UPTEC F 15069

Examensarbete 30 hp1 December 2015

Control Rod Effect at Partial SCRAM Upgrade of Plant Model for Forsmark 2 in

BISON After Power Uprate

Daniel Constanda

Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student

Abstract

Control Rod Effect at Partial SCRAM

Daniel Constanda

This study aims to improve the modeling of partial SCRAM in the BISON plant modelfor the Forsmark 2 nuclear reactor after power uprate. Validation of the BISONmodel against tests performed from March to May in 2013 have shown that this isone of the areas in which there is room for improvement. After partial SCRAM isperformed, the model underestimates the reactor power, recirculation flow andsteam flow when compared to the measurement data.

In BISON the partial SCRAM is modeled using a relative control rod effect vector(ASC vector). The aim is to replace the old values in this vector to improve themodel. The new model was shown to give an improved result for the reactor power,recirculation flow and steam flow. The study gives recommendations on how to applythe new model and what values of the relative control rod effect vector that can beused in the future.

ISSN: 1401-5757, UPTEC F 15069Examinator: Tomas NybergÄmnesgranskare: Staffan QvistHandledare: Anna Aspman, David Palko

Popularvetenskaplig sammanfattning

I kokvattenreaktorer (engelska: BWR, boiling water reactors) kan det uppsta storningarsom kan uttrycka sig i exempelvis tryckokning, tryckminskning och temperaturokning ireaktorn. Berakningsprogrammet BISON anvands for att simulera dessa.

Anlaggningsmodellen i BISON for Forsmark reaktor 2 har under senaste aren genomgattstora uppdateringar pa grund av anlaggningens effektokning. Modellen har nyligen jamfortsmot matvarden fran reaktorn vid 120 % effekt. Jamforelsen har funnit skillnader mel-lan anlaggningsmodellens beteende och matningar utforda i anlaggningen i samband medeffekthojning av Forsmark 2. En av skillnaderna var i styrstavsinverkan vid delsnabb-stopp, vilket denna rapport fokuserar pa. Delsnabbstopp ar nar nagra av styrstavarnaskjuts in i reaktorn, vilket gor att effekten sanks. Detta kan jamforas med snabbstoppdar alla stavar skjuts in och effekten sanks helt, reaktorn blir s.k. underkritisk och densjalvstandiga karnreaktionen upphor.

Denna rapport syftar till att forbattra modellen sa att delsnabbstoppet hamnar narmarematvardena fran jamforelsen. Styrstavsinverkan i den tidigare anlaggningsmodellen i BI-SON beraknas med antagandet att den varierar proportionellt med styrstavar som skjutsin. Den nya styrstavsinverkan togs fram genom att BISON jamfordes med ett annatsimuleringsprogram som simulerar harden (branslet till reaktorn) noggrannare. Dettasimuleringsprogram anvandes alltsa som referens for att undersoka vilken styrstavinverkansom BISON borde fa. Med en automatiserad jamforelse mellan dessa program sa togsstyrstavsinverkan fram for flera olika fall.

Darefter anvandes den nya styrstavsinverkan i den tidigare anlaggningsmodellen i BISONoch jamfordes med samma matdata som forut. Den nya styrstavinverkan visade sig ge enforbattring gentemot den tidigare, darmed har malet med rapporten uppfyllts. Slutligeninnehaller rapporten en narmare analys av resultaten samt rekommendationer kring hurmetoden och resultaten bor anvandas. Det finns aven mojligheter att fortsatta dennastudie vidare, diskussion kring detta ges ocksa.

3

Contents

0.1 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1 Introduction 81.1 Boiling Water Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.2 The Reactor, Safety and Auxiliary Systems . . . . . . . . . . . . . . . . . . 91.3 BISON - Analysis Program for BWR . . . . . . . . . . . . . . . . . . . . . 121.4 Previous Results and Performed Tests . . . . . . . . . . . . . . . . . . . . . 121.5 Aim of the Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2 Theory 142.1 Transients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2 The SCRAM System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.3 SCRAM Modeling in BISON . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3.1 The Neutron Transport Equation . . . . . . . . . . . . . . . . . . . 162.3.2 Defintion of the ASC vector . . . . . . . . . . . . . . . . . . . . . . 172.3.3 The ASC vector in the Previous Model . . . . . . . . . . . . . . . . 18

3 Model and Simulations 193.1 Simulation Software Selection . . . . . . . . . . . . . . . . . . . . . . . . . 193.2 BISON Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.3 POLCA Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4 Method 214.1 Computation of ASC vector . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.1.1 Calculate New ASC vector . . . . . . . . . . . . . . . . . . . . . . . 224.2 Composition of the New Model . . . . . . . . . . . . . . . . . . . . . . . . 24

5 Results 255.1 ASC vector Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255.2 Comparison with Previous Results . . . . . . . . . . . . . . . . . . . . . . 275.3 Comparison of BISON and Simulate-3K Calculations . . . . . . . . . . . . 30

6 Discussion 316.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

7 Conclusions 34

A Comparison with Previous Results: Turbine Trip Case 36

B Comparison with Previous Results: House Load Operation Case 38

C Individual Control Rod Study 40C.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40C.2 POLCA Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40C.3 BISON Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40C.4 MATLAB Scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40C.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40C.6 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4

List of Figures

1 Overview of a BWR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 The reactor pressure vessel. . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Fuel assembly example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Overview of a reactor core. . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Algorithm for calculating the ASC vector. . . . . . . . . . . . . . . . . . . 226 Example of how the ASC and the reactor power given by BISON changes

with each iteration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 ASC vector for PSS during Cycle 32 and 34 . . . . . . . . . . . . . . . . . 258 ASC vector for PSS with and without runback . . . . . . . . . . . . . . . . 269 ASC vector for PSS and individual insertions of SCRAM bank 6 and 9 . . 2710 Loss of condensate pump: APRM . . . . . . . . . . . . . . . . . . . . . . . 2811 Loss of condensate pump: Recirculation flow . . . . . . . . . . . . . . . . . 2812 Loss of condensate pump: Steam flow from RPV . . . . . . . . . . . . . . . 2913 Comparison of the power given by BISON and Simulate-3K . . . . . . . . 3014 Turbine trip: APRM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3615 Turbine trip: Recirculation flow . . . . . . . . . . . . . . . . . . . . . . . . 3716 Turbine trip: Steam flow from RPV . . . . . . . . . . . . . . . . . . . . . . 3717 House load operation: APRM . . . . . . . . . . . . . . . . . . . . . . . . . 3818 House load operation: Recirculation flow . . . . . . . . . . . . . . . . . . . 3919 House load operation: Steam flow from RPV . . . . . . . . . . . . . . . . . 3920 Individual control rod study: APRM during loss of condensate pump . . . 41

List of Tables

1 Values of the ASC vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 Values of the ASC vector: Individual control rod study . . . . . . . . . . . 40

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0.1 Glossary

English term Swedish term ExplanationAPRM (Average PowerRange Monitor)

APRM Equivalent to the average neutronflux in the core. Usually mea-sured in % and equivalent to thereactor power in %.

