ML20076D268

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Encl 2-NP to LD-83-010,Rev 1, Statistical Combination of Uncertainties Part III - Uncertainty Analysis of Limiting Conditions for Operation C-E Sys 80 Nsss
ML20076D268
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Issue date: 08/31/1983
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.

COMBUSTION ENGINEERING. INC.

ENCLOSURE 2-NP TO LD-83-010 REVISION 01 STATISTICAL COMBINATION OF UNCERTAINTIES PART III Uncertainty An& lysis of Limiting Conditions for Operation C-E System 80 Nuclear Steam Supply Systems REACTOR DESIGN AUGUST 1983 i

l Combustion Engineering, Inc.

Nuclear Power Systems t ' .

. Windsor, Connecticut P

0308230328 830819 PDR ADOCK 05000470 E PDR

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 WAPRANTY 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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l ABSTRACT Part III of the Statistical Combination of Uncertainties (SCU) ~

reports describes the methodology for statistically-combining uncertainties .that are involved in the deterwination of the Limiting Conditions for Operation (LCO) on the Linear Heat Rate (LHR) and Departure from Nucleate Boiling Ratio (DNBR) for the Combustion Engineering (C-E) Nuclear Steam Supply Systems . (NSSS) . The overall uncertainty factors assigned to LHR and DNB Overpower Margin (DNB-OPM) establish that the adjusted LHR and DNB-OPM are conservative at a 95/95 probability / confidence level throughout the core cycle with respect to 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 statistica1 combination of state parameter 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 LCO overall uncertainty factors ,

  • Submitted as Enclosure 1-P to letter LD-82-054 , A. E. Scherer -

to D. G. Eisenhut, dated May 14, 1982.

ii

TABLE OF CONTENTS ,

, CHAPTER PAGE Abstract 11 Table of Contents 111 List of Tables v 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 Summary 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-l' 2.3.2 LHR LCO Statistical Methods , 2-2

- 2.3.3 DNB-0PM LCO Statistical Methods 2-3 2.4 Analyses Performed 2-4

. 2.4.1 LHR LCO Uncertainty Analysis 2-4 2.4.1.1 Power Distribution Synthesis Uncertainty 2-4 2.4.1.2 CECOR Fxy Measurement Uncertainty 2-5 ,

2.4.1.3 Other Uncertainty Factors 2-5 ,

iii

2.4.1.4 Overall LHR LCO Uncertainty Facter 2-6 2.4.2 DNS-OPM LCO Uncertainty Analysis 2-8 2.4.2.1 DNB-CPM Medeling Uncertainty with SCU 2-8 2.4.2.2 Other Uncertainty Factor 2-9 2.4.2.3 Overall DNS .0PM LCD Uncertainty Factor 2-10 3.0 .Results and Cenclusiens 3-1 3.1 LHR LCO 3-1

' 3-1 3.2 CNBR LCO l

R-1 References Aeoendires ,

Stechastic Si=ulatten of Uncertainties A-1 A. ~

A.1 Detector Signal Meas.ure=ent and C2A Sank Position A-1 Measurement Uncertainties A-1 A.2 State Para =eter Measurement Uncertainties A.3 DNS-CPM Algorithm Uncertainties A-2 A.4 FLARE / ROCS Modeling Error A-2 A.5 References for Appendix A A-3 B. Axial Shape Index Uncertainty B-l O

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4,

LIST OF TABLES TABLE PAGE 1 -1 Variables Affecting LHR and DNBR LCO and Monitored 1-4 NSSS Variables 2-1 Stochastically Modeled Variables 2-13 2-2 Ranges and Measurement Uncertainties of Statie 2-14

. Parameters 3-1 COLSS Synthesized Fq Modeling Error Analysis 3-2 3-2 Contribution of Individual Uncertainty to LCO Overall 3- 3 Uncertainty Factors ,

3-3 COLSS Synthesized DNB-OPM Modeling Error Analysis 3-4 B-1 Core Average ASI Error Analysis B-2 3

V

LIST OF FIGURES FIGURE PAGE 2-1 COLSS Simulation of Fq 2-15 2-2 COLSS Simulation of DNB-OPM 2-16 2-3 Flowchart for COLSS Overall Uncertainties for LHR and 2-17 DNB-OPM m

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DEFINITION OF ABBREVIATIONS ASI Axial Shape Index APHPD Axial Pseudo Hot-Pin Power Distribution 80C Beginning of Cycle CDF Cumulative Distribution Function C-E .

