ML20204H497

Nonproprietary Statistical Combination of Uncertainties, Part Iii,Uncertainty Analysis of Limiting Conditions for Operation

ML20204H497
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Issue date:	10/31/1984
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CEN-283(S)-NP, CEN-283(S)-NP-V03, CEN-283(S)-NP-V3, NUDOCS 8411120305
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San Onofre Nuclear Generating Station Units 2 and 3 CEN-283(S)-NP STATISTICAL COMBINATION OF UNCERTAINTIES

. PART III Uncertainty ' Analysis of Limiting Conditions for Operation San Onofre Nuclear Generating Station Units 2 and 3 REACTOR DESIGN OCTOBER 1984 Combustion Engineering, Inc.

Nuclear Power Systems Windsor, Connecticut 1

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_ . . . . . . . - J

LEGAL NOTICE s l

THIS REPORT WAS PREPARED AS AN ACCOUNT OF WORK SPONSORED BY COPEUSTION ENGINEERING, INC. NEITHER COMBUSTION ENGINEERING NOR ANY PERSON ACTING ON ITS 8EHALF:

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 USEFULNESS 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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ABSTRACT Part III of the Statistical Combination of Uncertainties (SCU) report

. describes the methodology for statistically combining uncertainties that are involved in the determination of the Limiting Conditions for Operation (LCO) on the Linear Heat Rate (LHR) and Departure from f?ucleate Boiling Ratio (DNBR) for San Onofre Nuclear Generating Station (SONGS) Units 2 and 3. 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 core conditions. .

The Statistical Combination of Uncertainties report describes a method for statistically combining uncertainties. Part I of this report describes the statistical combination of system parameter uncertainties in thermal margin Part II of this report describes the statistical combination of

~

analyses.

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.

The methods described here (Part III) are the same as those reviewed and approved for C-E System 80 plants.

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r-TABLE OF CONTENTS CHAPTER PAGE Abstract 11 Table of Contents iii 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 Sumary 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 LCO Statistical Methods 2-2 2.3.3 DNB-OPM LC0 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 2-6 2.4.1.4 Overall LHR LCO Uncertainty Factor 2-7 2.4.2 DNB-OPM LCO Uncertainty Analysis 2-8 2.4.2.1 DNB-OPM Modeling Uncertainty with SCU 2-8 2.4.2.2 Other Uncertainty Factors 2-9 2.4.2.3 Overall DNB-OPM LCO Uncertainty Factor 2-10 iii

~3.0. Results and Conclusions 3-1 3.1 -LHR LCO 3-1 3.2 DNBR LCO 3-1 References R-1 Appendices A. Stochastic Simulation of Uncertainties A-1 A.1 Detector-Signal Measurement and CEA Bank Position A-1 Measurement Uncertainties A.2 State Rarameter Measurement Uncertainties A-1 A.3. DNB-OPM Algorithm Uncertainties A-2 A.4 Reactor Core ' Simulator Modeling Error A-2 A.5 References for Appendix A A-2 B. Axial Shape Index Uncertainty B-1 4

i 9

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LIST OF TABLES TABLE PAGE 1-1 Variables Affecting LHR and DNBR LCO and Monitored NSSS 1-4 Variables

.2-1 Stochastically Modeled Variables 2-13 2-2 Pinges and Measurement Uncertainties of Parameters 2-14 3-1 COLSS Synthesized Fq Modeling Error Analysis 3-2 3-2 Contribution of Individual Uncertainties to LCO Overall 3-3 Uncertainty Factors 3-3 COLSS Synthesized DNB-OPM Modeling Error Analysis 3-4 B-1 Core Average ASI E'rror Analysis B-2 Y

LIST OF FIGURES

' FIGURE PAGE 2-1 COLSS Simulation for Fq 2-15 2-2 COLSS Simulation for DN8-OPM 2-16 2-3 Flowchart for COLSS Overall Uncertainties for LHR 2-17 and CNB-OPM e

b

/

,.e-vi

v DEFINITION OF ABBREV:ATIONS

y ASI Axial Shape Index t APHPD' Axial. Pseudo Hot-Pin Power Distribution

'BOC .Beginning of Cycle CDF Cumulative Distribution Function C-E- Combustion Engineering CEA-  : Control Element Assembly CETOP ~C-E Thermal On-Line Program CETOP-D Off-Line DNB Algorithm for Safety Analysis CETOP-1 DNB. Algorithm Used in COLSS (on-line) and Core Simulator -(off-line)

