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CEN-283(S)-NP, Part 2, Revision 0, Statistical Combination of Uncertainties Part 2; Uncertainty Analysis of Limiting Safety System Settings San Onofre Nuclear Generating Station Units 2 and 3
ML19214A145
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Issue date: 10/31/1984
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/J f:: A Cf{) I;;_,; Westinghouse Non-Proprietary Class 3 San Onofre Nuclear Generating Station Units 2 and 3 CEN-283 ( S }..NP STATISTICAL COMBINATION OF UNCERTAINTIES.

PART I I Uncertainty Analysis of Limiting Safety System Settings San Onofre Nuclear Generating Station Units 2 and 3 REACTOR DESIGN OCTOBER 1984 COMBUSTION ENGINEERING, INC. Nuclear Power Systems Windsor, Connecticut Westinghouse Non-Proprietary Class 3 LEGAL NOTICE THIS REPORT WAS PREPARED AS AN ACCOUNT OF WORK SPONSORED BY COMBUSTION ENGINEERING, INC. NEITHER COMBUSTION ENGINEERING NOR ANY PERSON ACTING ON ITS BEHALF: A. MAKES ANY WARRANTY OR REPRESENTATION, EXPRESS OR IMPLIED INCLUDING THE WARRANTIES OF FITNESS FOR A PARTICULAR PURPOSE OR MERCHANTABILITY, WITH RESPECT TO THE ACCURACY, COMPLETENESS OR 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. CEN-283(S)-NP, Part 2 Revision 0 i October 1984 Westinghouse Non-Proprietary Class 3 ABSTRACT Part II of the Statistical Combination of Uncertainties (SCU) report describes* the methodology used for statistically combining uncertainties involved in the determination of the Linear Heat Rate (LHR) and Departure from Nucleate Boiling Ratio (DNBR) Limiting Safety System Settings (LSSS) for San Onofre Nuclear Generating Station (SONGS) Units 2 and 3. The overall uncertainty factors assigned to LHR and DNBR establish that the adjusted LHR and DNBR are conservative at a 95/95 probability/confidence level throughout the.core cycle with respect to actual 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 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. The methods described here (Part II) are the same as those reviewed and approved for C~E System 80 plants. CEN-283(S)-NP, Part 2 Revision 0 ii October 1984 Westinghouse Non-Proprietary Class 3 TABLE OF CONTENTS CHAPTER Abstract Table of Contents List of Tables List of Figures Definition of Abbreviations 1.0 Introduction 1.1 Purpose 1.2 Background 1.3 Report Scope 1.4 Summary of Results 2.0 Analysis 2.1 General 2.2 Objectives of Analysis 2.3 Analysis Techniques 2.3.1 General Strategy 2.3.2 LHR LSSS Statistical Methods 2.3.3 DNBR LSSS Statistical Methods 2.4 Analyses Performed 2.4.1 LHR LSSS Uncertainty Analysis 2.4.1.1 Power Distribution Synthesis Uncertainty 2.4.1.2 CECOR Fxy Measurement Uncertainty 2.4.1.3 Startup Test Acceptance Band Uncertainty 2.4.1.4 Other Uncertainty Factors 2.4.1.5 Overall LHR LSSS Uncertainty Factor 2.4.2 DNBR LSSS Uncertainty Analysis CEN-283(S)-NP, Part 2 Revision 0 iii PAGE ii ii; V vi vii 1-1 1-1 1-1 1-2 1-3 2-1 2-1 2-1 2-1 2-1 2-3 2-5 2-6 2-6 2-6 2-7 2-8 2-11 2-12 2-14 October 1984 Westinghouse Non-Proprietary Class 3 2.4.2.1 DNB-OPM Modeling Uncertainty with SCU 2.4.2.2 Dynamic Pressure Uncertainty 2.4.2.3 Other Uncertainty Factors 2.4.2.4 Overall DNBR LSSS Uncertainty Factor 3.0 Results and Conclusions 3.1 LHR LSSS 3.2 ONBR LSSS References Appendices A. Stochastic Simulation of Uncertainties A.l Detector Signal Measurement and CEA Bank Position Measurement Uncertainties A.2 State Parameter Measurement Uncertainties A.3 DNB-OPM Algorithm Uncertainties A.4 Reactor Core Simulator Modeling Error A.5 References for Appendix A B. Core Power Level Measurement Uncertainty B.l Uncertainty Components B.2 Uncertainty Biases for DNBR Calculation B.3 Uncertainty Bias for LHR Calculation C. Axial Shape Index Uncertainty CEN-283(S)-NP, Part 2 Revision O iv 2-14 2-15 2-16 2-17 3-1 3-1 3-1 R-1 A-1 A-1 .A.-1 A-2 A-3 A-4 8-1 B-1 B-3 B-4 C-1 October 1984 Westinghouse Non-Proprietary Class 3 LIST OF TABLES TABLE PAGE 1-1 Variables Affecting LHR and DNBR LSSS 1-4 2-1 Stochastically Modeled Variables 2-20 2-2 Ranges and Measurement Uncertainties of Parameters 2-21 3-1 CPC Synthesized Fq Modeling Error Analysis 3-2 3-2 Contribution of Individual Uncertainties to LSSS Overall Uncertainty Factors 3-3 3-3 CPC Synthesized DNB-OPM Modeling Error Analysis 3-4 B-1 Core Power Synthesis Error.Analysis B-6 B-2 Power Measurement Uncertainty as a Function of Power B-7 C-1 Hot-Pin ASI Error Analysis C-2 C-2 Core Average ASI Error Analysis C-3 CEN-283(S)-NP, Part 2 Revision 0 V October 1984 FIGURE 2-1 2-2 2-3 2-4 A-1 B-1 Westinghouse Non-Proprietary Class 3 LIST OF FIGURES CPC Simulation for Fq CPC Simulation of DNB-OPM Flow Chart for CPC Overall Uncertainties for LHR and DNB-OPM Calculational Procedure for Penalty Factors due to RSF, SAM, and BPPCC Uncertainty DNB-OPM Algorithms Secondary Calorimetric Power Error vi CEN-283(S)-NP, Part 2 Revision 0 PAGE 2-22 2-23 2-24 2-25 A-5 B-8 October 1984 ASI APHPD BOC BPPCC CDF C-E CEA CETOP CETOP-0 CETOP-1 CETOP-2 COLSS CPC DNB DNBR DNB-OPM EOC ESFAS Fq Fxy LCO LHR LOCA LSSS MOC NSSS PDF PHPD PLR RCS RPS RSF RSPT Westinghouse Non-Proprietary Class 3 DEFINITION OF ABBREVIATIONS Axial Shape Index Axial. Pseudo Hot-Pin Power Distribution Beginning Of Cycle Boundary Point Power Correlation Coefficient Cumulative Distribution Function Combustion Engineering Control Element Assembly C-E Thermal On-Line Program Off-Line DNB Algorithm for Safety Analysis DNB Algorithm used in Core Simulator and COLSS on-line On-Line DNB Algorithm used in CPC Core Operating Limit Supervisory System Core Protection Calculator Departure from Nucleate Boiling DNB Ratio DNB Over Power Margin End Of Cycle Engineered Safety Features Actuation System Three Dimensional Power Peaking Factor Planar Radial Peaking Factor Limiting Conditions for Operation Linear Heat Rate (kw/ft) Loss Of Coolant Accident Limiting Safety System Setting(s)