ASC vector ASC vektor Relative control rod effect vector.Channel power Kanaleffekt The power generated by the fuel

in a certain coolant channel.Control rod Styrstav A neutron absorbing rod which

can be inserted/withdrawninto/from the reactor.

CPR (Critical Power Ra-tio)

Torrkokningskvot Ratio of the critical channelpower needed for dryout and ac-tual channel power.

Dryout Torrkokning Boiling on a heated surface dur-ing high steam concentration ina coolant channel, loss of waterlayer on the heated surface.

EFPH (Effective Full-Power Hour)

Ekvivalent fulleffekttid Ratio of extracted energy duringa given time and the rated outputof the reactor.

F1, F2, F3 F1, F2, F3 Forsmark Reactor 1, 2 and 3 re-spectively.

Feedwater Matarvatten (Mava) The water entering the RPV fromthe primary coolant loop.

Operating cycle Driftcykel The period from start of the reac-tor to refueling.

Operation point Driftpunkt The point on a coordinate systemwith power and RF on the y- andx-axis respectively.

Partial SCRAM (PSS) Delsnabbstopp Insertion of one or a few controlrods groups, decreasing the reac-tor power.

Reactor Pressure Vessel(RPV)

Reaktortank See Figure 2 for an illustration.

Reactor Coolant Pres-sure Boundary (RCPB)

RCPB/Primarsystemet Self explanatory.

Recirculation flow (RF) Huvudcirkulationsflode(HC-flode)

Water being circulated in the re-actor for cooling. Powered by re-circulation pumps.

Runback (of recircula-tion pumps)

Nedstyrning (av HC-pumpar)

Reduction of speed of the reactorrecirculation pumps.

Safety System Logic Sakerhetskedjor Shows which safety systems areactivated and in what order, de-pends on certain conditions suchas reactivity and pressure etc.

6

SCRAM Snabbstopp Rapid insertion of all control rodsinto the reactor, shutting downthe reactor quickly.

SCRAM bank Snabbstoppsgrupp A group of control rods used forSCRAM.

Void Void/Anginnehall The amount of vapor in the mod-erator. Higher void implies lesseffective moderation (thus lowerreactivity).

7

1 INTRODUCTION 8

1 Introduction

This section introduces the basics of the nuclear reactor and gives background to thestudy. It concludes with the aim of the study.

1.1 Boiling Water Reactor

A Boiling Water Reactor (BWR) is one of the two most common light water reactor types,the other is Pressurized Water Reactor (PWR). The most salient difference is what givesthem their names, the water inside the reactor of a BWR is boiling but in a PWR it is notdue to the higher pressure in the reactor. Another difference is that BWR is a single-loopsystem, see Figure 1, while PWR is a double-loop system. This is because the PWR needsa steam generator in order to get steam to drive the turbine. The BWR already generatessteam due to the boiling. All the reactors of the Forsmark Nuclear Power Plant (herebysimply referred to as Forsmark) are of BWR type. Thus this report will only focus on thisreactor type. Figure 1 shows an overview of a typical BWR with internal recirculationpumps.

Figure 1: Overview of a BWR with internal recirculation pumps.[1]

1 INTRODUCTION 9

1.2 The Reactor, Safety and Auxiliary Systems

The reactor pressure vessel is shown in Figure 2. This shows the most important partsof the reactor and the vessel. In the feedwater inlet the water enters from the primarycoolant loop, as shown in the overview in Figure 1. The same overview shows where thesteam leaves the RPV through the steam outlet.

The feedwater flows through the downcomer and is pumped through the reactor core,composed of fuel assemblies, by recirculation pumps. The recirculation pumps shown inFigure 2 are of the internal type. After the water has been heated enough to boil, thesteam generated will pass through the steam separators and steam dryers in order toremove liquid water. This is done since liquid water can damage the turbines. Then thesteam leaves through the steam outlet.

Figure 2 also shows the control rods. They are located at the bottom of the RPV andare inserted/withdrawn vertically upwards/downwards in order to regulate the reactivityin the core. In Figure 2, the illustrated control rod is inserted. The control rods are of across shape when viewed from above, as shown in Figure 3.

In the case of loss of off-site power the recirculation pumps can be powered by energystored in a flywheel, enabling runback. There is one flywheel for each of the four pairs ofrecirculation pumps. Each one of these is placed so that a failure of flywheel will not affectanother flywheel or other safety systems. [2] If the flywheels are not accounted for in thesafety analysis, then the design of the core (i.e. the placement of the fuel assemblies, seeFigure 3 and Figure 4) needs to be different in order to fulfill the safety criteria. The coreneeds to have more new fuel in order to keep the power level evenly spread out over thecore. There cannot be large local variations in power. This is less economical since notall fuel can be used optimally.

Before cycle 34, which started with the refueling of F2 in July 2015, The Swedish RadiationSafety Authority (Stralsakerhetsmyndigheten (SSM)) have not allowed the inclusion of theflywheels in the safety analysis. Thus the core designs have had different design conditionsuntil this cycle.

1 INTRODUCTION 10

Figure 2: The reactor pressure vessel.[3]

1 INTRODUCTION 11

Figure 3: Fuel assembly example. [4] The Forsmark reactors contain a similar but notidentical design for their fuel assemblies.

Figure 4: Overview of a reactor core.[5]

1 INTRODUCTION 12

1.3 BISON - Analysis Program for BWR

BISON is a one dimensional dynamic analysis program for BWR originally developed byASEA-ATOM, and is currently distributed and developed by Westinghouse. BISON isused for analyzing transients in the reactor. The modeling in BISON starts with withthe feedwater pumps and ends with the turbine control valves. It contains models for thedifferent parts in the RPV, such as steam separators etc. (see Figure 2), and detailedmodels of various safety relief valve systems and control systems. It also has a simplemodel for the feedwater system. BISON models both thermal-hydraulics and neutronkinetics. The neutron kinetics are explained further under 2.3.1 The Neutron TransportEquation. [6]

Some of the important physical processes which take place in these systems are thermal-ization, diffusion and absorption of neutrons in the core, with or without the influenceof control rods. The flow of the steam from the RPV, through the turbine system orthe safety and relief valves. The flow of the condensate and feedwater in their respectivesystems. These processes can be modeled in BISON.

