ML20079N358

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Nonproprietary Statistical Combination of Uncertainties Part Ii,Uncertainty Analysis of Limiting Safety Sys Settings C-E Sys 80 Nsss,Part II
ML20079N358
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Issue date: 01/31/1983
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COMBUSTION ENGINEERING. INC.

s%'.05URE l-NP

' TO LD 010

. STATISTICAL COMBINATION OF UNCERTAINTIES PART II Uncertainty Analysis of Limiting Safety System Settings

~ C-E System 80 Nuclear Steam Supply Systems REACTOR DESIGil JANUARY 1983 Combustion Engineering, Inc.

Nuclear Power Systems Windsor, Connecticut 4

DR ADO K O 00 DR  :

E

4 LEGAL NOTICE THIS REPORT WAS PREPARED AS AN ACCOUNT OF WORK SPONSORED BY COMBUSTION ENGINEERING, INC. NEITHER COMBUSTION ENGINEERING NOR ANY PERSON ACTING ON ITS BEHALF:

A. MAKES ANY WARRANTY OR REPRESENTATION, EXPRESS OR IMPLIED INCLUDING THE WARRANTIES OF FITNESS FOR A PARTICULAR PURPOSE OR MERCHANTABILITY, WITH RESPECT TO THE ACCURACY, COMPLETENESS OR USEFULLNESS OF THE INFORMATION CONTAINED IN THIS REPORT, OR THAT THE USE OF ANY INFORMATION, APPARATUS, METHOD, OR PROCESS DISCLOSED IN. THIS REPORT MAY NOT INFRINGE PRIVATELY OWNED RIGHTS; OR B. ASSUMES ANY LIABILITIES WITH RESPECT TO THE USE OF, OR FOR DAMAGES RESULTING FROM THE USE OF, ANY INFORMATION, APPARATUS, METHOD, OR PROCESS DISCLOSED IN THIS REPORT.

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A85 TRACT

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Part II of the Statistical Combination of Uncertainties (SCU) reports describes the methodology used for statistically combining uncertainties involved in the determination of the Linear Heat Rate (LHR) and Departure from Nucleate Boiling Ratio (DNBR) Limiting Safety System Settings. (LSSS) for the C6mbustion Engineering (C-E) Nuclear Steam Supply Systems (NSSS). The overall uncertainty factors assigned to LHR and DNB Overpower !iargin (DNS-OPM) establish that the adjusted LHR and DN8-OPM are conservative at a 95/95 probability / confidence level throughout the core cycle with respect to actual core conditions.

The Statistical Combination Of Uncertainties reports describe a method for statistically combining uncertainties. Part I* of this report describes the statistical combination of system parameter uncertainties in thermal margin analyses. Part II of this report describes the statistical combination of state parameter and modeling uncertainties I

for the detemination of the LSSS overall uncertainty factors.

Part III of this report describes the statistical combination of state parameter and modeling uncertainties for the determination af

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the Limiting conditions 'for Operation (LCO) overall uncertainty factors'.'

  • Submitted as Enclosure 1-P to letter LD-82-054l, A. E. Scherer to D. G. Eisenhut, dated May 14, 1982.

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TA8LE OF CONTENTS CHAPTER PAGE Abstract 11 Table of Contents 111 List of Tables y List of Figures vi Definition of Abbreviations vii 1.0 Introduction 1-1 1.1 Purpose 1-1 1.2 Background 1-1 1.3 Report Scope 1-2 1.4 Sumnary of Results 1- 3 2.0 Analysis 2-1 2.1 General 2-1 2.2 Objectives of Analysis 2-1 2.3 Analysis Techniques 2-1 2.3.1 General Strategy 2-1 2.3.2 LHR LSSS Statistical Methods 2-2 2.3.3 DNS-OPM LSSS Statistical Methods 2-5 2.4 Analysis Performed 2-6

2. 4.1 LHR LSSS Uncertainty Analysis 2-6
2. 4.1.1 Power Distribution Synthesis Uncertainty 2-6
2. 4.1. 2 CECOR Fxy Measurement Uncertainty 2-7
2. 4.1. 3 Startup Test Acceptance Band Uncertainty 2-8
2. 4.1. 4 Other Uncertainty Factors 2-9
2. 4.1. 5 Overall LHR LSSS Uncertainty Factor 2-10 2.4.2 ONS-OPM LSSS Uncertainty Analysis 2-12 iii

2.4.2.1 DN8-CPM Modeling Uncertainty with SCU 2 12 2.4.2.2 Oynamic Pressure Uncertainty 2-13

. 2.4.2.3 Other Uncertainty Factors 2-14 2.4.2.4 Overall CN8-OPM LSSS Uncertainty Factor 2-15

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3.0 Result

and conclusions 3-1 3.1 LHR LSSS 3-1 3.2 DNBR LSSS 3-1 References R-1 Accendices ,

A. Stochastic Simulation 'of Uncertainties A-1 ,

A.1 Detector signal Measurement and C2A Bank A-1 Positien Measurement Uncertainties A-1 -

A.2 State Parameter Measurement Uncertainties A-1 A.3 ONS-OPM Algorithm Uncertainties A-2 A.4 FLARE / ROCS Modeling Error A-2 A.5 References for Appendix A A-3

8. Core Power Level Measurement Uncertainty 8-1 C. Axial shape Index Uncertainty C-1

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LIST OF TABLES TABLE . PAGE 1 -1 Variables Affecting LHA and DN8R LSSS 1-4 1 Stochastically Modeled Variables 2-18 2-2 Rangesand Measurunent Uncertainties of State 2-19 Parameters 3-1 CPC Synthesized Fq Modeling Error Analysis 3-2 3-2 Contribution of Individual Uncartainty to LSSS Overall 3-3 Uncertainty Factors 3-3 CPC Synthesized DNS-0PM Modeling Error Analysis 3-4 8-1 Core Power Synthesis Error Analysis 8-3 8-2 Power Measurement Uncertainty as a Function of Power B-4 C-1 Hot-Pin ASI Error Analysis C-2 C-2 Core Average ASI Error Analysis C-3 o

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! 2-1 CPC Simulation of Fq s- N-s 2- 20 ,

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, 2-2 CPC Simulation of DNS-OPM ,

2-3 Flow chart for CPC Overall Uncartaintiet fon LHR 2-22 and CNB-OPM

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's A-1 DNS-OPM Algorithms A-4, " ' '