Middle Of Cycle Nuclear Steam Supply System Probability Distribution Function Pseudo Hot-Pin Power Distribution Part Length Rod (CEA) Reactor Coolant System Reactor Protection System Rod (CEA) Shadowing Factor Reed Switch Position Transmitter vii CEN-283(S)-NP, Part 2 Revision 0 October 1984 SAFDL SAM scu TSF Westinghouse Non-Proprietary Class 3 Specified Acceptable Fuel Design Limits Shape Annealing Matrix Statistical Combination of Uncertainties Temperature Shadowing Factor viii CEN-283(S)-NP, Part 2 Revision 0 October 1984 Westinghouse Non-Proprietary Class 3

1.0 INTRODUCTION

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(l). All uncertainty components considered in the determination of the overall uncertainty factors for the calculation of LHR and DNBR are listed as follows: 1. Uncertainty in the ex-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 Core Protection Calculator (CPC)(l) LHR calculation due to the CPC power distribution synthesis for CPC LHR algorithm
5. Uncertainty in the CPC DNB calculation due to the CPC power distribution synthesis for the CPC DNB algorithm
6. Uncertainty in the CPC DNB algorithm with respect to the safety analysis DNB algorithm
7. Uncertainty in the 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. Axial fuel densification uncertainty 12a Engineering factor due to manufacturing tolerance

1.2 BACKGROUND

The plant protection system in operation on the SONGS units 2 and 3 is composed of two sub-systems:

1. an Engineered Safety Features Actuation System (ESFAS) and 2. a Reactor Protection System (RPS). CEN-283(S)-NP, Part 2 Revision 0 1-1 October 1984 Westinghouse Non-Proprietary Class 3 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 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 lOCFRSO Appendix A (Criteria Number 10, 20, and 25)(2). The LSSS, combined with the LC0(3), establish 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 Units 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 penalty factors for the C-PC three-dimensional peaking factor {Fq) and DNBR calculations to ensure* conservative plant operation.

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(l-9). 1.3 REPORT SCOPE The scope of this report encompasses the following objectives:

1. to describe the methods used for statistically combining uncertainties applicable to the LHR and DNBR LSSS; 2. to evaluate the aggregate uncertainties as they are applied in the calculation of LHR and DNBR. CEN-283(S)-NP, Part 2 Revision 0 1-2 October 1984 Westinghouse Non-Proprietary Class 3 The probability distribution functions associated with the uncertainties defined in Section 1.1 are analyzed to obtain the LHR and DNBR overall uncertainty factors based on a 95/95 probability/confidence tolerance limit. The methods used for the determination of uncertainties on the power measurement, the core average Axial Shape Index (AS!), and the hot-pin ASI are also described.

The methods presented in this report are applicable 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. The stochastic simulation program results in overall uncertainties for the LHR LSSS and the ONBR LSSS of [ J and [ ], respectively, at a 95/95 probability/confidence level. CEN-283(S)-NP, Part 2 Revision 0 1-3 October 1984 CEN-283(S)-NP, Part 2 Revision 0 Westinghouse Non-Proprietary Class 3 TABLE 1-1 VARIABLES AFFECTING THE LHR AND DNBR LSSS LHR 1. Core Power Level 2. Axial Power Distribution

3. Radial Power Distribution 4
  • CEA Po s i ti on DNBR 1. Core Power Level 2. Axial Power Distribution
3. Radial Power Distribution 4
  • CEA Po s i ti on 5. Core Coolant Inlet Temperature
6. Core Coolant Pressure 7. Primary Coolant Mass Flow 1-4 October 1984 Westinghouse Non-Proprietary Class 3 2.0 -ANALYSIS 2.1 GENERAL The following sections describe the impact of the uncertainty components of 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 the calculation of LHR and DNBR are also discussed.

In addition, this chapter presents the analyses performed to determine overall uncertainty factors which are applied in the on-line CPC calculations of the LHR and DNBR to 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: 1. to document the stochastic simulation technique used in the overall uncertainty analysis associated with the LHR and DNBR LSSS and, 2. to determine the overall uncertainty factors used in the calculation of the LHR and DNBR, on the basis of a 95/95 probability/confidence level, so that the 11 adjusted 11 LHR and DNBR (i.e., the CPC synthesized value corrected by the respective overall uncertainty factor) will be conservative throughout the core cycle with respect to actual core conditions.

2.3 ANALYSIS TECHNIQUES 2.3.1 GENERAL STRATEGY The reactor core simulator(l) generates typical three-dimensional core power distributions which reflect a variety of plant operating conditions.

The uncertainty analyses are performed by comparing the three-dimensional peaking factor {Fq) and DNB-OPM obtained from the reactor core simulator to those culated by the off-line CPC as tuned to the reactor core simulator through a CEN-283(S)-NP, Part 2 Revision 0 2-1 October 1984 Westinghouse Non-Proprietary Class 3 simulation of the appropriate startup testing (see section 2.4.1.3).

Figures 2-1 and 2-2 show an overview of the uncertainty analysis process. Note that the overall DNB uncertainty factor is calculated in overpower margin (DNB-OPM) and not DNBR un.its since the uncertainty factor is used [as a multiplier]

on heat flux in the on-line CPC ONBR calculation.

The 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 described in this report also involves the stochastic simulation of the state parameter measurement uncertainties for the LHR and DNB-OPM calculations.

The neutronic and thermal-hydraulic input parameters that are statistically modeled(4) are given in Table 2-1. A detailed tion of the individual measurement uncertainties is presented in Appendix A. A comparison of the on-line to off-line thermal-hydraulic algorithms is also presented in Appendix A. Approximately twelve hundred (1200) cases of power distributions at each of three burnups (BOC, MOC, and EOC) are used in the determination of the overall uncertainty factors for the LHR and DNB-OPM. These cases 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 configurations (first two lead banks full in to full out, PLR-90% inserted to full out), and xenon and iodine concentrations (equilibrium, load maneuver, oscillation).

The power measurement adjustment terms 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*. A detailed description of these uncertainty factors is given in Appendix B. The method used for the CPC calculation of the core average ASI and hot-pin ASI uncertainties is described in Appendix C.

  • This error component accounts for the error in the CPC power calculation during design basis events. CEN-283(S)-NP, Part 2 Revision 0 2-2 October 1984 Westinghouse Non-Proprietary Class 3 2.3.2 LHR LSSS 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 CPC synthesized Fq is compared with that of the reactor core simulator.

Figure 2-1 illustrates the tional sequence employed in the Fq model1ng uncertainty analysis.

The Fq modeling error (xi) between the CPC synthesized Fq and the actual Fq is defined as: Xi = ( If SYN II F g ) ; F ----(---11-AC_T_U-AL-1 ...... 1* -F-q )-i-. -l ( 2-1) where (11 SYN 11 Fq)i and (11 ACTUAL 11 Fq)i are the CPC Fq and the reactor core simulator Fq for the i-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 EOC). The mean Fq error(~) and the standard deviation (crF) of the Fq error can be calculated from: N I: Xi i=l F XF= N N

  • 2 L (X 1 -X) i=l F F N-1 where N = sample size ( 2-2a) 1/2 (2-2b) Sine~ the mean and standard deviation are estimated from the data~ the 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 mean (XF) and the standard deviation (aF). A normality test of the error distribution is performed by using the D-prime statistic value(lO-ll) to justify the assumption of a normal distribution.

CEN-283(S)-NP, Part 2 Revision 0 2-3 October 1984 Westinghouse Non-Proprietary Class 3 The k 95195 factor for a normal distribution(ll-l

2) is calculated as: k = kl-p + (ki-p -ab)l/2 a where k 2 a = 1 -(l 2 (N-1) 2 k 2 b a. = k1 .. p-N (2 .. 3a) (2-3b) (2-3c) kl-p = percentiles of a normal distribution for the probability p (1.645 for 95% probability) k = percentiles of a normal distribution for the confidence Cl coefficient (1.645 for 95% confidence)

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

Lower 95/95 tolerance limit= X -k 95195 a Upper 95/95 tolerance limit= X + k 95195 a (2-4a) (2-4b) where X, cr, and k 95195 are the sample mean, standard deviation, and one-sided tolerance limit factor, respectively.