'CETOP-27 .On-Line-DNB Algorithm.Used in'CPC COLSS' Core Operatin'g Limit Supervisory System CPC Core P.rotection Calculator Departure from Nucleate Boiling _

-DNB

'DNBR DNB Ratio

.DNB-OPM DNB Overpower Margin E0C End of Cycle

,, ESFAS Engineered Safety Features Actuation System Fq Three-Dimensional Power Peaking Factor jFxy V Planar Radial Power Peaking Factor LC0 Limiting Con'ditions for Operation LHR LinearHeatRate'(kw/ft)

, LOCA Loss of Coolant Accident y LSSS- Limiting Safety System Setting (s) yp 'MOC; Middle of Cycle MSSS -Nuclear Steam Supply System PDF. s, Probability Distribution Function

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.PHPD Pseudo Hot-Pin Power Distribution-PLR Part length Rod (CEA)

POL' V? Power Operating Limit

. .RCS- Reactor Coolant System-RPS Reactor Protection System SAFDL Specified Acceptable Fuel Design Limits SCU' Statistical Combination of Uncertainties

@ vii

& .= - -

F d -

1.0 INTRODUCTION

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

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certainty components considered in the determination of the overall

-uncertainty factors for the core Power _0perating Limits (POL) based on the

.LHR and DNBR calculations are listed as follows:

1. .'~ Uncertainty in the in-core detector signal measurement

2. Uncertainty.in the Control Element Assembly.(CEA) position measurement

~3. Uncertainties in the temperature, pressure, and flow measurements 4.

Uncertainty (in the' measurement-of planar radial peaking factors (Fxy) using CECOR

5. Uncertainty in the Core Operating Limit Supervis'ory System (COLSS) LHR calculation due to the COLSS power distribution synthesis.-

6. .

Uncertainty in the COLSS DNB-OPM calculation due to the COLSS power-distribution synthesis'for COLSS DNB algorithm

7. Uncertainty in the COLSS DNB algorithm with respect to the safety analysis DNB algorithm

8. Computer processing uncertainty

9. Fuel and' poison rod bow uncertainties

10. Axial fuel densification uncertainty

11. -' Engineering factor due to manufacturing tolerance 1.2 -BACKGROUND

' 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, azimuthal-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.

1-1

Operation of the reactor core within these limits assures that no anticipated

-operational occurrence will result in exceeding the Specified Acceptable Fuel Design Limits (SAFDL) on DNBR 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 DNBR and LHR operating limits and monitored NSSS variables is given in Table 1-1.

The functional relationship between the monitoring systems (COLSS)(1) and the safety systems (CPC)(3) is as follows: Monitoring systems aid the operator during normal operation in maintaining the plant within established operating limits. On the other hand, safety systems are. designed to minimize the probability and magnitude of release of radioactivity to the environment during abnormal operation. The integrated functions of the monitoring and protective systems via the plant technical specifications assure that all safety requirements are satisfied I4) More detailed discussions of these systems may be found in References 1 and 3.

A generic SCU method for C-E System 80 plants has been applied and licensed for Palo Verde unit 1. The SCU methodology described in this report is the same as the methodology used for C-E System 80 NSSS(5-7) ,

The SCU method is applied to determine overall uncertainty factors for the LHR and DNBR operating limits. The overall uncertainty factors assigned to LHR and DNB-0PM establish that the adjusted LHR and DNB-0PM will be conservative throughout the core cycle with respect to actual core conditions.

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 DNBR LC0;

2. -to evaluate the aggregate uncertainties as they are applied in the calculation of the LHR and DNBR LCO.

1-2

The probability distribution functions associated with the uncertainties defined in Section 1.1 are analyzed to obtain the LHR and DNB-0PM 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 Shape Index (ASI) is also described. The methods presented in this report are applicable specifically to SONGS Units 2 and 3.

.1.4

SUMMARY

OF RESULTS The analysis techniques described in Section 2.0 were applied to SONGS Unit 2 cycle 2. Using the stochastic simulation program, overall uncertainties for the LHR LCO and the DNBR LCO of [ ']and[ ],respectively,were calculated at a 95/95 probability / confidence level.