There are of course several ways in which BISON performs approximations in order toperform accurate computations at a reasonable time. One example is that all flow pathsare considered to be strictly one dimensional. This approximation is motivated becausethe flow is close to being one dimensional in most sections of the coolant loop, withexception of the bottom of the lower plenum and in the liquid portion of the upperplenum. [6]

1.4 Previous Results and Performed Tests

This section covers the relevant tests performed from March to May in 2013 and the re-sults of the previous model. There were eleven tests performed which were relevant forthe testing of the BISON model. These tests show that there is room for improvementin the modeling of partial SCRAM in BISON. Out of these eleven test there were threein which partial SCRAM occurred in both the actual test and the previous model. Thusthese are the only measurements that can be used to verify the results of the BISONmodel for partial SCRAM with the uprated reactor. The tests were loss of condensatepump, turbine trip, and house load operation. [7]

A comparison of the previous model and the measurements can be seen under 5 Resultsfor the loss of condensate pump case. The other two cases are very similar and the resultsare analogous, see Appendix A and Appendix B. In each of these three cases the previousmodel underestimates the reactor power after partial SCRAM. As a consequence, themodel also underestimates the recirculation flow and steam flow. It is clear that thepartial SCRAM modeling needs improvement.

1 INTRODUCTION 13

1.5 Aim of the Study

The aim is to improve the modeling of partial SCRAM in the plant model in BISONfor the Forsmark 2 nuclear reactor after power uprate. Validation of the BISON modelagainst tests performed from March to May in 2013 have shown that this is one of theareas in which the model has room for improvement when compared to the tests. Afterpartial SCRAM is performed, the model underestimates the reactor power, recirculationflow and steam flow when compared to the measurements. In BISON the partial SCRAMis modeled using a relative control rod effect vector. The aim is to replace the old valuesin this vector to improve the model.

2 THEORY 14

2 Theory

This section explains several types of transient, the SCRAM system and how SCRAM ismodeled in BISON. For the SCRAM modeling in BISON it covers the neutron transportequation and the ASC vector.

2.1 Transients

In general the term transient is used to indicate time dependence or fast change. Here,however, the term takes on a more specific meaning. It is defined as an event which leadsto an imbalance in supplied and removed heat from the reactor core (with the exception ofloss of coolant accident). Usually these are in the order of a few seconds to a few minutes.

Transients can be grouped into the following categories: [8] [9]

1. Pressure increase.

2. Pressure decrease.

3. Feedwater flow increase or feedwater temperature decrease.

4. Feedwater flow decrease.

5. RF increase.

6. RF decrease.

However, it is worth to note that these categories are not precise because a transient cansometimes fit into more than one of these categories at the same time. Transients alsochange over time since there will be a response from the safety and control systems. Theeffect of the transient can also depend on the time scale involved. Some of the slowertransients might take minutes while some faster take seconds. Thus a transient can forexample be viewed as pressure increase if the time frame is only a few seconds. But itmight at the same time lead to a reduction of feedwater temperature in a few minutes.

The test case of loss of condensate pump falls into the 4th category of feedwater flowdecrease because it will eventually lead to a decrease in feedwater. This case is actuallysometimes referred to as ”loss feedwater or condensate pump” since they are very similar.

The general description is as follows, feedwater flow decrease leads to a lower water levelin the RPV. Since the feedwater is subcooled, the feedwater flow decrease implies lesssubcooling of the moderator. Thus there will be more water closer to the saturation tem-perature. The void increases and reactivity decreases.

This type of transient can sometimes be handled by the water level controller. However,if it is not able to counteract transient by changing the water level reaching a stable op-eration point, then runback of the recirculation pumps is activated. This is followed bypartial SCRAM. The decrease in reactivity and the decrease in the speed of water levelreduction can be enough to reach a stable operation point. If it does not, then other sys-tems would pump water into the RPV and SCRAM would be activated. This would leadto completely shutting down the reactor. For the test case runback is activated directlybefore the water level is affected by the loss of condensate pump, then partial SCRAM

2 THEORY 15

follows.

Turbine trip falls into 1st category of pressure increase and the 3rd of feedwater flowincrease or feedwater temperature reduction. That is because it takes on both character-istics, in the short term (in order of seconds) it will see a pressure increase. But in thelonger term (in order of minutes) it will have a feedwater temperature reduction as well.

Pressure increase transients are caused by a decrease in the extraction of steam from theRPV. During turbine trip the steam extraction is prevented by the closure of turbinecontrol valves. The increase in pressure will cause increase in subcooling and decrease invoid. Thus the reactivity increases.

The feedwater temperature reduction occurs since the turbine trip will stop the heatingof the feedwater. The feedwater is heated in pre-heaters before entering the RPV. It takesa few minutes for the colder water to enter the RPV however, which is why this is a slowtransient. The lower temperature gives a higher subcooling in the core, decreasing thevoid and increasing the reactivity. The increase in reactivity can be stopped by partialSCRAM or SCRAM depending on the severity of the transient.

House load operation falls into the 6th case of pressure increase. When the house loadoperation occurs, the reactor only supplies power to the plant itself. Therefore the power(i.e. the reactivity) must be decreased, in order to protect the turbines. Because if theconnection to the grid is lost and the reactor produces steam at the level of full power,then the turbine will speed up leading to turbine trip. The power decrease is achievedby runback of the recirculation pumps and partial SCRAM. Runback causes increase invoid and thus decrease in power. Partial SCRAM reduces the power through the neutronabsorption of the control rods.

2.2 The SCRAM System

The SCRAM system is used for complete shutdown (SCRAM) or for a power reductioncalled partial SCRAM. The systems consists of controls rods which can be hydraulicallyinserted into the core of the reactor. [10]

The control rods affect the reactivity in the core by absorbing neutrons. Thus the in-sertion of control rods leads to a reduction in neutrons in the core that are causing thechain reaction, decreasing the reactivity. Withdrawal will in the same manner increasethe reactivity. The material used is mostly boron carbide (B4C), containing the highlyneutron absorbing isotope B-10. [11]

The control rods are divided into control rod groups referred to as SCRAM groups orSCRAM banks. The insertion of these groups is how the system is operated. For SCRAMall groups (and consequently all rods) are inserted completely in a few seconds. For partialSCRAM only one or a few of the groups are inserted, as the name implies. This leadsto a fast and large reduction in reactivity, and thus in power, without shutting down thereactor. Thus if the reactivity does not need to be reduced as much it has the advantageover SCRAM that the rector can remain in operation. Then a stable operation point canbe reached.

