ML20204H428

Nonproprietary Statistical Combination of Uncertainties, Part Ii,Uncertainty Analysis of Limiting Safety Sys Settings

ML20204H428
Person / Time
Site:	San Onofre
Issue date:	10/31/1984
From:	ABB COMBUSTION ENGINEERING NUCLEAR FUEL (FORMERLY
To:
Shared Package
ML13309B466	List: ML20204H428 ML20204H497
References
CEN-283(S)-NP, CEN-283(S)-NP-V02, CEN-283(S)-NP-V2, NUDOCS 8411120289
Download: ML20204H428 (61)

Text

-

San Onofre Nuclear Generating Station Units 2 and 3 CEN-283(S)-NP STATISTICAL COMBINATION OF

, UNCERTAINTIES PART II-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

!$kk$o![o!ObbO61

,e PDR

f. -

LEGAL NOTICE s 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 T0 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.

1 i

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 /cenfidence level throughout the. core cycle c 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 these reviewed and approved for C-E System 80 plants.

e 11

TABLE OF CONTENTS CHAPTER PAGE Abstract .

ii 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.'O Analysis 2-1 2.1 General 2-1 2.2 Objectives of Analysis 2-1 2.3 . Analysis Techniques 2-1 2.3.1 General Strategy 2-1 2.3.2 LHR LSSS Statistical Methods 2-3 2.3.3 DNBR LSSS Statistical Methods 2-5 P.4 Analyses Performed 2-6 2.4.1 LHR LSSS Uncertainty Analysis 2-6 2.4.1.1 Power Distribution Synthesis Uncertainty 2-6 4

2.4.1.2 CECOR Fxy Measurement Uncertainty 2-7 2.4.1.3 Startup Test Acceptance Band Uncertainty 2-8 2.4.1.4 Other Uncertainty Factors 2-11 2.4.1.5 Overall LHR LSSS Uncertainty Factor 2-12 2.4.2 DNBR LSSS Uncertainty Analysis 2-14 iii b J

(

2.4.2.1 DNB-0PM Modeling-Uncertainty with SCU 2-14 2.4.2.2 Dynamic Pressure Uncertainty 2-15 2.4.2.3-'Other Uncertainty Factors 2-16 2.4.2.4 Overall DNBR LSSS Uncertainty Factor 2-17 3.0 Results and Conclusions 3-1 3.1 LHR LSSS 3-1 3.2- DNBR LSSS 3-1 References R-1 Appendices A. Stochastic Simulation of Uncertainties A-1 A.1 Detector Signal Measurement and CEA Bank Position Measurement Uncertainties A-1 A.2 State Parameter Measurement Uncertainties _

A-1 A.3 DNB-OPM Algorithm Uncertainties A-2 A.4 Reactor Core Simulator Modeling Error A-3 A.5 . References for Appendix A A-4 B. ' Core Power Level Measurement Uncertainty B-1 B.1 Uncertainty Components B-1 B.2 Uncertainty Biases for DNBR Calculation B-3 B.3 Uncertainty Bias for LHR Calculation B-4 C. Axial Shape Index Uncertainty C-1 iv

s .

LIST OF-TABLES TABLE PAGE 1-1 Variables Affecting LHR and DNBR LSSS 1-4 2-1 Stochastically Modeled Variables 2-20 2 Ranges and Measurement Uncertainties of Parameters 2-21 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-0PM 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 r

V

A LIST OF FIGURES FIGURE PAGE 2-1 . CPC Simulation for Fq 2-22 2-2 CPC Simulation of DNB-0PM 2-23 2-3 Flow Chart for CPC Overall Uncertainties for LHR and DNB-OPM 2-24 2-4 Calculational Procedure for Penalty Factors due to RSF,' SAM, and BPPCC Uncertainty 2-25 A-1 DNS-OPM Algorithms A-5 B-1 Secondary Calorimetric Power-Error B-8 e

I 8

vi

DEFINITION OF ABBREVIATIONS ASI- Axial Shape Index APHPD Axial. Pseudo Hot-Pin Power Distribution BOC Beginning Of Cycle BPPCC Boundary Point Power Correlation Coefficient CDF Cumulative Distribution Function C-E- Combustion Engineering CEA Control Element Assembly ,,

