Nuclear Engineering and Design 227 (2004) 285–300

Axial offset control of PWR nuclear reactor coreusing intelligent techniques

Mehrdad Boroushakia,∗, Mohammad B. Ghofrania, Caro Lucasb,Mohammad J. Yazdanpanahb, Nasser Sadatic

a Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11365-9567 Tehran, Iranb Department of Electrical and Computer Engineering, Tehran University, P.O. Box 14395-515 Tehran, Iranc Department of Electrical Engineering, Sharif University of Technology, P.O. Box 11365-9363 Tehran, Iran

Received 9 December 2002; received in revised form 27 August 2003; accepted 3 November 2003

Abstract

Improved load following capability is one of the main technical performances of advanced PWR (APWR). Controlling thenuclear reactor core during load following operation encounters some difficulties. These difficulties mainly arise from nuclearreactor core limitations in local power peaking, while the core is subject to large and sharp variation of local power density duringtransients. Axial offset (AO) is the parameter usually used to represent of core power peaking, in form of a practical parameter.This paper, proposes a new intelligent approach to AO control of PWR nuclear reactors core during load following operation.This method uses a neural network model of the core to predict the dynamic behavior of the core and a fuzzy critic based onthe operator knowledge and experience for the purpose of decision-making during load following operations. Simulation resultsshow that this method can use optimum control rod groups maneuver with variable overlapping and may improve the reactorload following capability.© 2003 Elsevier B.V. All rights reserved.

Abbreviations: ANNs, artificial neural networks; AO, axialoffset; APE, average power error; APWR, advanced pressurizedwater reactor; BOC, beginning of cycle; CAOC, constant axialoffset control; CGD, center of gravity defuzzifier; CRG, controlrods group; DYNCO, a dynamical core calculation code for VVERreactor; CODA, computerized operator decision aids; COSS, com-puterized operator support system; MLP, multi-layer perceptronneural network; NARX, nonlinear auto regressive with exogenousinputs neural network; NN, neural network; OL, overlapping be-tween the control rods groups; RNN, recurrent neural network;RMLP, recurrent multi-layer perceptron neural network;P, thermalpower of the reactor core; PIE, product inference engine; PIL, errorbetween predicted and lower limit of the core AO; PIR, error be-tween predicted and higher limit of the core AO; PT, error betweenpredicted and desired core thermal power; SF, singleton fuzzifier

∗ Coresponding author. Tel.:+98-913-2063587;fax: +98-21-6013128.

E-mail address:boroushaki@mehr.sharif.edu (M. Boroushaki).

1. Introduction

Controlling the nuclear reactor core during loadfollowing operation is an important area in nuclearengineering, particularly in advanced PWRs. Nu-clear reactor core is a complex nonlinear system andmultivariable nature with high interactions betweentheir state variable. Any maneuver of the control rodgroups (CRGs), can induce unintended time-space Xeoscillations, resulting in large local power peaking.Such a complexity cannot be duly represented bysimple few points models (Kuan et al., 1992). Modernintelligent techniques, using neural networks (NNs)and fuzzy systems, allow to satisfactory handle sucha problem (Akin and Altin, 1991; Na and Upadhyaya,1998).

0029-5493/$ – see front matter © 2003 Elsevier B.V. All rights reserved.doi:10.1016/j.nucengdes.2003.11.002

286 M. Boroushaki et al. / Nuclear Engineering and Design 227 (2004) 285–300

Nomenclature

A fuzzy set in input space ofUB fuzzy set in output space ofVdi desired value of neuroniE(m) error of neural network during the

training at time intervalmFC fuzzy critic outputhi(m) position of control rods group

numberi at the time intervalm�I normalized axial offset of the

reactor corel fuzzy IF-THEN rule numberm time intervalM total number of time intervals

during a load following transientoj activation function of neuroniR set of real numberst timeU input space of fuzzy inference engineu(m) input signal of neural network

at time intervalmV output space of fuzzy inference enginewij weight from neuronj to ix input variable of fuzzy systemx∗ real valued point (vector) inxXe(m) Xenon concentration of reactor core

at time intervalmy output variable of fuzzy systemy∗ real valued point (vector) inyY(m) output signal of neural network

at time intervalmZ−1 Z-transform of a taped-delay-line

Greek lettersδi error signal of neuroniη learning rateµAl(x) membership function of thelth

rule in IF sectionµBl(y) membership function of thelth rule

in THEN sectionρ(m) reactivity of the reactor core at the

time intervalm

SubscriptsE expected value of the reactor

core power

max maximummin minimumNN neural network outputr fraction of real to nominal value of

reactor core powerRE real value of the reactor core power

In load following mode, the reactor has to track theload changes while considering the core limitationsin local power peaking and safety margins. Axial off-set (AO) is the parameter usually used to representcomplex three-dimensional phenomena of core powerpeaking, in form of a practical parameter. In previouscontrol systems, usually crisp logics have been used tocontrol AO and the thermal power. However, in con-stant axial offset control (CAOC) strategy, in which thereactor AO is maintained within predetermined limits,via suitable maneuver of control rods, the variation ofAO versus reactor relative power during transients hasa fuzzy nature. Thus, using fuzzy control based meth-ods is more suited to this type of problem and mayimprove the plant control capability.

