ML20027C338

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Statistical Combination of Uncertainties,Part II, Uncertainty Analysis of Limiting Safety Sys Settings for C-E Sys 80 Nsss.
ML20027C338
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Site: 05000470
Issue date: 09/30/1982
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ABB COMBUSTION ENGINEERING NUCLEAR FUEL (FORMERLY
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ML19301B800 List:
References
LD-82-079, LD-82-79, NUDOCS 8210150313
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I i

l ENCLOSURE l-NP

! TO LD-82-079 i-

STATISTICAL COMBINATION

!O 0F UNCERTAINTIES l PART II i Uncertainty Analysis of Limiting Safety System Settings for C-E System 80 Nuclear Steam Supply Systems f

REACTOR DESIGN SEPTEMBER,1982 i Combustion Engineering, Inc.

Windsor, Connecticut +

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t I

f 8210150313 821008 PDR ADOCK 05000470 t

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LEGAL NOTICE

4. >

THIS REPORT WAS PREPARED AS AN ACCOUNT OF WORK SPONSORED BY COMBUSTION ENGINEERING, INC. NEITHER COMBUSTION ENGINEERING NOR ANY PERSON ACTING ON ITS BEHALF: i A. MAKES ANY WARRANTY OR REPRESENTATION, EXPRESS OR IMPLIED l INCLUDING THE WARRANTIES OF FITNESS FOR A PARTICULAR PURPOSE l OR MERCHANTABILITY, WITH RESPECT TO THE ACCURACY, COMPLETENESS l OR USEFULLNESS OF THE INFORMATION CONTAINED IN THIS REPORT, OR j 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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l ABSTRACT Part II of the Statistic ~al Combination of Uncertainties (SCU) reports i describes the methodology used for statistically combining uncertainties involved in the determination of the i.inear Heat Rate (LHR) and Departure from Nucleate Boiling Ratio (DNBR) Limiting Safety System Settings (LSSS) for the Combustion Engineering (C-E) Nuclear Steam Supply Systems (NSSS). The overall uncertainty factors assigned to LHR and DNB Overpower Margin (DNB-0PM) establish that the adjusted LHR and DNB-0PM 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 for the determination of the LSSS overall uncertainty factors.

Part III of this report describes the statistical combination of state parameter and modeling uncertainties for the determination of the Limiting Conditions 'for Operation (LCO) overall uncertainty factors.

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  • Submitted as Enclosure 1-P to letter LD-82-0541, A. E. Scherer to D. G. Eisenhut, dated May 14, 1982. l l

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.; TABLE OF CONTENTS

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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 Bactground 1-1 1.3 Report Scope 1-2 1.4 Summary of Results 1-3 2.0 Analysi s 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 i . 2.3.3 DNS-OPM LSSS Statistical Methods 2-5 2.4 Analysis Performed . 2-6 l . 2. 4.1 LHR LSSS Uncerte.inty Analysis 2-6 e 2. 4.1.1 Power Distribution Synthesis Uncertainty 2-6

2. 4.1. 2 CECOR Fxy F.easurement Uncertainty 2- 7 l 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 DNB-0PM LSSS Uncertainty Analysis 2-12 l iii

2.4.2.1 DNB-OPM Modeling Uncertainty with SCU 2-12 2.4.2.2 Dynamic Pressure Uncertainty 2-13

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2.4.2.3 Other Uncertainty Factors 2-14 2.4.2.4 Overall DNB-OPM LSSS Uncertainty Factor 2-15 u,.