Combustion Engineering CEA Control Element Assembly C-E Thermal On-Line Program CETOP CETOP-D Off-Line DNS-OPM Algorithm for Safety Analysis CETOP-1 On-Line DNB-OPM Algorithm Used in COLSS and Core Simulator CETOP-2 On-Line DNS-OPM Algorithm Used in CPC COLSS Core Operating Limit Supervisory System CPC Core Protection Calculator DNB Departure From Nucleate Boiling DNBR DNB Ratio DNB-OPM DNB Overpower 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 .

NSSS Nuclear Steam Supply System PDF Probability Distribution Function

. PHPD Pseudo Hot-Pin Power Distribution I PLR Part length Rod POL Power Operating Limit .

! RCS Reactor Coolant System RPS Reactor Protection System I SAFDL Specified Acceptable Fuel Design Limits SCU Statistical Combination of Uncertainties vii l

, .. -. . _ _ , _ - . , .. _ . - ~ . - _ - . _ _ - .- --- - - __

1.0 INTRODUCTION

1.1 PURPOSE The purpose of this report is to describe the methodology for statistically combining uncertainties associated with the LHR and DNBR LCO (1). All

- uncertainty components considered in the determination of the overall uncertainty factors for the core Power Operating Limits (POL) based on the LHR

. and DNSR calculations are listed as follows: .

1. Uncertainty in in-core detector signal measurement
2. Uncartainty in Control Element Assembly (CEA) position measurement
3. Uacertainties in temperature, pressure, and flow measurements
4. Uncertainty in measurement of planar radial peaking factors (Fxy) using CECOR(2)
5. Uncertainty in Core Operation Limit Supervisory System (COLSS) LHR calculation due to the COLSS power distribution synthesis for COLSS LHR algorithm.
6. Once-tainty in COLSS ONS-OPM calculation due to the COLSS power distribution synthesis for COLSS DNS-OPM algorithm
7. Uncertrinty in COLS$ DNS-OPM algoritcm with respect to safety analysis DNB-OPM algorithm
8. Computer processing uncertainty
9. Fuel and poison rod bow uncertainties
10. Global axial fuel densification uncertainty
11. Engineering factor due to manufacturing tolerance.

1.2 BACXGROUND The COLSS is a digital computer monitoring system. The purpose of COLSS is to assist the operator in maintaining specified operating limits during normal operation. The principal function of COLSS is to aid the operator in monitoring the limiting conditions for operation based on DNBR margin, LHR, and azimuthal f-

' tilt and maintaining core power at or below licensed power. COLSS results are presented to the operator via control room outputs such as alarms, meters, CRT -

displays, and printer reports. .

Operation of the reactor core within these limits assists in assuring that no anticipated operational occurrence will result in exceeding the Specified 1-1 l

1

Acceptable Fuel Design Limits (SAFDL) on DNB and centerline fuel melting. in addition, the consequences of postulated accidents such as a LOCA will be acceptable with respect to applicable criteria. A list of variables affecting DN8 and LHR operating limits and monitored NSSS variables is given in Table 1-1.

The functional relationship between monitoring systems (COLSS)(1) and safety systems (CPC)(3) is as follows: Monitoring systems are to aid the operator during normal operation, in maintaining the plant within established operating

- limits. On the other hand, safety systems are designed to respond to minimize the probability and magnitude of release of radioactivity to the environment.

The integrated functions of the monitoring and protective systems with the plant technical specifications assure that all safety requirements are satisfied (4) . More detailed discussion of those systems may be found in References 1 and 3.

The Statistical Combination of Uncertainties (SCU) is applied to determine overall uncertainty factors for the LHR and DNBR operating limits. The overall uncertainty factors assigned to LHR and DNS-OPM establish that the adjus'ted LHR and DNB-OPM will be conservative throughout the core cycle with respect to actual core conditons.

1.3 REPORT SCOPE The objectives of this report are:

1. to describe the methods used for statistically combining uncertainties applicable to the LHR and DNER LC0;
2. to evaluate the aggregate uncertainties as they are applied in the calculation of the LHR and DNBR LCO.

l The probability distribution functions associated with the uncert'ainties 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 method used for the determination of the uncertainties on the core average Axial Shapa Index (ASI) is also described.

The methods presented in this report are applicable specifically to CE System .

80.

1-2

l'. 4

SUMMARY

OF RESULTS The analysis techniques described in Section 2.0 were applied to C-E System

80. Using the stochastic simulation program:. overall uncertainties for the LHR LCD and the DNBR LCO of [ ] and [ ] , respectively, were calculated at a 95/95 probability / confidence level.