1-3

TABLE 1-1 VARIABLES AFFECTING LHR AND DNBR LCO AND MONITORED NSSS VARIABLES MONITOREDVARIABLE(S)

NSSS VARIABLES INFERRED FROM:

Core Average Power Turbine First Stage Pressure Cold Leg-Temperature Hot Leg Temperature Feedwat'er Flow

- Steam Flow Feedwater Temperature Steam Pressure Reactor Coolant Pump Head Reactor Coolant Pump Speed Pressurizer Pressure Radial. Peaking Factor CEA Positions Cold Leg Temperature

-Azimuthal Tilt Magnitude In-Core Neutron Flux Normalized Axial Power Distribution In-Core Neutron Flux CEA Group Positions Reactor Coolant System Mass Flow Reactor Coolant Pump Head Reactor Coolant Pump Speed Cold Leg Temperature Pressurizer Pressure

-Reactor Coolant System Pressure Pressurizer Pressure Reactor Coolant Inlet Temperature Cold Leg Temperature 1-4

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 COLSS modeling that  ;

affect the LHR and DNBR LCO. The effects of all individual uncertainties on the LCO overall uncutainty factors for LHR and DNBR are also discussed. In addition, this chapter presents the analyses performed to determine the everall uncertainty factors. These uncertainty factors when applied to the COLSS calculations of the LHR and DNB-0PM ensure at a 95/95 probability /

confidence level that the calculations are conservative. .

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

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'1. .to document the stochastic simulation technique used in the overall uncertainty analysis associated with the LHR and DNBR LC0 and,

2. to determine LHR and DNB-OPM overall uncertainty factors, on the basis of a 95/95 probability / confidence level, so that the " adjusted" LHR and DNB-OPM (i.e., the COLSS synthesizea 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 are performed by comparing the three-dimensional

. power. peaking factor (Fq) and DNB-0PM obtained from the reactor core simulator (3) to those calculated by COLSS (as tuned to the reactor core simulator through a

' simulation of the appropriate startup testing). Figures 2-1 and 2-2 show an

- overview of the uncertainty analysis process. The reactor core simulator generates typical three-dimensional core power distributions which reflect a variety of. operating conditio .s. Fq and DNB-OPM modeling uncertainties are statistically combined with other uncertainties in calculating overall 2-1

i uncertainty factors for the COLSS LHR and DNB-0PM calculations. The uncertainty analysis described in this report also includes the stochastic simulation of the state parameter measurement uncertainties for the LHR and DNB-0PM calculations IO) . The neutronic 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 nethod 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, E0C) are used in the determination of the overall uncertainty factors for' the LHR and DNB-OPM calculations. The cases (total

-of 3600) considered herein are chosen to encompass steady state and quasi-steady state plant operating conditions throughout the cycle lifetime. Power distributions are generated by changing power levels (20-100%), CEA con-figurations (first two lead banks full in to full out, PLR-90% inserted to full out), and xenon and iodine concentrations (equilibrium, load maneuver, andoscillation).

2.3.2 LHR LCO STATISTICAL METHODS The reactor core simulator is used to generate the hot-pin power distribution which serves 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. Figure 2-1 illustrates the calculational sequence employed in the Fq modeling uncertainty analysis. The Fq modeling error (X ip) between the COLSS synthesized Fq and the actual Fq is defined as:

(" SYN" F )I X -1 (2-1) p = (" ACTUAL" F )I q

2-2

where (" SYN" Fq)I and (" ACTUAL" Fq)I are the COLSS Fq and the rea: tor core simulator Fq for the 1-th case. The Fq error is analyzed for each case at each time-in-life. Approximately 1200 cases are analyzed at each time-in-life (BOC, MOC, and E0C). Each error distribution is evaluated to obtain the mean Fq error'(Xp) and tLe standard deviation (op).

The mean Fq error (X p ) and the standard deviation (op) of the Fq error can be calculated from:

N .

