politecnico di milano, italy object-oriented modeling ... · 3.1 point kinetics neutronic the point...

Proceedingsof the 4th International Modelica Conference,

Hamburg, March 7-8, 2005,Gerhard Schmitz (editor)

A. Cammi, F. Casella, M. Ricotti, F. SchiavoPolitecnico di Milano, ItalyObject-Oriented Modeling, Simulation and Control of the IRIS NuclearPower Plant with Modelicapp. 423-432

Paper presented at the 4th International Modelica Conference, March 7-8, 2005,Hamburg University of Technology, Hamburg-Harburg, Germany,organized by The Modelica Association and the Department of Thermodynamics, Hamburg Universityof Technology

All papers of this conference can be downloaded fromhttp://www.Modelica.org/events/Conference2005/

Program Committee

• Prof. Gerhard Schmitz, Hamburg University of Technology, Germany (Program chair).

• Prof. Bernhard Bachmann, University of Applied Sciences Bielefeld, Germany.

• Dr. Francesco Casella, Politecnico di Milano, Italy.

• Dr. Hilding Elmqvist, Dynasim AB, Sweden.

• Prof. Peter Fritzson, University of Linkping, Sweden

• Prof. Martin Otter, DLR, Germany

• Dr. Michael Tiller, Ford Motor Company, USA

• Dr. Hubertus Tummescheit, Scynamics HB, Sweden

Local Organization: Gerhard Schmitz, Katrin Prolß, Wilson Casas, Henning Knigge, Jens Vasel,Stefan Wischhusen, TuTech Innovation GmbH

Object-Oriented Modeling, Simulation and Control of the IRISNuclear Power Plant with Modelica

Antonio Cammi∗, Francesco Casella†, Marco E. Ricotti∗, Francesco Schiavo†‡

Politecnico di Milano,Piazza Leonardo da Vinci 32

20133 MilanoItaly

Abstract

The paper presents the application of the Modelica lan-guage to the modeling, simulation, and control of thenew IRIS nuclear power plant, under development byan international consortium. The plant model, devel-oped by using components from the ThermoPower li-brary, as well as custom-built nuclear components, isdescribed, as well as the digital control system model,which will eventually become very realistic. Specialemphasis is put on the use of inheritance and replace-able objects for the management of a family of modelvariants over the project life-time. Selected simulationresults are included.

1 Introduction

The IRIS project [3] involves 21 organizations from10 countries and refers to the design of an innova-tive, light water reactor with a modular, integral pri-mary system configuration. The reactor pressure ves-sel houses the nuclear fuel, control rods and con-trol rods drive mechanisms, but also all the ma-jor reactor coolant system components, including thecoolant pumps, the steam generators and the pressur-izer (Fig.1).IRIS is basically a PWR (Pressurised Water Reactor):in the primary loop, liquid water is heated by the nu-clear fuel rods in the core, and is then sent by thepumps to the primary side of heat exchanger; the sec-ondary loop actually generates steam which is sent toturbines to produce power.

∗Dipartimento di Ingegneria Nucleare “E. Fermi”CESNEF,{antonio.cammi,marco.ricotti }@polimi.it

†Dipartimento di Elettronica e Informazione,{casella,schiavo }@elet.polimi.it

‡Corresponding author

Figure 1: The IRIS Reactor

Compared to conventional PWR plants, however, IRIShas a set of distinctive features, which directly affectthe control system design:

• the integral configuration requires a large waterinventory in the primary loop, whose residencetime is much greater than usual;

• a helicoidal once-through steam generator is em-ployed on the secondary side, which has a veryshort residence time, compared to the morewidespread U-tube recirculating steam genera-tors;

• sprayers are not available to reduce the pressurein the primary loop during fast transients.

Object-Oriented Modeling, Simulation and Control of the IRIS Nuclear Power Plant with Modelica

The Modelica Association 423 Modelica 2005, March 7-8, 2005

The control strategy must take these facts into account,and a dynamic simulation tool is essential to ensurethat the control objectives can be achieved.

