*) is better than f(x), is carried out. In some problems,evaluation of the entire neighborhood becomes veryexpensive in terms of time and computing resources. Inthat case, it is possible to reduce the size of SN takingthe rst move that improves the current solution. If thisis not possible, then it will be necessary to examine thewhole neighborhood.During search process, the TS technique allows cyclingprevention using a short-term memory, an array with eitherxed or variable length. The purpose of this memory is tostore certain prohibited movements (the reason why thisarray is called tabu list). In this sense, a movement remainstabu (forbidden) during n iterations (tabu tenure). It is verycommon also to apply a long-term memory to diversifyneighbors search, being the objective of this memory tomove toward unvisited regions.It is important to mention that the TS technique mayforbid some interesting moves because of their tabu sta-tus. In such case, if a move produces the best solution ofthe whole process, but it is forbidden, it is possible tocancel its tabu status and take it into account (aspirationcriterion).In the present analysis a tabu list with variable lengthfrom 7 to 15 is used. These values were obtained after a sta-tistical analysis in the development process of QuinalliBTsystem. Since function evaluation is a process that takesso much time and computing resources, the neighborhoodwas not revised in its entirety, neither for FL nor for CRPdesigns, but only 10% and 40%, respectively. During FLdesign, four CM-PRESTO simulator executions arerequired in order to evaluate the objective function. ForCRP design only one CM-PRESTO execution is required.In order to penalize the high frequency movements thatdo not improve the objective function during the iterative210 A. Castillo et al. / Annals of Nprocess, an aspiration criterion and a long-term memorywith a FVEC (Frequency VECtor) array were applied in5. ResultsTo test the QuinalliBT system, data of a real operationcycle were used. The chosen FL design (including itsCRPs) corresponds to an 18-month cycle length, with108 fresh fuel assemblies, a cycle burnup of 11,020MWD/T and ke = 0.9986. This ke value was obtainedfrom the simulation of the reference cycle with CM-PRE-STO simulator. The QuinalliBT system was executed sev-eral times, with all executions having similar results. Bestresults obtained are shown however.Table 1 shows the results obtained for the rst stage,according to Haling calculation. It can be seen that thermallimits, hot excess reactivity and cold shutdown margin weresatised. The corresponding limit values for each parame-ter are shown in this table. Eighty-four iterations were car-ried out to obtain these results, and the objective functionwas evaluated 1996 times using CM-PRESTO simulator.In this stage the eective multiplication factor obtained ishigher than the target value for ke.Once seed FL is obtained, QuinalliBT system performsan iterative process, until coupled FL-CRP is optimized.Fig. 2 presents the results obtained after four CRP-FL iter-ations. It can be seen that through the iterative process,eective multiplication factor decreases at the end of cycle,due to the fact that in the rst iterations some thermal lim-its are violated. In the last iteration, the thermal limits aresatised and ke values in the intermediate burnup steps areadjusted to the target ke. At the end of cycle, ke value ishigher than target ke. In the last CRP optimization caseexecuted, 637 iterations were performed and the objectivefunction was evaluated 10,867 times. The number ofCRP iterations decreases when the CRP-FL optimizationprocess is almost nished. In Table 2, ke values, burnupsteps and thermal limits are shown.Finally, Fig. 3 shows ke behavior through the CRP-FLiterative process, when FL is obtained. The optimized CRPis taken into account in this stage instead of Halings prin-Table 1Results in the Halings calculationParameter Limit Obtained valueMFLPD k eff behaviour0.99801.00001.00201.00401.00601.00801.01000 2000 4000 6000 8000 10000burnup (MWd/T)k effkcritkeff first iterationkeff second iterationkeff third iterationkeff fourth iterationFig. 