E i 7, i=1 F (2-2)

F N N 1/2 E I

, 4,g(Xp - 7 p)2 I (2-3)

N-1 where N = sample size Since the mean and standard deviation are estimated from the data, the one-sided tolerance limit can be constructed from the k-factor. - For normal distributions, the one-sided tolerance limit factor, k, accounts for the sampling variations in the sample mean (Xp ) and the standard deviation (o).

p A normality test of the error distribution is performed by using the D-prime statistic value(9-10) to justify the assumption of a normal distribution. If the error distribution is normal, the k 95/95 factor is calculated from an analytical expression (9-11) (see Section 2.3.2 of Part II).

If the error is not normally distributed, a one-sided 95/95 tolerance limit is obtained by using non-parametric techniques [.

3 2.3.3 DNB-OPM LCO STATISTICAL METHODS The three-dimensional reactor core simulator provides a hot-pin power distribution for its DNB-0PM calculation and the corresponding in-core 2-3

detector signals for the COLSS power distribution algorithm. In the reactor core simulator, the DNB-0PM calculation is perfonned with the simplified, relatively fast running DNB algorithm CETOP-1(13) ,

{

]

A flowchart representing the reactor core simulator DNB-0PM calculation is

- shown in Figure 2-2. ,,

The Reactor Coolan.t System (RCS) inlet temperature, pressure, and flow rate are [

. ] for both the reactor core simulator and COLSS. [

]

Operating ranges and measurement uncertainties of the LCO parameters are given in Table 2-2.

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

, (" SYN" DNB-0PM)I

-1 (2-4)

(" ACTUAL" DNB-0PM)9 where (" SYN" DNB-0PM)i and (" ACTUAL" DNB-0PM)I represent the COLSS DNB-0PM and the reactor core simulator DNB-OPM for the 1-th case. The DNB-0F:1 errors are analyzed separately for each time-in-life. Each error distribution is analyzed for nonnal or non-parametric behavior to calculate the mean DNB-0PM error (X D), standard deviation (CD), and one-sided upper 95/95 tolerance

. limit.

2.4 ANALYSES PERFORMED 2.4.1 LHR LC0 UNCERTAINTY ANALYSIS 2.4.1.1 POWER DISTRIBUTION SYNTHESIS UNCERTAINTY 2-4

The reactor core simulator calculates in-core detector signals for the COLSS ,

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

[ ] and added to the in-core signal. . An error. component for each CEA bank position measurement (pulse counters) is obtained [

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

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) are obtained. By analyzing the Fq modeling errors, the COLSS modeling error distributions (histogram) of Fq are obtained for each time-in-life. The mean Fq error (%p), the standard deviation (op), and the lower 95/95 tolerance limit (TL p) for the Fq modeling uncertainty are obtained by analyzing each error distribution. The COLSS Fq modeling uncertainty is determined by combining uncertainties associated with the COLSS power synthesis algorithm, the in-core detector signal measurement, and the CEA position measurement.

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

Therefore, the CECOR Fxy measurement uncertainty (2) which accounts for the difference between the CECOR Fxy and the actual Fxy is combined with the Fq modeling nncertainty to obtain a net conservative uncertainty on Fq.

The CECOR Fxy error is defined as:

I XFC " P i ,

where P and Gj are the actual Fxy and the CECOR calculated Fxy for the i-th 4

case, respectively.

2-5

i 2.4.1.3. 'OTHER UNCERTAINTY FACTORS l

AXIAL FUEL DENSIFICATION UNCERTAINTY The axial fuel densification uncertainty factor (16) considers the global effect of the shrinka'ge of the fuel pellet stack, due to heating and

-irradiation, on the Fq since the COLSS Fq calculation does not account for it directly._ [.

4 1

FUEL AND POISON R00 80W UNCERTAINTIES The fuel and' poison rod' bow uncertainties (17) consider the effect of " bowing" of_ the fuel and poison. rods, due to heating and irradiation, on Fq since the COLSS' Fq~ calculation does not account for. it dircctly. The factors,

- calculated based on the methodology described in Reference 17, will be part of the composite COLSS Fq modeling uncertainty.

COMPUTER PROCESSING UNCERTAINTY The comput'er processing uncertainty considers the effect of the computer machine precision of the C-E CDC-7600 computer and the on-site computer on the COLSS Fq calculations. The' computer processing uncertainty will be part of the composite Fq modeling uncertainty.