2 THEORY 16

In F2 the SCRAM system consists of 161 control rods which are divided into 18 groupsconsisting of 9 rods each, except for one group of 8 rods. Partial SCRAM consists of twogroups, one of 8 rods and one group of 9, making the total 17 rods. [12]

The SCRAM system should not be confused with the fine motion control rod drive system.This system uses the same control rods but it is physically separated from the SCRAMsystem and it is of another design and has another purpose. The rods are inserted andwithdrawn using an electric system. [10] This system is used to control the power level, thepower distribution, and to compensate for the long term reactivity changes due to burnup of the fuel. [11] This system can also shutdown the reactor, however the minimuminsertion time is 4 minutes rather than a few seconds as is the case of the SCRAMsystem.[10]

2.3 SCRAM Modeling in BISON

2.3.1 The Neutron Transport Equation

To understand how SCRAM is modeled, the neutron transport modeling needs to beshown first. In BISON it is modeled using the 2-group diffusion equations with timedependence and one dimension in space. 2-group means that the neutrons are dividedinto the two groups: group 1 (fast) and 2 (thermal) depending on whether their energyis high or low. Please note that it is not essential to understand this complicated set ofequations in detail in order to follow this study. It is included in order to give a formaldefinition of the ASC vector and to give a complete picture of the SCRAM modeling. Theequations have the following form [6]

1

v1

∂φ1

∂t= ∇·D∇φ1−D1B

2rφ1−ΣA1φ1+

1

keff(νΣF1(1−β1)φ1+νΣF2(1−β2)φ2)+

m∑i=1

λiCi−ΣR1φ1

(1)

1

v2

∂φ2

∂t= ∇ ·D∇φ2 −D2B

2rφ2 − ΣA2φ2 + ΣR1φ1 (2)

where the equations for the delayed neutrons are

∂Ci

∂t= −λiCi +

1

keff(νΣF1β1iφ1 + νΣF2β2iφ2) (3)

(i = 1, ...,m)

2 THEORY 17

The variables in the equations are the following

φ1 = Neutronflux in group 1

φ2 = Neutronflux in group 2

Ci = Precursor density for group i of delayed neutrons

λi = decay constant for group i of delayed neutrons

m = number of groups of delayed neutrons (6 groups are included)

β1i = fraction of delayed neutrons in group 1 from fast fission

β2i = fraction of delayed neutrons in group 2 from thermal fission

β1 =m∑i=1

β1i

β2 =m∑i=1

β2i

B2r = equivalent radial buckling

1/keff = first eigenvalue for equations (1) through (3) in the steady state (time

derivatives = 0).

The code iterates to find 1/keff in the steady state and holds it constant in

the transient.

v1, v2 = average velocities for the neutrons in groups 1 and 2.

D1, D2,ΣA1,ΣA2,ΣF1,ΣF2 and ΣR1 are diffusion coefficients and neutrons cross

sections, respectively.

ν = average number of neutrons released per fission.

2.3.2 Defintion of the ASC vector

The coefficients (macroscopic neutron cross sections D1, ΣA1 etc.) in the Equations 1 to 3given in the previous section are calculated by 2-dimensional nodal code (softwares suchas CASMO or PHEONIX) for two cases

i) Cross sections in every axial node in BISON with control rods withdrawn (relativelylow absorption cross section), Σunrodded.ii) Cross sections in every axial node in BISON with control rods completely inserted(high absorption cross section), Σrodded.

The insertion of a control rod group (such as a SCRAM bank) is then modeled by usingthe relative control rod effect vector (ASC vector) in the following way for each coefficient

Σ = (1− ASC) · Σunrodded + ASC ∗ Σrodded (4)

where Σ is a macroscopic cross section such as D1, ΣA1 etc. The ASC in the equationrepresents the element in the ASC vector corresponding to the control rod group being

2 THEORY 18

inserted.

In BISON the number of elements in the ASC vector is determined by the creator of themodel. The number can be between 1 to 25. For the models used in this study it contains5 elements representing SCRAM banks number 9, 6, 12, 18, and the remaining. Like this:

ASC = [A9, A6, A12, A18, Aremaining] (5)

The first two are the banks being inserted during partial SCRAM, the second two canalso be used for partial SCRAM but are not currently in use, the last element representsthe rest of the SCRAM banks. The sum of the vector must be 1 since the sum of allelements corresponds to all control rods being inserted (SCRAM), as described in Equa-tion 4. Thus the individual elements in the vector can have values between 0 and 1, giventhe constraint that the sum of all elements is 1.

Lastly, it is important to note that if a SCRAM bank is inserted, all of its rods arecompletely withdrawn beforehand. This is the case for the two banks used in partialSCRAM for both the tests and the simulations. However, if this was not the case then itwould be possible for BISON to take it into account.

2.3.3 The ASC vector in the Previous Model

In the previous model the ASC vector is assumed to be proportional to the number ofcontrol rods inserted into the core. This gives the following vector

ASC = [8/161, 9/161, 9/161, 9/161, 126/161] (6)

where each element contains the number of control rods in the group or groups it corre-sponds to, divided by the total number of control rods in order to get the sum of 1.

This assumption is equivalent to assuming that all control rods are the same and affectthe core same. This is only approximative due to three main reasons. First of all theplacement of the control rods matter. The neutron flux is not uniform in the core, itcan be higher in the center of the core compared to its boundary for example. The fuelassemblies also have different burn up, affecting the neutron flux.

Secondly, there will be diminishing returns for each rod being inserted. Take for examplethe action of inserting one control rod alone. This rod will have a lot of neutrons toabsorb. Now take the same rod and insert all the other rods except this one. Then aftera while insert the rod. This time it will have a lot fewer neutrons to absorb since all theother rods already have absorbed many of the neutrons. Every time the number of rodsinserted is increased the returns will diminish since the amount of available neutrons de-creases. However, by assuming that all rods have the same effect, the diminishing returnsis not taken into account.

Lastly, there is also the fact that all the control rods ability to absorb neutrons changeswith time. It depends on how many they have already absorbed. Control rods need tobe changed with time just like the fuel of the reactor [11]. This and the other two factorsare not considered with the assumption in the previous model.

3 MODEL AND SIMULATIONS 19

3 Model and Simulations

This section concerns the selection of the software for the simulations used to calculatethe ASC vector. It also briefly covers the models in the software used for the simulations.

3.1 Simulation Software Selection

There are several kinds of software available for simulating the changes in the core of thereactor. As described in 2.1 Transients there are several things going on in the core, thereactivity, pressure and temperature and other quantities changes and affect each other.Safety and control systems will also interact with the core. Thus software can often sim-ulates different aspects such as thermo-hydraulics and neutron kinetics in more detailthan the other, it might also choose to include more details about the safety and controlsystems or exclude them completely.