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

[ CEN-283(S)-NP, Part 2 Revision 0 2-4 October 1984 Westinghouse Non-Proprietary Cl.ass 3 ] The locator Lis calculated from the following equation which is derived from the methods in Reference

13. [ ] (2-5) where 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 11 ko 11 is calculated from equation (2-4) by using the determined one-sided tolerance limit and the known mean error. 2.3.3 DNBR LSSS STATISTICAL METHODS 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, relatively fast running DNB algorithm CETOP-l(I 4). [ J A flowchart representing the reactor core simulator DNB-OPM calculation is shown i n Fi g u re 2-2 . The Reactor Coolant System (RCS) input temperature, pressure, and flow rate are [* __ _ ] for both the reactor core simulator and CPC. [ CEN-283(S)-NP, Part 2 Revision 0 2-5 October 1984 Westinghouse Non-Proprietary Class 3 : ] Operating ranges and measurement uncertainties of 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 algorithms (on-line to off-line).

c* ] Thus, the effects of the error components associated with the temperature, pressure, and flow measurements and the on-line to off-line DNB algorithm are accounted for in the determination of the CPC DNB-OPM modeling error via the SCU program. The CPC DNB-OPM modeling error (with SCU) is defined as: = ______ (_11 _SY_N_11_DN_B_-_O_PM

__ ) __ i_ (11 ACTUAL 11 DNB-OPM)i 1 (2-6) where (11 SYN 11 DNB-OPM)i and (11 ACTUAL 11 DNB-OPM)1 represent the CPC DNB-OPM and the reactor core simulator DNB-OPM for the i-th case. The DNB-OPM errors are analyzed separately for each time-in-life.

Each error distribution is tested for normality and the mean DNB-OPM error (X 0), standard deviation (o 0), 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 the CEN-283(S)-NP, Part 2 Revision 0 2-6 October 1984 Westinghouse Non-Proprietary Class 3 ex-core signal. An error component of each Control Element Assembly (CEA) bank measurement (reed switch position transmitters) is obtained[~

J The CEA position error component is then added to. its respective CEA bank position.

The CPC synthesizes a pseudo hot-pin power distribution (PHPD) by using (as input) the adjusted ex-core detector signals and the adjusted CEA bank positions.

The CPC hot-pin power distributions are obtained by using a cubic spline fitting technique in conjunction with constants such as planar radial peaking factors (Fxy), Rod Shadowing Factors (RSF), Boundary Point Power Correla~1on Coefficients (BPPCC), and Shape Annealing Matrix (SAM). A Temperature Shadowing Factor (TSF) correction is used in the CPC to account for the inlet temperature effect on neutron flux power. By comparing the reactor core simulator calculated Fq with the CPC synthesized Fq for each case, the Fq modeling error defined in equation (2-1) is obtained.

By analyzing the Fq modeling errors, the CPC modeling error distributions (histogram) of Fq are obtained for each time-in-life.

The mean Fq error (XF), the standard deviation (crF), and the lower 95/95 tolerance limit (TLF} for the Fq modeling uncertainty are obtained by analyzing the error distribution at each time-in-life.

The CPC Fq modeling error is composed of the uncertainties associated with the CPC power synthesis algorithm, the ex-core detector signal measurement, and the CEA position measurement.

2.4.1.2 CECOR Fxy MEASUREMENT UNCERTAINTY In the calculation of the CPC Fq modeling uncertainty, the CPC uses predicted values of Fxy. The Fxy values used by CPC are verified by the CECOR(ll) measured Fxy values during startup testing. Therefore, the CECOR Fxy measurement uncertainty which accounts for the differences between the CECOR Fxy and the actual Fxy is statistically combined with the Fq modeling uncertainty to obtain a net conservative uncertainty on Fq. The CECOR Fxy error is defined as: G. P. 1 -1 CEN-283(S)-NP, Part 2 Revision 0 (2-7) 2-7 October 1984 Westinghouse Non-Proprietary Class 3 where P; and G; are the actual Fxy and the CECOR calculated Fxy for the i-th case, respectively.

2.4.1.3 STARTUP TEST ACCEPTANCE BAND UNCERTAINTY The CPC power distribution algorithm(!)

requires values of the RSF, TSF, SAM, and BPPCC constants as input data. These constants are assumed to be known exactly for the CPC calculation of core hot-pin power distributions and core power. These CPC power distribution algorithm constants are therefore verified during startup testing. The acceptance band criteria on these constants also ha~e associated uncertainties which affect the CPC calculated Fq and DNB-OPM. Penalty factors due to RSF, TSF,* SAM, and BPPCC acceptance band uncertainties are considered in the CPC overall uncertainty analysis.

(1) Rod (CEA) Shadowing Factor (RSF) The CPC RSF constants used in the power synthesis algorithm are verified during startup testing. The predicted RSF values are calculated by simulating the RSF test and analyzing the ex-core detector response for various CEA configurations.

The calculation of the LHR penalty associated with the RSF measurement uncertainty (P 1) includes ex-core detector measurement error, depletion, and feedback effects. Figure 2-4 shows the calculational procedure for determining penalty factors due to RSF uncertainty.

The three-dimensional reactor core simulator provides reference values of Fq, DNB-OPM, and ex-core detector signals for each of the 1200 cases analyzed at each time-in-life.

The CPC Fq calculations with the predicted nominal RSF values are performed for the same 1200 cases at each time-in-life (CPC base cases). These CPC Fq values calculated with the nominal RSF values are compared with those of the reactor core simulator to generate a base error distribution.

In order to calculate the sensitivity of Fq with respect to RSF, the RSF value (R) for a given rod configuration is changed from the nominal CPC data base constant value (base case value) to a new RSF value (R + ~R) and the CPC Fq is re-calculated for 1200 cases at each time-in-life.

[ CEN-283(S)-NP, Part 2 Revision 0 2-8 October 1984 Westinghouse Non-Proprietary Class 3 J: [ J (2-Ba) where [ J (2-8b) [ ] The RSF uncertainty

[ J typically has been chosen based on differences between predicted and measured RSF values from previous startup test power ascension results. (2) Temperature Shadowing Factor (TSF) The TSF algorithm has been modified for SONGS-2 cycle 2 (Ref. 20). This modification will accommodate any uncertainty factors associated with the TSF in the data base constants.

Therefore, no penalty factor is required to correct the neutron flux power calculation due to the TSF uncertainty~

(3) Shape Annealing Matrix (SAM) The CPC Shape Annealing Matrix (SAM) elements used in the power synthesis algorithm are verified during power ascension testing. The predicted SAM elements are calculated by simulating a free unrodded xenon oscillation similar to SAM startup test measurement procedure.

The predicted SAM elements CEN-283(S)-NP, Part 2 Revision 0 2-9 -=c>ctober 1984 Westinghouse Non-Proprietary Class 3 are then determined from a regression analysis of the ex-core signals and the corresponding bottom, middle and top third integrals of the core peripheral power. In the calculation of the LHR penalty factor associated with the SAM measurement uncertainty (P 2), ex-core/in-core detector measurement error, feedback, depletion, and shape annealing error effects are considered.

Figure 2-4 shows the calculational procedure for determining the penalty factors due to SAM uncertainties.