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1 DEFINITION OF ABBREVIATIONS ASI Axial Shape Index APHPD Axial Pseudo Hot-Pin Power Distribution BOC Beginning of Cycle BPPCC Boundary Point Power Correlation Coefficient

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CDF Cumulative Distribution Function C-E Combustion Engineering l

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CEA Control Element Assembly CETOP C-E Thermal On-Line Program CETOP-0 Off-Line DNS-OPM Algorithm for Safety Analysis j CETOP-1 On-Line DNS-OPM Algorithm Used in Core Simulator and COLSS CETOP-2 On-Line DNB-OPM Algorithm Used in CPC COLSS Core Operating Limit Supervisory System CPC Core Protection Calculator

DNB Departure from Nucleate Boiling DNBR DNS Ratio DNB-OPM DNB Over Power Margin EOC End of Cycle ESFAS Emergency Safety Features Actuation System .

Fq Three Dimensional Power Peaking Factor Fxy Planar Radial Power Peaking Factor x

LCO Limiting Conditions for Operation LHR Linear Heat Rate (kw/ft)

LOCA Loss of Coolant Accident LSSS Limiting Safety System Setting (s)

MOC Middle of Cycle l NSSS Nuclear Steam Supply System PDF Probability Distribution Function PHP0 Pseudo Hot-Pin Power Distribution

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PLR Partial Length Rod RCS Reactor Coolant System j RPS Reactor Protection System j RSF Rod Shadowing Factor RSPT Reed Switch Position Transmitter vii

SAFDL Specified Acceptable Fuel Design Limits SCU Statistical Combination of Uncertainties TSF Temperature Shadowing Factor e

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viii

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1.0 INTRODUCTION

i 1.1 PURPOSE t

The purpose of this report is to describe the methodology used for

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statistically combining uncertainties associated with the WR and DN8R l L5SS(l). All uncertain'
y components considered in the determination of the overall uncertainty factors for UR and DNS-OPM are listed as follows:
1. Uncertainty in ex-core detector signal measurement
2. Uncertainty in Control Element Assembly (CEA) position measurement l 3., Uncertainties in temperature, pressure, and flow measurements
4. uncertainty in Core Protection Calculator (CPC)(l) UR calculation due to the CPC power distribution synthesis for CPC UR algorithm l 5. Uncertainty in CPC ONS-OPM calculation due to the CPC pcwer distribution synthesis for CPC ON8-OPM algorithm
6. Uncertainty in CPC DNS-CPM algorithm with respect to safety analysis GN8-OPM algorithm
7. Uncertainty in measurement of planar radial peaking factors using CECOR
8. Computer processing uncertainty i
9. Startup test acceptance band uncertainties
10. Fuel and poison rod bow uncertainties
11. Global axial fuel densification uncertainty l

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12. Engineering factor due to manufacturing tolerance.

I 1.2 BACXGROUND The plant protection system in operation on the C-E NSSS is composed of two sub-l l

systems:

l 1. an Engineered Safety Features Actu'ation System (ESFAS), and

2. a Reactor Protection System (RPS) l 1-1

The CPC initiates two of the ten trips in the reactor protection system, the low DNBR trip and the high local power density trip. The RPS assesses the LHR

. and DN8R LSSS as a function of monitored reactor plant parameters. The CPC I

uses these monitored parameters as input data and calculates the on-line LHR and DN8R margin to trip limits. A list of variables which affect the CPC calculation of LHR and DNBR in terms of the LHR and DNBR LSSS is given in Table 1-1.

These two protective functions assure safe operation of a reactor in accordance with the criteria established in 10CFR50 Appendix A (Criteria Number 10, 20, and 25)(2). The LSSS, combined with the LC0(3) establishes the thresholds for automatic protection system actions to prevent the reactor core from exceeding the Specified Acceptable Fuel Design Limits (SAFDL) on centerline fuel melting and Deoarture from Nucleate toiling (DN8). A more detailed discussion of CPC may be found in Reference 1.

A stochastic simulation of particular reactor parameters was used to evaluate uncertainties in earlier C-E analog protection systems (4) (Calvert Cliffs Unit 1 and 2)(5). A similar method was al'so employed to evaluate state parameter response functions and their uncertainties in relation to the LHR and DN8R LSSS for Arkansas Unit 2, Cycle 2(6). Results obtained from the

, stochastic simulation were used to obtain penalty factors for the CPC three -

dimensional peaking factor (Fq) and DNB-OPM calculations to ensure conservative pient operation.

1.3 REPORT SCOPE The scope of this report encompasses the following objectives:

1. to describe the methods used for statistically combining uncertainties applicable to the LHR and DNBR LSSS;
2. to evaluate the aggregate uncertainties as they are applied in the calculation of LHR and DNBR, The probability distribution functions associated with the uncertainties defined in Section 1.1 are analyzed to obtain the LHR and DNB-OPM overall uncertainty factors based on a 95/95 probability / confidence tolerance limit.

The methods used for the determination of uncertainties on the power

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1-2

measurement, the core average Axial Shape Index (ASI), and the hot-pin ASI are also described since these parameters are used in the determination of the overall uncertainty factors.

The methods presented in this report are applicable to C-E System 80 NSSS.

1.4

SUMMARY

OF RESULTS The analysis techniques described in Section 2.0 were applied to C-E System 80 NSSS. The stochastic simulation program results in overall uncertainties for the LHR LSSS and the DNBR LSSS of [ ".) and ( d , respectively, at a 96/95 probability / confidence level.-

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TABLE 1-1 VARIABLES AFFECTING THE LHR AND DNBR LSSS l

LHR

1. Core Power i

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2. Axial Power Distribution
3. Radial Power Distribution .

l DNBR l

1. Core Power
2. Axial Power Distribution 1
3. Radial Power Distribution j 4. Core Coolant Inlet Temperature
5. Core Coolant Pressure
6. Primary Coolant Mass Flow l

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2.0 ANALYSIS 2.1 GENERAL The following sections describe the impact of the uncertainty components on the system parameters, the state parameters, and the modeling that affect the LHR and DN8R LSSS. The effects of all individual uncertainties on the LSSS overall uncertainty factors for LHR and DNBR are also discussed. In addition, this chapter presents analyses performed to determine overall uncertainty factors which are applied to the CPC calculations of the LHR and DNS-CPM to ensure a 95/95 probability / confidence level that the calculations are conservative.