Highly detailed dynamic simulators have been devel-oped for the IRIS reactor [6]. Such simulators, basedon the complex computational fluid-dynamics codenamedRELAP[10], are perfectly suited for accidentanalysis and safety-oriented evaluations of the reac-tor design features. On the other side, due to theamount of the details involved, they cannot be profi-ciently used for control-oriented dynamic simulation.

Within this framework, the use of the Modelica lan-guage offers a viable solution, allowing the develop-ment of dynamic simulators that are detailed enoughfor control-oriented analysis and yet with limited com-putational requirements.

To provide the required capabilities for the analysis,specific models for nuclear reactor components havebeen developed, to be applied for the dynamic simula-tion of the IRIS integral reactor, albeit keeping generalvalidity for PWR plants. In addition to that, specificdigital control blocks have been developed, so that acomplete model of the plant and of its digital controlsystem is available.

The paper is organized as follows. An overview of theplant model is presented in Section 2, while in Sec-tion 3 the models specifically developed for nuclearcomponents are analyzed in detail. Section 4 containsan overview of the plant digital control system and, inSection 5, the problem of managing a library of plantmodels with different detail levels is tackled. Section 6presents some closed-loop simulation results. Finally,Section 7 draws some conclusions and outlines possi-ble future developments.

2 Plant Model

The model of the IRIS plant basically describes theprimary circulation loop, i.e. the reactor coolant loop,and the secondary loop, i.e. the once-through evapo-rators, along with the feedwater and turbine systems.Most of the required models have no specificnuclearfeatures, and were thus borrowed from the general-purpose ThermoPower library, designed for the mod-elling of generic thermo-hydraulic power plants; thelibrary is an open-source project, described with moredetail in [4]. The only notable exceptions are the reac-tor core and the pressurizer, which are described in thenext section.

Figure 2: Plant flow diagram

2.1 Primary loop

The primary loop (see Fig. 2) starts with the pressur-izer (top of the diagram); the pressurizer is connectedby a pressure-loss component to the upper mixing vol-ume, taking into account the mass and energy bal-ances. Starting from the top of the diagram, counter-clockwise, the centrifugal pump model can be found,followed by another plenum model. The primary sideof the heat exchanger between the primary and sec-ondary loop is then encountered, modelled by threecascaded, finite-volume pipe models; the middle onedescribes the section where the coolant is actually incontact with the secondary side tube bundle. Proceed-ing onwards, other two plenum models followed by apressure loss can be found, leading to the inlet of thecore model (see next Section). This in turn is followedby another pressure loss, another plenum, and the tworiser sections, modelled by two pipes having differentdiameter. The loop is closed by a simple model ofthe chemical and volume control system (CVCS), ba-sically a mixer and an ideal flow source. The fluid inthe whole loop is one-phase water, with the exceptionof the steam filling the upper pressurizer dome.

The heat transfer between the primary and secondaryloop is modelled by two heat transfer modules andby the thermal model of the tube metal mass. Theprimary-side heat transfer coefficient is held constantto its nominal value, since the Reynolds and Prandtlnumbers does not vary substantially; on the secondaryside, the heat transfer coefficients can be computed ac-

A. Cammi, F. Casella, M. Ricotti, F. Schiavo


cording to different laws, e.g. Chen’s correlation, ormuch simpler, empirically tuned curves.

2.2 Secondary loop

The secondary loop is composed of the feedwater sys-tem, the helical coil once-through steam generator andthe turbine system. The once-through generator is rep-resented by a finite-volume, 10-node model of the two-phase fluid flow, assuming homogeneous flow, i.e. thesame velocity for the liquid and vapor phases.Currently, the feedwater system is represented by anideal flow source, whose flow rate is determined bythe control system, and whose enthalpy is a function ofthe plant load level, determined from balance-of-plantcalculations. The turbine system includes a simplified,linear model of the high- and low-pressure turbines,plus simplified models of the connection to the grid,including an idealized synchronous generator, localloads, and a grid model. The latter ones are includedto provide suitable boundary conditions for the (muchslower) plant dynamics; therefore, they only model ac-tive power flows, neglect the electro-mechanical dy-namics, and assume perfect synchronism between thegenerator and/or the grid.In the near future, it is planned to replace the feed-water and turbine system models with more realisticcounterparts, including steam bleedings and conden-sate train, to better represent the actual steam genera-tor dynamics under large load variations. On the otherhand, the finite-volume fluid evaporator model couldbe replaced by a simpler version, with moving bound-aries between the liquid, 2-phase, and vapor sections,and an averaged description of each section.