BISON performs dynamic simulations of the core in 1D and includes many safety andcontrol systems. It does not model the neutron kinetics in detail, the focus is more onthermo-hydraulics. Thus it will not give a very detailed picture of the core but it will givegood estimates of pressure changes in pipes and similar types of changes.

POLCA performs steady state 3D simulations of the core, with focus on neutron kinetics,but does not include other systems in the analysis. It does not perform dynamic simula-tions.

Simulate-3K (Simulate 3D Kinetics) performs dynamic 3D simulations of the core. Sum-marily it can be described as: it models the core in the same amount of detail as POLCAbut it models systems outside of the core in less detail than BISON does.

The choice of software for comparison with BISON was POLCA. The idea of using POLCAis that when it’s modeling partial SCRAM it could get a better estimate of the reactivitychanges (and power changes) in the core.

However a brief comparison between the reactor powers given by BISON and Simulate-3Kwas also done, in order to see whether the choice of POLCA would have a huge impacton the results or not. Because POLCA will decide what power BISON ends up with thischoice is very important.

The versions of the softwares used are BISON 6.9.4.1, POLCA 4.13.1, Simulate-3K2.06.00.

3.2 BISON Models

The BISON models used are the same as the ones which were used for the validation withsome minor modifications. Instead of modeling the exact events which took place duringthe measurements, it only models the event of interest: partial SCRAM. The model sim-ulates what happens when the reactor goes from normal operation to partial SCRAM.

However, the most important difference is that another control rod model is used. Insteadof using a proportional relative control rod density for each SCRAM group (based onthe number of control rods in the group only), a calculated control rod density is used.

3 MODEL AND SIMULATIONS 20

The vector with these values can be changed. The models also includes the options ofindividual insertion of SCRAM bank 6 and 9 (which replaces PSS in such a case), changingthe steam separator model, keeping the main circulation flow constant (no runback), andchanging the core data (the configuration of the core changes every time the core isrefueled).

3.3 POLCA Models

POLCA is used in the following way: First the model takes the RF, feedwater temperatureand reactor power as input given by the run of the BISON model. Then it performs anoption called POWERSEARCH where the given RF and the feedwater temperature areheld constant, and the given reactor power is an initial guess at what the power should beafter PSS (or individual SCRAM bank insertion). POLCA then iterates on reactor powerto keep the same effective multiplication factor as prior to the insertion. The given poweris the output of the model and the value which the BISON model should correspond to.

The POLCA models need to be able to simulate the same cases as the BISON models ifthey are to be compared. Thus it can perform PSS, individual insertion of SCRAM bank6 and 9, keeping the main circulation flow constant (no runback), and changing the coredata.

4 METHOD 21

4 Method

This section describes the study in more detail. First how POLCA is used together withBISON in order to compute the new ASC vector, including both how the algorithm itselfworks and how the actual calculation of the ASC vector is done. Second, how the newBISON model is composed.

4.1 Computation of ASC vector

The computation of the ASC vector is done with an algorithm described in Figure 5. Thisalgorithm calculates the ASC vector for each point of burn up in the operating cycle. Itis done in the same way for every point.

This is algorithm falls under the general optimization algorithm of the form: [13]

1. Specify some initial guess of the solution x0.

2. For k = 0, 1, · · ·

i) If xk is optimal, stop.

ii) Determine xk+1, a new estimate of the solution.

But in Figure 5 it is described in more detail.

The first step 1 simply includes an initial guess of the ASC vector. If this is done for thefirst burn up point then the guess will be the proportional assumption, see Equation 6.But for all subsequent points the guess will be the ASC vector of the previous point. Thisis done on the assumption that this guess is better and thus will save some computationtime since fewer iterations will be needed if the guess is good. 1 In step 2 the iterationsstart with a loop-structure, described by roman numerals.

The next step i) is to insert the ASC vector into the BISON model, i.e. the BISON script.This model is described under 3.2 BISON Models. Then the model runs in step ii) andreturns results in step iii). The results for the RF, feedwater temperature and reactorpower are extracted.

In step iv) POLCA runs with the RF and feedwater temperature given by BISON. This isneeded in order to make them simulate the same scenario. The POLCA model is describedunder 3.3 POLCA Models. In step v) the extracted power from POLCA is compared withthat of BISON. If they are the same within a tolerance of 0.1 % then the algorithm ter-minates and we have calculated the ASC vector. If on the other hand the power fromPOLCA and BISON are not within the tolerance then the algorithm continues to step vi).

In step vi) a new guess for the ASC vector is calculated based on the previous ASC vectorguesses and the power given by POLCA and BISON. How this is done is described indetail under 4.1.1 Calculate New ASC vector. It then precedes to the beginning of theloop and the same procedure starts again but with a different ASC vector from last time.

1This also turned out to be the case. The number of iterations was about 3-5 with the proportionalassumption as the initial guess, but with the ASC vector of the previous point it was about 1-3.

4 METHOD 22

Figure 5: Algorithm for calculating the ASC vector. This is performed for each point ofburn up in the operating cycle.

4.1.1 Calculate New ASC vector

This is done with a MATLAB script which extrapolates or interpolates based on the val-ues of the ASC vector and the power given by the POLCA and BISON runs.

When the first guess is done the script only has one data point for the ASC vector value,the initial guess against the difference between power from POLCA and BISON. Thus itis not possible to interpolate to guess the next answer. Instead the relation between thereactor powers given by POLCA and BISON is used. If for example the power given byPOLCA is higher than that given by BISON, then that means that BISON underesti-mates the power. Thus the ASC vector needs to be lower, since a lower value implies ahigher power. The script then divides the value by two.

If the relation between the power from POLCA and BISON would be the other wayaround, then the value should be increased instead. This is done by multiplying by two.The reason that the value increases (or decreases) by a factor of 2 is to give a an overes-timation or underestimation of the ASC vector. Then there will be values to interpolatebetween. If the factor was smaller (or a small number was added or subtracted) thenthere would be the risk of having to iterate many times before interpolation could replaceextrapolation.

4 METHOD 23

In Figure 6 there is an example of how the values of the reactor power and the ASC changesas iteration proceeds. The process described in the previous paragraph is shown. Firstthe value underestimates the reactor power, then in the second iteration it overestimatesit a lot. However, after the interpolation starts in the third iteration, the changes to thevalue of the ASC (and thus the reactor power) is much smaller and the values is fine-tuned.