Using SAM values with and without detector measurement error, and shape annealing error effects, approximately twelve hundred (1200) cases at each time-in-life are run to calculate.

values of CPC LHR and DNB-OPM. The cases used in this analysis include changes in power distribution due to changes in fuel depletion, core power, CEA configuration, load maneuvers and xenon/iodine concentrations.

[ .] (4) Boundary Point Power Correlation Coefficient (BPPCC) The CPC Boundary Point Power Correlation Coefficient (BPPCC) values used in the power synthesis algorithm are verified during power ascension testing. The predicted BPPCC values are calculated by simulating a free unrodded xenon oscillation similar to the SAM measurement procedure.

The predicted BPPCC values are then determined from a regression analysis of the top and bottom one-third core average power integrals and the boundary point powers at the top and bottom of the core. In-core detector measurement error feedback and depletion effects are considered in the calculation of the LHR penalty factor associated with the BPPCC measurement uncertainty (P 3). Figure 2-4 shows the calculational CEN-283(S)-NP, Part 2 Revision 0 2-10 October 1984 Westinghouse Non-Proprietary Class 3 procedures for penalty factors due to BPPCC uncertainty.

CPC LHR and DNB-OPM are calculated for 1200 cases at each time-in-life with the BPPCC values with and without in-core detector signal measurement error. The cases used for the BPPCC penalty factor calculation include changes in power distribution due to changes in fuel depletion, core power level, CEA configuration, load maneuvers, and xenon/iodine concentrations.

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

[ ] (2-9) where [ ] J 2.4.1.4 OTHER UNCERTAINTY FACTORS Axial Fuel Densification Uncertainty The axial fuel densification uncertainty factor(lB) considers the global effect of the shrinkage of the fuel pellet stack, due to heating and tion, on Fq since the CPC Fq calculation does not account for it directly.

[ CEN-283(S)-NP, Part 2 Revision 0 2-11 ]-------------------------October 1984 Westinghouse Non-Proprietary Class 3 Fuel and Poison Rod Bow Uncertainties The fuel and poison rod bow uncertainties(l

9) consider the effect of 11 bowing 11 of the fuel and poison rods, due to heating and irradiation, on Fq since the CPC Fq calculation does not account for it directly.

These factors, lated based on the methodology described in Reference 19, will be part of the composite Fq modeling uncertainty.

Computer Processing Uncertainty The computer processing uncertainty considers the eff~~t of the computer machine precision of the C-E CDC-7600 computer and the on-site computer on the CPC Fq calculations.

The computer processing uncertainty will be part of the composite Fq modeling uncertainty.

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 fissile material and variations in the gap conductance.

This factor, calculated based on the methodology described in Reference 18, will be part of the composite Fq modeling uncertainty.

2.4.1.5 OVERALL LHR LSSS UNCERTAINTY FACTOR An overall CPC Fq uncertainty factor is determined by combining 95/95 probability/confidence tolerance limits of the error components.

This overall uncertainty factor includes a Fq modeling uncertainty, a CECOR Fxy measurement uncertainty, the startup test acceptance criteria uncertainty, the axial fuel densification uncertainty, fuel and poison rod bow uncertainties, a computer processing uncertainty, an engineering factor uncertainty and a reactor core simulator modeling uncertainty.

Figure 2-3 shows the calculational sequence to determine an overall LHR LSSS uncertainty factor. The Fq modeling error {xiM) defined in equation (2-1) can be rewritten as: i C; -Fi XFM = F. 1 CEN-283(S)-NP, Part 2 Revision 0 (2-10) 2-12 October 1984 Westinghouse Non-Proprietary Class 3 where Fi and Ci are the reactor core simulator calculated Fq and the CPC inferred value of Fq for the i-th case, respectively.

A composite error (xtr) of the Fq modeling uncertainty and the CECOR Fxy measurement certainty can be.deterministically calculated as follows: . C. G. X, -1

  • 1 1 -..,......

~. -FT r _. t'. 1 1 ( 2-11) By applying equations (2-7) and (2-10), this leads to: xtT = x:M + xic + (x~M

  • xtc (2-12) The mean of the composite Fq modeling uncertainty is determined by: (2-13) The 11 ka 11 of the composite Fq modeling uncertainty is detennined by combining the 11 kcr 11 for CECOR Fxy (kcrFC), CPC power distribution synthesis (kcrFM), engineering factor (kcrFE)' rod bow penalties (kcrPF' kopp), computer processing (kocp), and reactor core simulator(!)

modeling error (koFR).**

By using the [ ] technique this (kcr)FT is calculated by: [. ] (2-14) The resultant composite Fq modeling penalty factor (PMF) is determined by using the lower 95/95 composite tolerance limit for Fq (TLF) as follows: PMF = 1 + TLF 1 (2-15) where (2-16) The lower tolerance limit is used to assure conservative CPC Fq calculations at a 95/95 probability and confidence level. The last step in determining an overall Fq uncertainty factor (BERR3) is to combine the composite modeling uncertainty (PMF), the startup acceptance criteria uncertainty (PSF) and the axial fuel densification uncertainty (PA). Consequently, [ ** See Appendix A.4 CEN-283(S)-NP, Part 2 Revision 0 2-13 J (2-17) October 1984 Westinghouse Non-Proprietary Class 3 The LSSS LHR overall uncertainty factor (BERR3) is used [ the CPC calculated LHR (KW/FT} such that: Jon CPC tt SYN 11 LHR * ( BERR3) > 11 ACTUAL II LHR 95/95 ( 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 11 ACTUAL 0 LHR. 2.4.2 DNBR LSSS UNCERTAINTY ANALYSIS 2.4.2.1 DNB-OPM MODELING UNCERTAINTY WITH SCU The CPC DNB-OPM modeling uncertainty with SCU is made up of uncertainties associated with power distribution synthesis, DNB algorithm, ex-core detector signal measurement, CEA position measurement, RCS inlet temperature measurement, RCS pressure measurement, and RCS flow measurement techniques.

In order to include the RCS inlet temperature, pressure, and flow rate effects in the DNB-OPM modeling uncertainty, a [ J program is employed.

[ J By comparing the reactor core simulator calculated DNB-OPM 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) ] A detailed description of the SCU DNB-OPM modeling uncertainty is presented in Appendix A.3. CEN-283(S)-NP, Part 2 Revision 0 2-14 October 1984 Westinghouse Non-Proprietary Class 3 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 ature, pressure, and flow measurements must be accounted for in the calculation of the net CPC DNB-OPM uncertainty.

These errors are implicitly included in the modeling uncertainty via the SCU program. For the CPC DNBR calculation during a transient, the ~~essurizer pressure sensed by the precision pressure transducer is adjusted to get the 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 for the dynamic pressure may be represented by: [ J (2-20) where [ J [ ] 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. Wide ranges of radial peak and ASI are also considered in this analysis.

[ [ [ CEN-283(S)-NP, Part 2 Revision 0 J 2-15 ] (2-21) J October 1984 Westinghouse Non-Proprietary Class 3 The dynamic pressure compensation offset (AP 0) is defined as the pressure difference between sensor measured pre~sure and the RCS pressure during a transient.

In order to calculate 6P 0 , the RCS pressure change rate during the worst transient (such as a pressurizer spray valve malfunction) is calculated.

Next, the dynamic pressure compensation is obtained by multiplying the sure change rate by the dynamic pressure compensation offset. [ 2.4.2.3 OTHER U~CERTAINTY FACTORS DNBR Computer 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 DNBR calculations.