3.0 Results and Conclusions 3-1 3.1 LHR LSSS 3-1 3.2 DNBR LSSS 3-1 References R-1 Appendices A. Stochastic Simulation of Uncertainties A-1 A.1 Detector Signal Measurement and CEA Bank A-1 Position Measurement Uncertainties A-1 A.2 State Parameter Measurement Uncertainties A-1 A.3 DNB-0PM Algorithm Uncertainties A-2 A.4 References for Appendix A A-2

B. Core Power Level Measurement Uncertainty B-1 C. Axial Shape Index Uncertainty C-1 e

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LIST OF TABLES TABLE . PAGE ,

1 -1 Variables Affecting LHR and DNBR LSSS 1-4

, 2-1 Stochastically Modeled Variables 2-18 2-2 Rangesand Measurement Uncertainties of State 2-19 Parameters 3-1 CPC Synthesized Fq Modeling Error Analysis 3-2

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3-2 Contribution of Individual Uncertainty to LSSS Overall 3-3 Uncertainty Factors 3-3 CPC Synthesized DNB-OPM Modeling Error Analysis 3-4 B-1 Core Power Synthesis Error Analysis B-3 B-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 4

a m

V

I LIST OF FIGURES FIGURE PAGE 2-1 CPC Simulation of Fq 2-20 2-2 CPC Simulation of DNB-0PM 2-21 2-3 Flow chart for CPC Overall Uncertainties for LHR 2-22 and DNB-OPM A-1 DNB-OPM Algorithms A-3 -

f h

P e

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DEFINITION OF ABBREVIATIONS ASI Axial Shape Index APHPD Axial Pseudo Hot-Pin Power Distribution 50C Beginning of Cycle BPPCC Boundary Point Power Correlation Coefficient CDF Cumulative Distribution Function C-E Combustion Engineering -

CEA Control Element Assembly CETOP C-E Thermal On-Line Program CETOP-D Off-Line DNB-OPM Algoritin for Safety Analysis CETOP-1 On-Line DNB-0PM Algorithm Used in Core Simulator and COLSS CETOP-2 On-Line DNB-0PM Algorithm Used in CPC i COLSS Core Operating Limit Supervisory System CPC Core Protection Calculator i DNB Departure from Nucleate Boiling DNBR DNB Ratio DNB-0PM 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 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 j NSSS Nuclear Steam Supply System l PDF Probability Distribution Function PHPD Pseudo Hot-Pin Power Distribution PLR Partial Length Rod ,

RCS Reactor Coolant System +

RPS Reactor Protection System 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

0 l

A i

e P

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=

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i viii

1.0 IN1R000CTION 1.1 PURPOSE The purpose of this report is to describe the methodology used for statistically combining uncertainties associated with the LHR and DNBR LSSS(I). All uncertainty components considered in the determination of the overall uncertainty factors for LHR and DN8-OPM are listed as follows: ,

1. Uncertainty in ex-core detector signal measurement
2. Uncertainty in Control Element Assembly (CEA) position measurement 3., Uncertainties in temperature, pressure, and flow measurements f
4. Uncertainty in Core Protection Calculator (CPC)(I) LHR calculation due to i the CPC power distribution synthesis for CPC LHR algorithm
5. Uncertainty in CPC DN8-OPM calculation due to the CPC power distribution synthesis for CPC DN8-CPM algorithm
6. Uncertainty in CPC DN8-OPM algorithm with respect to safety analysis DN8-OPM algorithm
7. Uncertainty in measurement of planar radial peaking factors using CECOR
8. Computer processing uncertainty
9. Startup test acceptance band uncertainties
10. Fuel and poison rod bow uncertainties
11. Global axial fuel densification uncertainty
12. E,ngineering factor due to manufacturing tolerance.

1.2.BACXGROUND The plant protection system in operation on the C-E NSSS is composed of two sub-systems:

1. an Engineered Safety Features Actu'ation System (ESFAS), and
2. a Reactor Protection System (RPS)

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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 DNBR LSSS as a function of monitored reactor plant parameters. The CPC

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uses these monitored parameters as input data and calculates the on-line LHR and DNBR 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 Departure from Nucleate Boiling (DNB). 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 i Unit 1 and 2)(5). A similar method was also employed to evaluate state parameter response functions and their uncertainties in relation to the LHR and DNBR LSSS for Arkansas Unit 2, Cycle 2(6). Results obtained from the stochastic simulation were used to obtain pdnalty factors for the CPC three

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

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

l. 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 apolied in the ,

l calculation of LHR and DNBR.