CETOP C-E Thermal On-Line Program CETOP-D. Off-Line DNB Algorithm for Safety Analysis CETOP-1 DNB Algorithm used in. Core Simulator and COLSS on-line CETOP-2 -On-LineDNBdigorithmusedinCPC COLSS Core Operating Limit Supervisory System CPC Core Protection Calculator DNB Departure from Nucleate Boiling DNBR DNB Ratio DNB-OPM DNB Over Power Margin

- EOC - End Of Cycle p ESFAS Engineered Safety Features Actuation System Fq Three Dimensional Power Peaking Factor Fxy Planar Radial Peakirg Factor LCO Limiting Conditions for Operation

LHR Linear Heat Rate (kw/ft)

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

[ MOC Middle Of Cycle

.NSSS Nuclear Steam Supply System

• - PDF Probability Distribution Function PHPD Pseudo Hot-Pin Power Distribution PLR Part length Rod (CEA)

RCS Reactor Coolant System RPS Reactor Protection Sys' tem RSF Rod (CEA) Shadowing Factor j RSPT Reed Switch Position Transmitter I

i vii

es- -

SAFDL Specified Acceptable-Fuel Design Limits SAM . Shape Annealing Matrix

SCU Statistical Combination of Uncertainties TSF Temperature Shadowing Factor G

G e

6 e.

viii

l' r

1.0 INTRODUCTION

h 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(1) . ~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. Uncertain'ty 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)(1) LHR calculation Idue to the CPC power distribution synthesis for CPC LHR algorithm

5. Uncertainty in the CPC DN8 calculation due to the CPC power distribution synthesis for the CPC DNB algorithm

6. Uncertainty in the CPC DN8 algorithm with respect to the safety analysis DN8 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

12. Engineering factor due to manufacturing tolerance  !

2 -

1.2 BACKGROUND

4

! 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 t

! 2. a Reactor Protection System (RPS).

t I I I

1-1

The CPC initiates two of the ten trips in the Reactur 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 10CFR50 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 systemsI4)(CalvertCliffs Units'l 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 CPC three-dimensional peaking factor (Fq) and DNBR calculations to ensure l

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 i described in this report is the same as the methodology used for C-E System 80 NSSS(7-9) ,

1.3 REPORT SCOPE l

The scope of this report encompasses the following objectives:

L 1. to describe the methods used for statistically combining uncertainties l applicable to the LHR and CNBR LSSS; i 2. to evaluate the aggregate uncertainties as they are applied in the

l. calculation of LHR and DNBR.

1-2

. 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 (ASI), and the hot-pin ASI are also described.

The methods presented'in this report are applicable to SONGS Units 2 and 3.

1.4 SUM ARY OF RESULTS, The analysis techniques descrit re applied to SONGS Unit 2 cycle 2. The stochastic simulat.. ts in overall uncertainties for the LHR LSSS and the ON8R LSSS '[ ],respectively,ata 95/95 probability / confidence level'.

1 I s

i 1-3

h.

r k.

TABLE 1-1

. g VARIABLES AFFECTING THE LhR AND DNBR LSSS t

F LHR ,

' )

1. Core Power Level e

~

2. Axial Power Distribution.

. 3. Radial Pcwer Distribution x

4.s CEA Position x w ,

E DNBR

([ e.. 4 h

r%a At i it M h 1. Core Power Level if[,Jf.'(

k92;

2. Axial Power Distribution ya

- 3. Radial Power Distribution 5 ; )! ' ,

4. CEA Position F.k .& . ; w -

+

i 5. Core Coolant Inlet Temperature J

'- 6. Core Coolant Pressure f ;;n..

%g y 7. Primary Coolant Mass Flow ,

]p'e ..y O

e, .

=

} .- .?.:. .:3

. > i.'. /:.;

V'

u '

• A; '.? :4

, a;: q E

,5 k.

Ma h

F L r

~

l h-

" I A

?:

- , 4 ,

S

,. 1-4  :

7

2.0 -ANALYSIS 2.1- GENERAL p .b . 8

x.,.; ?

The following sections describe the impact of the uncertainty components of } T(.{ ;

the system parameters, the state parameters, and the modeling, that affect the JY li t.%,.