In recent years, many intelligent control method-ologies have been proposed for controlling differentcomplex plants (e.g., steam generator). Most of thesemethodologies have used generalization capabilitiesof the neural network and decision-making abilitiesof fuzzy systems (Narendra and Parthasarathy, 1990;Akin and Altin, 1991; Cho and No, 1997; Na andUpadhyaya, 1998). In this research, we proposed anew intelligent approach to AO control of PWR nu-clear reactors core during load following operation.

We used a recurrent neural network (RNN) formodeling and fast prediction of a PWR nuclear reactorcore dynamics. This model was trained by an accuratethree-dimensional core calculation code. This modelcan capture three-dimensional dynamics effects of thecore (i.e., the effects of spatial power distribution andshadowing of the control rods, on core dynamics) ina large rang of thermal power variation. We used afuzzy system, based on the operator knowledge andexperience for decision-making during load followingoperations. The intelligent core controller uses thefuzzy system and the neural network core model ina control algorithm. This controller proposes a suit-able CRGs maneuver and variable overlapping for

M. Boroushaki et al. / Nuclear Engineering and Design 227 (2004) 285–300 287

the next time interval (Boroushaki, 2003a, b). Simu-lation results show that this controller may improvethe responses, comparing to other control systems.

2. Artificial neural networks and fuzzy systems

In this section, some concepts related to artificialneural networks (ANNs) and fuzzy systems are brieflyreviewed.

2.1. Artificial neural networks

ANNs consist of a great number of processingelements (neurons), connected to each other. Thestrengths of the connections are calledweights. Forthe modeling of physical systems, a feed-forwardmulti-layered network is commonly used. It consistsof a layer of input neurons, a layer of output neu-rons and one or more hidden layers. In a multi-layerperceptron “MLP” (Fig. 1), there is no connectionbetween the neurons in a given layer, so that the in-formation is transferred from the (l − 1)th layer tothe lth one. External data enter the network throughthe input nodes and, through nonlinear transforma-tions, output data are generated by the output nodes(Yegnanarayana, 1999).

In ANNs, the knowledge lies in the interconnectionweights between neurons. Therefore, learning processis an important characteristic of the ANN methodol-ogy, whereby representative examples of the knowl-edge are iteratively presented to the network, so that itcan integrate this knowledge within its structure (train-ing phase).

In most applications of MLP, the weights are deter-mined by means of the back-propagation algorithm,

Inputs

Input Laye

Hidden Layer

Output Layer

Output

Fig. 1. A multi-layer perceptron (MLP) neural network.

which minimizes a quadratic cost function by a gra-dient descent method. During the training phase, theweights are successively adjusted based on a set ofinputs and the corresponding set of desired output tar-gets. First, the inputs are presented to the network andpropagated forward to determine the resulting signal atthe output neurons. The difference between the com-puted output vectors and the desired output targets rep-resents an error that is back-propagated through thenetwork in order to adjust the weights. This process isrepeated and the learning continues until the desireddegree of accuracy is achieved (Haykin, 1999).

According to the back-propagation algorithm, whenan input is presented to the network, the activation ofeach neuron is determined by:

oi = yi

J∑

j=0

wijoj

(1)

whereoi is the activation of uniti, yi is the activationfunction of unit i, wij is the weight from unitj to i,andJ is the total number of inputs (excluding the bias)applied to neuroni. The synaptic weightwi0 (corre-sponding to the fixed input) equals the bias applied tothe neuroni. Back propagation is then invoked to up-date all the weights in the network according to thefollowing rule:

�wij (n + 1) = η(δioj) + �wij (n) (2)

wheren is the iteration number,η is the learning rateandδi is the error signal for uniti. The error signalδkfor an output unitk is calculated from the differencebetween the desired valuedk and actual valueyk forthat unit, while the error signalδh for a hidden unithis a function of the error signals of those units in thenext higher layer connected to unith and the weightsof those connections.