The probability distribution functions associated with the uncertainties '

i 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 L

0-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.

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

l.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 uncertaintiet for -

the LHR LSSS and the DNBR LSSS of [ 5)* and [ %3*, respectively, at a 5 5/95 probability / confidence level. -

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  • The values will be provided later.

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. i 1-3

T TABLE 1-1 VARIABLES AFFECTING THE LHR AND ONBR LSSS ,

l LHR

1. Core Power
2. Axial Power Distribution
3. Radial Power Distribution i

DNBR

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

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1-4

'r 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 DNBR 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 DND-OPM to ensure a 95/95 probability / confidence level that the calculations are conservatiye.

2.2 OBJECTIVES OF ANALYSIS The objectives of the analysis reported herein are:

1. to document the stochastic simulation technique used in the overall uncertainty analysis associated with the LHR and DNBR LSSS and
2. to determine LHR and DNB-OPM overall uncertainty factors on the basis of a 95/95 probability / confidence level that the " adjusted" LHR and DNB-OPM (i.e., the CPC synthesized value corrected by the respective overall uncertainty factor) will be conservative throughout the core cycle with respect to actual care conditions.

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

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2-2. The reactor core simulator generates the three-dimensional core power

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distributions which reflect changes in' typical plant operating conditions.

Fq and DNB-OPM modeling uncertainties are statistically combined with other uncertainties in calculating CPC overall uncertainty factors for LHR and DNB-OPM. The uncertainty analysis performed in this report also involves the stochastic simulation of the state parameter measurement uncertainties j for the LHR and DNB-OPM calculations. The neutronic and thennal-hydraulic input parameters that

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l 2-1

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 uncettainty section is also presented in Appendix A.

Approximately twelve hundred (1200) cases of power distributions at each of three burnups (BOC, MOC, EOC) were used in the determination of the overall

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uncertainty factors for the LHR and DNB-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, PLR-90% insertec to full out), and xenon and iodine concentration (equilibrium, Iced maneuver, oscillation).

The power measurement errors used for the LHR and DNB-OpM calculations are obtained from the CPC core power synthesis error, the secondary calorimetric power measurement error, the secondary calorimetric 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 method 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 pcwer distributions 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 l . defined as:

t

(" SYN"Fq)I Xp i= _-1 (2-1)

(" ACTUAL" Fq)I

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

2-2

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, MCC, and EOC).

The mean Fq error (T) p and the standard deviation (op ) of' the Fq error can be calculated from:

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

N l ,

9 7 (Xp - Xp)2 op * ( 2-2b)

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 for the sampling variations in the mean (h) and the standard deviation (op). A normality test of the error distribution is performed by using the D-prime statistic value(7-8) to justify the assumption of a normal distribution.

The K 95/95 factor for a normal districution(8,9) is calculated as:

K= (2-3a) a 2-3

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

(2-3b)

K b = K _p - N (2-3c) >

Kj,p = percentiles of a normal distribution for the probability P (1.645 for 95% probability).

K, = percentiles of a normal distribution for the confidence coefficient (1.645 for 95% confidence).

N = sample size ~

If the error distribution is normal, the upper and lower one-sided 95/95 tolerance limits are calculated using the following equations:

Lower 95/95 tolerance limit = I - K 95/95 (2-4a)

Upper 95/95 tolerance limit = X + K ( 2- 4b )

95/95 where Y, o, and K are the sample mean, standard deviation, and one-95/95 sided tolerance limit factor, respectively.

If the error is not normally distributed,one-s,ided 95/95 tolerance limits are calculated by using non-parametric techniques , .

D 5

The locator L is calculated from the following equation (10)

( 2- 5) 2-4 .

l l

,1

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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 "Ke" is calculated from equation ( 2-4) by using '

the determined one-sided tolerance limit and the known mean error. l:

2.3.3 DNB-OPM LSSS STATISTICAL METH005 The three-dimensional reactor core simulator provides a hot-pin power distribution for its DNB-OPM calculation and the corresponding ex-core detector signals for the CPC power distribution algorithm. In the reactor core simulator, the DNB-OPM calculation is performed with the simplified, fasterrunningDNBalgorithmCETOP-1(II).b J^

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

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, The Reactor Coolant System (RCS) input temperature, prissu're, and flos rate are

( ]forboththe reactorcoresimulatorandCPC.{

i 2-5  !