The computer processing uncertainty is represented by the term (kcr)CP and is part of the DNB-OPM composite modeling uncertainty (kcr 0 T). This computer processing uncertainty (kcrcp) is calculated by using the following equation:

[ J (2-22) [-] [ ] (2-23) Startup Test Acceptance Band Uncertainty The startup test acceptance band uncertainty for DNB-OPM is determined by the method described in Section 2.4.1.3. Fuel and Poison Rod Bow Uncertainties The fuel and poison rod bow uncertainties for DNB-OPM are determined by the method described in Section 2.4.1.4. CEN-283(6)-NP, Part 2 Revision 0 2-16 October 1984 Westinghouse Non-Proprietary Class 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 DNB correlation(l 5)_ 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, the following uncertainties are combined statistically in 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 uncertainties in fuel clad diameter 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-OPM overall uncertainty factor. 2.4.2.4 OVERALL DNBR LSSS UNCERTAINTY FACTOR The off-line overall CPC uncertainty factor for DNB-OPM (BERRl) is determined by combining all one-sided (upper) 95/95 probability/confidence tolerance limits of the error components.

This overall uncertainty factor includes a DNB-OPM modeling uncertainty, a CECOR Fxy measurement uncertainty, the dynamic pressure uncertainty, a computer processing uncertainty, the startup test acceptance band uncertainty, fuel and poison rod bow uncertainties and a reactor core simulator modeling uncertainty.

Figure 2-3 illustrates the calculational sequence to determine the overall DNB-OPM uncertainty factor. A composite DNB-OPM modeling uncertainty is obtained by following a similar strategy to that used for the Fq uncertainty analysis.

The CECOR Fxy CEN-283(S)-NP, Part 2 Revision 0 2-17 October 1984 Westinghouse Non-Proprietary Class 3 measurement uncertainty is calculated in terms of DNB-OPM units using the sensitivity of DNB-OPM to Fxy { a(%DNB-0PM)/a(%Fxy)

}. The mean of the CECOR Fxy error is given by: [ ] ( 2-24a) [ ] (2-24b) The composite mean error.for the composite DNB-OPM modeling uncertainty can then be calculated as: (2-25) The composite (kcr) is made up of uncertainties for DNB-OPM modeling algorithm (kcr 0 M), CECOR Fxy (ko 0 c), rod and poison bow penalties (kcrPF' kapp), DNBR computer processing (kcrcp), and a reactor core simulator modeling error (kcrFR). Using [ ], this composite (ko)DT is calculated as: [ ]( 2-26) The upper 95/95 composite modeling tolerance limit for DNB-OPM (TL 0) is used for conservative CPC DNB-OPM calculations and determined by: (2-27) The composite DNB-OPM modeling penalty factor (PM 0) can then be determined as: CEN-283(S)-NP, Part 2 Revision 0 2-18 (2-28) October 1984 Westinghouse Non-Proprietary Class 3 In order to determine an overall ONB-OPM uncertainty, the composite DNB-OPM modeling penalty factor (PM 0) is [ ] combined with the dynamic pressure penalty (PP 0) and the startup acceptance band uncertainty (PS 0). An overa 11 DNB-OPM uncertainty factor for CPC ( BERRl ) is determined by combining PM 0 , PP 0 , and PS 0: [ ] (2-29) Use of the overall uncertainty factor (BERRl) for the off-line CPC calculated DNB-OPM assures at. least a 95% probability, at a 95% confidence level, that the 11 ACTUAL II DNB-OPM wil 1 be 1 a rger than the CPC DNB-OPM: CPC II SYW' DNB-OPM corrected with ( BERRl ) 95195 < 11 ACTUAL II DNB-OPM ( 2-30) Therefore, the use of the overall uncertainty factor (BERRl) [ J on the on-line CPC hot pin heat flux distribution used in the DNBR calculation assures at 1 east a 95% probability, at a 95% confidence 1 eve 1., that the CPC calculated DNBR < actual core minimum DNBR: CPC calculated hot pin DNBR corrected with (BERR1)95195 < actual core minimum DNBR (2-31) CEN-283(S)-NP, Part 2 Revision 0 2-19 October 1984 CEN-283(S)-NP, Part 2 Revision 0 Westinghouse Non-Proprietary Class 3 TABLE 2-1 STATISTICALLY MODELED VARIABLES NEUTRON I CS CEA Positions Ex-Core Detector Signals THERMAL-HYDRAULICS RCS Pressure Core Inlet Temperature Core Flow 2-20 October 1984 PARAMETERS CEA Positions Ex-Core Detector Signals Core Inlet Cool~nt Temperature Primary Cool ant Pressure Primary Coolant Flow Rate CEN-283(S)-NP, Part 2 Revision 0 Westinghouse Non-Proprietary Class 3 TABLE 2-2 RANGES AND MEASUREMENT UNCERTAINTIES OF PARAMETERS UNIT (in) (% power) (o F) (PSIA) (GPM) 2-21 RANGES MEASUREMENT UNCERTAINTY October 1984 CEN-283(S)-NP, Part 2 Revision 0 Westinghouse Non-Proprietary Class 3 FIGURE 2-1 CPC SIMULATION FOR Fq 2-22 October 1984 CEN-283(S)-NP, Part 2 Revision 0 Westinghouse Non-Proprietary Class 3 FIGURE 2-2 CPC SIMULATION OF DNB-OPM 2-23 October 1984 CEN-283(S)-NP, Part 2 Revision 0 Westinghouse Non-Proprietary Class 3 FIGURE 2-3 FLOW CHART FOR CPC OVERALL UNCERTAINTIES FOR LHR AND DNB-OPM 2-24 October 1984 Westinghouse Non-Proprietary Class 3 FIGURE 2-4 CALCULATIONAL PROCEDURE FOR PENALTY FACTORS DUE TO RSF, SAM. AND BPPCC UNCERTAINTY CPC BASE RUN WITH PARAMETERS R* t CPC F~ DNB-OPM FOR 1200 CASES WITH BASE VALUE (R) + *COMPARE CPC RESULTS WITH THOSE OF REACTOR CORE SIMULATOR

  • CALCULATE ERROR *ANALYZE ERROR DISTRIBUTION t TO LE RANCE LIMIT (Tlo)
  • NOMINAL VALUE (R) ** CHANGED VALUE (R+tt.R) CEN-283(S)-NP, Part 2 Revision O REACTOR CORE SIMULATOR F , DNB-OPM, AND EX*CDRE DETE~OR SIGNALS FOR 1200 CASES PENAL TY FACTOR ?.-25 CPC RUN WITH PARAMETERS R'** ' CPC F~ DNB-OPM fOR 1200 CASES WITH R' +
  • COMPARE CPC RESULTS WITH THOSE OF REACTOR CORE SIMULATOR
  • CALCULATE ERROR *ANALYZE ERROR DISTRIBUTION

+ TOLERANCE LIMIT (TL) October 1984 .*

Westinghouse Non-Proprietary Class 3 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 SONGS Unit 2 cycle 2 are presented in this section. 3.1 LHR LSSS Following the analysis techniques described in Section 2.4.1, CPC synthesized Fq modeling errors.were tabulated (Table 3-1) for the three times in core life (BOC, MOC, and 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 most non-conservative 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 LSSS results in an aggregate uncertainty of [ ] at a 95/95 probability/confidence level. This overall uncertainty factor of[_. ], when applied to the CPC synthesized Fq, will assure that the CPC Fq will be larger than the actual Fq at a 95/95 probability/confidence level at all times during the fuel cycle. 3.2 DNBR LSSS Following the analysis techniques presented in Section 2.4.2, the CPC synthesized DNB-OPM modeling errors 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 non-conservative modeling uncertainty was considered in the calculation of the overall CPC DNB-OPM uncertainty.