The back-propagation process will generally con-verge to a minimum that satisfies the criterion im-posed by the user which usually renders the sum of thesquares of the error of the output signals,

∑k (dk−ok)

2

less than a predetermined value. In this work, the biasof all neurons was set to−1.

RNN are neural networks with one or more feed-back connections. Given an MLP as the basic buildingblock, we may have feedback from the output neu-rons of the MLP or from the hidden neurons of thenetwork to the input layer. When the MLP has two or

288 M. Boroushaki et al. / Nuclear Engineering and Design 227 (2004) 285–300

Z-1

Z-1

Z-1

Z-1

Z-1

Z-1

Multilayer Perceptron

(MLP)

y (m-q+1)

u (m-p+1)

y (m-q+2)

u (m-p+2)

y (m-1)

u (m-2)

y (m)

u (m-1)

u (m)

y (m+1)

Input

Output

Fig. 2. Nonlinear autoregressive with exogenous inputs (NARX) structure.

more hidden layers, the possible forms of feedbacksexpand even further. The recurrent networks have arich repertoire of architectural layouts (Medsker andJain, 1999).

Fig. 2 shows the architecture of a type of RNN,based on a MLP. In this figure, the Z−1 repre-sents the Z-transform of a single taped-delayed-line.The model has a single input that is applied to atapped-delay-line memory of p units. It has a sin-gle output that is fed back to the input via anothertapped-delay-line memory of q units. The content ofthese two tapped-delay-line memories are used to feedthe input layer of the MLP. The present value of themodel input is denoted by u(m), and the correspond-ing value of the model output is denoted by y(m+ 1);that is, the output is ahead of the input by one timeunit. Thus, the signal vector applied to the input layerof the MLP, consists of a data window made up aspresent and past values of the plant inputs, repre-senting exogenous inputs originated from outside thenetwork and delayed values of the model outputs, onwhich the model outputs is regressed. This recurrentnetwork is referred to as a “nonlinear auto regressivewith exogenous inputs (NARX) model” . The dynamic

behavior of the NARX model is described by:

y(m + 1) = F(y(m) . . . y(m − q + 1), u(m), . . . ,

u(m − p + 1)) (3)

where F is a nonlinear function of its arguments.

2.2. Fuzzy systems

Fuzzy systems are knowledge-based or rule-basedsystems (Wang, 1997; Zimmermann, 1996). The in-puts and outputs of a fuzzy system are linguisticvariables (i.e., low, high, etc.), which are definedvia membership functions. The heart of a fuzzy sys-tem is a knowledge base consisting of the so-calledfuzzy IF-THEN rules. A fuzzy IF-THEN rule is anIF-THEN statement in which some words are char-acterized by continuous membership functions. Thestarting point of constructing a fuzzy system is to ob-tain a collection of fuzzy IF-THEN rules from humanexperts or based on domain knowledge. These rulesuse the membership functions for different input andoutput of the system to determine the state of out-put parameters for any state of the input parameters.

M. Boroushaki et al. / Nuclear Engineering and Design 227 (2004) 285–300 289

Fuzzy Inference Engine

Defuzzifier Fuzzifier

x in U y in V

Fuzzy sets in V

Fuzzy sets in U

Fuzzy Rule Base

Fig. 3. The basic configuration of a fuzzy system with fuzzifierand defuzzifier.

The next step is to combine these rules into a singlesystem. Different fuzzy systems use different prin-ciples for this combination. There are two types offuzzy systems that are commonly used in the litera-ture: Takagi–Sugeno–Kang (TSK), and expert fuzzysystems with fuzzifier and defuzzifier. In this work,we used second type of fuzzy systems. The basicconfiguration of a fuzzy system with fuzzifier anddefuzzifier is shown in Fig. 3.

The fuzzy rule-base represents a collection of fuzzyIF-THEN rules as follows:

IF x1 isA1 and . . . and xn isAn, THEN y isB

where Ai and B are fuzzy sets in Ui ⊂ R and V ⊂ R,and x = (x1, x2 . . . , xn)

T ∈ U and y ∈ V are the inputand output (linguistic) variables of the fuzzy system,respectively.

The fuzzy inference engine combines these fuzzyIF-THEN rules into a mapping from fuzzy sets in theinput space U ⊂ Rn to fuzzy sets in the output spaceV ⊂ R based on fuzzy logic principles. Therefore,fuzzy inference engine combines the rules in the fuzzyrule-base into a mapping from fuzzy set A′ in U tofuzzy set B′ in V. Since in most applications, the inputand output of the fuzzy systems are real-valued num-bers, we must construct interfaces between the fuzzyinference engine and the environment. The interfacesare the fuzzifier and defuzzifier depicted in Fig. 3. Thefuzzifier is defined as a mapping from a real-valuedpoint x∗ ∈ U ⊂ Rn to a membership grade repre-senting fuzzy set A′ in U. The defuzzifier is definedas a mapping from fuzzy set B′ in V ⊂ R (which isthe output of the fuzzy interface engine) to crisp pointy∗ ∈ V . Conceptually, the task of the defuzzifier isto specify a point in V that best represents the fuzzyset B′.