]Operatingrangesandmeasurementuncertaintiesof the state parameters are given in Table 2-2.

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

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

]Theeffectsoftheerrorcomponentsassociatedwiththe temperature, pressure, and flow measurements and the on-line to off-line DNS-0Pl1 algorithm are ,

accounted for in the determinatici, of the CPC DNB-0PM modeling error via the l SCU program.

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

i (" SYN" DNB-OPM)I .

X D= -1 (2-6)

(" ACTUAL" DNB-OPM)I where (" SYN" DNB-0PM)I and (" ACTUAL" DNB-OPM)I represent the CPC DNB-OPM and the reactor core simulator DNB-OPM for the 1-th case. The DNB-OPM errors are analyzed separately for each time-in-life for conservatism. Each error

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distribution is tested for normality and the mean DNB-OPM error (XD )'

standard deviation (oD), and one-sided upper 95/95 tolerance limit are

- computed.

. 2.4 ANALYSES PERFORMED 2.4.1 LHR LSSS UNCERTAINTY ANALYSIS 2.4.1.1 POWER DISTRIBUTION SYNTHESIS UNCERTAINTY The reactor core simulator calculates ex-core detector signals for the CPC '

power distribution synthesis. An error component for each ex-core signal is

[ and added to 2-6

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

By comparing the reactor core simulator _ calculated Fq with the CPC synthesized Fq for each case, the Fq modeling errors defined in equation (2-1) are ,

obtained. By analyzing the Fq modelinq errors, the CPC modeling error I distributions (histogram) of Fq are obtained for each time in cycle. The mean Fq error (77), the standard deviation (op), and the lower 95/95 tolerance limit (TL )p for the Fq modeling uncertainty are obtained by analyzing the

- error distribution at each time'-in-life. The Fq modeling error is ccmposed of the uncertainties associated with the CPC power synthesis algorithm, the i 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 o f Fxy . The Fxy usea oy CPC are verified by a CECOR(l4) calculation of Fxy during startup testing. Therefore, the CECOR Fxy measurement uncertainty is combined with the Fq modeling uncertainty.to account for the differences between the CECOR Fxy and the actual Fxy.

. The CECOR Fxy error is defined as:

l XFC " P (~)

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

l 2-7 1

2.4.1.3 STARTUP TEST ACCEPTANCE BAND UNCERTAINTY J-The CPC power distribution algorithm (I) 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 factor due to RSF uncertainty, the CPC and '

reactor core simulator Fq calculations for base case are performed using the }.

nominal CPC data base constants for twelve hundred (1,200) cases at each time-in-l i fe. The RSF value (R) for a given rod configuration is changed from the CPC data base constant value (base case value) and the CPC Fq are then calculatedwiththischangedRSFvalue(R+s1R).((

] -

(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

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 2.4.1.4 OTHER UNCERTAINTY FACTORS Axial Fuel 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,ontheCPCFqcalculations.[,'_

Fuel and Poison Rod Bow Uncertainties 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 j The computer processing uncertainty considers the effect of the computer machire 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 l composite Fq modeling uncertainty.

2-9

1

.I 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 F q modeling uncertainty.

2. 4.1. 5 OVERALL LHR LSSS UNCERTAINTY FACTOR An overall CPC Fq uncertainty factor is determined by combining all lower 95/95 probability / confidence tolerance limits of the error components. This overall -

uncertainty factor includes the composit? Fq modeling uncertainty, the startup test acceptance criteria uncertainty, and the axial fuel densification uncertainty. Figure 2-3 shows the calculational sequence to determine an overall LHR LSSS uncertainty factor.