The individual uncertainty components of the overall DNB-OPM uncertainty factor are presented in Table 3-2. Combining the uncertainties associated with the DNBR LSSS gives an overall uncertainty factor of [ J at a 95/95 probability/confidence level. This overall uncertainty factor, when applied to the heat flux input to the on-line CPC DNBR calculation, will assure that the CPC DNBR will be smaller than the actual DNBR at a 95/95 probability/confidence level at all times during the fuel cycle. CEN-283(S)-NP, Part 2 Revision 0 3-1 October 1984

0 () CD m ~-z en I -* I\.) 0 OJ :J u) o-(f) ..........

z "'U "'U Q) ;::::i I\.) 0 (') 0 CT CD -, ....lo. <D OJ vJ l N TIME IN CORE LIFE BOC MOC EOC TABLE 3-1 CPC SYNTHESIZED Fq MODELING ERROR(l) ANALYSIS NUMBER OF DATA POINTS (N) MEAN ERROR (X)FM % 11 SYN 11 F (1) ERROR = (IIUTll/\1 C"n -1 ) 95/95 TOLERANCE(Z),(3) LIMIT (TL) FM (2) See References 12 and 13. Most conservative of normal or non-parametric values presented.

(3) If the error distribution is determined to be non-parametric, the value for (kcr)FM is calculated as (ko)FM =-(TL)FM + XFM CD :J (0 ::::,-0 C en CD z 0 :J I "'U a ""O -, ro* ar '< () ru en en u)

Westinghouse Non-Proprietary Class 3 TABLE 3-2 CONTRIBUTION OF INDIVIDUAL UNCERTAINTIES TO LSSS OVERALL UNCERTAINTY FACTORS UNCERTAINTY LHR Ls*ss Modeling Error (X) FM, (X) DM (kcr)FM,(kcr)DM CECOR Fxy (X) FC , (X) DC (kcr)FC,(kcr)DC Engineering Factor ( ko) FE Fuel Rod Bow (kcr)PF Poison Rod Bow ( ka )pp Computer Processing ( kcdcp Reactor Core Simulator (ka)FR Modeling Axial Densification PA Rod Shadowing pl Shape Annealing Matrix p2 Boundary Point Power P3 Dynamic Pressure PP 0 DNBR LSSS (1) includes power distribution synthesis uncertainty, ex-core signal noise, CEA position error. (2) includes [ Jin addition to errors of (1). CEN-283(S)-NP, Part 2 Revision 0 3-3 October 1984

0 () CD m :::. z U) I -* N 0 OJ :::::J (.,J 0:0 I z "'U "'U Q) ::i N w I TIME IN CORE LIFE BOC MOC EOC TABLE 3-3 CPC SYNTHESIZED DNB-OPM MODELING ERROR(!) ANALYSIS NUMBER OF DATA POINTS (N) MEAN ERROR (X)DM "SYW DNB-OPM (1) ERROR = ( 11 l\f'TIII\I II hKib hbKA -1 ) 95/95 TOLERANCE(2),(3) LIMIT (TL)DM (2) See References 12 and 13. Most conservative of the normal or non-parametric values presented.

(3) If the error distribution is considered non-parametric, the value for (ka)0 M is calculated as: (ko)DM = (TL)DM -XDM 0 C" CD """I ....... <D OJ +::>,. CD :::::J <O :::::; 0 C U> CD z 0 :::::J -b """I 0 ""O """I ro* or '< () ru U> U> (.,J Westinghouse Non-Proprietary Class 3 REFERENCES

1. Combustion Engineering, Inc., 11 Assessment of the Accuracy of PWR Safety System Actuation as Perfomied by the Core Protection Calculators 11 , CENPD-170-P and Supplement, July, 1975. 2. Southern California Edison Company, "Final Safety Analysis Report (FSAR) for San Onofre Nuclear Steam Generating Station Units 2 and 3 11 , January, 1984. 3. Combustion Engineering, Inc., 11 COLSS, Assessment of the Accuracy of PWR Operating Limits as Determined by the Core Operating Limit Supervisory System", CENPD-169-P, July, 1975. 4. Combustion Engineering, Inc., 11 Statistical.

Combination of Uncertainties Methodology", Parts 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 11 , June 30, 1978. 6. Combustion Engineering, Inc., 11 Response to Questions on Documents Supporting the AN0-2 Cycle 2 Licensing Submittal", CEN-157(A)-P, Amendment 1, June, 1981. 7. Combustion Engineering, Inc., "Statistical Combination of Uncertainties, Part II; Uncertainty Analysis of Limiting Safety System Settings, C-E System 80 Nuclear Steam Supply Systems 11 , Enclosure 1-P to LD-83-010, January, 1983. 8. Combustion Engineering, Inc., "Response to NRC Questions on CESSAR-F Statistical Combination of Uncertainties in Thennal Margin analysis for System 80 11 , Enclosure 1-P to LD-83-037, April, 1983. 9. Combustion Engineering, Inc., "Responses to NRC Questions on CESSAR-80 Uncertainties 11 , Enclosure 1-P to LD-83-082, August, 1983. 10. American National Standard Assessment of the Assumption of Normality, ASI-NlS-15, October, 1973. 11. Sandia Corporation, "Factors for One-Sided Tolerance Limits and for 'Variable Sampling Plans", SCR-607, March, 1963. 12. C. L. Crow, et al, "Statistical ManuaP, Dover Publications, Inc., New York, 1978. 13. R. E. Walpole and R. H. Myers, 11 Probability and Statistics for Engineers and Scientists 2ed 11 , Macmillan Publishing Company, Inc., New York, 1978. 14. C. Chiu, "Three-Dimensional Transport Coefficient Model and Prediction Correction Numerical Method for Thermal Margin Analysis of PWR Cores 11 , Nuclear Eng. and Design, P103-115, 64, March, 1981. CEN-283(S)-NP, Part 2 Revision 0 R-1 October 1984 Westinghouse Non-Proprietary Class 3 15. Combustion Engineering, Inc., 11 CETOP-D Code Structure and Modeling Methods for San Onofre Nuclear Generating Station Units 2 and 3 11 , CEN-160(5)-P, May, 1981. 16. Combustion Engineering, Inc., 11 Functional Design Specification for a Core Protection Calculator", CEN-147(S)-P, January 1981. 17. Combustion Engineering, Inc., "INCA/CECOR Power Peaking Uncertainty 11 , CENPD-153-P, Rev. 1-P-A, May, 1980. 18. Combustion Engineering, Inc., "Fuel Evaluation Model", CENPD-139-P, October, 1974. 19. Combustion Engineering, Inc., 11 Fuel and Poison Rod Bowing", CENPD-225-P-A, June, 1983. 20. Combustion Engineering, Inc., "CPC/CEAC Software Modifications for San Onofre Nuclear Generating Station Unit No. 2 and 3 11 , CEN-281(s)-P, June, 1984. CEN-283(S)-NP, Part 2 Revision 0 R-2 October 1984 Westinghouse Non-Proprietary Class 3 APPENDIX A Stochastic Simulation of Uncertainties A.1 Detector Signal Measurement and CEA Bank Position Measurement Uncertainties In the SCU program, error components of ex-core detector signals are [ ]. This error component is then added to the ex-core signal generated by the reactor core simulator and is used as input to the CPC power distribution algorithm.

The location of each CEA bank is measured using the Reed Switch Position Transmitters (RSPT). An error component of each CEA bank measurement is selected r .] The sampled error is then added to the respective CEA bank position for input to the CPC power distribution algorithm.

A.2 State Parameter Measurement Uncertainties The on-line ONB algorithm(A-l) 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 DNBR, errors associated with these state parameters must be accounted for in the CPC DNB-OPM uncertainty analysis.

