# Development of a BWR control rod pattern design system based on fuzzy logic and knowledge

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The development of a system for the control rod pattern design of Boiling Water Reactorsbased on fuzzy logic and knowledge is presented in this paper. The fuzzy logic module makes

Annals of Nuclear Energy 31 (2004) 343356

www.elsevier.com/locate/anuceneuse of membership functions and fuzzy rules to control the neutron multiplication factor and

the maximum relative nodal power by acting over the control rods relative movement and thein-core water ow. The Mamdani implication process is used to evaluate the membershipfunctions. The multiplication factor is controlled in order to bring the reactor to the criticalstate, and the maximum relative nodal power is controlled to maintain the main thermal limits

in the core under their design values. Knowledge rules are implemented to govern the controlrods movement and the coolant ow in the core. The fuzzy logic control system is linked to thethree dimensional neutronic and thermal-hydraulic steady state simulator CM-PRESTO. The

system was tested with the cycle 10 of Laguna Verde Nuclear Power Plant, Unit 1. The resultsobtained show that a very reasonable control rod programming can be achieved with a quitesimple methodology. The obtained cycle length is comparable with that achieved with a Haling

based simulation.# 2003 Elsevier Ltd. All rights reserved.Development of a BWR control rod patterndesign system based on fuzzy logic

and knowledge

Juan-Luis Francois*, Cecilia Martn-del-Campo,Antonio Tavares

Laboratorio de Analisis en Ingeniera de Reactores Nucleares, Universidad Nacional Autonoma

de Mexico- Facultad de Ingeniera, Paseo Cuauhnahuac 8532. 62550 Jiutepec, Mor. Mexico

Received 18 August 2003; accepted 8 September 2003

Abstract0306-4549/$ - see front matter # 2003 Elsevier Ltd. All rights reserved.doi:10.1016/j.anucene.2003.09.004

* Corresponding author.

E-mail addresses: jl@-b.unam.mx (J.-L. Francois), cmcm@-b.unam.mx (C. Martn-del-Campo).

1. Introduction

Control rod pattern (CRP) design is an important task of the cycle managementof a Boiling Water Reactor (BWR). It proposes the way the operator has to movethe control rods (CR) to obtain the maximum energy from the core under the safetyand ux constraints. On the other hand during the fuel reload pattern design stage;the control rod programming must be taken into account in order to obtain a realand optimum reload designSeveral works have been developed for the BWR control rod programming since

several years ago. Motada (1972) used the Method of Approximate Programming(MAP) limited to a simple 1D reactor model of one energy group. Afterwards,Kawai et al. (1976) using the MAP, developed the OPROD code based on a 3DBWR core simulator, the convergence of the MAP was the issue in this approach.Hayase and Motada (1980) included a heuristic search algorithm to improve theMAP algorithm. Kiguchi et al. (1984) developed a system to optimize the powerdistribution in the sense that it is the closest to a target one. They use a linear searchalgorithm with a simplied model based on sensitivity analyses of local power andthermal margins using a 3D simulator. On the side of the heuristic rules based sys-tems, Zhong and Weisman (1984) developed a 3D computer code RODPRO forautomatically generate a control rod program for BWR using a Control Cell Coredesign. The system was based on heuristic rules to simplify complex theoreticalapproaches while eliminating trial and error studies. Fukusaki et al. (1988) devel-oped a knowledge based system more exible than the MAP based systems, in thesense that it can incorporate easily core design and operation policy changes byadding new rules. Lin and Lin (1991) showed that heuristic based expert systems canreproduce the experts work for generate control rod patterns with the advantage ofcomputational time savings. Finally Karve and Turinsky (2000) have shown theeectiveness of their CRP sampling capability added to the FORMOSA-B code,using heuristic rules based on common engineering practices used in industry.Concerning control methods, in general they use crisp and exact denitions to

represent the operation of a system. In practice, however, it is not always easyto represent the crisp mathematical model of a system like the control of aBWR; such systems are mainly controlled by skilled human operators. Fuzzylogic theory (Zadeh, 1965) suggests a method to represent vague or fuzzy conceptsand decision mechanisms. Mamdani and Assilian (1975) applied this theory to thedesign of fuzzy logic controllers for processes based on the control behaviors of askilled human operator. The main behaviors of human operators are represented bylinguistic rules. Therefore fuzzy logic oers several advantages that can be used forthe CRP design problem:

Fuzzy logic provides an environment to compute with words (operatorslanguage), when there is no mathematical formula to express expertise.

A fuzzy rule-based system is very easy to understand compared to that of thetraditional rule-based approach.