2.2 OBJECTIVES OF ANALYSIS ,

The objectives of the analysis reported herein are:

1. to doevrent the stochastic simulation techniase used in the overall uncertainty analysis associated with the LHR and DNBR LSSS and
2. to detactine LER and DR8-CPM overall uncertainty factors :n <the basis of a

'95/96 probauility/cenfidence level that the " adjusted" LMR and DNS-OPM (f.e., tne C?C synthesized v lue corrected by the respective overall uncertainty factor) will be conservative throughout the core cycle with respect to actual core conditions.

2.3 ANALYSIS TECHNIQUES 2.3.1 GENERAL STRATEGY The uncertainty analyses were performed by comparing the three-dimensional peaking factor (Fq) and DN8-OPM obtained fran the reactor core simulator (I) to those calculated by the CPC as shown in Figures 2-1 and i

2-2. The reactor core simulator generates the three-dimensional core power distributions which reflect changes in' typical plant operating conditions.

. Fq and DNS-OPM modeling uncertainties are statistically ccmbined with other uncertainties in calculating CPC overall uncertainty factors for LHR and DNS-OPM. The uncertainty analysis performed in this report also involves the stochastic simulation of the state parameter measurement uncertainties for the LHR and DNS-OPM calculations. The neutronic and thermal-hydraulic input parameters that 2-1 e

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are statistically modeled(4) are given in Table 2-1. The detailed description of the individual measurement uncertainties is presented in

- Appendix A. The on-line to off-line thermal-hydraulic algorithm uncertainty section is also presented in Appendix A.

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Approximately twelve hundred (1200) cases of power distributions at each of three burnups (B0C, MOC, EOC) were used in the determination of the overall uncertainty factors for the LHR and DNS-OPM. These cases were chosen to encompass steady state and quasi-steady state plant operating conditions throughout the cycle lifetime. Power distributions were generated by changing power levels (20-100%), CEA configurations (first two lead banks full

in to full out, PLb90% inserted to full out), and xe1o.1 and icdiae concentration (equilibrium, Icad maneuver, escillstion).
The power measurement errors used for the LMR and DNS-0PM calculations are obtained from the CPC core power synthesis error, the seccndary calorimetric power measurement error, the secondary calcrimetric power to the' CPC power calibration allowance., and a' thermal power transient offset.* The detailed description of these uncertainty factors is given in Appendix B. The mothed used for the calculation of the core average ASI and hot-pin ASI uncertainties is described in Appendix C.

2.3.2 LHR LSSS STATISTICAL METHODS The reactor core simulator was used to generate th'e hot-pin power distributions I which , served as the basis for comparison in establishing the uncertainty factors documented in this report. The CPC synthesized Fq is compared with that of the reactor core simulator Fq. Figure 2-1 illustrates the calculational sequence employed in the Eq modeling uncertainty analysis. The i

Fq modeling error (Xp ) between the CPC synthesized Fq and the actual Fq is defined as:

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(" SYN"Fq)I Xpi= -1 ( 2-1 )

(" ACTUAL" Fq)I

  • This error component accounts for the error in the CPC power calculation during design basis events.

2-2

, , . , , . . _ _ . _ _ , _ . _ . , . . . _ _ _ _ . . _ _ - -- - _ - .--_y

Y where (" SYN" Fq)I and (" ACTUAL" Fq)I are the CPC Fq and the reactor core simulator Fq for the i-th case. The Fq errors are analyzed for each case of

, each time-in-life. Approximately 1200 cases are analyzed at each time-in-life (BOC, MOC, and EOC).

The mean Fq error (Q) and the standard deviation (e7 ) of the Fq error can be calculated from:

N 2 XI (2-2a) 7 , i=1 F N

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i  :

I (XF~I) F '

( 2-2b) op " ( N-1

)

where N = sample size Since the mean and standard deviationi are estimated from the data, the one-sided tolerance limit. can be constructed from the K factor. For normal distributions, one-sided tolerance limit factor, K, is a number which accounts

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for the sampling variations in the mean (X p) and the standard deviation (ep). A normality test of the error distribution 'is performed by using the 0-prime statistic value(7-8) to justify the assumption of a normal di stribution. ,

The K factor for a nomal distribution (8,9) is calculated as:

95/95 K=

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(2-3a) a 2-3

I where 2 a=1 2(N-1) (2-2)

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.g 2 2

  • b = X ,, . (2-x)

Kj,p = percantiles of a normal distribution for the probab.ility P (1.645 for 955 probability).

X, = percent 11es of a normal distribution for the confidence coefficient (1.645 for 955 confidence).

N = sample size If the error distribution is normal, the upper and lower ons-sided 95/95 tolerance Ifmits are calculated using the following equations:

. (I-4)

L6wer 95/95 tolerance limit = X - X95/95' Upper 95/95 tolerance limit = X + X95/95' (2-8) whereT,e,andb5/95 an de sample mean, standard deviation, and one-sided tolerance limit factor. 'respectively.

If the error is not normally distributed,one-sided 95/95 tolerance limits are ,

calculated by using non-parametric techniques ,

The locator L is calculated from the following equation which is derived from the methods in Reference 10.

j , ( 2- 5) 2-4

4

..e The one-sided (upper or lower) 95/95 tolerance limit is.obtained by selecting the error value (from the ordered error distribution) corresponding to the locator L. A non-parametric "Ka" is calculated from equation (2-4) by using the determined one-sided tolerance limit and the known mean error. ,

2.3.3 DNS-OPM LSSS STATISTICAL MriliODS The three-dimensional reactor ccre sinulator provides a hot-pin pcwer distribution for its ONB-CPM calculation and the corresponding ex-:oN dstecter .

.ignals for the CPC power aistribution algorithm. In the reactor core simulator, the ONB-CPM calculation is performed'with the simplified, faster running DNS algorithm CETOP-1(Il). b

]A flowchart representing the reactor core simulator DNB-OPM calculation is shown in Figure 2-2. '

The Reactor Coolant System (RCS) input temperature, pressure, and flow rate are

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~ ( for both the reactor core simulator and CPC.

I l 2-5

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Operating ranges and measurement uncertainties of the state parameters are g5ven in Table 2-2.