[ ] This procedure allows for direct simulation of the effects of the CPC on-line inlet temperature, pressure, and flow measurement, and their respective uncertainties on the CPC DNB-OPM overall uncertainty.

Therefore, uncertainties with respect to temperature, pressure, and flow are implicitly accounted.for in the DNB-OPM modeling uncertainty.

CEN-283(S)-NP, Part 2 Revision 0 A-1 October 1984 Westinghouse Non-Proprietary Class 3 A.3 DNB-OPM Algorithm Uncertainties Ideally, the DNB-OPM overall uncertainty calculation would use three distinct thermal-hydraulic algorithms:

The off-line design T-H algorithm (CETOP-D) represents the base-line DNB-OPM calculation.

CETOP-l(A-

2) and CETOP-2(A-l) are simplified versions of CETOP-0, and perform the on-line thermal-hydraulic calculations for the plant monitoring and protection

.systems, ely(A-3).

[ 1 The actual calculational scheme is shown in Figure A-1. CETOP-D is a fast running, accurate, core thermal-hydraulics calculator.

It is used as the setpoint DNB-Overpower Margin calculator for all CPC/COLSS plants. As such, CETOP-D is benchmarked against detailed TORC/CE-1.

The general CETOP methodology is described in Reference A-2. The CETOP-D code is described in detail in References A-4 and A-5. [ CEN-283(S)-NP, Part 2 Revision 0 A-2 October 1984 Westinghouse Non-Proprietary Class 3 1 These differences between CETOP-1 and CETOP-D result in CETOP-1 having a shorter execution time while essentially maintaining the accuracy of CETOP-D. CETOP-2 is also a fast running version of CETOP-0. This version has been streamlined in order to meet the timing and core memory storage requirements of the on-line CPCs. CETOP-2 has been described in References A-6 and A-7. The primary use of CETOP-1 is in COLSS, which is a control grade monitoring system. CETOP-1 w~s chosen to be used in the reactor core simulator because of its short execution time compared to CETOP-D, and very high accuracy compared to CETOP-2. [ ___ _ .] [ J A.4 Reactor Core Simulator Modeling Error The reactor core simulator uses the FLARE neutronic model to predict tative power distributions.

The FLARE model is tuned to a more accurate and rigorous ROCS neutronic simulator code. The reactor core simulator modeling CEN-283(S)-NP, Part 2 Revision 0 A-3 October 1984 Westinghouse Non-Proprietary Class 3 error accounts for the effect of the reactor core simulator modeling uncertainty on the reference LHR and DNB-OPM calculations.

A.5 References for Appendix A A-1 Combustion Engineering, Inc., "Functional Design Specification for a Core Protection Calculator", CEN-147(S)-P, February, 1981. A-2 C. Chiu, "Three-Dimensional Transport Coefficient Model and Prediction-Correction Numerical Method for Thermal Margin Analysis of PWR Cores 11 , Nuclear Eng. and Design, P103-115, 64, March, 1981. A-3 Combustion Engineering, Inc., "Response to. NRC Questions on CESSAR-F Statistical Combination of Uncertainties in Thermal Margin analysis for System 80 11 , Enclosure 1-P to LD-83-037, April, 1983. A-4 Combustion Engineering, Inc., 11 CETOP-D Code Structure and Modeling Methods for San Onofre Nuclear Generating Station Units 2 and 3 11 , Docket No. 50-361, 50-362, CEN 160(S)-P, Rev.1-P, September 1981. A-5 Combustion Engineering, Inc., 11 CETOP-D Code Structure and Modeling Methods for Arkansas Nuclear One -Unit 2," CEN-214(A)-P, July 1982. A-6 Combustion Engineering, Inc., 11 CPC/CEAC Software Modifications for Arkansas Nuclear One -Unit 2, 11 CEN-143(A)-P, Rev. 1-P, September 1981. A-7 Combustion Engineering, Inc., "Response to Questions on Documents Supporting the AN0-2 Cycle 2 License Submittal 11 , CEN-157(A)-P with Amendments 1-P, 2-P and 3-P, 1981. A-8 M. G. Kendall and A. Stuart, "The Advanced Theory of Statistics, Vol. II 11 , Hafner Publishing Company, New York, 1961, p. 457. CEN-283(S)-NP, Part 2 Revision 0 A-4 October 1984

.. , ,*;'}I'. .' -.1 .. ,l. CEN-283(S)-NP, Part 2 Revision 0 Westinghouse Non-Proprietary Class 3 FIGURE A-1 DNB-OPM ALGORITHMS A-5 October 1984 Westinghouse Non-Proprietary Class 3 APPENDIX B Core Power Level Measurement Uncertainty B.l Uncertainty

.Components The CPC utilizes two different calculations of core power, thermal power and neutron flux power, for the LHR and DNBR calculation.

The CPC thermal power is calculated based on the reactor coolant temperature and the reactor coolant mass flow rate. The CPC thermal power measurement error is calculated by detenninistically combining the secondary calorimetric power measurement error, the secondary calorimetric power to CPC power calibration allowance, and the thermal power transient offset. The CPC neutron flux power is calculated based on the sum of the tri-level ex-core detector signals. The CPC neutron flux power measurement error is calculated from the CPC neutron flux power synthesis error, the secondary calorimetric power measurement error, and the secondary calorimetric power to the CPC power calibration a 11 owance. Secondary Calorimetric Power Measurement Error The secondary calorimetric power measurement error (Xsc) consists of the uncertainty components for the following parameters:

1. Feedwater Flow 2. Feedwater Temperature
3. Secondary System Pressure 4. Pressurizer Heaters 5. Reactor Coolant System Loss 6. Coolant Pump Heat 7. Component Cooling Water The result of a typical analysis of the secondary calorimetric power error, based on the above uncertainty components and secondary instrument accuracies, is provided in Figure B-1. Verification of the secondary calorimetric power error is performed during startup testing. CEN-283(S)-NP, Part 2 Revision 0 B-1 October 1984 Westinghouse Non-Proprietary Class 3 The secondary calorimetric power measµrement error is conservatively bounded by the following core power error function (Xsc): ------~-The application of this error has been modified for the SONGS-2 cycle 2 CPCs {Ref. 20). This modification allows the secondary calorimetric power measurement error to vary as a function of core power as shown above. In previous CPC power. uncertainty analyses, the maximum penalty [ ] was conservatively applied over the entire power range. Calibration Allowance The secondary calorimetric power to the CPC power calibration allowance (XCA) is based on Technical Specification allowances.

Adjustments are made to the CPC thermal power and CPC neutron flux power values if the absolute difference with the secondary calorimetric power calculation is greater than [ ]. This allowance is consistent with that for other CPC plants. Thermal Power Transient Offset The thermal power transient offsets on CPC DNBR and LHR calculations are evaluated to assure that the CPC Design.Basis Events (DBEs) are adequately mode1ed4 The DBEs that are limiting for the determination of these offsets are those which involve single CEA misoperations.

The limiting DBE for the thermal power transient offset on the CPC DNBR calculation is the single CEA withdrawal from full power, which gives the most non-conservative CPC calculation of heat flux. The thermal power transient offset on the CPC DNBR calculation (Xro> was determined as [ ] which covers the maximum non-conservatism involved.

The DNBR thermal power transient offset is used in the evaluation of the addressable uncertainty bias constant for the CPC thermal power (BERRO). Since the neutron flux power response is essentially instantaneous, the addressable uncertainty bias constant for the CPC neutron flux power (BERR2) does not require a transient bias offset component.