3 Nuclear Components

TheModelicamodels for “nuclear” components havebeen developed to provide solutions which are suitableboth for “general” use and specifically for the IRIS nu-clear plant modelling. The main components are thecore, (with separate models for the point kinetic neu-tronic generation, the fuel thermal dynamics and themoderator, as depicted in Fig. 3) and thepressurizer;the main modelling principles are summarized here,for more details see [1, 2].

3.1 Point Kinetics Neutronic

The point kinetic neutronic model describes the dy-namics of the neutron generation processes in thecore. The model is based on standard point kinetic

Figure 3: The Core Model Internal Structure

dynamic balance equations, describing the evolutionof the neutronic population and of the precursor con-centration. Reactivity feedback from coolant density,fuel Doppler effect, and rod insertion are accountedfor. The dynamic terms can be switched off, to obtaina simplified static model, neglecting the fast dynamics.The neutronic power generated into the fuel is propor-tional to the neutronic populationn, which responds tothe point reactor kinetics balance equations :

dn

dt=

ρ−βΛ

n+6

∑i=1

λi ci

dci

dt=

βΛ

n−λici i = 1, · · · ,6 ,

(1)

wherec is the precursor concentration leading to adelayed neutron source,ρ is the total reactivity of thecore,β is the fraction of delayed neutrons,λ is the de-cay constant of the precursors andΛ is the character-istic period of the reactor or mean neutron generationtime.Reactivity feedbacks are taken into account as well, byconsidering linear or non linear feedback coefficients,always negative, for the coolant density effect (αc), thefuel Doppler effect (α f ), the effect of the boron con-centration (αB) into the primary fluid as a neutronicpoison and the level of insertion of the control rodbanks into the core (αCR). These relations are

ρ = ρCR+ρ f +ρc +ρB ,

ρ f = α f(Te f f −Te f f0

),

ρc = αc

(1

vc−

1

vc0

),

ρB = αB (C−C0) ,

(2)

whereTe f f andTe f f0 are the instantaneous and refer-ence effective fuel temperature, respectively, obtained



from the fuel model,vc andvc0 are the instantaneousand reference specific volumes of the coolant,C andC0 are the instantaneous and reference boric acid con-centration in the coolant. The boric acid concentrationin the coolant depends mainly on the control rods in-sertion.

The reference values are those corresponding to thenominal, full power operation of the reactor.

3.2 Fuel model

The fuel model describes the dynamics of the thermalpower generated within the core by the nuclear chainreactions. The neutronic generation model and the fuelmodel are linked by a connection between twoMod-elicastandardHeatPort , where the connectors vari-able are the total power generated and the fuel tem-perature. AThermoPowerDHTdistributed heat trans-fer connector is used as well, as an interface with themoderator, modelled by a 1-D flow model.

The model is based on the application of the time de-pendent Fourier equation (in monodimensional cylin-drical geometry) to the three fuel zones: pellet, gapand cladding (Fig. 4).

Figure 4:Fuel pellet radial scheme for heat transfer mod-elling

The main assumption of the model is to consider onlythe radial heat transfer, thus disregarding both the ax-ial and the circumferential diffusions. Fourier’s equa-tion is discretized radially in five zones, and longitudi-nally in a user-decidable number of segments (N). Forthe pellet, gap and cladding the corresponding balance

equations read:

ρpcp,p∂Tp

∂t=

1

r

∂∂r

(rkp

∂Tp

∂r

)+q

′′′,

∂∂r

(kg

∂Tg

∂r

)= 0 ,

ρccp,c∂Tc

∂t=

1

r

∂∂r

(rkc

∂Tc

∂r

).