There are a variety of choices in the fuzzy in-ference engine, fuzzifier, and defuzzifier modules.Specifically, we can propose five fuzzy inference en-gines (product, minimum, Lukasiewicz, Zadeh, andDienes-Rescher), three fuzzifiers (singleton, Gaus-sian and triangular), and three types of defuzzifiers(center-of-gravity, center average, and maximum).Not all of the 45 possible combinations proved equallyuseful for using in our fuzzy system. In the rest ofthe paper, we shall only report the results obtained byone of the more suitable fuzzy systems.

In this paper, a fuzzy system with a singleton fuzzi-fier, a product inference engine and a center of gravitydefuzzifier (SF-PIE-CGD), has been used. In a single-ton fuzzifier (SF), the membership function µA(x) ofa fuzzy set A has a value equal to 1 at point x0 andequal to 0 for points other than x0. The product in-ference engine (PIE) is based on Mamadani method.The Mamadani product inference calculates the max-imum value of the products of membership functionswithin IF-THEN rules (Wang, 1997). Therefore, themembership function of a fuzzy set B′ in V, may becalculated at the output of the fuzzy engine:

µB′(y) = MaxMl=1

[n∏i=1

µAli(x∗)µBl(y))

](4)

where l is the rule number, x∗ is the input vector to thesystem, µAl

i(x) and µBl(y) are membership functions

of the lth rule in the IF and THEN sections, respec-tively (Wang, 1997). The system output is calculatedthrough a center of gravity defuzzifier (CGD). Thisdefuzzifier specifies the y∗ as the center of the areacovered by the membership function of B′, that is:

y∗ =∫syµB′(y)dy∫sµB′(y)dy

(5)

where∫s

is the conventional integral.

3. Axial offset control in PWRs during loadfollowing operations

A nuclear power reactor core controller has to con-trol the core thermal power along with the safety lim-itation on local power peaking during load followingoperation. Local power peaking in nuclear reactors,is a complex three-dimensional phenomena, resulting

290 M. Boroushaki et al. / Nuclear Engineering and Design 227 (2004) 285–300

from different reactor parameters (fuel loading, powerlevel, temperature distribution, position of CRGs, fuelburn up, spatial Xe oscillations, etc.). To simplify thisphenomenon, local power peaking is usually dividedinto two radial and axial components. While radialpower peaking is usually flattened (via optimum fuelloading/reloading pattern) once at the beginning of cy-cle (BOC), the axial power peaking is continuouslychanging by perturbations created by CRG manoeu-vres. Axial offset (AO), is the parameter usually usedto determine the core power peaking. This parameteris defined as:

AO = PT − PB

PT + PB(6)

where PT and PB represent the fraction of thermalpower generated in the top and bottom halves of thecore, respectively (Sipush et al., 1976). This parameter,which could be easily measured on-line, via ex-coreinstrumentation, still reduces the complexity of theproblem and provides an efficient practical mean tocontrol the reactor. Thus, the main challenge of thereactor control, during load following operation, is tomaintain the axial power peaking (represented by AO)within certain limits, about a reference target value.

The limitations on the core AO can be analysed inPr −�I coordinates, where �I is the normalized AOdefined by:

�I = AO × Pr = PT − PB

PT − PB× Pr (7)

where Pr is relative core thermal power (the ratio of theactual core thermal power to nominal thermal power).

In CAOC strategy, the limitations on the core AOvalue can be shown by two parallel lines in Pr − �I

coordinates (Sipush et al., 1976). This means that thecore working conditions in Pr −�I coordinates mustlie within a certain band (e.g., ±5%) during any powertransient (Fig. 4). The chosen target AO would occurat full power, equilibrium Xe, and all rods out. Thiscontrol strategy protects the reactor from any divergentXe oscillation and would ensure safe operation of thereactor during load following transients. Figs. 5 and 6exhibit CAOC strategy in a 100 to 50% load followingoperation in a typical VVER-1000 (Yousefpour andGhofrani, 2000). As shown in these figures, �I ex-ceeds the upper margin in absence of AO control andis maintained within �I band with AO control.