Figure 6: Example of how the ASC and the reactor power given by BISON changes witheach iteration.

Because then there will be two values between which interpolation can be done. If theextrapolation is done in too small steps a lot of computations can be wasted in order toget to the other side of the sought value. It is when the sought value lies between datapoints which interpolation can be used. This value is assumed to be where the differencebetween the reactor power of POLCA and BISON is zero, they have the same value. Thevalue of the ASC vector for which this is true is chosen to be the next guess.

The interpolation is done using the spline function in MATLAB since the shape of thecurve is unknown and thus a polynomial of a certain degree cannot be chosen. The ex-trapolation is done by using a simple first order polynomial since the spline function cangive strange values outside the data points, it relies on piecewise polynomials.

Lastly, it is important to note that the interpolation or extrapolation of the ASC valuesis done on a single element for the case of individual SCRAM bank insertion, since onlyone element is used. However, for partial SCRAM two elements are used. Thus theinterpolation or extrapolation is done on the sum of the two elements, since BISON usesthe sum of them in this case.

4 METHOD 24

4.2 Composition of the New Model

The new model is simply the previous model with a new ASC vector. Thus when evalu-ating this model against the three test cases the ASC vector is the only thing that needsto be changed. The models are kept the same in all other aspects, in contrast to the ASCcalculations where several things such as point of burn up etc. were changed.

The important question is how the ASC vector should be chosen. Due to the large numberof different conditions for which the ASC was calculated there are hundreds of differentchoices. The conditions which clearly should apply are PSS and runback, since both ofthese occurred during the tests. Cycle 32 is chosen because it is more similar to cycle 31,when the tests were performed, than cycle 34. The core designs of cycle 31 and 32 donot take the flywheels into account, while 34 does. The mean of all points of burn up ischosen, so that no one point will have a large effect on the result. This gives the ASCvector shown in Table 1.

Table 1: Values of the ASC vector. The new value is the calculated value, the previousvalue is the value with the proportional assumption.

ASC groups 9 6 12 18 remainingNew value 0.0187913 0.0440809 0.0440809 0.0440809 0.848966

Previous value 0.0497 0.0559 0.0559 0.0559 0.7826

5 RESULTS 25

5 Results

5.1 ASC vector Results

In this section the results of the ASC vector calculations are presented. If the ASC vec-tor is given by the proportional assumption, see Equation 6, then it is shown as dottedline. The steam separator type is AS01, as in the previous model, unless stated otherwise.

At PSS the ASC vector is presented as the sum of the two first elements. For individualSCRAM bank insertion the element corresponding to the SCRAM bank is presented. Insome of the points of burn up the BISON calculations did not converge2, therefore theyare missing in the figures.

Figure 7: The ASC vector for PSS during Cycle 32 and 34 at the burn up of 0 to 7000EFPH.

2This convergence issue was due to the default initial guess of the burn up which does not work forsome points of burn up. While this could easily be changed manually for individual cases of convergenceissues. It wasn’t deemed important enough to correct since the number of points affected is low and thescripts would need to be changed for this to be automated. The points affect are in cycle 32 2500 and3500 EFPH, and in cycle 34 it is 0 EFPH.

5 RESULTS 26

Figure 8: The ASC vector for PSS with and without runback during cycle 34 at the burnup of 0 to 7000 EFPH.

5 RESULTS 27

Figure 9: The ASC vector for individual insertion of SCRAM bank 9 and 6, the sum ofthe ASC vectors for the individual insertions, and PSS. The values are for cycle 34 atthe burn up of 500 to 7000 EFPH. Note that there are three black lines representing theproportional assumption for PSS, individual insertion for SCRAM bank 6, and for 9.

5.2 Comparison with Previous Results

The most interesting results for evaluation are APRM, RF and steam flow. These areshown for the case of loss of condensate pump in figure 10, 11, and 12. In these figures themeasurements are shown together with the previous and the new model. The results forthe turbine trip case and the house load operation case are very similar. For this reasonthey aren’t included here. But they can be viewed in Appendix A where the same figuresare included for turbine trip, and in Appendix B for house load operation.

All three figures show that the new model produces results closer to the measurements.In figure 10 the APRM for the new model is much closer than in the previous model,although it is still a bit below the measurements. The same is true for the RF, figure 11,while the steam flow is a bit higher than the measurements, figure 12.

5 RESULTS 28

Figure 10: APRM (power) in % during loss of condensate pump. The red lines are themeasured APRMs (four different measurements), black is the previous model, and blueis the new model.

Figure 11: Recirculation flow in kg/s during loss of condensate pump. The red line is themeasured RF, black is the previous model, and blue is the new model.

5 RESULTS 29

Figure 12: Steam flow from reactor pressure vessel in kg/s during loss of condensatepump. The red line is the measured steam flow, black is the previous model, and blue isthe new model.

5 RESULTS 30

5.3 Comparison of BISON and Simulate-3K Calculations

The BISON calculations are compared with some calculations done in Simulate-3K. Thecase used for comparison was PSS with runback in cycle 32, and with steam separatortype AA. The Simulate-3K model uses a correlation equivalent to the AA type, so BISONneeds to use AA in this case for the comparison to be valid. In these calculations the coredata from POLCA has been converted for use in Simulate-3K, thus the programs use thesame core data (since BISON uses the same as POLCA). The points of burn up differ abit however, since they are shifted by +250 EFPH relative to the points of burn up inPOLCA and BISON (except the last step where it is only +105 EFPH). In figure 13 thecomparison is shown.

Figure 13: Comparison of the power given by BISON and Simulate-3K, for the case PSSwith runback during cycle 32, and with steam separator type AA

6 DISCUSSION 31

6 Discussion

It is very clear from Figure 7, 8 and 9 that all results for the ASC vector are smaller thanthe previous values of the proportional assumption. This means that the reactor powerafter insertion of the control rods will be higher than in the previous model. Thereforethe new model gives improved results when evaluated against the measurements in Figure10, 11 and 12. The same results for the other test cases can be seen in Appendix A andAppendix B.

The results from Figure 7, 8 and 9 also show that the proportional assumption of theASC vector is flawed. It is not possible to assume that the relative effect of the controlrod insertion changes linearly with the number of control rods inserted. This is apparentin Figure 9 where it is shown that the individual insertion of SCRAM bank 6 has a muchlarger effect than the insertion of 9, although it only contains one more control rod. Fur-thermore, the sum of the individual insertion of SCRAM bank 6 and 9 is not the sameas the value given for their simultaneous insertion, i.e. PSS, even though the number ofrods is exactly the same.