(3)

whereρ is the density,cp is the specific heat,T is thetemperature,k is the thermal conductivity,q′′′ is thevolumetric source term,r is the radial dimension andtthe time, while the subscriptsp, g andc stand for thepellet, the gap, and the cladding, respectively.The heat transfer model is represented in Fig. 4, withthe pellet discretized into three zones of equal volume.Eqs.(3), together with the conditions of heat flux van-ishing at the pellet center and the continuity of thetemperatures and heat fluxes at the three boundariespellet-gap-cladding-coolant allow the determination ofTp(r, t), Tg(r, t) andTc(r, t).In addition to the above equations, five correlationssynthesizing the dependance ofcp,p, kp, cp,c andkc asa function of the fuel temperature and ofkg as a func-tion of both the reactor power and the burn-up havebeen adopted.The condition at the cladding-coolant interface is de-termined by the distributed heat transfer connectorvariables.Finally, the effective fuel temperature, used to evalu-ate the Doppler feedback contribution on neutronics,is defined as follows:

Te f f =4

9T|r=0 +

5

9T|r=R . (4)

3.3 Moderator

The core moderator is modelled by the ThermoPowerlibrary Water.Flow1D , with a small extension tomake the fluid density available to the point kineticsmodel. The coolant model has the same number ofvolumes as the fuel. The convective heat transfer be-tween the two components is calculated at each nodeby

φmod = −φc ,

φmod = γ(Tc−Tmod) ,(5)

whereφmod andφc are, respectively, the moderator andthe fuel cladding heat flux,γ is the heat transfer co-efficient, andTmod andTc are the moderator and fuel



cladding temperatures. DetailedRELAPsimulationshave shown that the heat transfer coefficient is approx-imately constant for all the operating conditions thecontrol system is concerned with.

3.4 Pressurizer Model

The pressurizer model is based on a lumped param-eter approach, which is appropriate to the IRIS case.Both water properties in the liquid volume and in thesteam volumes are assumed as homogeneous, at equalpressure but not at thermodynamic equilibrium.The model is based on two groups of dynamic massand energy balance equations, the first for the liquidphase and the second for the vapor phase inside thetank. Mass and energy transfer between the two phasesis provided by bulk condensation and surface conden-sation of the vapor phase, and by bulk boiling of theliquid phase. Additional energy transfer can take placeat the surface if the steam is superheated.External interfaces are provided for connections to thehydraulic loop by a bottom flange and to a safety cir-cuit by a safetyflange; also available are a heatingpower command input and a level signal probe output.The heating power input is processed by a limiter anda low pass filter block to simulate the delay in heatingeffect and the limited heaters power. The resulting ef-fective heating power signal drives the production ofsaturated steam by the heaters at a rate correspond-ing to the difference between the enthalpy of the liquidholdup and the enthalpy of saturated steam. For sim-plicity, the corresponding steam flow enters directlythe steam holdup, without causing heating of the liq-uid holdup.The bottom flange’s flow enters directly the liquid vol-ume; its pressure is increased depending on the liquidholdup’s level.The metal wall dynamics is taken into account, assum-ing uniform temperature. Heat transfer takes place be-tween the metal wall and the two phases and betweenthe wall and the external ambient at fixed temperature.

4 Control

The control design of the IRIS nuclear power plant isa complex task, with objectives that, depending on theplant operating conditions, vary from the managementof start-up sequences to the recover from turbine or re-actor trips and to the grid power/frequency regulationat full nuclear power.

Classic design concepts, for early nuclear units, re-lied on separate control systems for each control loop,and limited signal interaction between the loops [9].This simplified the design of each loop, particularlywith analog control systems where each interconnec-tion added hardware expense. On the other side, thecurrent trend is for more integrated systems that cantake advantage of coordinating the different controlloops [7]. This allows for more effective plant control,but complicates the control system failure analysis. Aviable solution for IRIS is the choice of a hierarchicalcontrol system, as depicted in Fig. 5.

Figure 5:Control system architecture

At the top level is located a supervisory control systemwith the following functions:

• Establish the plant electric power reference sig-nal. Such reference signal will be used to derivereference and/or feedforward signals for the othermajor control loops.

• Monitor plant conditions and deter-mine/coordinate the appropriate operatingmodes for the major control systems.