Normalized axial offset (∆l)

Target value of ∆I ± 5% ∆I

0

100

Relative power (Pr)

+5% -5%

Fig. 4. Principles of CAOC strategy, using normalized AO (�I).

4. Intelligent approach to AO control

To implement CAOC strategy in real nuclear re-actor, the operator can use CRGs and/or boric acidas control agents. Although the use of boric aciddoes not affect the power distribution in the core,but would cause some delays in the reactor response.Using CRGs will lead to a faster reactor response butany CRG maneuver affect the reactor power distribu-tion, i.e., the core AO. Moreover, there is a tendencyin some cases to limit the use of the boric acid, toavoid accumulation of liquid wastes. Thus, the CRGs,with different overlapping, constitute the main con-trol agent for the load following operation. It is tobe noted that in some cases, the operator may allowthe core AO to leave the band for a short period, pro-vided that it returns back to the band, by the effect ofthermal feedbacks and/or Xe build up.

The variation and control of AO during transientshas a fuzzy nature. Thus the process can be suitablymodeled and implemented by an intelligent controller,using a fuzzy critic. We designed an intelligent con-troller, which can use the knowledge and experiencesof the operator in a fuzzy decision maker to select thebest maneuvers of the CRGs. This intelligent core con-troller (Boroushaki, 2003a, b) includes: a NARX coremodel, a control rod groups (CRGs) maneuver gener-ator, a fuzzy critic and an optimum CRGs maneuverfinder. The NARX is updated with real plant data atany time interval, for capturing any process dynam-ics not included in the training set. The fuzzy criticconsiders all of the possible CRGs maneuvers, andproposes the optimum CRGs maneuvers and overlap-

M. Boroushaki et al. / Nuclear Engineering and Design 227 (2004) 285–300 291

Fig. 5. Simulation results of a daily load following operation in a typical VVER-1000 without AO control.

ping, for the next time interval. This is an innovativemethod for controlling PWR nuclear reactor core, andmay improve the responses, compared to other controlapproaches.

5. Intelligent core controller structure

Fig. 7 shows the structure of the designed intelligentcore controller. The control algorithm used includes

the following steps:

Step 1: Defining: the expected core thermal power(PE); the maximum and minimum overlap-ping between the CRGs (OLmin, OLmax) andthe maximum and minimum of allowable coreaxial offsets (AOmin, AOmax) during the nexttime interval. This step is performed by theModules 1 and 2, which constitute the inputsof the controller.

292 M. Boroushaki et al. / Nuclear Engineering and Design 227 (2004) 285–300

0 3 6 9 12 15 18 21 24

Rel

ativ

e po

wer

0.0

0.5

1.0

0 3 6 9 12 15 18 21 24

Con

trol

rod

s gr

oup

p

ositi

on (

cm)

0

100

200

300

400

Time(hr)

0 3 6 9 12 15 18 21 24Bor

on c

once

ntra

tion(

g/kg

)

0.0

0.5

1.0

1.5

2.0

0 3 6 9 12 15 18 21 24

∆Ι

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

∆Ι

Upper margine

Lower margine

Preference

Pactual

CRG # 10

CRG # 9

CRG # 8

Fig. 6. Simulation results of a daily load following operation in a typical VVER-1000 with AO control.

Step 2: Generating all possible CRGs maneuvers (h8,h9 and h10 indicate the positions of the CRGsnumbers 8, 9 and 10, respectively), taking intoaccount the initial CRGs positions, and themaximum and minimum overlapping betweenthe CRGs. This is performed by the Module 3.

Step 3: Implementing each of CRGs maneuversto a fast core model and predicting thecore response during the next time interval(Module 4).

Step 4: Finding optimum response of the core modeland the related CRGs maneuver (Modules5–7).

Step 5: Implementing the best CRGs maneuver tothe real plant (Module 8).

Step 6: Updating the core model, using the responseof the real plant (see Section 6).

The above steps are executed at each time intervalduring the transient. Detailed descriptions of the othermodules are explained in following sections.

In this research, the proposed intelligent approachhas been implemented to a Russian PWR (VVER) coreat beginning of cycle. We have used DYNCO codefor simulation of the plant. DYNCO is dynamic codedesigned to simulate Russian 3000 MWt PWR core

M. Boroushaki et al. / Nuclear Engineering and Design 227 (2004) 285–300 293

1- Maximum and minimum of control rod groups overlapping

(O.L), and core axial offsets (A.O).

3- Control rod groups (CRGs) manoeuvre generator.

4- Core dynamic behavior predictor ( a fast core model)

5- Plant prediction analyzer.

7- Optimum control rod groups manoeuvre finder.