It is therefore clear that the proportional assumption will not yield accurate results forthe relative control rod effect. Instead it needs to be calculated from core simulations inorder to give a better result, as shown when compared to measurements in figure 10, 11and 12.

It should also be noted that the results for the RF and steam flow can be improved furtherby changing the steam separator model. This has been shown in a study performed atForsmark [14]. Although this falls outside the scope of this study and is therefore notexplored further.

The comparison of the power given by the computations in BISON and Simulate-3K, inFigure 13, shows that the results are close to each other. Although the points of burnup aren’t exactly the same, they follow the same trend where the difference between theprograms is about the same for the whole cycle. Simulate-3K gives a higher value for thepower during the whole cycle, however only about 2 %.

This is good result since this indicates that the choice of POLCA as a reference for thecomputation of the ASC vector shouldn’t have a too large effect on the results, comparedto if Simulate-3K had been used. While the simulation tools will never precisely modelreality, it is much less likely that they are incorrect if two of them give similar results.Then the calculations does not solely rely on one of the softwares. It is also notable thatthe average difference in power is only about 2 %. Because during safety analysis, theAPRM values should be assumed to be either 2 % higher or 2 % lower than full power,with the choice being the alternative which would have the most negative effect on safety.This is done in order to account for instrument errors etc. [15] Thus the result of 2 %difference between the softwares can be said to close to each other.

The choice of the ASC vector for future simulations should probably be different fromthe ASC vector used during the evaluation in this study. This is because ASC vectorvaries between cycles, as shown in Figure 7. Furthermore the flywheel is accounted for inthe safety analysis from cycle 34 and onward. This will make the core design look a bit

6 DISCUSSION 32

different. Besides, there are many other reasons the design might change. Such as changein various safety criteria, such as CPR, or change in operation length of the cycle.

However, if no new value is calculated, it is recommended that the minimum value ofthe ASC vector for cycle 34 is used. Cycle 34 should be used instead of 32 due to theflywheel being included, and the minimum value results in a higher power after PSS,which is a more conservative assumption. However, what is conservative might dependon the scenario analyzed, in general PSS is used to significantly reduce power. Thereforeit would in general be better from a safety perspective to have a higher control rod effect,and a lower would be more conservative.Thus the vector in Equation 7 could be used inthe future. 3

ASC = [0.0187913, 0.0440809, 0.0440809, 0.0440809, 0.848966] (7)

Note that the elements for SCRAM bank 12 and 18 are the same as for 6, this is onlybecause they need a value. These values have not been evaluated and cannot be assumedto be correct.

6.1 Future Work

There are several possibilities for future studies on this topic. One would be to performthe same or similar calculations of the ASC vector for other operating cycles. Then theconclusions in this work could be confirmed and expanded on. It might shine more lighton how important it would be to perform these calculations for each cycle. There is a lotof time that can be saved if the amount of ”cycle specific” analyses are limited.

There is also the possibility of doing the same study for other reactors, such as Forsmarkreactor 3. The design of this reactor is similar but still a bit different from F2. F1 is verysimilar to F2, so a comparison between them might not be as interesting. It would beinteresting to see if the same conclusions can be drawn for F3 as for F2. The design ofthe reactor could be important for the ASC vector. It is very likely that the proportionalassumption will yield disappointing results in this case too. However, it might be the casethat the difference between the proportional assumption and the calculated ASC vactoris much larger or much smaller for F3 than for F2. If so, then there is room for a lot moreto study in order to find the cause for this.

Finally there is also the possibility of improving the algorithm and method itself. Theremight be some improvements which could give results even closer to the measurementsor there might be some way of making it more efficient. The latter could improve theease of usage in implementing the method as a standard, if progress is possible in that area.

Westinghouse has announced that BISON 6.10.0 will include an additional feature for theSCRAM modeling, called FCR. [16] This would change Equation 4 to Equation 8.

Σ = (1−ASC0)·Σunrodded+ASC0 ·Σrodded+FCR·(ASC−ASC0)(Σrodded−Σunrodded) (8)

3The distribution of the ASC value on the elements for SCRAM bank 9 and 6 was chosen as:

ASC9 =ASCPSS ·ASCindiv9

ASCindiv9 + ASCindiv6, ASC6 =

ASCPSS ·ASCindiv6

ASCindiv9 + ASCindiv6

6 DISCUSSION 33

where ASC0 is the steady state ASC. FCR is the nodal SCRAM reactivity multiplier. IfFCR = 1 then Equation 8 turns back into Equation 4. This feature would be interestingto explore since it wasn’t available at the time of this study.

7 CONCLUSIONS 34

7 Conclusions

The assumption that the ASC vector is proportional to the number of inserted controlrods is flawed. It does not vary linearly with the number of rods. To get a more accuratePartial SCRAM the control rod effect should instead be calculated by core simulations.

The flywheels will be taken into account starting with cycle 34. Thus it is recommendedthat new ASC values should be calculated for future cycles, or that the values for cycle34 are used. This is important since the core design influences the values.

Instead of the mean value, the smallest value should be used. It is more conservative sincea smaller value results in a higher power after Partial SCRAM.

There are a few avenues available for future study. The same or similar studies to thisone can be performed for more cycles or for other plants. The algorithm used in thisstudy might have room for improvements, future studies could look for these. The FCRfeature, explained in 6.1 Future Work, could also be studied. It was not available duringthis study and thus could not be taken into consideration.

References

[1] Karnkraftsakerhet och Utbildning AB (KSU). Gemensam reaktorutbildning, del 1,2010. Image source. In Swedish, translation of image performed by the thesis author.

[2] Forsmarks Kraftgrupp. Forsmark 2 - Sakerhetsrapport, System 649 - Frekvensom-riktare flr HC-pumpar inkl transformatorer. Technical report, 2013. In Swedish.

[3] Karnkraftsakerhet och Utbildning AB (KSU). GK3 Reaktorsystem, 2013. Imagesource. In Swedish, translation of image performed by the thesis author.

[4] MIT OpenCourseWare. 2D view of four bundle module, 8 x 8 lattice, with controlblade. http://ocw.mit.edu. Image source.

[5] Nejdet Erkan. Typical Control Cell Core Lay. Lecture in Nuclear Plant Engineeringat The University of Tokyo. Image source.

[6] H. Svensson. BISON - A One Dimensional Dynamic Analysis Code for Boiling WaterReactors. Technical report, ABB Atom, 1991.

[7] Marielle Perup Lars Furedal. Validering av anlaggningsmodell for BISON av Fors-mark 2, 3253 MWt. Technical report, Westinghouse Electric Sweden AB, 2014. InSwedish.