The control sub-systems have different settings and avarying structure (i.e., different inputs and differentcontroller structure) depending on the specific operat-ing mode of the plant.All the operating modes to drive the plant during thenon-emergency maneuvers have been designed [8];nevertheless, only the “full-power” control mode (nu-clear flux from 20% to 100%) has been fully imple-mented, simulated and tested yet, so, from here on, thedescription will cover only such operating mode.

4.1 Supervisory Control

The supervisory control system uses the normalizeddesired power as an input signal to derive the refer-ence and feedforward signals for the lower-level con-trol systems. On the base of the desired power the tem-perature and nuclear flux reference for the reactor con-trol are derived, along with a pressure reference for the



turbine and steam dump control systems and with theflow rate reference for the feedwater control. The sig-nals to be fed to the lower systems are derived fromthe desired power reference with linear filtering andthrough look-up tables based on steady-state plant bal-ances.

4.2 Reactor Control

The aim of the reactor control is to control the coolanttemperature, and thus the reactor nuclear power, bydriving the control rods stepping system. As a matterof fact, the reference is a temperature signal comingfrom the upper level, while the measurements includethe core coolant average temperature (obtained as themean between the temperature at the core inlet and theone at the core outlet) and the nuclear neutron flux (ob-tained through special sensors enclosed within the coreshielding).The temperature error, with suitable dynamic compen-sation, is used to generate an error signal for determin-ing the speed request for the control rods, along witha power mismatch signal which is used to improve thestability and the velocity of the reactor control systemresponse. The power mismatch signal (i.e. the dif-ference between the reference and the measured neu-tronic flux) is fed into a rate compensation filter, toeliminate steady-state influence, and then into a non-linear, power-dependant gain, to improve low-powerresponse while avoiding high frequency excitation ofthe rod stepping system.The combined error signal enters a rod speed pro-gram that features a small dead band to avoid highfrequency rod stepping. The speed request thus gen-erated is then serviced by a servo control system em-bedded within the control rods drive mechanism. Thisservo is currently described by a high-level behav-ioral model, which could be eventually replaced by aphysical-based model.

4.3 Turbine Admission Valve Control

The turbine system for the IRIS power plant has notbeen completely designed yet and it is reasonable toassume that the turbine supplier will provide most ofthe requirements for the turbine control system; how-ever, the design must be compatible with the overallIRIS plant control strategy. The most important con-straint is that the IRIS turbine control will have theresponsibility for controlling steam pressure by actingon the turbine admission valve (TAV).

The control is based on a PID, its input being the refer-ence pressure signal coming from the supervisory con-trol system and the actual steam pressure measured atthe turbine inlet, with suitably low-pass filtering ac-tion. The PID output is then summed to the amplifiedfrequency mismatch (i.e., the difference between theactual generator frequency and the desired frequency),with the gain depending on the grid droop setting. Theresulting signal is fed to the TAV drive system after be-ing filtered by a non-linear algebraic function, whichis an approximate inverse of the TAV characteristic.

4.4 Steam Dump Control

The steam dump control system must control steampressure when the turbine admission valve control isnot doing so, and must provide a backup in all othercases. Experience shows that a simple PID control per-forms well, particularly if the system uses hydraulicsteam dump valves, as it will be in the IRIS case.The controlled variable is the steam dump valve open-ing, while the controller inputs are the pressure refer-ence (from the upper level) and the turbine inlet steampressure (low-pass filtered). Additional steam-dumpaction is available in case of need: the power refer-ence, filtered through a rate compensator and a suit-able gain, is added to the steam dump valve controlsignal, to provide a faster response in case of suddenchanges in the requested power (e.g., when a reactor ora turbine trip occur and the supervisory control systeminstantaneously lowers the power reference).

4.5 Feedwater Control

The feedwater control system directly controls thefeedwater flow in the secondary side by acting on avalve located at the feedwater pumps. The structure isbased on two PID controllers in cascade configuration.The inner loop acts to control feedwater flow to the ref-erence value obtained from the supervisory control. Inthe ideal case with perfect settings in the supervisorycontroller, this would result in the plant operating atthe desired power, at least in steady state. Of course,such an open loop control on power would be sensi-tive to parameter variations, so the outer loop providesa trim signal to adjust feedwater flow to achieve the de-sired power by the action of a PID controller with thereference and the actual power as inputs. The feedwa-ter valve control signal is then filtered by a non-linearalgebraic function, which is an approximate inverse ofthe valve characteristic.