LHR and DNBR LSSS. The effects of all individual uncertainties on the LSSS if 5 o g.D J ,A overall uncertainty factors for the calculation of LHR and DNBR are also ;v.e .J.y discussed. In addition, this chapter presents the analyses performed to E.. [

determine overall uncertainty factors which are applied in the on-line CPC yt$

calculations of the LHR and DNBR to ensure at.a 95/95 probability / confidence

%. '.'l .

level that the calculations are conservative. ,

p..$.,: Q.

' f w 't wg _.y

, s .. :. : -

1,W. i 2.2 OBJECTIVES OF ANALYSIS

ya l ',Iq t , yy

., .,.r The objectives of the analysis reported herein are: .h.ph;..S.

1. .to document the stochastic simulation technique used in the overall J.ao, n .c ,.  :

uncertainty analysis associated with the LHR and DNBR LSSS and, g.gy

2. to determine the overall uncertainty factors used in the calculation of 'yAO CI the LHR and DNBR, on the basis of a 95/95 probability / confidence level, Jgg?

y ..

so that the " adjusted" LHR and DNBR (i.e., the CPC synthesized value e..!F :

t .. .:p corrected by the respective overall uncertainty factor) will be G~ vg ~.// w conservative throughout the core cycle with respect to actual core 1*e.9.

- gM ..

conditions. #7 QC3

& . 7W .'i, ?

2.3 ANALYSIS TECHNIQUES # .n.a W ;;

.., 6 3, .% ,,

2.3.1 GENERAL STRATEGY y- p,y 3 ;; : - f. .

. w ;

The reactor core simulator (1) generates typical three-dimensional core power $*Q*

distributions which reflect a variety of plant operating conditions. The  %.' 't , fi uncertainty analyses are performed by comparing the three-dimensional peaking N...

y g?-

a ~p., ' ;

3 '; . N 2-1 [M .:: y'M.

. p.a

. . . . . . . di

c .n- 53

.. E5q

• fy . >. .

F1j Y!k simulation of the appropriate startup testing (see section 2.4.1.3). Figures ' 6. ,

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-0PM) "f 6 and not DNBR units since the uncertainty factor is used [as a multiplier] on I% b.-il heat flux in the on-line CPC DNBR calculation. The F and q DNB-0PM modeling .h...[

s.p s t.

uncertainties are statistically combined with other uncertainties in y,, j ]

calculating CPC overall uncertainty factors for LHR and DNB-0PM. The [M uncertainty analysis described in this report also involves the stochastic y/4ygg simulation of the state parameter measurement uncertainties for the LHR and *f.N,~-

DNB-0PM calculations. The neu nic and thermal-hydraulic input parameters gf that are statistically modeled are given in Table 2-1. A detailed descrip- -;e. e "s tion of the individual measurement uncertainties is presented in Appendix A. { l..] .

A comparison of the on-liae to off-line thermal-hydraulic algorithms is also A5

,p presented in Appendix A. .#4 Approximately twelve hundred (1200) cases of power distributions at each of three burnups (B0C, MOC, and E0C) 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-0PM 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.

2-2

h.

1 k

i f.

(

2.3.2 LHR LSSS STATISTICAL METHODS y c

The reaci.or 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 I

that of the reactor core simulator. Figure 2-1 illustrates the calcula-tional sequence employed in the Fq modeling uncertainty analysis. The Fq l modeling error (X p) between the CPC synthesized Fq and the actual Fq is f defined as: -

1

(" N" Fq)i Xp = -1 (2-1) -

(" ACTUAL".Fq)I where (" SYN" Fq)I and (" ACTUAL" Fq)I are the CPC Fq and the reactor core [-

simulator Fq for the 1-th case. The Fq error is inalyzed for each case at each time-in-life. Approximately 1200 cases are analyzed at each time-in-life [

(B0C, MOC, and E0C). -

r e

The mean Fq error ({} and the standard deviation (op ) of the Fq error can be  ;

calculated from: .

i i

N E

X I  :

i=1 Y=p N

( - a) }

i 1/2 I (Xp - Rp)2 li=1 (2-2b)  ;

'F "' N-1 _

L.

where N = sample size Since' the mean and standard deviation are estimated from the data, the one- g A

sided tolerance limit can be constructed from the k factor. For normal distributions, the one-sided tolerance limit factor (k) accounts for the i sampling variations in the mean (ip ) and the standard deviation (op ). A normality test of the error distribution is performed by using the D-prime kk statistic value(10-11) to justify the assumption of a normal distribution.

2-3

6 :. ; > . .