344 J.-L. Francois et al. / Annals of Nuclear Energy 31 (2004) 343356 Fuzzy logic can handle approximate solutions eciently.

the entire rule-based system must be searched to nd out that there is no

matching premise, thus there will be no action for a given input.

Fuzzy logic algorithms are easy to implement. Fuzzy logic algorithms are notlanguage dependent.

Based on these features and the importance of the control rod pattern design taskfor the BWR cycle management and reload pattern design we decided to develop afuzzy logic control system and apply it to a real case for a typical BWR.

2. Fuzzy logic control system description

The fuzzy logic control system (FLCS) was designed to act over the control rodsaxial relative movement and the in-core water ow, in order to bring the neutronmultiplication factor (K) to the critical state, and to maintain the maximum relativenodal power (MRNP) under a xed value, to assure that the main thermal limits inthe core will be under their design values.Fig. 1 shows the main components of the system, which are the fuzzy logic con-

troller module (FLC), based on the FUZZLE software (Modico, 1997) andCM-PRESTO, a three dimensional neutronic and thermal-hydraulic steady statesimulator (Scandpower, 1993).The fuzzy logic controller is composed by three parts:

The FUZZIFY task, where the variables are converted from crisp valuesobtained from the CM-PRESTO simulator into fuzzy values by mean of themembership functions.

The INFERENCE task, where the rules are combined to produce a control Fuzzy logic allows freedom in applying dierent composition techniques.Freedom comes from the membership (belief) function concept. The designercan incorporate his/her expertise, belief, or evidence into the inferencemechanism by designing membership functions. The traditional rule-basedsystems operate based on exact match between a given situation and its rules.

Fuzzy logic allows freedom in applying dierent implication techniques.Here, implication means the decision making process often symbolized byTHEN clause. In traditional rule-based systems, THEN is a searchprocess. When the left hand side of a rule is satised, a search is performed tond the corresponding action. In fuzzy logic, the implication process can bedesigned in any reasonable form to obtain the best approach for a givenproblem.

The mechanics of fuzzy logic algorithms is dierent than that of the tradi-tional rule-based systems. In fuzzy logic, all the rules are evaluated for a giveninput; therefore the speed of the algorithm is not a function of the number ofinputs. On the other hand, the process speed of the traditional rule-basedsystems is a function of the input because of the search process. In some cases,

J.-L. Francois et al. / Annals of Nuclear Energy 31 (2004) 343356 345action.

(FLOW). This action value has a major impact over the core reactivity. The DEFUZZIFY task, where the output variables are converted from fuzzyvalues into crisp or scalar values, to be reinserted in the reactor simulator.

2.1. Fuzzy variables

Two types of fuzzy variables were dened in the system, the input variables and theaction or output variables. The input variables are the neutron multiplication factorand the maximum relative nodal power as have already introduced. The action vari-ables regarding control rods movement are dened as the increment or decrement innotches (control rod movement unit), that will be applied to a control rod in order toachieve the desired core reactivity and to maintain the peak power under a limit value.The action values are the relative movement of the shallow control rods (SCR) andthe relative movement of the deep control rods (DCR). Concerning the water owin the core, the output value is a fractional change around the nominal 100% value

Fig. 1. Flow diagram of the fuzzy logic control system.

346 J.-L. Francois et al. / Annals of Nuclear Energy 31 (2004) 3433562.2. Fuzzication

A membership function must be dened for each variable in the system in order tofuzzify them, it means to convert from a crisp value to a fuzzy value. In fuzzy logicthe range or universe of a variable can be divided in several regions or fuzzy sets, aslow, medium and high. For instance consider a variable X that can take anyvalue between 1 and 10, it can be dened that the interval 15 is interpreted aslow, the interval 38 as medium and the interval 710 as high. The denitionof low or any other term solely depends on the user judgement. Such a judgementis formulated by a possibility distribution function, often taking values between 0and 1, and is referred to as membership function. In FUZZLE, the shapes of themembership functions are piece-wise linear with 4 break points (coordinates) thatinclude triangles and trapezoidal of any form. The maximum value of a membership

function is equal to one.

2.2.2. Maximum relative nodal powerFig. 2. Membership function of K.The membership function used for MRNP is shown in Fig. 3. The range of thisinput variable was divided in three fuzzy sets: low power (LP), normal power (NP)2.2.1. Neutron multiplication factorThe membership function used for K is shown in Fig. 2. The range of this input

variable was divided in three fuzzy sets: subcritical (SBC), critical (CRIT) andsupercritical (SPC). The bounds of the universe are 0.99 and 1.01.