4.6 Digital PI controller

Models for digital PI and PID controllers, in ISA form,have been implemented. Here, for the sake of brevity,only the PI development is briefly showed: the PIDmodel development is quite similar.The model is based on the standard industrial ISA for-mulation, with the output calculation formula obtainedwith a Tustin discretization:

CS(s) =Kp

((bSP(s)−PV(s))+

1

TI s(SP(s)−PV(s))

)

⇓

(Tustin: s=

2

Ts

z−1

z+1

)

CS(z) =SP(z)a0 +a1 z−1

1−z−1 +PV(z)b0 +b1 z−1

1−z−1

(6)

with

a0 =2 Kp b TI +Kp Ts

2 TI, a1 =

−2 Kp b TI +Kp Ts

2 TI,

b0 =−2 Kp b TI −Kp Ts

2 TI, b1 =

2 Kp b TI −Kp Ts

2 TI.

The complete controller model includes also advancedfeatures likemanualandtrackingworking mode, out-put saturation, and anti wind-up mechanism.The resulting block has two boolean inputs (automaticand tracking switch signals), four discrete real inputs(set-point, process value, manual and tracking signals)and a discrete real output (control signal).The Modelica implementation exploits the languagefeatures for digital blocks, using discrete variables andwith the instructions enclosed within a sampling loop:

when {initial(),sampleTrigger} then...[PI computations]...end when;

The anti wind-up mechanism is implemented via anauxiliary variable:

CSwind=pre(CS)+a0*SP+a1*pre(SP)+b0*PV+b1*pre(PV);

whereCswind is the auxiliary variable,CS the con-trol variable, SP the set-point andPV the processvalue.The actual control value is chosen depending on thecontroller logic state (automatic, manual or tracking)and on the saturation values, e.g. :

if AUTO thenif CSwind >= CSmax then

CS = CSmax;CSport.signal[1] = CSmax;

elseif CSwind <= CSmin then

CS = CSmin;CSport.signal[1] = CSmin;

elseCS = CSwind;CSport.signal[1] = CS;

end;else

...

where the parametersCSmaxandCSmin, are the up-per and lower saturation limits for the control action.With this implementation structure, the controller inte-gral state is automatically updated at every executioncycle so to be coherent with the last output sample.

5 Model Management through theproject life-cycle

Object-oriented features such as inheritance and re-placeable components are often described as key fac-tors in the development of reusable model libraries.In fact, they can also be extremely useful for theproper management of families of application modelsthroughout an engineering project’s lifetime, as it willbe explained in this section with reference to the IRISproject.

5.1 Requirements

During the IRIS project lifetime, a considerable num-ber of model variants will have to be built and ana-lyzed; some of them will become obsolete and willhave to be discarded, while others should be kept con-sistently up-to-date. The motivations of the modelvariants are now briefly discussed.Depending on the specific simulation to be performed,different accuracy vs. computational load trade-offsare required. Reference simulations should be per-formed with the maximum level of accuracy and de-tail, and cross-checked with the results of the refer-ence simulations performed with the certified RELAPcode. When performing simulations around a certainoperating point, some approximations could then beintroduced, which are only valid for that operating re-gion; it should be possible to easily check simplifiedversions against their more accurate counterparts.Some of the plant parameters (e.g. the pump character-istics, or some plenum volumes) are not yet definitive,and could change in the future; when one of such pa-rameters is changed, it is essential that all the currentmodel variants are updated consistently.Once the initial phase of the control system design hasbeen carried out, a systematic simulation campaign



must be performed to check that the operational con-straints (i.e., the activation thresholds of the protectionsystem) are never violated in all the predicted oper-ating conditions and transients; thousands of differentsimulation runs can be required. To carry out this task,the simplest and fastest possible variant of the plantmodel should be used.It should be also kept in mind that the plant mod-els will be developed, used, and maintained by dif-ferent people over a wide time span (several years)and at widely spaced sites (US, Europe). For instance,the model presented in this paper will be presumablyfrozen for some months, and then possibly resumedwhen the project will enter the commercial phase. Itis therefore essential to avoid building a plethora ofdistinct models, differing only by some details, whichwould be extremely difficult to maintain and documentconsistently.