,79 - 9

-Yf}

.g -

The k factor for a normal distribution (11-12) is calculated as: },[J$.4 ,

98/95 .. - g 1 ,. y k 1-p 2

+ (k1-p - ab)l/2 h$

k= (2-3a) 'I.t/-

a - - ; -s

- y, ;'

p where Q . .' &

2 k M~ u: .

a=1- *

(2-3b) A /; ' -

2 (N-1) f.

. -q -

4.. y.

~:r 4 r '

i::s k

2 gg,. ,%- ,

b=k 1-p2 ,.a N

(2-3c) "G*

.. 4...;

. . ..;. .N:

.g s.

9 ' ;> g%

k 1-p

= percentiles of a normal distribution for the probability p (1.645 for 95% probability) 1. %. -*M 7 ".c..: g.%

3 1. .

k = percentiles of a normal distribution for the confidence @ ' '.

s.

a coefficient (1.645 for 95% confidence) h..m.6.3

• R+

g

, .r.y.5 .s.r

+-

N = sample size  %

. . w_ , .

,. v_ . s . -.

hm .

If the error distribution is normal, the upper and lower one-sided 95/95 l f.;1.y .

tolerance limits are calculated using the following equations: f.:8

,p.!

}7.-( g ;

(2-4a)

Lower 95/95 tolerance limit = X - k95/95o Upper 95/95 tolerance limit = X + k95/95o (2-4b) 'y

'k=C .;

1.... .

where X, o, and k 95/95 are the sample mean, standard deviation, and one-sided g.y'j;<

tolerance limit factor, respectively. $ 9' .'.)

k :' .c If the error is not normally distributed, one-sided 95/95 tolerance limits are Ny ^.,

calculated by using non-parametric techniques [

2-4

] The locator L is calculated from the following equation which is derived from the methods in Reference 13.

[ ] (2-5) where -

.. .;;c . .;

Bthr':

ll#:p W

g,t-+$9 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 M locator L. A non-parametric "ke" is calculated from equation (2-4) by using ..

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

w w .c.. , .q 2.3.3 DNBR LSSS STATISTICAL METHODS R,(M-

. . w. v ;

The three-dimensional reactor core simulator provides a hot-pin power hi T.j ,.- l[:

f distribution for its DNB-0PM calculation and the corresponding ex-core f.y3.h detector signals for the CPC power distribution algorithm. In the reactor ffs-- F: am core simulator, the DNB-OPM calculation is performed with the simplified, $$ . k relatively fast running DNB algorithm CETOP-1(14) . [

h W.% -

n.s

.f/k'.U

~

] A  !

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

.s? r.i Jr9y. ' d r, c. ;

in Figure 2-2. W[-

Q y '.

n.%

The Reactor Coolant System (RCS) input temperature, pressure, and flow rate gg:p are[- 3.Q(,j r ..a

] for both the reactor core simulator and CPC. [ . ? 9..

rg.jpg .  :: .

1. ,f  : l'

] Operating ranges and measurement uncertainties of the state parameters are given in Table 2-2. , g.3_ -

z;c., s.; .:.

.4.~.; ' 4 The SCU program also involves a stochastic simulation of the error components  ;}.}jl 5".

associated with the DNB algorithms (on-line to off-line). [ ,. ..y ,

%.J? :k

." i.' /,Nl

.N y'hY r.

9. :c y.4 {f.

] Thus, the effects of the error components Qi}

P.PW

.j p y . g .

associated with the temperature, pressure, and flow measurements and the y gb on-line to off-line DNB 'lgorithm a are accounted for in the determination of h5W7 Rr ?- ' O. 5-the CPC DNB-0PM modeling error via the SCU program. .."m.;/" .

.i i;k. a y .

~e #i t y i The CPC DNB-0PM modeling error (with SCU) is defined as:

%,R

.- iti,

(" SYN" DNB-0PM)

(2-6)

=

(" ACTUAL" DNB-0PM)9- 1 .p.g

@6 a.

.a s where (" SYN" ONB-0PM)j and (" ACTUAL" DNB-0PM)9 represent the CPC DNB-0PM and VW4 the reactor core simulator DNB-0PM for the i-th case. The DNS-0PM errors are . .48 l#d:-

analyzed separately for each time-in-life. Each error distribution is tested (( 4 .s%

for normality and the mean DNB-0PM error O(X ), standard deviation (onw ), and .J [p4 f2

" ' ?.