The SCU program also involves a stochastic simulation of the error components

. associated with the DNS-OPM algorithms (on-line to off-line ) . b

]Theeffectsoftheerrorcomponentsassociatedwiththe temperature, pressure, and flow measurements and the on-line to off-line DNB-OPM algorithm are ,

accounted for in the detennination of the CPC D!!D-OPM modeling error via the SCU progrua.

The DNB-OPM modeling error (with SCU) is defined as:

(" SYN" ON3-0PM)I I -1

.X D=

(2-6)

(" ACTUAL" DNB-OPM)I where (" SYN" DNS-OPM)I and (" ACTUAL" DNS-OPM)I represent the CPC DNB-OPM and the reactor core simulator DNB-OPM for the i-th case. The DNB-OPM errors are analyzed separately for each time-in-life for conservatism. Each error distribution is tested for normality and the mean DNB-OPM error (XD )'

i standard deviation (eD), and one-sided upper 95/95 tolerance limit are computed.

2.4 ANALYSES PERFORMED I

2.4.1 LHR LSSS UNCERTAINTY ANALYSIS 2.4.1.1 POWER DISTRIBUTION SYNTHESIS UNCERTAINTY l

The reactor core simulator calculates ex-core detector signals for the CPC power distribution synthesis. An error component for each ex-core signal is l

, ,and added to j 2-6

the ex-core signal. An error component of each Control Element Assembly (CEA)

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bankmeasurement(reedswitchpositiontransmitters)isobtained(

^

]TheCEApositionerrorcomponent  ;

is then added to its respective CEA bank positon. The CPC synthesizes a hot-pin power distribution (PHPD) by using (as input) the adjusted ex-core detector signals and the adjusted CEA bank positions. The CPC hot-pin power distributions are obtained by using a cubic spline fitting technique in conjunction with constants such as planar radial peaking factors (Fxy), Rod Shadowing Factors (RSF), Boundary Point Power Correlation Constants (BPPCC),

Shape Annealing Matrix (SAM), and Temperature Shadowing Factors (TSF).

l By comparing the reactor core simulator calculated Fq with the CPC synthesized l Fq for each case, the Fq modeling errors defined in equation (2-1) are obtained. By analy:Ing the Fq modeling errors, the CPC codeling e.ror ,

distributions (histogram) of Fq are obtained fcr each time in cycle. The mean

. Fq error (I ),p the standare. deviation (ay), and the lower 95/95 tolerance limit (TI.7) for the Fq modeling uncertainty are obtained by analyzing the

- error distribution at each time-in-life. The Fq modeling error is composed of

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the uncertainties associated with the CPC power synthesis algorithm, the ex-core detector signal measurement, and the CEA position measurement.

. 2.4.1.2 CECOR Fxy UNCERTAINTY In the calculation of the CPC Fq modeling uncertainty, the CPC uses predicted values of Fxy . The Fxy used by CPC ire verified by a CECOR(I4) calculation of Fxy during startup testing. Therefore, the CECOR Fxy measurement uncertainty is combined with the Fq modaling uncertainty.to account for the differerces between the CECOR Fxy and the actual Fxy.

. The CECOR Fxy error is defined as:

Xk=Gi*P (2-7) p i

where Pj and Gj are the actual Fxy and the CECOR calculated Fxy for the 1-th case. respectively.

l 2-7 .

2.4.1.3 STARTUP TEST ACCEPTANCE BAND UNCERTAINTY The CPC power distribution' algorithm (l) requires RSF, TSF, SAM, and BPPCC as input ,

data. These constants are assumed to be known exactly for the CPC calculation of the core hot-pin power distributions. These CPC power distribution

. algorithm constants are therefore verified during startup testing. The CPC constants for RSF, TSF, SAM, and BPPCC should agree with the respective measured values within the startup test acceptance criteria. The acceptance band criteria on these constants also have associated uncertainties which affect the CPC calculated Fq and DN8-OPM. Penalty factors due to RSF, TSF, SAM, and BPPCC uncertainties are considered in the CPC overall uncertainty analysis.

In order to obtain the penalty facter due to RSF ' uncertainty, the CPC and reactor core simulator Fq calculations for base case are perfcrmed using the  ;

nominal CPC data base ccnstants foa twelve hundred (1,200) cases at each time-in-li fe. The RSF value (R) for a given rod configurstien is changed fran the CPC data base constant value (base casa value) and the CPC Fq are then i calculated with this changed RSF value (R +a6R). ,

. =

l (2-8a)

(2-8b)

The penalty factors due to the TSF, SAM, and BPPCC uncertainties are also obtained by following a similar procedure, 2-8 *

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The startup test acceptance band uncertainty (PS) is calculated by statistically combining the penalty factors due to RSF, TSF, SAM, and BPPCC uncertainties and is represented by the following equation: -

, , (2-9) where I

2.4.1.4 GTHER IlhCERTAIllT( FAC. TORS Axf al %el Densification Uncertainty The axial fuel densification uncertainty factor (15) considers the global effect of the shrinkage of the fuel pellet stack, due to heating and irradiation, on the CPC Fq calculations. ,_

]

Fuel and Poison Rod Bow Uncertainties i

The fuel and poison rod bow uncertainties (16) consider the effect of " bowing" of the fuel and poison rods,due to heating and irradiation,on the CPC Fq calculations. These factors will be part of the composite Fq modeling uncertainty.

Computer Processing Uncertainty The computer processing uncertainty considers the effect of the computer machine precision of the C-E 7600 computer and the on-site computer on the CPC Fq calculations. The computer processing uncertainty will be part of the composite Fq modeling uncertainty.

., 2-9

Engineering Factor Uncertainty The engineering factor considers the effect on the CPC Fq calculation due to fuel manufacturing tolerance (15) . This factor will be part of the composite Fq (o modeling uncertainty.