5.2 Implementation

The top-level structure of the simulator is representedin Fig. 6: the TGFWS block contains the Tur-bine/Generator/Feedwater system model; the NSSSblock contains the Nuclear Steam Supply Systemmodel, i.e. the nuclear reactor, with the primary andsecondary loops. The two are connected to each otherby thermo-hydraulic connectors. The control side isrepresented by the CS (Control System) block, col-lecting all the control loops, and the SS (Supervi-sory system) block, which generates the set points forthe CS based on the plant load request. Three busconnectors carry the sensor, actuator, and referencesignals. This structure is common to all the possi-ble variants of the model, and thus contained in theIRISSimulatorBase partial model. Different ver-sions of the simulator can be instantiated by select-ing the actual content of each block; for instance, onecould use the simplified TGFWS model described inSection 2, or a more detailed one.The NSSS model contains a replaceable model(HelicalCoil ) for the secondary side of the once-through steam generator, which can be implementedby either the finite-volume or the moving boundarymodel, and by adding through inheritance the desiredequations to compute the heat transfer coefficient.Besides that, it is possible to vary dramatically thedegree of detail and the computational load of themodel by changing the number of nodes in the coreand once-through generator models, as well as byredeclaring the medium models in the primary andsecondary loop components. The default medium

Figure 6: The Base Simulator Model

models are the IF97-based water models taken fromModelica.Media , but it is possible to use muchfaster models, based either on table interpolation or onequation-based simplified medium models. The ther-modynamic conditions of the fluid in the primary loopconditions vary in a rather narrow range (140 to 160bar, 270 to 330 degrees Celsius), so that extremelysimplified models can still be acceptable; the fluid con-ditions in the secondary loop vary in a broader range,from subcooled liquid to superheated steam, albeit in anarrow pressure range around 58 bar, due to the pres-sure control system action.

Last, but not least, if an incompressible fluid model isadopted for the primary loop, the fast pressure statescaused by the small compressibility of the fluid, cou-pled with the small hydraulic resistances around thecirculation loop, are automatically avoided, withoutany need to change the component models. This is es-sential to allow the use of the faster explicit integrationalgorithms (e.g. forward Euler).

The simulation suite is then organized as a small li-brary (Fig. 7), containing the “empty” base models,and the actual models of the different parts, withoutany unnecessary duplicate of data. Any specific vari-ant of the simulation model can be instantiated fromthis library by using suitable modifiers. For exam-ple, the variant V2 of the simulator, using a simpleincompressible water model for the primary loop, 7nodes in the core model, a finite volume model of thesteam generator with 15 nodes using Chen’s correla-



Figure 7: Iris Simulation Suite

tion for the heat transfer coefficient, the variant V1 ofthe TGFWS, and the variant 2 of CS and SS, is instan-tiated as follows:

model IRISSimulator_V2extends IRISSimulatorBase(

redeclare Plants.NSSS_V1 NSSS(redeclare package PrimaryMedium =

Media.SimpleIncompressibleWater,Core(N = 7),redeclare Plants.HelicalCoilFVChen

HelicalCoil(N=15)),redeclare Controls.CS_V2 CS,redeclare Controls.SS_V2 SS,redeclare Plants.TGFWS_V1 TGFWS);

end IRISSimulator_V2;

IRISSimulatorBase is the empty base model de-scribed at the beginning of the section, and its fourreplaceable componentsNSSS, TGFWS, CS, SSare of typeNSSSBase, TGFWSBase, CSBase andSSBase, which again only contain the interfaces. TheNSSS model in turn contains the replaceable steamgenerator modelHelicalCoil .

In this way, it is straightforward to maintain a con-sistent state for a potentially large family of simulatorvariants, as well as documenting all of them efficiently.