The breakpoints of the subcritical region are: 0.99, 0.99, 0.9985, 0.9995 The breakpoints of the critical region are: 0.9985, 0.9995, 1.0005, 1.0015. It

means that the membership function CRIT must yield the maximum value1, at the location in the universe between 0.9995 and 1.0005 which representsCRIT the best. In other words, the reactor will be critical at 1.00.0005

The breakpoints of the supercritical region are: 1.0005, 1.0015, 1.01, 1.01

J.-L. Francois et al. / Annals of Nuclear Energy 31 (2004) 343356 347Fig. 3. Membership function of MRNP.

rods. One is used for the MRNP control, which is in most of the cases the so called

shallow control rods (SCR) (in the case that the axial power prole is top peaked,the SCR can move along the core length). The other membership function is used forthe core reactivity control using the deep control rods (DCR). The whole axial lengthwas divided in two zones. The shallow rods are allowed to move from 24 to 48 notchesof withdrawn, nevertheless it is preferable that they move from 32 to 48 notches. Thedeep rods can move from 2 to 24 notches of withdrawn, however they must preferablymove from 4 to 16 notches. The fully inserted control rod (zero notches of withdrawn)is forbidden. Three fuzzy sets were used for these membership functions: negative(NEG), zero (ZERO) and positive (POS). The bounds of the universe are 0 and 24. Anegative value of the action variable means that the rod or group of rods must beinserted, then a negative reactivity is added, on the opposite, a positive value meansthat the rods must be extracted, adding a positive reactivity to the core. Fig. 4 showsthe membership function for the shallow control rods, where the breakpoints are:

For the negative fuzzy set: 0, 0, 8, 10 For the zero fuzzy set: 8, 12, 16 For the positive fuzzy set: 14, 16, 24, 24and high power (HP). The bounds of the universe are 1.5 and 3.0. The maximum valueassigned for the normal power is 2.25 (1.5 1.5), which is a value that must assurethat the main thermal limits: the maximum lineal heat generation rate (MLHGR), theratio of the average planar lineal heat generation rate (RAPLHGR) and the minimumcritical power ratio (MCPR) must be under their limit design values.

The breakpoints of the low power fuzzy set is: 1.5, 1.5, 1.85, 2.1 The breakpoints of the normal power fuzzy set: 1.85, 2.1, 2.25, 2.5 The breakpoints of the high power fuzzy set: 2.25, 2.5, 3.0, 3.0

2.2.3. Control rod relative movementTwo membership functions were used for the relative movement of the control

348 J.-L. Francois et al. / Annals of Nuclear Energy 31 (2004) 343356Fig. 4. Membership function of shallow control rods.

Fig. 6. The range of this input variable was divided in three fuzzy sets: low ow

Fig. 5. Membership function of deep control rods.Fig. 5 shows the membership function for the deep control rods, where thebreakpoints are:

For the negative fuzzy set: 0, 2, 10, 12 For the zero fuzzy set: 8, 12, 16 For the positive fuzzy set: 12, 14, 22, 24

It must be pointed out that the real zero movement of the control rod is located atthe value 12 of the membership function. This is done because FUZZLE does notallow negative values in the range of the membership functions.

2.2.4. Water ow changeThe membership function used for the coolant change in the core is shown in

J.-L. Francois et al. / Annals of Nuclear Energy 31 (2004) 343356 349Fig. 6. Water ow membership function.

igh fu t: 1 107

zy r

uzz ic ller namby t o isti ptio

wheractioExThe rules can be written in the fuzzy associative memory (FAM) form, for thedeep control rods we have:

KSBC CRIT SPC

LP POS ZERO NEGMRNP NP POS ZERO NEG

HP POS ZERO NEGDCR

2.4. Inferencing

The evaluation of membership functions, sometimes called cuts or clipping, for agiven numerical value is done in this step. The reactor variables are computed with theIF K is SPC THEN FLOW is LOWIF MRNP is HP THEN SCR is NEG

IF MRNP is LP THEN SCR is POS

IF K is SBC THEN FLOW is HIGHIF X is Ai OR=AND Y is Bi THEN Z is Ci

e X and Y are process variables, Ai, Bi and Ci are fuzzy sets and Z is the controln of the rule.amples of rules are:

IF K is SBC THEN DCR is POS

IF K is SBC THEN DCR is NEGIFTHEN statements. The IF portion is the antecedent and the THEN part is theconsequent. In this work, control rules are chosen as follows:acterized a se f lingu

, the dyc descri n rules. A fuzzy control action consists ofIn a f y log contro ic behavior of the fuzzy system is char-2.3. Fuz ules H ow zzy se 00, 107,

N al fuzzy : 95.5, 1 104.5(LOW), normal ow (NORM) and high ow (HIGH). The bounds of the universeare 93.0% and 107.0%, these are percentages around the nominal water ow value.The break...

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