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2. 4.1. 5 OVERALL UiR LSSS UNCERTAINTY FACTOR An overall CPC Fq uncertainty factor is determined by combining all lower 95/95 l probability / confidence tolerance limits of the error components. This overall uncertainty factor includes the composite Fq modeling uncertainty, the startup test acceptance criteria uncertainty, and the axial fuel densification uncertainty. Figu. e 2-3 shows the calculational sequence ta determine an overall LHR LSSS uncertainty factor.

l The Fq modeling arrar (Xh) defined in equation (2-1) can be rewritten as:

. a i 61 . Fj x5 (2-10)

. F3 l

where Fj and C$ are the reactor core simulator calculated Fq and the CPC ,

inferred value of Fq for the 1-th case, respectively. A composite error (XFTI ) of the Fq modeling uncertainty and the CECOR Fxy ' measurement uncertainty can be deteministically calculated as follows:

Xh = -1 (2-11)

By applying equations (2-7) and (2-10), this leads to:

X FT = Xpgi+X FC + (Xpgf*XFC ) (2*I 2) 2-10

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The mean of the composite Fq modeling uncertainty is determined by:

, IFT

  • IFM + IFC+(IFM
  • FC I) (2-13)

The "5r" of the composite Fq modeling uncertainty is determined by combining the "4" for CECOR Fxy (X'FC), CPC power distribution synthesis (km),

engineering factor (XaFE)* #. bow penalties (Xapp. Kapp), computer processing (KoCP),andFLARE/R0bS II) modeling error (KoFR)*

(2-14)

L .

The resultant composite Fq modeling penalty factor (PMp ) is datermined by

using the lower 95/95 composite tolerance limit (TLp) for Fq as foilcws

PN# = I

! (2-15)

. 1 + "L 7 where .

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TLp = IFT-(Ka)FT (2-16)

The lower tolerance limit is used te assure conservative CPC Fq calculations at a 95/95 probability and confidence level.

The last step to deterstne an overall Fq uncertainty factor (SERR3) is to combine the composite modeling uncertainty (PMp), the startup acceptance criteria uncertainty (PS) and the axial fuel densification uncertainty (PA).

Consequently, (2-17) l *See Appendix A.4 ,

l 2-11 l

l

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The LSSS LHR overall uncertainty factor (BERR3) is used ,

, on the CPC calculated LHR (KW/FT):

CPC " SYN" LHR * (BERR3)95/95 > " ACTUAL" LHR (2-18)

Use of the overall uncertainty factor (BERR3) for the CPC calculated LHR assures at least a 95% probability, at a 95% confidence level, that the CPC LHR will be larger than the " ACTUAL" LHR.

  • 2.4.2 DNS-OPM~LSSS UNCERTAINTY ANALYSIS 2.4.2.1 DNB-OPM MODELING UNCERTAINTY WITH SCU  ;

The CPC DNB-OPM modeling uncertainty with SCU is made up of uncertainties associated with power aistribution synthesis, ONB algorithm, ex-core detector signal measurement, CEA position measuremeat, RCS tenperature measurement, RCS pressure measure.nent,and RCS ficw measurement. In orcer to include the RCS inlet temperature, p.esture, and flow rate effects in the DNB-OPM modeling uncertainty,a[ _

program is employed. ,

By comparing the reactor core simulator calculated DNB-OPM with the CPC calculated DNB-OPM for each case, the DNS-OFM modeling arror is obtained. The mean of the DNB-OPM modeling, error is represented by: ,,

(2-19)

(

The detailed description of the SCU DNB-OPM modeling uncertainty is presented in Appendix A.3.

2-12

2.4.2.2 DYNAMIC PRESSURE UNCERTAINTY Core inlet temperature, primary system pressure, and primary coolant flow rate affect the calculation of DNB-OPM. Errors associated with the static temperature, pressure, and flow measurements must be accounted for in the calculation of the net CPC ONS-OPM uncertainty. However, these errors are implicitly included in the modeling uncertain 4.y via the SCU program .

For the CPC ON8-OPM calculation during a transient, the pressurizer pressure sensed by the precision pressure transducer is adjusted to get RCS pressure by considering dynamic pressure campensation offset. In order to take account for RCS pressure change during a transient, an additional uncertainty in the DNB-OPM overall uncertainty analysis is considered.

-The uncertainty for the dynamic pressure may be represented by:

(2-20) where By using the CETOP-0 code, the calculation of DNB-OPM is carried out over the parameter range of plant operation presented in Table 2-2. The wide ranges of ,,

radial peak and ASI are also considered in this analysis. ,

m 4

(2-21 )

MM m b

ED g 2-13

The dynamic pressure compensation offset Q1P D

) is defined as the pressure difference between sensor measured pressure and the RCS pressure during a transient.In order to calculates &P D, the RCS pressure change rate during the l worst transient (such as a pressurizer spray valve malfunction) is calculated.

Then, the dynamic pressure compensation is obtained by multiplying the pressure change rate by the total sensor delay- time.

l

= -

2.4.2.3 OTHER UNCERTAINTY FACTORS I

OLBR Comouter< Processing Uncertainty The computer processing uncertainty considers the effect of the off-line (CDC 7C00 computer) to the on-line computer machine precision . en the CPC ONB-OPM  :

calculations. The computer processing uncertainty is represented by the term l (Ka)DT and is part of the DNB-OPM composite modeling uncertainty. This computer processing uncertainty (KaCP) is calculated by using the following equation

(2-22)

~

l (2-23)

Startua Test Acceotance Band Uncertainty

! The starcup test acceptance band uncertainty for DNB-OPM is determined by the same method described in Section 2.4.1.3.

l 2-14

Fuel and Poison Rod Bow Uncertainties The fuel and poison rod bow uncertainties for DNS-OPM are determined by the same method described in Section 2.4.1.4.

. System Parameter Uncertainties In order to determine the minimum DNBR (MON 8R) limit, C-E thermal margin methods utilize the detailed TORC code with the CE-l DNS correlation (12).

The MDNBR for LSSS includes the uncertainties associated with system parameters vhich describe the physical system. These system parameters are composed of reactor core geometry, pin-by-pin radial power distributions, inlet and exit flow boundary conditions,etc. In the statistical combination of system parameter encartainties(I7), the following uncertainties are coa.bined statistically in the MDNBR limit:

1. Inlet f1cw distribution uncertainties
2. Fuel pellet density uncer:ainties i 3. Fuel pellet enrichment uncertainties.
4. Fuel pellet diameter ur.certaintles-
5. Random and systematic uncertainties in fuel clad diameter
6. Random snd systematic uncertainties in fuel red pitch I
7. ON8 correlation uncertainties i

The SCU MONBR limit provides, at a 95/95 probability and confidence level, that the limiting fuel pin will avoid DNS. Since the SCU MONBR limit includes system parameter uncertai_nties as described in Part I of this report, these uncertainties are not considered in the determination of the CPC ONB OPM overall uncertainty factor.