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- ENGINEERING FACTOR UNCERTAINTY The engineering' factor uncertainty accounts for the effect of variations in

- the fuel pellet and clad manufacturing process. Variations in fuel pellet

- diameter and enrichment are included in this allowance, as are variations in clad diameter and thickness. These result in variations in the quantity of

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- fissile material and variations ~ in the gap conductance. This factor,

' calculated based on the methodology described in Reference 16, will be part of the composite Fq modeling uncertainty.

2-6

'2.4.1.4~ OVERALL LHR LCO UNCERTAINTY FACTOR An' overall COLSS Fq uncertainty factor is determined by combining all lcwer 95/95 probability / confidence tolerance limits of the error components. This overall . uncertainty factor includes a Fq modeling uncertainty, a CECOR Fxy measurement uncertainty, a reactor core simulator modeling error, fuel and poison rod bow uncertainties, a computer processing uncertainty, an axial fuel densification uncertainty, and an engineering factor uncertainty. Figure 2-3 shows the calculation sequence to determine an overall LHR LCO uncertainty

. factor.

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

C F I

Xpg = F (2-6) 1

- where F, and C j are the reactor core simulator calculated Fq and the COLSS in-ferred value of Fq for the i-th case, respectively. Acompositeerror(Xh) of the Fq modeling uncertainty and the CECOR Fxy uncertainty can be deter-ministically calculated as follows:

XFT =

.* -1 (2-7)

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

X FT

=X pg +X FC *I M C) (2-8)

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

IFT

• TFM + FC + ( FM FC) (2-9)

The composite (ko)FT f r the Fq modeling error is made up of uncertainties for'COLSS power algorithm (kopg), CECOR Fxy error (k FC),rodbowpenalties (kopp,kopp),computerprocessing(koCP), and reactor core simulator (3) modeling error *(koFR). By using the [ ] technique, this (ko)FT is calculated by:

[ ](2-10)

• See Appendix A (Section A.4) 2-7

The resultant composite Fq modeling penalty factor (PMp ) is determined by using_ the lower 95/95 composite tolerance limit for Fq (TL p ) as follows:

1 PM (2-11) p = 1 + TL p

where TLp=TFT - (ko)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 in determining 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,

[ ] (2-13)

This LCO LHR overall uncertainty factor (UNCERT) is used as [ .

] on the COLSS calculated LHR (KW/FT) such that:

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 DN8-0PM LCO UNCERTAINTY ANALYSIS 2.4.2.1 DN8-OPM MODELING UNCERTAINTY WITH SCU The COLSS DNB-0PM modeling uncertainty with SCU is made up of uncertainties associated with power distribution synthesis, in-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 [ ]programisemployed. The 5C0 program 2-8

[ ] the measurement uncertainties and operating ranges associated with RCS state parameters along with the on-line to off-line DNB algorithm error components.

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

[ ] (2-15)

[

]

2.4.2.2 OTHER UNCERTAINTY FACTORS DNBR COMPUTER PROCESSING UNCERTAINTY The computer processing uncertainty for the calculation of DNB-0PM considers the effect of the off-line (CDC 7600 computer) to the on-line computer machine precision on the~ COLSS DNB-0PM calculations. The computer processing uncertainty is represented by the terms of (ko)CP and is part of the DNB-0PM composite modeling uncertainty (ko)DT. This computer processing uncertainty (ko)CP is calculated using the following equation:

[ ] (2-16) where[

] defined in the following equation:

[ ] (2-17)

- 2-9

FUEL AND POISON ROD BOW UNCERTAINTIES The fuel'and poison rod bow uncertainties for DN8-0PM are determined by the same method described in Section 2.4.1.3.

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 DNBR correlation (14) .

The M)NBR for the LCO includes the uncertainties associated with system parameters which describe the physical system. These system parameter

, uncertainties include: core geometry, pin-by-pin radial power distributions, inlet and exit flow boundary conditions, etc. In the statistical combination of system parameter uncertainties, the following uncertainties are combined statistically in the MDN8R 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 uncertainties in fuel clad diameter

6. Random and systematic uncertainties in fuel rod pitch 7.- DN8 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 MDN8R limit includes system parameter uncertainties as described in Part I of this report, these uncertainties are implicitly included in the calculation of the COLSS DNB-OPM

>- overall uncertainty factor.