8- DYNCO code (as a real VVER reactor core).

2- Expected core thermal power (PE).

6- Fuzzy critic.

O.L min

O.L h8-h9-h10

PIR PT

h8-h9-h10 O.L

Updating the core model

O.L max

A.Omin

A.Omax

PIL

STEP 1

STEP 2

STEP 3

STEP 4

STEP 5

STEP 6

FC

t A.ONN PNN

t PE

Fig. 7. Intelligent core controller structure.

294 M. Boroushaki et al. / Nuclear Engineering and Design 227 (2004) 285–300

(VVER type 320) by means of 3260 nodes distributedsymmetrically in the core. In this type of reactor, tengroups of control rod plus boric acid, are used to con-trol the reactor power level and spatial power distri-bution in the core, while satisfying the safety criteria(Yousefpour and Ghofrani, 2000). DYNCO can showthe effects of movement of any CRGs on the core pa-rameters, as a function of time. Criticality of the plantis maintained by 1000 ppm boron acid concentrationand the reactor is controlled by using three CRGs 8,9 and 10 (other groups are fixed at the top of the coreas safety rods).

We used the C++ language to build the intelli-gent core controller (Fig. 7) and the DYNCO codeto represent the real plant. To evaluate validity of theresults of the core controller, during different loadfollowings, we defined an average power error (APE)parameter as:

APE = 1

M

M∑m=1

|PrRE(t(m)) − PrE(t(m))| (8)

where M is the total number of time intervals,PrRE(t(m)) and PrE(t(m)) are the real and the ex-pected core thermal powers at the mth time interval,respectively.

5.1. Prediction of the core dynamic behaviors usingNARX

Fig. 8 shows the neural network designed for identi-fication of the plant (Module 4). This model includes aRNN type NARX with 33-45-30-4 structure. We usedfour reactor dynamic state variables, Xenon (Xe), corereactivity (ρ), thermal power (P) and AO for identifica-tion of long-term core dynamics with a time step equalto 300 s (Kerlin et al., 1977). This structure includes:two hidden layers, each composed of 45 and 30 neu-rons; 4 output units considered for Xe, P, ρ and AO;and 33 input units, foreseen for the present and twopast delayed CRG positions of the CRGs numbers 8, 9,and 10 (h8, h9 and h10), plus the present and five pastdelayed NARX outputs. This model predicts the coredynamics behavior much faster than the DYNCO code(about 800 times), with an acceptable error. Although,a 33-78-78-78-4 structure for NARX has been alreadyused by Boroushaki et al.(2002, 2003a, b), further re-searches showed that a smaller structure (33-45-30-4)

is possible and improves the response and learningtime of the model.

This designed NARX had been already trained by anoff-line batch learning, using 64 transients generatedby the DYNCO code (Boroushaki, 2002 and 2003b).These transients include all possible core dynamicconditions by movement of CRGs during a fixed pe-riod of 10,000 s. This model will then be updated by anon-line learning, using the plant responses in each timeinterval (step 6). The starting point of the batch learn-ing is fixed at the beginning of the load following tran-sient, using the initial off-line batch learning weightsmatrix. The on-line learning is accomplished after ac-quisition of a new data set for capturing any processdynamics, which was not included in the training set.

We have not used boric acid as a control agent,to avoid sharp increase in number of required train-ing transients and training time. The detailed descrip-tion and characteristics of this model are provided byBoroushaki et al. (2002, 2003b).

5.2. Plant prediction analyzer

Each of CRGs maneuvers generated in Module 3,causes a different transient in the reactor core (varia-tion of the AO and power). We need a suitable methodto analyze the predicted plant response with regard tothe core AO limitation and to find the optimum CRGmaneuver. We defined two parameters PIR and PIL,to compare the predicted core model responses withAO limitation:

PIR=k1×�Imax(Pr[(m+1)])−INN(Pr[t(m + 1)])�(9)

PIL=k2×�INN(Pr[(m+1)]) − Imin(Pr[t(m + 1)])�(10)

where t(m) and t(m + 1) are the mth and the nexttime intervals, Pr[t(m+1)] is the relative core thermalvalues at the (m + 1)th time interval, Imax(Pr[t(m +1)]) and Imin(Pr[t(m + 1)]) are the maximum andminimum limitations of the core �I at the (m + 1)thtime intervals, INN is the predicted core �I for a CRGsmaneuver and k1, k2 are positive constant coefficientsthat are used for scaling the parameters. Each of thesetwo parameters can be positive, zero or negative. IfPIR and PIL were both positive then the predicted coreworking condition would be within the AO limitation