The Fq modeling error (Xpg) defined in equation (2-1) can be rewritten as:

I i j Xg= (2-10) where Fg and C4 are the reactor core simulator calculated Fq and the CPC inferred value of Fq for the 1-th case, respectively. A composite error I '

(XFT ) of the Fq modeling uncertainty and the CECOR Fxy ' measurement uncertainty can be deterministically calculated as follows:

Xh = -1 (2-11)

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

XFT = Xpgi+X FC + (Xpg i*XFC ) (2-12) i l

i 2-10

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

IFT

  • YFM + EFC + (5FM
  • FC
5) (2-13)

., The "Ko" of the composite Fq modeling uncertainty is determined by combining the "Ko" for CECOR Fxy (KoFC), CPC power distribution synthesis (2pg),

, engineering factor (KoFE), rod bow penalties (Kopp, Kopp),andcomputer processing (KoCP):

(2-14)

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

using the lower 95/95 composite tolerance limit (TLp ) for Fq as follows: '

I PMg= (2-15) ,

. 1 + TL p I where f' i'

TLp = TFT - (K')FT (2-16)

The lower tolerance limit is used to assure conservative CPC Fq calculations at a 95/f 5 probability and confidence level.

The last step to determine an overall Fq uncertainty factor (BERR3) is to combine the composite modeling uncertainty (PM p ), the startup acceptance criteria uncertainty (PS) and the axial fuel densification uncertainty (PA).

Consequently, (2-17) l-9 wi 2-11

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The LSSS LHR overall uncertainty factor (BERR3) is used _as a multiplier 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 DNB-OPM LSSS UNCERTAINTY ANALYSIS 2.4.2.1 DNB-0PM MODELING UNCERTAINTY WITH SCU The CPC DNB-0PM modeling uncertainty with SCU is made up of uncertainties ,

associated with power distribution synthesis, DNB algorithm, ex-core detector  !

signal measurement, CEA position measurement, RCS temperature measurement, RCS pressure measurement, and RCS flow measurement. In order to include the RCS inlet temperature, pressure, and flow rate effects in the DNB-OPM modeling uncertainty, a , _

program is employed. ,

By comparing the reactor core simulator calculated DNB-0PM with the CPC calculated DNB-OPM for each case, the DNB-OPM modeling error is obtained. The mean of the DNB-OPM modeling error is represented by: ,,

(2-19) i 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 DNB-0PM uncertainty. However, these errors are implicitly included in the modeling uncertainty via the SCU program .

For the CPC DNB-0PM calculation during a transient, the pressurizer pressure sensed by the precision pressure transducer is ad, justed 'o get RCS pressure ,

by considering dynamic pressure compensation 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 fer the dynamic pressure may be represented by:

(2-20) where By using the CETOP-D 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. ,

I

. j l

' (2-21 )  ;

N

  • = t 1

l i l

1 i

2-13

s The dynamic pressure compensation offset Q1P D

) is defined as the pressure difference between serisor measured pressure and the RCS pressure during a transient.In order to calculateadP ,Dthe RCS pressure change rate during the 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 t,he total sensor delay time.

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2.4.2.3 OTHER UNCERTAINTY FACTORS DNBR Comouter Processing Uncertainty The computer processing uncertainty considers the effect of the off-line (CDC 7600 computer) to the on-line computer machine precision . on the CPC DNB-0PM calculations. The computer processing uncertainty is represented by the term (Ka)DT and is part of the DNB-OPM composite modeling uncertainty. Thi s computer processing uncertainty (KaCP) is calculated by using the following equation:

[ (2-22)

- ~

-u l

(2-23)

Startuo Test Acceptance Band Uncertainty The startup test acceptance band uncertainty for DN8-OPM is determined by the I

same method described in Section 2.4.1.3.