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1 1-3

TABLE 1-1 VARIABLES AFFECTING LHR AND DNBR LCO AND MONITORED NSSS VARIABLES NSSS VARIABLES ENITURED VARIABLE (S) '

INFERRED FROM:

Core Average Power Turbine First Stage Pressure '

Cold Leg Temperature Hot Lag Tammerature Feedwater Flow Staam Flow Feedwater Temperature Steam Pressure Radial Peaking Factor CEA Positions Azimuthal Tilt Magn 1tuce In-Core Neutron Flux Nomalized Axial Poweri Distribution In-Core Neutron Flux CEA Group Positions Reactor Coolant System Mass Flow Reactor Coolant Pum Head

! Reactor Coolant Pumo Speed Cold Lag Temperature Pressurizar Pressure Reactor Coolant System Pressure Pressud zer Pressure Reac*ar Coolant Inlet Temperature Cold Leg Temperature 9

l l-4

2.0 ANALYSIS 2.1 GENERAL The following sections describe the impact of the uncertainty components on the systes parameters, the state parameters, and the COLSS modeling that affect the LHR and DN8R LCO. The effects of all individual uncertainties on the LCO overall uncertainty factors for LHR and DN8R are also discussed. In addition, this chapter presents analyses performed to determine overall uncertainty factors which are applied to the COLSS calculations of the LHR and DN8-OPM to ensure a 95/95 probability / confidence level that the calculations are conservative. -

2.2 OBJECTIVES OF ANALYSIS i 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 DN8R LCO and
2. to detennine LHR and DNS-OPM overall uncertainty factors on the basis of a 95/95 probability / confidence level that the " adjusted" LHR and DNB-OPM

! (i.e., the COLSS synthesized value corrected by the respective 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 power peaking factor (Fq) and DNS-OPM obtained from the reactor core .

l simulator (II to those calculated by COLSS as shown in Figures 2-1 and 2-2.

i The reactor core simulator generates the three-dimensional core power distributions which reflect changes in. typical operating conditions. Fqand l

DNB-OPM modeling uncertainties are statistically combined with other uncertainties in calculating COLSS overall uncertainty factors for the COLSS ,

LHR and DNB-OPM calculations. The uncertainty analysis performed in this ,

report also involves the stochastic simulation of the state parameter measurement uncertainties for the LHR and DNB-OPM calculations (5) . The neutronic 2-1

.c- .-- , , - ,,,,c. ,n.--. m - .-r-,-.--.-.e - _

and thermal hydraulic input parameters that are statistically modeled are given in Table 2-1. A 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. The method used for the determination of the core average ASI uncertainty is described in Appendix B.

. Approximately twelve hundred (1200) cases of power distributions.at each of three burnups (BOC, MOC, EOC) were used in the determination of the overall uncertainty factors for the LHR and DNB-0PM calculations. The cases (total of 3600) considered herein 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% inserted to full out), and xenon and iodine concentration (equilibrium, load maneuver, oscillation).

2.3.2 LHR LCO STATISTICAL METHODS The reactor core simulator was used to generate the hot pin power distribution which served as the basis for comparison in establishing the uncertainty factors documented in this report. The COLSS synthesized Fq is compared with that of the reactor core simulator Fq. Figure 2-1 illustrates the calculational sequence employed in the Fq modeling uncertainty analysis. The Fq modeling error (Xp i) between the COLSS synthesized Fq and the actual Fq is defined as:

X Ip = (" SYN" F")I *

(2-1) j (" ACTUAL" q F )9 -l where (" SYN" Fq)i and (" ACTUAL"Fq)I are the COLSS Fq and the reactor core simulator Fq for the 1-th case. The Fq errors are analyzed for each case of .

each time-in-life. Approximately 3600 cases are analyzed at BOC, MOC, and EOC conditions. Each error distribution is evaluated to obtain the mean Fq error

(%) and the standard deviation (op).

l The mean Fq error (G) and the standard deviation (ap ) of the Fq error can .

be calculated from:

! 2-2 l

N 2 1 yF , i=1 Fx (2-2)

M 1/2 4 g (Xp-I) p (2-3)

  • F y.1  ;

/

where N = sample size Since the mean and standard deviation are estimated from the data, the one-sided tolerance lir;it 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 sample mean (Xy) and the standard deviation (ep ). A normality test of the error distribution is performed by using the 0-prime statistic value( 6-7) to justify the assumption of a normal di stribution. If the error distribution is normal, the K95/95 factor is calculated from an analytical expression (M) (see Section 2.3.2 ofPartII). If the error is not normally distributed, a one-sided 95/95, tolerance, limit is obtained by using ncn-parameteric techniques ,