CEN-283(S)-NP, Part 2 Revision 0 B-2 October 1984 Westinghouse Non-Proprietary Class 3 The limiting DBE for the thermal power transient offset on CPC LHR calculation (XTF) is the single CEA withdrawal.

This event gives the most tive power for the CPC calculation of LHR. The thermal power transient offset on the CPC LHR calculation was determined as [ _], which covers the maximum non-conservatism involved.

This thermal power transient offset on CPC LHR calculation is used in the evaluation of the addressable uncertainty bias constant for the power used in CPC LHR calculation (BERR4). Neutron Flux Power Synthesis Error The neutron flux power synthesis error {XNF) is.obtained by comparing the CPC synthesized neutron flux power level to the reactor core simulator power for 1200 cases at each time-in-life.

The most non-conservative value of the sided tolerance limit at a 95/95 probability/confidence level is used at each power level. The CPC neutron flux power synthesis error for SONGS Unit 2 cycle 2 is presented in Table B-1. B.2 Uncertainty Biases for DNBR Calculation The uncertainty biases for power used in the DNBR calculation are added to the calculated power level as: where [ [ J ] POWERTH = Adjusted thermal power POWERNF = Adjusted neutron flux power BOT = Calculated thermal power BNF = Calculated neutron flux power BERRO = Thermal power measurement uncertainty factor for the CPC DNBR calculation BERR2 = Neutron flux power measurement uncertainty factor for the CPC DNBR calculation XSC = power level dependent core power measurement error 8-3 CEN-283(S)-NP, Part 2 Revision 0 October 1984 Westinghouse Non-Proprietary Class 3 The thermal power measurement uncertainty constant for the CPC DNBR calculation (SERRO) is determined by selecting the maximum value of the thermal power measurement errors (XCA+XTD) for the core power range (0-100% fu 11 power). [' ] The neutron flux power measurement uncertainty constant for the CPC DNBR calculation (BERR2) is determined by selecting the maximum neutron flux power measurement error (XCA+X..,c-}

at each power level for the core power range (0-130% full power). [ ---] For the DNBR calculation, the CPC selects the larger of the thermal power (POWERTH) or the neutron flux power (POWERNF).

B.3 Uncertainty Biases for LHR Calculation The uncertainty biases for power used in the LHR calculation are added to the uncorrected power level: where [ POWERLHR = POWERCALC

= *BERR4 = = CEN-283(S)-NP, Part 2 Revision 0 J power level input to the LHR calculation corrected for power measurement uncertainties power level calculated from thermal or neutron flux power measurements (BDT or BNF' whichever is greater) core power measurement uncertainty factor for the LHR calculation power level dependent core power measurement error 8-4 October 1984 Westinghouse Non-Proprietary Class 3 The core power measurement uncertainty factor for the LHR calculation (BERR4) is obtained by selecting the largest of the CPC thermal power error (XCA+XTF) or the CPC neutron flux power errors (XcA+XNF+XTF) over the core power range from 0-130% full.power. [ ] The CPC power measurement errors for SONGS Unit 2 eye~~ 2 are given in Table B-2 as a function of power. CEN-283(S)-NP, Part 2 Revision 0 B-5 October 1984

0 () CD m :::.z U) I -* N 0 OJ :::J (.,J o-!!] I z "'U "'U ID ;::::i N 0 () 0 C" CD """I ....... <D OJ CD I °' LIFE BOC MOC EOC TABLE B-1 CORE POWER SYNTHESIS ERROR ANALYSIS(!)

NUMBER OF DATA POINTS MEAN ERROR (1) Power Synthesis Error= (CPC NEUTRON FLUX POWER -SIMULATOR POWER SIMULATOR POWER ) (2) See References 12 and 13. Most conservative of the normal or non-parametric values presented.

LOWER 95/95(2) TOLERANCE LIMIT :§: CD :::J <O :::J"' 0 C U> CD z 0 :::J -b """I 0 ""O """I ro* w """I '< () ru U> U> (.,J

o () TABLE B-2 CD m
5. z CJ) I -* I\) 0 CX) POWER MEASUREMENT UNCERTAINTY AS A FUNCTION OF POWER ::J w o-(f) -I z ""U FOR DNBR ""U ru :::i SECONDARY I\) TRUE CALORIMETRIC THERMAL POWER** NEUTRON FLUX POWER(%) ERROR (%) ERROR(%) POWER ERROR { % ) 0 r 20 I 40 I 60 I 0:, I 80 " 100 I 130 I (Xsc) (XCA + XTO) (XCA + XNF) 0 0 0 [ *Largest value installed in the CPCs. (0 CX) **Power error for Thermal Power includes a transient power offset of [ ***[ ] ] . FOR LHR -POWER ERROR*** J%) I CD ::J (0 I :::J" 0 C CJ) I CD z 0 ::J I ""U -, 0 I "'O -, ro* ar I -, '< () ru \ XCA CJ) CJ) max w XCA + XNF
0 () CD m :5. z en I -* N 0 CX) ::J c.v o-cn ..........

I z "'U "'U ll) ::::i N 0 (") 0 C" CD .., (0 CX) CD I CX) 5 4 I-I er 0 0:: ex w oc. 3 w 3 0 Q. 2 ,-I 1 0 10 20 C *' FIGURE B-1 SECONDARY CALORIMETRIC POWER ERROR ..... CD ::J I I co :::::r 0 C en CD z 0 ::J I "'U .., 0 ""O .., ro* ii> '< () I I ii> en en c.v 30 40 50 60 70 80 90 100 t OF DESIGN RATEO POWER Westinghouse Non-Proprietary Class 3 APPENDIX C Axial Shape Index Uncertainty The axial shape index (ASI) for the core average and the hot-pin power distributions is computed from the power generated in the lower and upper halves of the core: ASI ( C-1) 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 Error= CPC ASI -Reactor Core Simulator ASI (C-2) The core average and hot-pin ASI uncertainty analyses are performed by comparing the CPC synthesized ASI and the reactor core simulator ASI. The resulting error distributions are analyzed to obtain the upper and lower 95/95 tolerance limits. The hot-pin ASI and the core average ASI uncertainties are presented in Tables C-1 and C-2. CEN-283(S)-NP, Part 2 Revision 0 C-1 October 1984

0 () CD m :5. z U) I -* N 0 CX) :::J (.,J o-!B I z -u -u Q) ;::::::i..

N 0 n. 0 C" CD """I ....... (0 CX) n I N BURNUP BOC MOC EOC NUMBER OF DATA POINTS TABLE C-1 HOT-PIN ASI ERROR(l) ANALYSIS MEAN ERROR (1) ASI ERROR= (CPC ASI -SIMULATOR ASI) LOWER 95/95(2) LIMIT . UPPER 95/95(2) LIMIT (2) See References 12 and 13. Most conservative of normal or non-parametric val~es presented. CD :5" co :::::; 0 C U> CD z 0 :::J I -u """I 0 ""O """I ro* or '< () ru U> U> (.,J

o () ro m
5. z C/J I -* N 0 ()) ::J c.v o-!!J z "'U "'U !l) N 0 u n I w BURNUP BOC MOC EOC NUMBER OF DATA POINTS TABLE C-2 CORE AVERAGE AS! ERROR(l) ANALYSIS MEAN ERROR LOWER 95/95(2) LIMIT g (1) ASI ERROR= (CPC ASI -SIMULATOR ASI) UPPER 95/95(2) LIMIT (2) See References 12 and 13. Most conservative of normal or non-parametric values presented. Cl) :5* (0 :::J" 0 C C/J Cl) z 0 ::J I "'U a ""O ro* or '< () ru C/J C/J c.v
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