M. Boroushaki et al. / Nuclear Engineering and Design 227 (2004) 285–300 295

Nuclear Reactor Core

Multi Layer Perceptron

(MLP)

33-45-30-4

Z -1

Z -1

Z -1

h8(t)

h9(t)

h10(t)

h10(t -p)

h8(t -p)

h9(t -p)

Xe(t -q)

Xe (t+1)

Z -1

Z -1

P (t+1)

Z -1

Z -1

A.O(t+1)

Z -1

Z -1

P(t -q)

A.O(t -q)

E (t+1)

Z -1 Z -1

P (t+1)

A.O(t+1)

+

+

+

-

-

-

-

(t+1)

(t+1)

Xe (t+1)

+

(t-q)

Fig. 8. Nonlinear autoregressive with exogenous inputs (NARX) structure designed for reactor core modeling.

band. If one were positive and the other negative, thepredicted core working condition would be out of theallowable AO limitation band.

We defined another parameter (power error) be-tween the predicted and the expected core power asfollows:

PT = k3 × �PrNN(t(m + 1)) − PrE(t(m + 1))� (11)

where PrNN(t(m+ 1)) and PrE(t(m+ 1)) are the pre-dicted and the expected relative core thermal powersat the (m + 1)th time interval and k3 is a positiveconstant coefficient that is used for scaling the param-eter. This parameter can be positive, zero or negative.If PT were zero, the predicted core thermal powerwould be matched with the expected one, during thenext time interval.

296 M. Boroushaki et al. / Nuclear Engineering and Design 227 (2004) 285–300

Table 1Twenty-four fuzzy critic rules

Rule number PIR PIL PT r Rule number PIR PIL PT r Rule number PIR PIL PT r1 P P P Z−1 9 P N N Z−4 17 Z N Z Z1

2 P P Z Z4 10 Z P P Z−1 18 Z N N Z−4

3 P P N Z−1 11 Z P Z Z4 19 N P P Z−4

4 P Z P Z−1 12 Z P N Z−1 20 N P Z Z1

5 P Z Z Z4 13 Z Z P Z−1 21 N P N Z−4

6 P Z N Z−1 14 Z Z Z Z4 22 N Z P Z-4

7 P N P Z−4 15 Z Z N Z−1 23 N Z Z Z1

8 P N Z Z1 16 Z N P Z−4 24 N Z N Z−4

Module 5 calculates three parameters of PIR, PILand PT for each of the transients predicted by theNARX core model.

5.3. Fuzzy critic

The Module 6 is a fuzzy system designed for ana-lyzing each of the transient generated by CRG maneu-ver. This module examines any core model responsewith regard to the core AO limitations and the powererror. This fuzzy system contains a singleton fuzzifier,a product inference engine and a center of gravity de-fuzzifier (SF-PIE-CGD). Inputs of the fuzzy systeminclude PIR, PIL and PT parameters, and output of de-fuzzifier is a crisp value that shows the suitability de-gree of the input parameters (core model responses).The most important part of this fuzzy system is thefuzzy rule-base, which should be written by an expert(the operator) using his knowledge and experience fordecision-making at any core states, during load fol-lowing operations. Table 1 includes 27 rules, definedto this purpose. The inputs of the fuzzy rule-base areGaussian membership as follows:N(x) = 1 if x ≤ −0.3

N(x) = exp

{−

(x + 0.3

0.2

)2}

if x > −0.3

(12)

Z(x) = exp −( x

0.2

)2(13)

P(x) = 1 if x ≥ 0.3

P(x) = Exp −(x − 0.3

0.2

)2

if x < 0.3(14)

where x is one of the three parameters: PIR, PIL andPT. The membership functions of the fuzzy critic out-

put FC are also Gaussian membership functions as:

Zd(y) = exp

{−

(y − d

0.25

)2}

(15)

where d is equal to ±1 and ±4.These membership functions are used in fuzzy

IF-THEN rules. Twenty-four rules in Table 1 coverall different possible state with three inputs PIR, PILand PT. These IF-THEN rules are used in inferenceengine of the fuzzy critic to determine the status ofthe output parameter FC, in any states of the inputparameters PIR, PIL and PT. The fuzzy critic output(FC) shows the suitability degree of CRGs maneu-vers. The Gaussian membership functions in (15) willimply the crisp output value of FC vary between −1and +4.