2.4.2.3 OVERALL DNS-OPM LCO UNCERTAINTY FACTOR The overall COLSS uncertainty factor for DNS-OPM (EPOL2) is determined by I combining all' one-sided (upper) 95/95 probability / confidence tolerance limits.

This overall uncertainty factor includes a DNB-0PM modeling uncertainty, a CECOR Fxy measurement uncertainty, a reactor core simulator modeling error,a 2-10

.. .= -_. .

DNBR computer processing uncertainty, and fuel and poison rod bow uncertainties. Figure 2-3 shows the calculational sequence used to determine the overall.DN8-OPM uncertainty factor.

The composite DN8-OPM modeling uncertainty is obtained by following a similar

. strategy to that used for the Fq uncertainty analysis. The CECOR Fxy measurement uncertainty is calculated in terms of DNB-0PM 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: ,,

-[l ] (2-18a) and the CECOR F xy "koDC" is given by:

[ ] (2-18b)

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

• (2-19)

' TDT " DM + DC + DM DC)

Thecomposite(ko)DT is made up of uncertainties for the DNS-OPM modeling algorithm (koDM), CECOR Fxy (koDC), rod and poison bow penalties (kop p, kopp),

DN8R computer processing uncertainty (koCP), and a reactor core simulator modelingerror(koFR). Using[ ], this composite (ko)DT is calculated as:

[ ] (2-20)

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

) is used for conservative COLSS DNB-0PM calculations and is determined by:

(2-21)

TLD" DT+(ko)DT 2-11

- - - 1 I

1 l

)

.The penalty factor (PM D

) f r this composite tolerance limit can be determined

.as:  ;

(2-22)

PMD = 1 + (TL)D Therefore, the overall DNB-0PM. uncertainty factor for COLSS (EPOL2) is:

[ ] (2-23)

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

COLSS " SYN" DNB-0PM * < " ACTUAL" DNB-0PM (2-24)

Use of the overall uncertainty factor (EPOL2) for the COLSS calculated DNB-0PM assures, at least a 95% probability, at a 95% confidence level, that the

" ACTUAL" DNB-OPM will be larger than the COLSS DNS-OPM.

12

y _ _

l l

TABLE 2-1 STATISTICALLY MODELED VARIABLES NEUTRONICS CEA POSITIONS IN-CORE SIGNALS

. THERMAL HYDRAULICS RCS PRESSURE CORE INLET TEMPERATURE CORE FLOW 2-13

TABLE 2-2 RANGES AND MEASUREMENT UNCERTAINTIES OF PARAMETERS MEASUREMENT PARAMETERS UNIT RANGES UNCERTAINTY In-core Signal (% power)

CEA Posi:fon -

(in)

Core Inlet . (*F)

Coolant Temperature Primary Coolant (psia)

. Pressure Primary Coolant (GPM)

Mass Flow _ _

2-14

._. a A ,A p.L_. . o ,

- a 9

FIGURE 2-1 COLSS SIMULATION FOR Fq e

t h eum 2-15

g _

FIGURE 2-2 COLSS SIMULATION FOR DNB-0PM ig Mi 2-16

i FIGURE 2-3 FLOWCHART FOR COLSS OVERALL UNCERTAINTIES FOR LHR AND DNB-0PM s

EI 2-17

-g 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 LCO at a 95/95 probability /

confidence level. ' The results of the analyses perfor1ned for SONGS Unit 2 cycle 2 are presented in this section.

3.1 LHR LCO FollowingtheanalysistechniquesdescribedinSectio[2.4.1,theCOLSS synthesized Fq modeling errors are tabulated in. Table 3-1 for three times in corelife(80C,M0C,EOC). All time-in-life dependent Fq modeling uncer-tainties were considered in evaluating the overall Fq penalty. However, the time-in-life that led to the most non-conservative modeling uncertainty was p 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 LCO results in anaggregateuncertaintyof[ ] at a 95/95 probability / confidence level.

This uncertainty factor of [ ] when applied to the COLSS synthesized Fq, will assure that the COLSS Fq wil1 be larger than the actual Fq at a 95/95 probability / confidence level at all times during the fuel cycle.

3.2 DN8R LCO Following the analysis techniques presented in Section 2.4.2, the C0iSS synthesized DN8-OPM modeling errors were calculated and are summarized in Table 3-3. The modeling error was analyzed as a function of time-in-life, but only the time-in-life which led to the most non-conservative modeling uncerta.nty was considered in calculation of the DN8-0PM overall uncertainty.