2.3.3 DNB.0PM LCO STATISTICAL METHODS The three-dimensional reactor core simulator provides a hot-pin power distribution for its DNB-OPM calculation and the corresponding in-core detector signals for the COLSS power distribution algorithm. In the reactor core simulator, the DNS-OPM calculation is performed with the simplified', faster running DNB-0PM algoritta CETOP-1.(10) , {

J A flowchart representing the reactor core simulator DNS-OPM calculation is shown in -

Figure 2-2.

The Reactor Ccolant System (RCS) inlet temperature, pressure, and flow rate are

,for both the 2-3

l reactor core simulator and COLSS. ,

[Operatingrangesandmeasurementuncertaintiesof the LCO state parameters are given in Table 2-2.

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

, (" SYN" DNS-OPM)i

-1 (2-4)

(ACTUAL"DNB-OPM)I where'(" SYN" DNB-OPM)iand (" ACTUAL" DN8a0PM)I represent the COLSS DNB-OPM and the reacor 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 distribution is analyzed for normal or non-parametric behavior to calculate the mean DNB-OPM error ($), standard deviation ( a0), and one-sided 95/95 tolerance limit.

2.4 ANALYSES PERFORMED 2.4.1 LHR LCO UNCERTAINTY ANALYSIS 2.4.1.1 POWER DISTRIBUTION SYNTHESIS UNCERTAINTY The reactor core simulator calculates in-core detector signals for the COLSS power distribution synthesis. An error component fpr each in-core signal is

[ ]andaddedtothe in-core signal . An error component for each CEA bank'meisurement (pulse counter position) is obtained ,

The CEA position error component is then added to its respective CEA bank position. The COLSS synthesizes a hot-pin power distribution by using (as input) the adjusted in-core detector signals and the adjusted CEA bank positions. A simple five element Fourier fitting technique

~

is employed in COLSS to get the core axial power shape.

24

l

  • j By comparing the calculated reactor core simulator Fq with the COLSS synthesized Fq for each case, the Fq modeling errors defined in equation (2-1) l are obtained. By analyzing the Fq modeling errors, the COLSS modeling error distributions (histogram) of Fq are obtained for each time-in-cycle. The mean j Fq error (5), the standard deviation ( ap), and the lower 95/95 tolerance limit (TL )p for the Fq modeling uncertainty ars obtained by analyzing each error distribution. The COLSS Fq modeling uncertainty ts determined by combining uncertainties associated with the COLSS power synthesis algorithm, the in-core

~ -

de'tector signal, and tNi CEA-~ position measurement.

2.4.1.2 CECOR FXY UNCERTAINTY In the calculation of the COLSS Fq modeling uncertainty, the COLSS uses predicted values of planar radial peaking factors (Fxy). The Fxy used by COLSS are verified by a CECOR calculation of Fxy during startup testing.

Therefore, the CECOR Fxy measurement uncertainty (2) is combined with the Fq modeling uncertainty to account for the difference between the CECOR Fxy and the actual Fxy.

The CECOR Fxy error is defined as:

G P XFC " P (2-5) i where Pj and G$ are the actual Fxy and the CECOR calculated Fxy for the 1-tn case, respectively.

2.4.1.3 OTHER UNCERTAINTY FACTORS AXIAL FUEL DENSIFICATION UNCERTAINTY '

The axial fuel densification uncertainty factor (I3) considers the global effect of the shrinkage of the fuel pellet stack, due to in-pile sintering, on theCOLSSFqcalculations.[

2-5

__-.m , , , , . . - . _ , _ _ _ _ . _ ~ . _ _ - - . ,_,_._m ,. . - , , _, ,, , ,, , _ . , _ _ _ . . , . _ _ - - _ . - _ _ . - _ , , , _ . . . _ _ . , _ _ . - - . . . ~ , ,

FUEL AND POISDN R00 80W UNCERTAINTIES The fuel and poison rod bow uncertainties (14) consider the effect of " bowing" of the fuel and poison rods, due to heating and irradation, on the COLSS Fq calculations. The factors will be used as part of the composite COLSS Fq modeling uncertainty.

~

C0sUTER 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 COLSS Fq calculations. The computer processing uncertainty will be used as part of the composite Fq modeling uncertainty.