2. ke Behavior after four iterations.0 1.0076 1.009A. Castillo et al. / Annals of Nuclear Energy 34 (2007) 207212 211Table 2ke and thermal limits valuesBurnup step ke MFLPD MPGR MFLCPR0 1.0080 0.8967 0.7823 0.8795ciple. In the last FL optimization executed case, QuinalliBTsystem performed 170 iterations and evaluated the objec-tive function 8279 times. ke value decreases during theCRP-FL iterative process, due to some thermal limits vio-lated in the rst iterations. Later on, thermal limits are sat-ised and ke at the end of cycle is higher than target ke.1037 1.0090 0.8758 0.8774 0.83912093 1.0080 0.8449 0.8541 0.85623052 1.0070 0.7290 0.7350 0.86744081 1.0060 0.7651 0.7778 0.90105032 1.0050 0.8318 0.8742 0.87286065 1.0060 0.8341 0.8836 0.88587096 1.0040 0.7667 0.8204 0.87748157 1.0030 0.7711 0.8374 0.89919279 1.0020 0.7569 0.8432 0.883810,307 1.0010 0.7567 0.8751 0.896611,020 1.0000 0.7439 0.8681 0.8818k eff behaviour0.99600.99901.00201.00501.00800 2000 4000 6000burnup (MWd/T)k effFig. 3. ke Behavior throughTable 3Parameters obtained in the last iterationBurnup step kcrit ke obtainedTable 3 shows the parameters obtained in this stage andit can be seen that all of these parameters are satised. Itis necessary to comment that, according to the stop criteriaof QuinalliBT system, the third stage of FL optimizationwas only performed three times.8000 10000kcritkeff first iterationkeff second iterationkeff third iterationout the iterative process.1037 1.0091 1.0092093 1.0085 1.0093052 1.0073 1.0074081 1.0061 1.0065032 1.0053 1.0056065 1.0045 1.0047096 1.0042 1.0048157 1.0033 1.0049279 1.0018 1.00210,307 1.0011 1.00111,020 0.9986 1.001HER 1.0024SDM 1.7316. ConclusionsA new system to optimize a FL-CRP design in a coupledway for BWRs was developed. Tests showed a convergentbehavior of the system throughout CRP-FL iterative pro-cess. Although at the beginning of the process some ther-mal limits are not satised, once iterative process isnished all parameters are satised. The eective multipli-cation factor ke so obtained is better than the target valuefor ke used to test the QuinalliBT system.According to Table 3, the ke obtained with QuinalliBTsystem is 0.0024 Dk/k greater than target ke. This valuerepresents around 10 full power days of reactor operation,with the corresponding extra energy generated. The suc-cessful executions of QuinalliBT system through dierentcases suggest the robustness of the system.During the performed tests, it could be seen that the rststage of the process can be eliminated, because seed FL isindependent of the last FL design. New proposals to obtainseed FL in a simpler way are under study, in order toreduce CPU time. Actually, the maximum number of iter-ations in the dierent executed tests was 10, which still rep-resents a considerable amount of CPU time.AcknowledgementReferencesOrtiz, J.J., Requena, I., 2004. Using a multi-state recurrent neural networkto optimize fuel reloads in BWRs. Annals of Nuclear Energy 31,789803.Ortiz, Juan Jose, Requena, Ignacio, 2006. Azcatl-CRP: an ant colony-based system for searching full power control rod patterns in BWRs.Annals of Nuclear Energy 33, 3036.Ortiz, J.J., Requena, I., 2004. An order coding genetic algorithms tooptimize fuel reload in a nuclear boiling water reactor. Nuclear Scienceand Engineering 146, 8898.Castillo, Alejandro, Alonso, Gustavo, Morales, Luis B., Campo, CeciliaMartin del, Francois, J.L., Valle, Edmundo del, 2004. BWR fuelreloads design using a tabu search technique. Annals of NuclearEnergy 31, 151161.Castillo, J.A., Ortiz, J.J., Alonso, G., Morales, L.B., del Valle, E., 2005.BWR control rod design using tabu search. Annals of Nuclear Energy32, 741754.Francois, J.L., Martin-del-Campo, C., Tavares, A., 2004. Development ofa BWR control rod pattern design based on fuzzy logic and heuristics.Annals of Nuclear Energy 31, 343356.Haling, R.K., 1964. Operational strategy for maintaining an optimumpower distribution through core life. In: Proc. ANS Topl. Mtg.Nuclear Performance of Core Power Reactors, TID-7672. US AtomicEnergy Commission.Specker, S.R., Fennern, L.E., Brown, R.E., Stark, K.L., Crowther, R.L.,1978. The BWR control cell core improved design. Transactions ofAmerican Nuclear Society 30, 336338.Scandpower, A.S., 1993. User Manual CM-Presto 9. Version CM914B.212 A. Castillo et al. / Annals of Nuclear Energy 34 (2007) 207212This research has been partly supported through theresearch project SEP-2004-C01-46694 by CONACYT,Mexico.Rev. 6, July 16.Kobayashi, Y., Aiyoshi, E., 2002. Optimization of boiling water reactorloading pattern using two-stage genetic algorithm. Nuclear Science andEngineering 142, 119139.Glover, F., 1968. Tabu search part I. ORSA, Journal of Computing 1,190206.Fuel loading and control rod patterns optimization in a BWR using tabu searchIntroductionProblem descriptionQuinalliBT systemTabu searchResultsConclusionsAcknowledgementReferences


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