[8] Michael Timm Dag Ribbing. Forsmark 1/2, Underlag till referensrapport i sakerhet-sredovisningen, Transienter och haverier, Huvudmetodikrapport, Metodik. Technicalreport, Westinghouse Atom AB, 2000. In Swedish.

[9] Anna Aspman. Forsmark 3 - 3775 MWt, Huvudmetodikrapport for verifiering avbranslets och RCPB:s integritet vid transienter. Technical report, WestinghouseElectric Sweden AB, 2011. In Swedish.

[10] Swedish Nuclear Power Inspectorate (SKI). Storningshandboken - BWR. 2003. InSwedish.

[11] Sten Lundberg. Praktisk reaktorfysik. Lund University, 1986. In Swedish.

[12] Forsmarks Kraftgrupp. Forsmark 2 - Sakerhetsrapport, System 532 - Manovreringoch indiktering av styrstavar. Technical report, 2014. In Swedish.

[13] Ariela Sofer Igor Griva, Stephen G. Nash. Linear and Nonlinear Optimization. So-ciety for Industrial and Applied Mathematics, second edition, 2009.

[14] Anghel Ionut. Forsmark 2 - Anlaggningsspecifika berakniningsforutsattningar vidbestamning av torrkokningsgransvarden infor cykel 34 (RA15). Technical report,Forsmarks Kraftgrupp, 2014. In Swedish.

[15] Forsmarks Kraftgrupp. Forsmark 2 - Sakerhetsrapport, Allman del kapitel 4 - Saker-hetskrav. Avsnitt 4.4 - Reaktorsakerhetsstyrda konstruktionskrav. 4.4.5 USNRC Reg-ulatory Guides, Division 1. Technical report, 2015. In Swedish.

[16] Carl Hals. BISON 6.10.0, News in coming release. In BISON Users Group 2015,2015.

A Comparison with Previous Results: Turbine Trip

Case

The case of turbine trip is shown in figure 14, 15, and 16. In these figures the measure-ments are shown together with the previous and the new model. All three figures showthat the new model produces results closer to the measurements. In figure 14 the APRMfor the new model is much closer than in the previous model, although it is still a bitbelow the measurements. The same is true for the RF, figure 15, while the steam flow isa bit higher than the measurements, figure 16.

Figure 14: APRM (power) in % during turbine trip. The red lines are the measuredAPRMs (four different measurements), black is the previous model, and blue is the newmodel.

Figure 15: Recirculation flow in kg/s during turbine trip. The red line is the measuredRF, black is the previous model, and blue is the new model.

Figure 16: Steam flow from reactor pressure vessel in kg/s during turbine trip. The redline is the measured steam flow, black is the previous model, and blue is the new model.

B Comparison with Previous Results: House Load

Operation Case

The case of house load operation is shown in figure 17, 18, and 19. In these figures themeasurements are shown together with the previous and the new model. All three figuresshow that the new model produces results closer to the measurements. In figure 17 theAPRM for the new model is much closer than in the previous model, although it is stilla bit below the measurements. The same is true for the RF, figure 18, while the steamflow is a bit higher than the measurements, figure 19.

Figure 17: APRM (power) in % during house load operation. The red lines are themeasured APRMs (four different measurements), black is the previous model, and blueis the new model.

Figure 18: Recirculation flow in kg/s during house load operation. The red line is themeasured RF, black is the previous model, and blue is the new model.

Figure 19: Steam flow from reactor pressure vessel in kg/s during house load operation.The red line is the measured steam flow, black is the previous model, and blue is the newmodel.

C Individual Control Rod Study

C.1 Introduction

This study was conducted in a very different fashion than the main study. The attemptwas to compute the ASC vector independently of BISON by only using POLCA, insteadof iteratively comparing BISON with POLCA. However these efforts were abandoned afterunsatisfactory results. But it is presented here as it might gain some further insight intothe workings of the ASC vector and why the main study was needed instead of this one.

C.2 POLCA Model

The POLCA model used the POWER option instead of the POWSEARCH option. Thecontrol rods were inserted individually and not by group basis. Everything else in themodel is kept constant: the power, recirculation flow, pressure, carry under, and feedwatertemperature. The idea being that since we are only interested in the relative change ofreactivity for the individual rods, and not the absolute, any error due to the simplificationof the model will be negated.

C.3 BISON Model

The same as in the main study, see 3.2 BISON Models.

C.4 MATLAB Scripts

There were three different MATLAB-scripts, one for creating the POLCA-scripts, one forrunning them, and one for calculating the ASC vector and plottning the results.

The first script creates a POLCA-script with the specifications given under C.2 POLCAModel, only inserting one rod for each run. After the POLCA scripts have been exe-cuted using the second script, the third script calculates the ASC vector. This is doneby extracting the difference in reactivity before and after the insertion of the rod. Thesereactivity changes are then added together by SCRAM bank basis, to get the contributionfrom each SCRAM bank. Each bank is then normalized with respect to the sum of thereactivity change for all rods.

Even if the absolute numbers for each rod contain some error, we are only interested inthe values of the rods relative to each other. Thus with the normalization we shouldexpect the errors of the POLCA computations not to be a big issue.

C.5 Results

In table Table 2 the results are displayed. One comparison with the previous model isdone in figure Figure 20.

Table 2: Values of the ASC vector. The new value is the calculated value of the individualcontrol rod study, the previous value is the value with the proportional assumption.

ASC groups 9 6 12 18 the restNew value 0.04722 0.06000 0.05139 0.06342 0.77798

Previous value 0.0497 0.0559 0.0559 0.0559 0.7826

Figure 20: APRM (power) in % during loss of condensate pump. The red lines are themeasured APRMs (four different measurements), black is the previous model, and blueis the new model with the new values in Table 2.

C.6 Discussion and Conclusions

The results are very similar to that of the previous model, there is no improvement. Notethat the sum of the values in group 6 and 9 for the new values is 0.10722 compared to0.10560 for the proportional assumption. In contrast to the same value in the main studyused for evaluation which is 0.06287, see Table 1. In the main study the difference is muchlarger.

However there are some interesting observations from these results. It appears that theassumption that the contributions of the rods could be added up independently to forma bank is not accurate. The ASC vector does not appear to change linearly with theincrease or decrease of number of rods. Thus adding the individual reactivity decreasecontributions cannot be done to get the reactivity decrease contributed by a whole bank.These calculations gave the same results as simply assuming that the ASC vector can bedetermined by simply adding the number of rods by the total number of rods. This isessentially the same assumption, they both assume linearity.

This study gives good grounds for taking another approach to calculating the ASC vector.It gave rise to the main study of this problem because this simpler approach did not work.