ENGINEERING FACTOR UNCERTAINTY The engineering factor considers the effect on the COLSS Fq calculation due to i fuel manufacturing tolerance (13). This factor will be part of the composite Fq modeling uncertainty.

t i

2.4.1.4 OVERALL LHR LCD UNCIRTAINTY FACTOR  :

An overall COLSS Fq uncertainty factor is detemined by combining all . lower 95/95 probability / confidence tolerance limits of error components. This overall uncertainty factor is made up of a composite Fq modeling uncertainty and axial fuel densification uncertainty. Figure 2-3 shows the calculation sequence to determine an overall LHR LCD uncertainty factor.

The COLSS Fq modeling uncertainty defined in equation (21) can be rewritten as:

l I

~ i (2-6) f Xh =

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

i inferred value of Fq for the i-th case, respectively. A composite error (X p7i ) of the Fq modeling uncertainty and the CECOR 'Fxy uncertainty can be detaministically calculated as follows:

2-6

I -l (2-7)

By applying equations (2-5) and (2-6), this leads to:

xp71xpyi + xFC' + (4M'*4C) 1 (2-s)

The mean of the composite Fq modeling uncertainty can be then determined by:

~

xFT" XFM+ N C+ FM(I *FCI) (2*9)

The composite (Ke)FT for the Fq modeling error is made up of uncertainties for CECOR Fxy (K' FC), COLSS power algorithm (Ka py), FLARE / ROCS (3) modeling error * '

(Ke FR), rod bow penalties (Ka pp K a g ,), and computer processing (Ka CP). By using tne , ,

technique, this (Ka)FT is calculated by:

(2-10)

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 PMy= (2-11 )

1 + TL p where TLp=TFT-(E#)FT (2-12)

The lower tolerance limit is used to assure conservative COLSS Fq calculations at a 95/95 probability / confidence level. -

The last step to detennine an overall Fq uncertainty factor (UNCERT) is to combine the composite modeling uncertainty (PM p ), the axial fuel densifi-cation uncertainty (PA), and the engineering factor (PE). Consequently,

  • See Appendix A4.

2-7

7, ,

i (2-13)

~

This LCO LHR overall uncertainty. factor (UNCERT) is used as a multiplier'on the

[

~

COLSS calculated LHR ('KW/FT): ,

, N e COLSS " SYN" LHR * (UNCERT)95/95 > " ACTUAL".LHR (2-14)'

Use of the overall uncertainty factor (UNCERT).for the COLSS calculated LHR assures at least a 95% probability, at a 95% confidence level, that '

the COLSS LHR will be larger than the " ACTUAL" LHR. <

2.4.2 DNB-OPM LCO UNCERTAIN 1Y ANALYSIS 2.4.2.1 DNB-0PM MODELING UNCERTAINTY WITH SCU' -.

The COLSS DNS-0PM modeling uncertainty with SCU is"sade up of Uncertainties associated with power distribution synthesis, in-core ' detector signal '

measurement, CEA position measurement, RCS temperature ite6surement, RCS '

pressure measurement, and RCS flow maar,urement. ~In order to include the RCS inlet temperature, pressure, and-flow. rate effects in DNS-OPM modeling ,

uncertainty..a stochastic simulation program was employed. The SCU progran stochastically simulates the measurement uncertainties and operating ranges associated with RCS state parameters along with the on-line to off-line DNB 0PM _

algorithm error components.

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

(2-15) .

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2.4.2.2 OTHER UNCERTAINTY FACTORS DNBR COMPUTER PROCESSING UNCERTAINTY ,

The computer processing uncertainty for the calculation of DNS-OPM considers the effect of the off-line (CDC 7600 computer) to the on-line comr. uter machine

-- precision on the COLSS ONS-OPM calculations. The computer processing uncertainty is represented by the terms of (Ka)DT and is part of the DNB-OPM composite modeling uncertainty. This computer processing uncertainty (KaCP) is calculated using the following equation:

(2-16)

+ -

r (2-17)

, , FUEL AND POISON ROD BOW UNCERTAINTIES

! - - The fuel and poison rod bow uncertainties for DNB-OPM are determined by the

_ same method described in Section 2.4.1.3.

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w'-- ym,- -----w-- ww,e----y-'-

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1 SYSTEM PARAMETER UNCERTAINTIES In order to datarmine the minimum DN8R (MNBR) limit, C-E thermal margin methods utilize the detailed TORC code with the CE-1 DNS correlation (II). .