. 2.4.2.4 OVERALL DNS-OPM LSSS UNCERTAINTY FACTOR The overall CPC uncertainty factor for DN8-OPM (BERRl) is determined by combining all one-sided (upper) 95/95 probability / confidence tolerance limits.

This overall uncertainty factor is made up of the composite DNB-OPM modeling 2-15

a uncertainty, the dynamic pressure uncertainty, and the startup test acceptance band uncertainty. Figure 2-3111ustratas the calculational sequence to determine the overall DN8-OPM LSSS uncertainty fa.ctor.

A composita DNS-CPM modeling was obtained by following a similar strategy to that used for the Fq uncertainty analysis. The CECOR Fxy measurement uncertainty was calculated in tenns of DN8-OPM units using the sensitivity of DNS-OPM ~

to Fxy {3(%DN8-OPM)/a(%Fxy)}, The mean of the CECOR Fxy err'or is given by:

(2-24a) and the CECOR Fxy *Ke* is given byi i

(2-24b) l l

The composita mean error for the c::mposite DNS-OPM modeling uncertainty can then be calculated as:

(2-25)

IDT

  • X0M+ %C+ %M* DC ,

. The composita (Xe)DT is made up of uncertainties for DN8-OPM modeling algorithm (XeDM), C2COR Fxy (Xe 0 C), rod bow penalties (Xepp, Xepp), and ONBR computer procassing (XeCp)., and FLARE / ROCS modeling error (XeFR). Using the root-sum-squa"e techniqus, this composite (Ke ) DT is calculated as:

M (2-26) 2-16

The upper 95/95 composite modeling tolerance limit for DNB-OPM (TL D

) is used for conservative CPC DNB-OPM calculations and determined by:

TLD" DT + (D)DT (2-27)

The composite DNB-OPM modeling penalty factor (PM D ) can then be determined as:

PMD = 1 + TLD (2-28)

, In order to determine an overall DNB-OPM uncertainty, the composite DNB-OPM modeling penalty factor (PM ) is [ combined with the dynamic D

pressure penalty (PPD ) and the startup acceptance band uncertainty.

An overall DNB-OPM uncertainty factor for CPC (BERRl) is determined by combining PM D

, PPD , and PS:

(2-29)

This LSSS DNB-OPM overall uncertainty factor (BERR1) is used as a multiplier on the CPC hot pin heat flux distribution used in the DNBR calculation:

CPC " SYN" DNB-OPM * (BERRl)95/95 <- " ACTUAL" DNB-OPM (2-30)

Use of the overall uncertainty factor (BERR1) for the CPC calculated DNB-0Pfi assures at least a 95% probability, at 95% confidence level, l

that the " ACTUAL" DMB-OPM will be larger than the CPC DNB-0PM.

l, l

l' l

2-17

TABLE 2-1 STATISTICALLY MODELED VARIABLES NEUTRONICS CEA Positions Ex-Core Detector Signals THERMAL HYDRAULICS RCS Pressure Core Inlet Temperature Core Flow e

2-18

. . , . _ . - - - , - . , . - - . _ . _ g , _ ,

TABLE 2-2 RANGES AND MEASUREMENT UNCERTAINTIES OF STATE PARAMETERS

. MEASUREMENT PARAMETERS UNIT RANGES UNCERTAINTY Core Inlet Coolant (*F)

Temperature Primary Coolant (PSIA)

Pressure .

Primary Coolant (GPM)

Flow Rate , , , ,,

l l

l i

6 2-19

E 4

O Figure 2-1 CPC~ SIMUt.ATION FOR Fq Wp W

G e

O 6

ammmen m

2-20

2 l

4 W

e 9

y ee a.

C E

M 2:

C QC N O I L N

E 5

= i-CFI

(

b m

N O

CL.

W 1

t i

a e

t i

2-21

t i

I t

9 l

x O

I M

==

4 M

-rI

=

4 Wa --

w *9 g w M g*

  • 5-l

< E'.

M l

s h

9

[

G f I _

. 2-22 w

m--~m --

y- w, w yn- - wwenu- w-- -- n -

3.0 RESULTS AND CONCLUSIONS The analysis techniques described in Section 2 have been used to obtain uncertainties associated with the LHR and DN8R LSSS at a 95/95 probability /

confidence level. The results of the analyses perfonned for C-E . System 80 NSSS are presented in this section.

3.1 LHR LSSS Follcwing the analysis techniques described in Section 2.4.1, CPC synthesized Fq modeling errors are tabulated in Table 3-1 for the three times in core life (80C,MOC,EOC). All time-in-life dependent Fq modeling uncertinties were considered in evaluating the overall Fq penalty. However, the time-in-life that led to the worst modeling uncertainty was used to determine the overall Fq uncertainty factor. The individual uncertainty components of the Fq overall uncertainty factor are listed in Table 3-2. Combining the uncertainties associatedwiththeLHRLSSSresultsinanaggregateuncertaintyof[  %]ata 95/95 probability / confidence level. This overall uncertainty factor of

[  %], when applied to the CPC synthesized Fq, will assure that the CPC Fq will be larger than the actual Fq at a 95/95 probability / confidence level at all times during the fuel cycle.

3.2 DNBR LSSS Following the analysis techniques presented in Section 2.4.'2, the mean values, standard deviations, and upper tolerance limit of the CPC synthesized DNS-OPM modeling error were calculated and are summarized in Table 3-3. The modeling error was analyzed as a function of the time-in-life, but only the time-in-life that led to the most conservative modeling uncertainty was considered in the calculation of the overall CPC ONS-OPM uncertainty. The individual uncertainty components of the overall DN8-OPM uncertainty factor are presented in Table 3-2. Combining the uncertainties associated with the DN8-OPM LSSS gives an overall uncertainty factor of [  %) at a 95/95 probability / confidence level.

This overall uncertainty factor, when applied to the CPC synthesized DNB-OPM, will assure that the CPC DNS-OPM will be smaller than the actual DNB-OPM at a

. 95/95 probability / confidence level at all times during the fuel cycle.