' 14 i

Fuel and Poison Rod Bow Uncertainties The fuel and poison rod bow uncertainties for DNB-0PM are determined by the same method described in Section 2.4.1.4

. System Parameter Uncertainties .*

In order to determine the minimum DNBR (MDNBR) limit, C-E thermal margin methods utilize the detailed TORC code with the CE-1 DNB correlation (12). -

The MDNBR for LSSS includes the uncertainties associated with system parameters which 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 uncertainties (17), the following uncertainties are combined statistically in i the MDNBR limit:

1. Inlet flow distribution uncertainties
2. Fuel pellet density uncertainties
3. Fuel pellet enrichment uncertainties
4. Fuel pellet diameter uncertainties
5. Random and systematic uncert11nties in fuel clad diameter i
6. Random and systematic uncertainties in fuel rod pitch
7. DNB correlation uncertainties The SCU MDNBR limit provides, at a 95/95 probability and confidence level, that the limiting fuel pin will avoid DNB. Since the SCU MDNBR limit includes system parameter uncertainties as described in Part I of this report, these uncertainties are not considered in the determination of the CPC DNB-0PM l -

overall uncertainty factor.

i 2.4.2.4 OVERALL DNB-OPM LSSS UNCERTAINTY FACTOR The overall CPC uncertainty factor for DNB-0PM (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 j.

2-15

J uncertainty, the dynamic pressure uncertainty, and the startup test acceptance band uncertainty. Figure 2-3 illustrates the calculational sequence to determine the overall DNB-0PM t.SSS uncertainty factor.

k A composite DNB-0PM modeling was obtained by following a similar strategy to that used for the Fq uncertainty analysis. The CECOR Fxy measurem.:nt uncertainty was calculated in terms of DNB-OPM units using the sensitivity of.DNB-0PM -

to Fxy {a(%DNB-0PM)/a(t/xy)l .

The mean of the CECOR Fxy error is

~

given by:

(2-24a) and the CECOR Fxy "Kc" is given by:

(2-24b)

The composite mean error for the composite DNS-0PM modeling uncertainty can then be calculated as:

XDT = XDM + XDC + XDM

  • XDC (2-25)

The composite (Ka)DT is made up of uncertainties for DNB-0PM modeling

. algorithm (KoDM), CECOR Fxy (KoDC). rod bow penalties (Kop , Kopp), and DNBR computer processing (KoCP). Usingthe( __

technique, this composite (Ka)DT is calculated as:

I

- ~

(2-26) i 2-16

M 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"IDT + (D)DT (2-27) l 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 (PMD ) IS -

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

An overall DNB-0PM uncertainty factor for CPC (BERRl) is determined by combining PM D

, PPD , and PS:

(2-29)

This LSSS DNB-OPM overall uncertainty factor (BERRI) 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

';NB-0Pf1 assures at least a 95% probability, at 95% confidence level,

. tnat the "ACTUAt." DNB-0PM will be larger than the CPC DNB-0PM.

\

l  !

i 2-17 l

l

TABLE 2-1 '-

STATISTICALLY MODELED VARIABLES

}-

NEUTRONICS CEA Positions Ex-Core Detector Signals .

I THERMAL HYDRAULICS RCS Pressure Core Inlet Temperature Core Flow o.- ,

e e

1 i

f 2-18 f

e

l TABLE 2-2 RANGES AND MEASUREMENT UNCERTAINTIES OF STATE PARAMETERS

- MEASUREMENT PARAMETERS UNIT RANGES UNCERTAINTY

' ~ ' '

Core Inlet Coolant ('F) * * .

Temperature Primary Coolant (PSIA) j' Pressure -

Primary Coolant (GPM)

Flow Rate , , , ,

i

  • The values will be provided later.

G l-t

~

2-19

  • Figure 2-1 i CPC SIMULATION FOR Fq t

EX CORE i SIMULATOR DET CT R _

$IMULATE I DETECTOR SIGNAL E -

POWER SIGNALS A005 RANDOM RANDOM - POWER,

~

DISTRIBUTION UNCERTAINTY COMPONENT ALGORITHM

~ <0MPONENT CEA -

~

TO INPUTS CEA POSITIONS _

- pq POSITIONS RANDOM 5

' pq COMPONENT COMPARE f,PHPD*9 (F qERROR) PHPDy*

l

.v HISTOGRAM PDF(Y)

Y = F ERROR q

~

i PHPD** - CPC PSEUD 0 HOT-PIN POWER DISTRIBUTION ,

A PHPD* - HOT-PIN DISTRIBUTION (1/PER ASSEMBLY)

G 2-20

nr i 1 0

9 0

e

1. -

f

..E c.