6. Case study and discussion

Figs. 9 and 10 show the results of the designed in-telligent core controller with on-line learning in twodifferent cases. The overlap between CRGs number 8,9, 10 has been limited between 0 and 40% and the al-lowable core �I to −17% ± 5% (−17% correspondsto the AO at nominal power). Selection of the timeinterval for controlling the core during a transient de-pends on the: execution time of the control algorithmand maximum rate of power change during load fol-lowing. In the following simulations, a time intervalof 300 s was selected. The constants k1, k2 and k3 in(9), (10) and (11) were selected as 10, 10 and 5, re-spectively.

Case 1: The first load following considered was a16-2-4-2 transient shown in Fig. 9. This tran-sient includes a slow decrease of the core

M. Boroushaki et al. / Nuclear Engineering and Design 227 (2004) 285–300 297

Fig. 9. Core controller results for a 16-2-4-2 load following, using on-line learning: (a) expected and real core thermal powers; (b) core�I limitations and real core�I; c) control rod groups (CRGs) number 8, 9 and 10 positions; (d) core working conditions and core �I

limitations in Pr − �I coordinates; (e) CRGs overlap value; (f) fuzzy critic output value.

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Fig. 10. Core controller results for a 16-8 load following, using local on-line learning: (a) expected and real core thermal powers; (b) core�I limitations and real core�I; (c) control rod groups (CRGs) number 8, 9 and 10 positions; (d) core working conditions and core �I

limitations in Pr − �I coordinates; (e) CRGs overlap value; (f) fuzzy critic output value.

M. Boroushaki et al. / Nuclear Engineering and Design 227 (2004) 285–300 299

power from 100 to 50% during 2 h, constantpower at 50% for 4 h, and slow return to fullpower during 2 h. The total transient timewas 35,800 s divided in 119 (=35,800/300)time intervals. This case resulted in an APEequal to 43.3 MWt (less than 1.5% of nomi-nal power).

Case 2: The second load following considered was a16-8 transient shown in Fig. 10. This transientincludes a fast decrease of the core powerfrom 100% to 70% with a rate of 2%/min,constant power at 70% for 8 h, and fast re-turn to full power with a rate of 5%/min. Thetotal transient time was 34,600 s, divided in115 (=34,600/300) time intervals. This caseresulted in an APE equal to 28.1 MWt (lessthan 1% of nominal power).

As can be seen in Figs. 9 and 10, the intelligent con-troller succeeded to keep the AO within the specifiedbands in both cases, using solely CRGs maneuvers,i.e., without using Boric acid as a control agent. Itshould be noted that Boric acid can play an importantrole in controlling the reactor power level, as shownin Fig. 6. In case we allow the use of Boric acid, theintelligent controller will better track the load and theAPE may still be reduced.

We had two limitations to compare our results withother real case studies. First, load following mode ofcontrol has not to date been implemented to VVERplants. Therefore, we had to limit ourselves to transientsimulation using DYNCO code. Second, we had notaccess to western benchmarked case studies and rel-evant computer codes. However, we strongly believethat our proposed method, allowing the use of vari-able overlapping CRGs maneuvers, may improve theload following capability of modern PWRs. Becausevariable overlapping of CRGs would add a new inputcontrol agent to the control system and this would inturn increase the degree of freedom and controllabilityof the plant.

The total execution time of the designed intelligentcore controller on a Pentium IV 1.4 MHz PC falls toless than 115 s, from which 25 s is spent for on-linelearning and the remaining 90 s for other algorithmsteps. Computation time may be considerably reducedby using parallel processing of the control algorithm,and/or faster computers.

Finally, the following additional points are to beconsidered in practical application of the proposedmethod: The RNN can be trained by data recordedfrom the plant load following operations during a suf-ficient time period; the control algorithm may be ex-ecuted by parallel processing or by a very fast com-puter, and the boric acid may be added as a core con-trol agent.

7. Conclusions

In this research, we tried to develop a new methodto tackle one of the important problems of modernPWRs, i.e., improvement of load following capabil-ity of the plant, using advanced intelligent controllers.The proposed method represents an innovative ap-proach for identification and control of complex non-linear plants (i.e., nuclear reactor core).

The proposed intelligent core controller may im-prove the plant maneuverability during load followingoperations, using variable overlapping of CRGs, evenwithout use of boric acid as a control agent. The resultof the cases studied based on CAOC strategy showsthat the intelligent controller succeeded to control thecore AO within the specified bands during sever loadfollowing operation (case 2 above). One of the poten-tial applications of this method may be in design anddevelopment of computerized operator decision aids(CODA) or support system (COSS).

The drawbacks of this method are mainly: the needfor big amount of data for training of RNN; the rel-evant long training time and complexity of the con-troller structure. Further steps, i.e., uncertainty analy-sis, stability analysis, use on a reactor simulator, are tobe undertaken toward practical application in nuclearpower plants.

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