3-1 t

TABLE 3-1 CPC SYNTilESIZED. Fq MODELING ERROR (

ANALYSIS i

95/95 '

TIME IN NUMBER OF MEAN ERROR STANDARD (3) TOLERANCE (2)*(3)

CORE LIFE DATA POINTS (N) (Ir). 1 DEVIATI0ll(a).1 UNIT fTLir BOC HOC EOC b

l ~I *

(1) ERROR = fuAL Fq (2) See References 9 and 10 Normal or non-parametric values presented.

(3) If error distribution is detemined to be non-parametric, the value for (Ka)p is calculated as

(L8)y --(TL)p + F ,

k

, . , f ~J 7s . M ' a-y

~

i TABLE 3-2 CONTRIBUTION OF INDIVIDUAL UNCERTAINTY

! TO LSSS OVERALL UNCERTAINTY FACTORS UNCERTAINTY LHR LSSS DNB-0PM LSSS 3-D Peak (Fq) Modeling(Il  ! ,I --

Ke --

CECOR Fxy iI

\ Ka Engineering Factor Fuel Rod Bow Poison Rod Bow Axial Densification .

Rod Shadowing Temperature Shadowing i Boundary Point Power I Shape Annealing Matrix Computer Processing DNB-0PM Modeling with SCU(2) 'y Ko Dynamic Pressure l FLARE / ROCS Modeling (1) includes pcwer distribution synthesis uncertainty, ex-core signal noise, CEA position error.

(2) includes [. . '

r

]in addition to e'rors of (1).

2- 3

. s c

  • TABLE 3-3 CPC SYNTHESIZED DNS-0PM MODELING ERRORII} ANALYSIS

' 95/95 TIME IN NUMBER OF MEAN ERROR STANDARD (3) TOLERANCE (2)*(3)

CORE LIFE DATA POINTS (N) (fp). 1 DEVIATION (a ). 1 LJMIT (TL)o DOC HOC EOC l -.

'f s.

i

~I *

(1) ERROR = ~

i. C UA 8 OPM (2) See References 9 and 10. Normal and non-parametric values presented.

(3) If error distribution is considered non-parametric, the value for (Ka)D is calculated as:

(Ko)D = (TL)D - YD

l REFERENCES

1. Combustion Engineering, Inc., " Assessment of the Accuracy of PWR Safety System Actuation as Performed by the Core Protection Calculators", CENPD-

. 170-P and Supplement, July,1975.

2. Combustion Engineering, Inc., " System 80, Combustion Engineering Standard

, , Safety Analysis Report (CESSAR), Final Safety Analysis Report (FSAR)",

March 31,1982.

3. Combustion Engineering, Inc., "COLSS, Assessment of the Accuracy of PWR Operating Limits as Determined by the Core Operating Limit Supervisory System", CENPD-169-P, July,1975. .
4. Combustion Engineering, Inc., " Statistical Combination of Uncertainties Methodology", Part-I and III, CEN-124(8)-P,1980.

l

5. Docket No. 50-317, " Safety Evaluation by the Office of Nuclear Regulation for Calvert C1tffs Unit 1. Cycle 3", June 30,1978.
6. Combustion Engineering, Inc., " Response to Questions on Documents Supporting The ANO-2 Cycle 2 Licensing Submittal", CEN-157(A)-P, Amendment 1, June, 1981.
7. American National Standard Assessment of the Assumption of Normality, ASI-N15-15, October,1973.
8. Sandia Corporation, " Factors for One-Sided Tolerance Limits and for Variable Sampling Plans", SCR-607, March,1963.
9. C. L. Crow, et al, " Statistical Manual", Dover Publications, Inc., New York, 1978.
10. R. E. Walpole and R. H. Myers, " Probability and Statistics for Engineers and Scientists 2ed", Maconillan Publishing Company, Inc., New York,1978.
11. Chong Chiu, "Three-Dimensional Transport Coefficient Model and Prediction-Correction Numerical Method for Thermal Margin Analysis of PWR Cores",

Nuclear Eng. and Design, P103-115, 64 , March, 1981.

12. Combustion Engineering, Inc., "CETOP-0 Code Structure and Modeling Methods for San Onofre Nuclear Generating Station Units 2 and 3", CEN-160(S)-P, May, 1981.
13. Combustion Engineering, Inc., " Functional Design Specification for a Core Protection Calculator", CEN-147(S)-P, January,1981.
14. Combustion Engineering, Inc. , " INCA /CECOR Power Peaking Uncertainty", CENPD-153-P , Rev. 1-P-A, May, 1980.

1 R-1

15. Combustion Engineering, Inc., " Fuel Evaluation Model", CENPD-139-P, October,1974.
16. Combustion Engineering, Inc., " Fuel and Poison Rod Bowing", CENPD-225-P and Supplements, June,1978.
17. Combustion Engineering, Inc., " Statistical Combination of Uncertainties, Combination of System Parameter Uncertainties in Thermal Margin Analyses for System-60", Enclosure 1-P to LO-82-054, May 1982.

4 4

N i

4 R-2

APPENDIX A A,1 Detector Signal Measurement and CEA Bank Position Measurement Uncertainties

" In the SCU program, error components of ex-core detector signals are [

]Thiserrorcomponentis then added to the ex-core signal generated by the reactor core simulator and is used as input to the CPC power distribution algorithm.

The location of each CEA bank is measured using the Reed Switch Position Transmitters (RSPT). An error component of each CEA bank measurement is selected * -

The sampled error is then added to the respective CEA bank position for input to the CPC power distribution algorithm.

A.2 State Parameter Measurement Uncertainties The on-line DNB-OPM algorithm (A-1) used for CPC requires primary system pressure, core inlet temperature, core power, primary coolant flow rate, and hot pin power distribution as input. Since pressure, temperature, and flow affect the calculation of DNB-OPM, errors associated with these state parameters must be accounted for in the CPC ONB-OPM uncertainty analysis. _

~

This procedure o allows for direct simulation of the effects of the CPC on-line inlet temperature, pressure, and flow measurement and their respective uncertainties

, on the calculation of the CPC ON8-OPM. Therefore, DNS-CPM uncertainties with respect to temperature, pressure, and flow are implicitly accounted for in the l DN8-OPM modeling uncertainty.

l A-1

i l

A.3 DNS-OPM Algorithm Uncertainties Ideally the ONS-OPM overall uncertainty calculation would use three distinct thermal hydraulic algorithms. The off-line safety-analysis algorithm (CETCP-0) represents the base-line DNS-CPM calculation. CITCP-1(A-2) and CITCP-2(A~

I) are simplified versions of CITOP-0 and perform the on-line thermal hydraulic calculations for the plant monitoring and protaction systems,

~

respectively.(:

The actual calculaticnal scheme is shown in Figure A-1.