~ The individual contributing uncertainty factors to the DN8-OPM overall l.

uncertainty factor are presented in Table 3-2. Combining the uncertainties

- associated with the DN8-OPM LCO gives an overall uncertainty factor of [ ]

at a 95/95 probability / confidence level. This overall uncertainty factor, when applied to the COLSS synthesized DN8-0PM, will assure that the COLSS DN8-0PM will be smaller than the actual DN8-OPM at a 95/95 probability /

confidence level at all times during the fuel cycle.

3-1

TABLE 3-1 COLSS SYNTHESIZED Fq MODELING-ERRORII) M YSIS 95/95 Nt#SER OF MEAN ERROR TOLERANCE (2),(3)

TIME I.1 .

CORE LIFE DATA POINTS (N) Rpg) . LIMIT (E)pg

~ ~

BE MOC EE _

Y m

N" q (1) ERROR = (". p pq

,3) ,

(2) See References 9 and 10. Most conservative of normal or non-parametric values presented.

(3) If the error distribution is determined to be non-parametric, the value for (ka)pg is calculated as (ka)pg =-(TL)pg TX py s

TABLE 3-2 CONTRIBUTION OF INDIVIDUAL UNCERTAINTIES TO LCO OVERALL UNCERTAINTY FACTORS UNCERTAINTY LHR LCO DNBR LCO Modeling Error (T)pg,(T)DM (ko)pg,(ko)DM CECOR Fxy .

(T)FC,@)DC (ko)FC,(ko)DC Fuel Rod Bow (ko)pp Poison Rod Bow (ko)pp Computer Processing (ko)CP Reactor Core Simulator (ko)pg Modeling Axial Densification PA Engineering Factor PE (1) includes power distribution synthesis uncertainty, in-core signal noise and CEA position error.

(2) includes [ ]inadditiontothe errorsof(1).

3-3

TABLE 3-3 COLSS SYNTHESIZED DNB-OPM MDDELING ERRORII) ANALYSIS ,

95/95 TIME IN NLM ER OF . MEAN ERROR TOLERANCE (2),(3)

CORE LIFE DATA POINTS (N) (XDM)

LIMIT (TL)DM MOC E0C w

i (1) ERROR = (" SYN" DNB-0PM -1)

(2) See References 9 and 10. Most conservative of the normal or non-parametric values presented.

(3) Same as LHR except (ko) ,= (TL)DM - TDM

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 Engineering, Inc., " INCA /CECOR Power Peaking Uncertainty",

CENPD-153-P, Rev. 1-P-A, May, 1980.

3. Con 6ustion Engineering, Inc., " Assessment of the Accuracy of PWR Safety System Actuation as Performed by the Core Protection Calculato'rs",

CENPD-170-P and Supplement, July,1975.

4. Southern California Edison Company, " Final. Safety Analysis Report (FSAR) for San Onofre Nuclear Generating Station Units 2 and 3", January, 1

1984.

5. Combustion Engineering, Inc., " Statistical Combination of Uncertainties, Part III;-Uncertainty Analysis'~of Limiting Conditions for Operation, C-E System 80 Nuclear Steam Supply Systems", Enclosure 2-P to LD-83-010,

,3 Revision 01, August, 1983.

6. Combustion Engineering Inc., " Response to NRC Questions on CESSAR-F Statistical Combination of Uncertainties in Thermal Margin Analysis for

, System _80", Enclosure 1-P to LD-83-037, April,1983.

7. Combustion Engineering. Inc., " Responses to NRC Questions on CESSAR-80 Uncertainties", Enclosure 1-P to LD-83-082, August,1983.

-8. Combustion Engineering, Inc., " Response to Questions on Documents SupportingtheANO-2 Cycle 2LicensingSubmittals",CEN-157(A)-P,

. Amendment'1,'une, J 1981.

9.: American National Standard Assessment of the Assumption of Normality,

. ASI, N15-15, October,1973.