The WN8R for LCD includes the uncertainties associated with system parameters whic'h describe the physical system. These system parameters are composed of

- core geometry, pin-by-pin radial power distributions, inlet and exit flow

~

boundary conditions, etc. In the statistical combination of system parameter uncertairities(15), the following uncertainties are combined statistically irr the ENBR 1Imit:

1. Inlet f1'ow distribution uncertainties
2. Fuel pellet-density uncertainties ,
3. Fuel pellet enrichment uncertainties
4. Fuel pellet diameter uncertainties
5. Random and systematic uncertainties in fuel clad diameter
6. Random and systematic uncertainties in fuel rod pitch
7. CHF correlation uncertainties The SCU WNBR limit provides, at a 95/95 probability and confidence level, that

! the limiting fuel pin will avoid DNB. Since the SCU E NBR limit includes system parameter uncertainties, these uncertainties are implicitly included in the calculation of the COLSS ONS-OPM overall uncertainty factor.

2.4.2.3 OVERALL ONS-0PM LCD UNCERTAINTY FACTOR The overall COLSS uncertainty factor for DNB-OPM (EPOL2) is determined by combining all one-sided (upper) 95/95 probability / confidence tolerance limits.

j Figure 2-3 shows the calculational sequence to detennine the overall DNB-OPM uncertainty factor.

The composite DNS-CPM modeling uncertainty was obtained by following a similar strategy to that used for the Fq uncertaint; e alysis. The CECOR Fxy measurement uncertainty was calculated in terms of DNS-OPM units using the sensitivity of DNB-OPM to Fxy { a(';DNB-OPM)/a(".Fxy) } , The mean value of the CECOR Fxy error is given by:

2-10 x

., n. -

, . . - - - , -- . -,- ,, -- _n, , - , ~ - - - - . , , - - - - - - - - - , . - - _ - - - _ _ -

l

- =,

1 (2-18a) and the CECDR Fxy " Xe " is given by:

<= .,

(2-18b)

~

The composite mean error of the composite DN8-DPM modeling uncertainty can then be obtained by:

YDT

  • YDM + kC * (IDM *DC I) (2-19)

The composite (Xa)DT is made up of uncertainties for CECDR Fxy (X'DC), DNS.

OPM algorithm (K DM), r d bow penalties (Kopp, Kopp). DNBR computer processing (KoCP), and FLARE / ROCS moceling error (KcFR). Using the root-sum-square technique, this composite (Ka)DT is calculated by:

(2-20)

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

) is used for conservative CDLSS DNS-DPM calculations and determined by:

g.37+(X,)37 (2-21) .

The penalty factor (PM D

) for this composite tolerance limit can then be determined as:

PMD = 1 + (TL)D (2-22) 2-11

Therefore,the overall DNS-OPM uncertainty factor for COLSS (EPOL2) is :

-- (2-23)

This LCO DNB-OPM overall uncertainty factor (EPOL2) conservatively adjusts the COLSS calculated power operating limit:

COLSS " SYN" DNS-OPM , < " ACTUAL" DN8-OPM (2-24)

Use of the overall uncertainty factor (EPOL2) for the COLSS calculated DNB-0PMassuresatleasta95%; probability,ata95%confidencelevel, that the " ACTUAL" DNS-OPM will. be larger than the COLSS DNB-OPM.

O 2-12

-- . ,_y-. .-_-__- - ._.,- , . - . , v . - - , _ _ . . . _ - , - . , - , _.- .__ . . . - . _ . - . . , - . _ . . . , , , _ - . . . . . . .

TABLE 2-1 STATISTICALLY MODELED VARIABLES NEUTRONICS CEA POSITIONS IN-CORE SIGNALS WERMAL HYDRAULICS RCS PRESSURE ,

CORE INLET TEWERATURE CORE FLOW l

l s

l 2-13

TABLE 2-2 RANGES AND MEASUREMENT UNCERTAINTIES OF STATE PARAMETERS PARAMETERS MEASUREMENT UNIT RANGES UNCERTAINTY

~

Core Inlet (*F)

~ '

Colant Temperature Primary Coolant (psia)

Pressure Primary Coolant (GPM)

Mass Flow O

l 2- 1.:

FIGURE 2-T CGLSS SIMUL.ATION FOR F 9

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e O

9 I

2 . _ _ _ . _ _ _ _ _ _ . _ _ _ _ _ _ . . _ _ - _ _ _ _ _ _ _ . _ - _ _ _ _ _ _ . . . _ _ _ . - , _ . . _ _ _ _ _ - _ . _ _ _ _ . _ - _ - - _ . _ _ - - _ _

5 1

5 2

W E

g

~.