A.4 FLARE / ROCS Modeling Error The reactor core sinulator uses the FLARE neutronic model to predict representativo

. power distributions. The FLARE model is tuned to a more accurate and rigorous ROCS code. The FLARE / ROCS modeling error takes account for the effect of the l

FLARE modeling uncertainty on the reference LHR and DNB-0PM calculations.

A-2

A. 5 References for Appendix A A-1 Combustion Engineering, Inc., " Functional Design Specification for a Core Protection Calculator", CEN-147(5)-T. . February,1981.

. A-2 Chong Chiu, "Three-Dimensional Transport Ccefficient Mcdel and Prediction.

Correction Numerical Method for Thermal Margin Analysis of PMt Cores",

~'

Nuclear Eng. and Design, P103-115, ft , March, 1981.

A-3 M. G. Xandall and A. Stuart, ",The Advanced Theory of $tatistics, Vol. II",

Hafner Publishing Ccmpany, New York,1961, p. 457.

e 6

6 e

[

l t

A- 3

- = r

1 Figure A-1 l l

DNS-OPM ALGORITHMS l w

M e

l M

W 4

e A-4

APPENDIX B Core Power Level Measurement Uncertainty The CPC utilizes two different calculations of core power, thermal power and neutron flux power, for the LHR and DNB-OPM calculation. The CPC thermal power is calculated based on the reactor coolant temperature and the reactor coolant mass flow rate. The CPC neutron flux power is calculated based on the sum of

the tri-level ex-core detector signals. The core power level measurement uncertainty factors are obtained from the CPC neutron flux synthesis error, the secondary calorimetric power measurement error, the secondary calorimetric power to the CPC power calibration allowance, and the thermal power transient offset.

The CPC thermal power measurement error is determined by determinist 1cally combining the secondary calorimetric power measurement error, the secondary calorimetric power to the CPC power' calibration allowance, and the thermal power transient offset. The secondary calorimetric power measurement error (X3c) is obtained as follows:

i l

The secondary calorimetric power to the'CPC power calibration allowance and o the thermal power transient offset used for C-E system 80 NSSS are [ %] and

( %], respectively. The the5 mal power measurement uncertainty factor for the

, CPC ONS-OPM calculation (BERRO) is determined by selecting the maximum value l

of the thermal power measurement errors for the core power range (0-130% full power).[ ,_

B-1

The CPC neutron flux power measurement error is calculated by deterministic

  • combining the neutron flux power synthesis error, the secondary calorimetric power measurement error, and the secondary calorimetric power to the CPC power calibration allowance.

, The one-sided (lower) tolerance limit for the CPC neutron flux power synthesis error (at a 95/95 probability / confidence level) is obtained by analyzing each neutron flux power distribution for each time-in-li fe.

The CPC neutron flux power synthesis error for C-E System 80 NSSS is presented in Table B-1.

The neutron flux power measurement uncertainty factor for the CPC ONB-OPM calculation (BERR2) is determined by selecting the maximum value of the neutron flux power measurement error for the core power i

range (0-130% full powedL (,'

F*

The core power measurement uncertainty factor for the LHR calculation (BERR4) is obtained by selecting the largest of the CPC thermal power errors or the CPC neutron flux power errors over the core power range from 0-130% full power.(

The CPC power measurement errors for C-E System 80 are given in Table B-2 as a function of power.

B-2

d' l 4 5

i" sw LD W

, *5

==

g W.

85 a-

=

  1. 8"%

N

=5 -

Ip <

-w 1

ma M

. =s Y

i 5 E m e- C w a

w 5 S m

' lc 3 =.

Mw mm

-. w A ~

i a 5

w

.4 E=

-m l 4 I v g i m

u. x = a O= C

=2 w

!E g

I<. Q

  1. l &

IIs.

s u

W 5=

m b

I 8 8 2 a - m . .

B-3

4 9

s.

, k a

I I a

i

~

~

3M W

=-

55 E SE E =

% 9 5 I e -

8

[ 5 r,-

8

~ Q 'c a-e , u

=

- Es

-. m.

O e E

2 E E o

a G B v "c k 5

. *W E

$~ 2 E ss ~

W" u- i i ,,

GJ E

. m 3

L

=

4 O t

- a e m 6, a

g b 3 N C C C g

  1. $ .C S 2 R
  • S S R E R S  : 0 -

B-4

APPENDIX C Axial Shape Index Uncertainty The axial shape index (ASI) for the core average and the hot-pin power distributions is computed from the power generated in the lower and upper halves of the core:

ASI .

L~ (C-1)

Pt+Pg where Pt and Pg are, respectively, power in the lower half and the upper half of the core.

The ASI error is defined by:

ASI Error = CPC ASI - Reactor Core Simulator ASI (C-2)

The core average and hot-pin ASI uncertainty analyses are performed by comparing the CPC synthesized ASI and the reactor core simulator ASI. The resulting error distributions are analyzed to obtain the upper and lower 95/95 tolerance limits. The hot-pin ASI and the core average ASI uncertainties for C-E System 80 NSSS are presented in Tables C-1 and C-2.

i i

l C-1

1 l' 5

9

/ -

5 9

RT EI PM PI UL c

5 9

/

5 9

RT EI WH O l.

Lt

- ~

)

(

N S DO I RI S AT Y DA L NI A AV N TE A SD 1 d C

- a

> R R

E E L

B I A S )

T A  %

(

N I

P R NO T- AR O ER H ME I,

S A

R O

- S .

_ T T FN A .

OI L O U RP H

_ t I EA S NT UA ND- .

I S

A

< C P

C

_ (

=

R O

R R

E r

i I

_ N S m C C C A i O O O B B H E *

~

< s > ..

TABIE C-2 CORE AVERAGE ASI ERROR ANALYSIS NUMBER MEAN STANDARD LOWER 95/95 UPPER 95/95 BURNUP DATA PolNTS ERROR (%) DEVIATION (%) _ LIMIT LIMIT 83C HOC EOC u

i

  • ASIERROR=(CPCASI-SIHutATORASI.)
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