10. Sandia Corporation, " Factors for One-Sided Tolerance Limits and for Variable Sampling Plans", SCR-607, March,1963.

11. E. L.- Crow, et al, " Statistics Manual". Dover Publications, Inc. , New York,- 1960.

I

12. R. E. Walpole and R. H. Myers, " Probability and Statistics for Engineers i and Scientists 2ed", Macmillan Publishing Company, Inc., New York, 1978.

13. . C. Chiu, "Three-Dimensional Transport Coefficient Model and Prediction f Correction Numerical Method for Thermal Margin Analysis of PWR Cores",

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

l R-1

14. Combustion Engineering, Inc., "CETOP-D Code Structure and Modeling Methods for San Onofre Nuclear Generating Station Units 2 and 3",

CEN-160, May, 1981.

15. M. G. Kendall and A. Stuart, "The Advanced Theory of Statistics, Vol III", Hafner Publishing Company, New York,1961, p. 457.

16. Combustion Engineering, Inc., " Fuel Evaluation Model", CENPD-139-P, October, - 1974.

17. Combustion Engineering Inc., " Fuel and Poison Rod Bowing",

CENPD-225-P-A, June, 1983. ,,

e e

R-2

h APPENDIX A ,

STOCHASTIC SIMULATION OF UNCERTAINTIES A.1 Detector Signal Measurement and CEA Bank Position Measurement Uncertainties ln the SCU program, error components of in-core detector signals are [

]. This error component is .y then added to the in-core signal generated from the core simulator and is used i-as input to the COLSS power distribution algorithm (A-1) ,

j The location of each CEA bank is measured using pulse counters. An error [

component of each CEA bank measurement is selected [ _k

]. The sampled error is then added to the respective CEA bank position for input to the COLSS power distribution  ;="

algorithm. _

A.2 State Parameter Measurement Uncertainties The DNB algorithm used for COLSS requires primary system pressure, core inlet temperature, core power, primary coolant flow rate, and hot-pin power a 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-0PM uncertainty analysis. 3

[  :

s C

] This procedure allows for direct simulation of the effect of the COLSS on-line temperature, pressure, and flow measurements and their uncertainties on the 5 resultant DNB-0PM uncertainty. Therefore, uncertainties with respect to _

temperature, pressure, and flow are implicitly accounted for in the DNB-0PM modeling uncertainty.

2 A-1

.-a-.

l l

A.3 DNB-0PM Algorithm Uncertair..ies In the DNB-0PM overall uncertainty calculation, two distinct thermal hydraulic algorithms are involved. The off-line design T-H algorithm (CETOP-D)(A-2) represents the base-line DNB-OPM calculation. CETOP-1(A-3) is a simplified version of CETOP-D and performs the thermal hydraulic calculations in the reactor core simulator and COLSS (See Appendix A.3 of Part II). [

]

E _. __ _

]

A4 Reactor Core Simulator Modeling Error The reactor core simulator uses the FLARE neutronic model to predict representative power distributions. The FLARE model is tuned to a more accurate and rigorous ROCS neutronic simulator code. The reactor core simulator modeling error accounts for the effect of the FLARE modeling uncertainty on the reference LHR and DNB-0PM calculations.

A.5 REFERENCES FOR APPENDIX A A-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.

A-2

A-2 Combustion Engineering, Inc., "CETOP-D Code Structure and Modeling Methods for San Onofre Nuclear Generating Station Units 2 and 3",

CEN-160, May, 1981.

A-3 C. 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.

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

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

A-3 l

L l.

{

APPENDIX B AXIAL SHAPE INDEX L'NCERTAINTY 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:

P -P ASI = p ,p (B-1)-

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

3 e ASI error is defined by:

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

The core average ASI uncertainty analysis is 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 are presented in Table B-1.

B-1

1 5 ~ _

9

/

5 9

RT EI PM PI UL 5

9

/

5 9

RT .

EI WM OJ LL S

I S

Y L

A N

A N

• DO R RI 1 O AT

- R DA B R NI E AV E TE L I SD B S A A T

E G

A R

E V

A E )

I R

O R S C NO A AR R ER ME O T

A L

U M

I S

S T I FN S OI A O

RP S E S BA L MT O -

UA ~ _ C ND (

=

R O

R R

E P

U I N S R C C C A U O O C B B M E

• T~ -

l l

A -

COMBUSTION ENGINEERING, INC.

_ _ _ _ . _ _ _ _ _