6 O

e C3 Z

Q Q

N O I W N

Z CJ O

% m

.J H C1 8C b

=

N O

Q.

W t

e 0

e i

2-21

r I 6

e .\ ,

N 8 m 1 a i E

w m l.

~

s E" "g .a

m. g-E "5

I W -

e e

G E

i i n l

2-22

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

., confidence level. The results of the analyses performed for C-E , System 80

  • NSSS are presented in this section.

3.1 LHR LSSS' Following 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 -

(BOC,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 associated with the LHR '.SSS results in an aggregate uncertainty of [ %]*ata 95/95 probability /confidece level. This overall uncertainty factor of

[ %3 when applied to the CPC synthesized Fq, will assure that the CPC Fq ,

will be larger than the actua' 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 DNB-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 ONB-OPM uncertainty. The individual uncertainty components of the overall DNB-0PM uncertainty factor are presented in Table i

~

3-2. Combining the uncertainties associated with the DNB-OPM LSSS gives an overall uncertainty factor of [ Q*at a 95/95 probability / confidence level.

This overall uncertainty factor, when applied to the CPC synthesized DNB-OPM, will assure that the CPC ONB-OPM will be smaller than the actual DNB-OPM at a 95/95 probability / confidence level at all times during the fuel cycle.

  • The values will be provided later. ,

3-1

,-r - . - .-

TABLE 3-1 CPC SYNT!!ESIZED Fq H0DELING ERRORANALYSIS

(

i TIME IN NUMBER OF HEAN ERROR STANDARD (3 0 ANCE( '(3}

CORE LIFE DATA POINTS (N) (Ip),1 DEVIATION (a),1 LIMIT (TLly BOC

~

(1) ERROR = "

AL Fq -1

  • 100 (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 (ro)p = (TL)p *YF ,

i The values will be provided later.

l TABLE 3-2 CONTRIBUTION OF INDIVIDUAL UNCERTAINTY TO LSSS OVERALL UNCERTAINTY FACTORS i' UNCERTAINTY LHR LSSS DNB.0PM LSSS 3-D Peak (Fq) Modeling(l) fi 1 Ke -

CECOR Fxy I I Ke , }

Engineering Factor Fuel Rod Row l i.

Poison Rod Bow Axial Densification Rod Shadowing Temperature Shadowing Boundary Point Power Computer Processing DNB-OPM tdeling with SCU(2) 1 y l

l Ka Dynamic Pressure

. (1) includes power distribution synthesis uncertainty, ex-core signal noise,

. CEA position error.

i (2) includes

]inadd [ ition to errors of (1).

l l

~i

  • The values will be provided later.

3- 3 l

L__ - - - _ _

i . . i TABLE 3-3 CPC SYNTilESIZED DNB-OPH H0DELING ERROR III ANALYSIS 95/9S TIME IN NUMBER OF MEAN ERROR STANDARD (3) TOLERANCE (2)*(3)

CORE LIFE DATA POINTS (N) S), % DEVIATION (a ), 1 LIMIT (TL)g

!!0C H0C E0C

't' s.

N" - PM (1) ERROR = " ACTUAL" DNB-OPN

-1

  • 100 (2) See Reterences 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 - XD .

'

  • The values will be provided later.

e

~ ~ ~

_j

,r 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 Saft*y 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 Er.gineering, Inc., " Statistical Combination of Uncertainties Methodology", Part-I and III, CEN-124(8)-P,1980.
5. Docket No. 50-317, " Safety Evaluation by the Office of Nuclear Regulation for Calvert Cliffs 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 g 1, June, 1981.
7. American National Standard Assessment of the Assumption of Normality,  !