L '

~

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

[AM

$ i.co..

.3 y . +p ,.

7 1, ., .e The reactor core simulator calculates ex-core detector signals for the CPC Nkke power distribution synthesis. An error component for each ex-core signal is

?;

[ ] and added to the .%h v.a i.; N.y.'

% 9, 'e i,. .

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

bank measurement (reed switch position transmitters) is obtained ['

] The CEA nosition 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 3 power distributions are obtained by using a cubic spline fitting technique in conjunction with constants such as planar radial peaking factors (Fxy), Rod .

Shadowing Factors (RSF), Boundary Point Power Correlation Coefficients 'MQ (BPPCC), and Shape Annealing Matrix (SAM). A Temperature Shadowing Factor hMk (TSF) correction is used in the CPC to account for the inlet temperature E effect on neutron flux power.

B:

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. l 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 (27 ),

the standard deviation (op ), and the lower 95/95 tolerance limit (TLp ) 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 'kk[

measurement, and the CEA position measurement.

2.4.1.2 CECOR Fxy MEASUREMENT UNCERTAINTY N

~

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(17) 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:

x,iC . G4,P9 2-7

- . _ _ _ . ,w

where P and G are the actual Fxy and the CECOR calculated Fxy for the i-th 9 9 case, respectively.

2.4.1.3 STARTUP TEST ACCEPTANCE BAND UNCERTAINTY The CPC power distribution algorithm (1) requires values of the RSF, TSF, SAM, ano 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 hav.e associated uncertainties wh.ich affect the CPC calculated Fq and DNB-0PM. 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 startuo 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 (Py ) includes ex-core detector measurement error, depletion, and 4- ooack 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-0PM, 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 + AR) and the CPC Fq is re-calculated for 1200 cases at each time-in-life. [  ;

2-8

7_.

=

z-1 m

3 l

c-

'w-5'

~

3: . d 3

[ ] (2-8a) N_

.where h

[ ] (2-8b) -

-=

[ ] 1 The RSF uncertainty [ ] typically has been chosen based on differences between predicted and measured RSF values from previous startup test power >

ascension results. ]

O (2) Temperature Shadowing Factor (TSF) g The TSF algorithm has been modified for SONGS-2 cycle 2 (Ref. 20). This 4 modification will accommodate any uncertainty factors associated with the TSF g in the data base constants. Therefore, no penalty factor is required to  %

correct the neutron flux power calculation due to the TSF uncertainty. -Q (3) Shape Anne 2 ling Matrix (SAM) s

_N _

The CPC Shape Annealing Matrix (SAM) elements used in the power synthesis algorithm are verified during power ascension testing. The predicted SAM h elements are calculated by simulating a free unrodded xenon oscillation _'

similar to SAM startup test measurement procedure. The predicted SAM elements 4

=

-s 5

2-9 4

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-0PM.

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 ). Figure 2-4 shows the calculational 3

2-10

.,r. ;e .

.';W" J Lhl; .)

k..

2*. -

procedures for penalty factors due to BPPCC uncertainty. CPC LHR and DNB-0PM  ? )*,b are calculated for 1200 cases at each time-in-life with the BPPCC values with f.c. ; h and without in-core detector signal measurement error. The cases used for the []..y-BPPCC penalty factor calculation include changes in power distribution due to  ? *ff-

, j9 - < .. ,

changes in fuel depletion, core power level, CEA configuration, load ;Jg:;

maneuvers, and xenon / iodine concentrations. [ j;.f)'f.(

.?

.v'F.5'

-i7.gj

' .Y 4y

,3t{ . ...

. 5.; N 9

] _v; y

. =; sw -

~

The startup test a:ceptance band uncertainty (PS) is calculated by statistic- .

ally combining the penalty factors due to RSF, SAM, and BPPCC uncertainties t ? * . [~- ,.

and is represented by the following equation: il y4;.

..?.3 k.

c y t, ,

-l

[ ] (2-9)  %.((W" where b*

[

]

l 2.4.1.4 OTHER UNCERTAINTY FACTOR!

Axial Fuel Densification Uncertainty The axial fuel densification uncertainty factor (18) considers the global effect of the shrinkage of the fuel pellet stack, due to heating and irradia-tion, on Fq since the CPC Fq calculation does not account for it directly.