7 I I W M s E 8 -

c 8e hm I

C e

9 I

I 2-i7

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

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

3.1 LHR LCD Following the analysis techniques described in Section 2.4.1,COLS$ 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 uncertainties 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. A stochastic simulation of uncertainties associated with the LHR LCO results in an aggregate uncertainty of[ lat a 95/95 probability / confidence limit. This uncertainty factor of

( }, when applied to the COLS$ synthesized Fq, will assure that the COLSS 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 LCO Following the analysis techniques presented in Section 2.4.2, the mean values, 1

standard deviations, and lower tolerance limit of the COLSS synthesized DNB-OPM modeling errors were obtained and are sunnarized in Table 3-3. The modeling error was analyzed as a function of the core life, but only the burnup which led to the most conservative modeling uncertainty was considered in calculation l of the DNB-OPM overall uncertainty. The individual contributing , uncertainty l

factors to the ONB-OPM overall uncertainty factor are presented in Table 3-2.

Comnining of the uncertainties associated with the DNS-OPM LCO gives an overall

, uncertainty factor of [ ] at a 95/96 probability / confidence limit. This overall uncertainty factor, when applied to the COLS5 synthesized DNB-OPM, will assure that the COLSS ONB-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

1 TABLE 3-1 ,

COLSS SYNTHESIZE 0 Fq MODELING ERRORIII ANALYSIS

  • i I

i TIME IN NUMBER OF GL IANCE(2),(3)

MEAN ERROR STANDAR0(3} .

l CORE Lire DATA POINTS (N) ('XE ), 1 DEVIATION 8(.g);.1 LIMIT ITL)p I BOC *

) y

~

EOC

  • m I

I i

i i

~

(1) ERROR = . gf4 pq -1

  • 100 I

(2) See References 8 and 9. . Normal or non-parametric values presented.

i (3)

If error distribution is determined to be non-parametric, the value for (Ka), is calculated as (K )F --(TL)r + Ir

)

i i

TABLE 3-2 CONTRIBUTION OF INDIVIDUAL UNCERTAINTY TO LCO OVERALL UNCERTAINTY FACTORS UNCERTAINTY LHR LCO DNBR LCO 3-0 Peak Modeling(*) iI

\

k CECOR Fxy (I M

Engineering Facter Fuel Red Scw Peisen Red Scw Axial Densificatien Computer Processing DNS-OPM Mcdeling with !CU(*) 'I FLARE / ROCS Medeling

~ ..

(*) includes pcwer distribudien synthesis uncertainty, in-ccre signal noise, CIA pcsition error,

(") includes "

in aedi:icn :c ereces of

(* ).

1 I

! 3-3

i i

TABLE 3-3 .

COLSS SYNTHES 12E0 DNB-OPH N00ElfMG ERROR (N ANALYSIS i

95/95 i

TIME IN NUMBER OF MEAN ERROR STANDARD (3) TOLERANCE (2)*(3) l CORE LIFE DATA PolNTS (N) (X D. AI o= UMI (TL)D 1 ~

BOC -

l '

MOC i

l EOC u

] L '

i l

i I

8-WM

  • 100 (1) ERROR =l -1
( " ACTUAL" DNB-0PM j ,

1

!, (2) See References 8 and 9. . . Normal and non-parametric values presented.

(3) Same as tilR except (Ka)D " -(TL)D - D'-

i 1 -

i I

4

REFERENCES

1. 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.
2. Combustion Ericineering, Inc., " INCA /CECOR Power Peaking Uncertainty", CENPD-153-P, Rev.1-P-A, May,1980.
3. 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. -

4. Combustion Engineering, Inc., " System 80, Combustion Engineering Standard Safety Analysis Report (CESSAR), Final Safety Analysis Report (FSAR)",

March 31, 1982.

5. Combustion Engineering, Inc., " Response to Questions,on Documents Supporting the ANO-2 Cycle 2 Licensing Submittals", CEN-157(A)-P, Amendment 1, June,1981.
6. American National Standard Assessment of the Assumption of Normality, ASI, N15-15, October,1973.
7. Sandia Corporation, " Factors for One-Sided Tolerance Limits and for Variabe Sampling Plans", SCR-607, March,1963.
8. E. L. Crow, et al, " Statistics Manual". Dover Publications, Inc., New York, 1960.
9. R. E. Walpole and R. H. Myers, " Probability and Statistics for Engineers and Scientists 2ed", Macmillan Publishing Company, Inc., New York,1978.
10. 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. , ,

11. Combustion Engineering, Inc., "CETOP-D Code Structure and Modelin'g Methods for San Onofre Nuclear Generating Station Units 2 and 3", CEN-160, May, 1981.
12. M. G. Kendall and A. Stuart, "The Advanced Theory of Statistics, Vol III",

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

13. Combustion Engineering, Inc., " Fuel Evaluation Model", CENPD-139-P, .

October,1974.