ASI-N15-15, October,1973. I

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.

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-80", Enclosure 1-P to LD-82-054, May,1982.

i e

e e

e R-2

APPENDIX A l

l A.1 Detector Signal Measurement and CEA Bank Position Measurement Uncertainties l 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 IRSPT). 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 i

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 DNB-0PM ' uncertainty analysis. [

[Thisprocedure 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 DNB-OPM. Therefore, DNB-OPM uncertainties with f respect to temperature, pressure, and flow are implicitly accounted for in the '

DNB-OPM modeling uncertainty.

A-1

A.3 DNB-OPM Algorithm Uncertainties Ideally the DNB-OPM overall uncertainty calculation would use three distinct thermal hydraulic algorithms. The off-line safety-analysis algorithm (CETOP-0) represents the base-line DN8-0PM calculation. CETOP-1(A-2) and CETOP-2(A-I) are simplified versions of CETOP-0 and perform the on-line thermal

~

hydraulic calculations for the plant monitoring and protection systems, respectively. .

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

A.4 References for Appendix A A-1 Combustion Engineering, Inc., " Functional Design Specification for a Core

, Protection Calculator". CEN-147(S)-F , February,1981.

A-2 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, 6_{ , March, 1981.

A-3 M. G. Kendall and A. Stuart, "The Advanced Theory of Statistics, Vol. II",

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

A-2

~

Figure A-1 DN8-OPM ALGORITHMS O M e

e e

W m S

I 1

1 e

l I

l A- 3 1

l l

, 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-0PM 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 allowanca, 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 (Xsc) is obtained as follows:

~

l l

The secondary calorimetric power to the'CPC power calibration allowance and

~

the thennal power transient offset used for C-E system 80 NSSS are [ %] %nd

[ ".],* respectively. The thermal power measurement uncertainty factor for the CPC DNB-OPM calculation (BERRO) is determined by selecting the maximum value  ;

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

]

l

'

  • The values will be provided later.

3-1

The CPC' neutron flux power measurement error is calculated by deterministically combining the neutron flux power synthesis error, the secondary calorimetric

. power measurement error, and the secondary calorimetric power to the CPC power calibration allow'ance. 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-l i 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 range (0-130% full power). [ ,

3  !

i J.

L 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 0-130f. full pow 2r. [

l t

3 i The CPC power measurement errors for C-E System 80 are given in Table B-2 l

l as a function of power.

I l . ,

. I l

P I e 1

l

TABLE B-1 CPC POWER SYNTilESIS ERROR ANALYSIS HUMBER OF MEAN STANDARD LOWER 95/95 BURNur DATA POINTS ERROR DEVIATION TOLERANCE LIMIT

~

~

HOC **

HOC EOC y - -

w CPC POWER - SIMULATOR POWER

  • Power Synthesis Error =

(SIMULATOR POWER j

    • Tlie values will be provided later.

1 0

eam- =pe a h Me W

. se -

TABLE B-2 9 POWER MEASUREMENT UNCERTAINTY AS A FUNCTION OF POWER

~'

FOR DNB-0PM FOR LilR TRUE CALORIMETRIC TilERMAL POWER NEUTRON FLUX POWER ERROR POWER (%) ERROR (1) ERROR (%) POWER ERROR (%) (1) 0 10 20 30 L AD .

50 60 70 80 90 100 110 120 130 The values will be provided later.

APPENDIX C I 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:

L U ASI = (C-1 )

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

The ASI error is defined by:

ASI Er:-or = 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.

1-I l-C-1

. > - s, I

TABLE C-1 l

HOT-PIN ASI ERROR

  • ANALYSIS NUMBER OF MEAN STANDARD LOWER 95/95 UPPER 95/95 BURNUP DATA POINTS ERROR DEVIATION LIMIT LIMIT BOC MOC

! EOC m

  • ASIERROR=.(CPCASI-SIMULATORASI) o* The values will be provided later.

t i

S

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s 5

9 -

/

5 9

RT EI PM PI UL

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