6 Simulation

The results of a closed-loop simulation, obtained withthe tool Dymola ([5]), are now presented. The refer-ence transient is a filtered step variation of the electri-cal load reference, from 90% to 100% and then backto 90%. Although such a rude transient will neverbe performed on the actual plant, it is usually em-ployed to assess the overall dynamic response of thecontrol system, in terms of speed of response, damp-ing, overshoot, and so on. The normalized transientsof the neutron flux (representative of the generated nu-clear power) and of the generated electrical power areshown in Fig. 8, along with the reference power signal.The responses are well-damped and with limited over-shoot. The neutron flux transient takes into accountthe effect of the step-by-step actuation mechanism, aswell as of the dead-band included to avoid persistentchattering around a specific operating point. The cor-responding normalized transients of some control vari-ables (i.e. TAV opening, feedwater flow rate, and rodinsertion) are shown in Fig. 9.

Figure 8: Normalized response to a step load variation:measured variables

7 Conclusions and Future Work

In this paper, the application of Modelica to thestudy of the control system of the new IRIS nuclearpower plant has been presented; this is also the firstindustrial-scale application of the ThermoPower Mod-elica library.The well-behaved nature of the closed-loop transients



Figure 9: Normalized response to a step load variation:control variables

has confirmed that the new reactor concept will notpose exceedingly difficult problems to the control en-gineers, compared with already existing PWR plants.On the other hand, the availability of a detailed dy-namic model will allow the study of more advancedcontrol concepts, to cope with situations such as. e.g.,load/frequency control in small grids, or improvedmanagement of blackout transients.The object-oriented features of the Modelica language(replaceable classes in particular) have been fully ex-ploited to allow the efficient management of all thevariants of the plant simulator, which will be neededthroughout the project’s life-time. The structure of thesimulation suite will allow an easier re-use and exten-sion of the models developed so far, when the projectwill eventually enter the detailed engineering phase,prior to the construction of the first plant.

Acknowledgements

The authors wish to thank Westinghouse ElectricCompany LLC (IRIS project partner), and particularlyGary D. Storrick, Luca Oriani and Mario D. Carelli,for their contribution and support.

References

[1] A. Cammi, F. Casella, M.E. Ricotti, and F. Schi-avo. New modelling strategy for IRIS dynamicresponse simulation. In 5th International Confer-ence on Nuclear Option in Countries with Small

and Medium Electricity Grids, Dubrovnik, Croa-tia, June 3-4, 2004.

[2] A. Cammi, F. Casella, M.E. Ricotti, and F. Schi-avo. Object-oriented modelling for integralnuclear reactors dynamic simulation. InIn-ternational Conference on Integrated Modeling& Analysis in Applied Control & Automation,Genoa, Italy, October 3-4, 2004.

[3] M.D. Carelli. IRIS: A global approach to nuclearpower renaissance.Nuclear News, 46(10):32–42,September 2003.

[4] F. Casella and A. Leva. Modelica openlibrary for power plant simulation: Designand experimental validation. In 3rd Model-ica Conference, Linkoping, Sweden, November3-4, 2003. http://sourceforge.net/projects/thermopower/ .

[5] Dymola. Dynamic Modelling Laboratory, v. 5.3.Dynasim AB, Lund, Sweden.

[6] D. Grgic, T. Bajs, and L. Oriani. Development ofRELAP5 nodalization for IRIS non-LOCA tran-sient analyses. InAmerican Nuclear Society Top-ical Meeting in Mathematics & Computations(M&C), Gatlinburg, USA, April 6-10, 2003.

[7] IAEA. Modern instrumentation and control fornuclear power plants: A guidebook. Tech-nical Report 387, International Atomic EnergyAgency, Vienna, 1999.

[8] F. Schiavo and G. Storrick. IRIS control systemsconceptual design. Internal report STD-ES-04-34, Westinghouse Electric Company, September,2004. Westinghouse Electric Company Propri-etary.

[9] M. A. Schultz. Control of Nuclear Reactors andPower Plants. McGraw Hill, New York, 1961.

[10] A. S. L. Shieh, R. Krishnamurthy, and V. H.Ransom. Stability, accuracy, and convergenceof the numerical methods in RELAP5MOD3.Nuclear Science and Engineering, 116(10):227–244, 1994.



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