14. Combustion Engineering, Inc., " Fuel and Poison Rod Bowing", CENPD-225-P and Supplements, October,1976.
15. Combustion Engineering, Inc., " Statistical combination of Uncertainties, Combination of System Parameter Uncertaintes in Thermal Margin Analyses for --

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

R-1

~

\

i APPENDIX A l

STOCHASTIC SIMULATION OF UNCERTAINTIES I

Al. Detector Signal Measurement and CEA Bank Position Measurement Uncertainties In the SCU program, error components of in-core detector signals are[ ,

This error component is then added to the in-core signal generated from the core simulator and is used as input to the COLSS power distribution algorithm.

The location of each CEA bank is measured using the pulse counter position. 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 COLSS power distribution algorithm.

A2. State Parameter Measurement Uncertainties The DNB-OPM algorithm (A-1) used for COLSS requires primary system pressure, core inlet temperature, core power, primary coolant flow rate, and hot pin power distribution as input. Since' RCS pressure, RCS temperature, and RCS flow affect the calculation of DNB-OPM, errors associated with these state parameters must be accounted for in the COLSS DNB-OPM uncertainty analysis.

]Thisprocedure

. allows for direct simulation of the effect of the COLSS on-line temperature, pressure, and flow measurements and their uncertainties on the resultant DNB-OPM uncertainty Therefore, DNS-OPM uncertainties with respect to temperature, pressure, and flow are implicitly accounted for in the DNB-OPM modeling .

uncertainty.

e A-1

A3. DNS-OPM Algorithe Uncartainties In the DNS-OPM overall uneartainty calculation, two distinct thermal hydraulic algorithms are involved. The off-line safety-analysis algorithm (CETOP-0)(A-2) represents the base-line DN8-OPM calculation. CITOP-1 fA~3) is a simplified version of CITOP-0 and performs the the,rmal hydraulic calculations in the reactor core simulator and COLS3. ,

t 1

A4. FLARE / ROCS Modeling Error The reactor core simulator uses the FLARE neutronic model to predict representa-tive 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 FLARE modeling uncertainty on the reference LHR and DNB-OPM calculations.

l l -

I I A-2

AS. REFERENCES FOR APPENDIX A A-1 Combustion Engineering, Inc., "CCL33, Assessment of the Accuracy of PWR Operating Limits as Determined by the Core Operating Limit Supervisory System", CENPD-169-P, July,1975. ,

A-2 Combustion Engineering, Inc., "CETOP-0 Ccde Structure and Modeling Methods for San Onofre Nuclear Generating Station Units 2 and 3", CEN-160, May, 1981.

A-3 Chong Chiu, "Three-0imensional Transport. Coefficient Model and Prediction-Corrections Numerical Method for Themal Margin Analysis of PWR Cores",

Nuclear Eng, and Cesign, P103-115, y , March 1981.

A-4 M. G. Xandall and A. Stuart, "The Advanced Theory of Statistics, Vol. II",

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

1 4

A-3 l _ _ _. _ _ _ - - _ - . - - - - _ - - - - - - - _ - - . _ - . - ~ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

APPENDIX B AXIAL SHAPE INDEX UNCERTAINTY The axial shape index (ASI) for the core average power distribution is computed from the power in the lower and upper halves of the core:

L U ASI .

(B-1)

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

The ASI error is defined by:

ASI Error = COLSS ASI - Reactor Core Simulator ASI (B-2)

The core average ASI uncertainty analyses are performed by comparing the COLSS calculated ASI and the reactor core simulator ASI. The resulting error distributions are analyzed to obtain the upper and lower 95/95 tolerance limits. The core average ASI uncertainties for C-E System 80 are presented in Table B-1 l

G e

t B1

W e

N

=>

k' h3 A

-=

m C

E =;-

g 5E a g MW w w 4

e *=

4 tsi W

E W

3e 4 W w E2 5

a W5 m

mm M

5 m= 4

=g g W

elC I0=<

8 u

M M

, .=J C

  • e W 8

8 a

Q. E W

E -

E v v a E $ S E I

B-2

-

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