[

]

2-11 l , _ . _ . E

Fuel and Poison Rod Bow Uncertainties ..e The fuel and poison rod bow uncertainties (19) consider the effect of " bowing" )dhk.

of the fuel and poison rods, due to heating and irradiation, on Fq since the E ~ T. f, CPC Fq calculation does not account for it directly. These factors, calcu- 4 g^ 1 lated based on the methodology described in Reference 19, will be part of the i r

N.%

composite Fq modeling uncertainty, g..-

g' . 31 Computer Processing Uncertainty The computer processing uncertainty considers the effect of the computer 4Az machine precision of the C-E CDC-7600 computer and the on-site computer on the ,m.

7 ,- - ,

CPC Fq calculations. The computer processing uncertainty will be part of the y .:.f. i composite Fq modeling uncertainty. ,

. a.n.m Ry? : s Engineering Factor Uncertainty ..g The engineering factor uncertainty accounts for the effect of variations in  %

b.,s

f:

the fuel pellet and clad manufacturing process. Variations in fuel pellet gj,;,g ..

diameter and enrichment are included in this allowance, as are variations in a., 4,; y clad diameter and thickness. These result in variations in the quantity of NOdde

.WA @ Le fissile material and variations in the gap conductance. This factor, yg calculated based on the methodology described in Reference 18, will be part of _

?-y s;;p

~'

the composite Fq modeling uncertainty. c -:

2.4.1.5 OVERALL LHR LSSS UNCERTAINTY FACTOR l' 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 a ceptance criteria uncertainty, the axial fuel densification uncertainty, 'sel 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 (XFM) defined in equation (2-1) can be rewritten as:

I CI~FI (2-10)

Xpg =

Fj 2-12

i are the reactor core simulator calculated Fq and the CPC where F$ and C9 "

inferred value of Fq for the i-th case, respectively. A composite error (XFT) of the Fq modeling uncertainty and the CECOR Fxy measurement un-certainty can be.deterministically calculated as follows: ]

I XFT =

C G

i

-1 (2-11) M ]j gpsa i333 i

By applying equations (2-7) and (2-10), this leads to: kg-c i =X i +X i i i (2-12) u -

[1 X + (X pg *XFC )

FT FM FC .

I.[$.1C ' " ' ; ,.

.;h.', i The mean of the composite Fq modeling uncertainty is determined by:

f .- hl.

YFT

• TFM + FC + FM FC) (2-13) 4; ",j.

The "ka" of the composite Fq modeling uncertainty is detennined by combining [ '

the "ka" for CECOR Fxy (kaFC), CPC power distribution synthesis (kaFM)' 'i '

engineering factor (koFE), rod bow penalties (kapp, kapp),computerprocessing (y ~ -[{

(kaCP), and reactor core simulator III modeling error (koFR). ** By using the .[.3[ I

[ ] technique this (ko)FT is calculated by: Q..}

E- 3(2-14) MI 3A The resultant composite Fq modeling penalty factor (PMp ) is determined by 4W'[fy g

using the lower 95/95 composite tolerance limit for Fq (TLp ) as follows: g i :{f.'.[.-

I (2-15) 7$g PMp=

1 + TL p ph. $.,

= ..

where - (#g TLp=RFT - (ka)FT (2-16) -u The lower tolerance limit is used to assure conservative CPC Fq calculations E ,

EM

.g.y .

at a 95/95 probability and confidence level. [ "y h,. ,i . f- ..

The last step in deter:nining an overall Fq uncertainty factor (BERR3) is to YN combine the composite modeling uncertainty (PM p ), the startup acceptance criteria uncertainty (PSp) and the axial fuel densification uncertainty (PA).

Consequently,

[ ] (2-17)

• • See Appendix A.4 2-13

The LSSS LHR overall uncertainty factor (BERR3) is used [ ] on the CPC calcui46ted LhR (6//I) abu. Ud.

(2-W CPC " SYN" LHR * (BERR3)95/95 > "ACWAL" LHR Use of the overall uncertainty factor (BERR3) for the CPC calculated LHR assures at least a 95% probability, at a 95% confidence level, that the CPC LHR will be larger than the " ACTUAL" LHR. .

2.4.2 DNBR LSSS UNCERTAINTY ANALYSIS 2.4.2.1 DNB-OPM MODELING UNCERTAINTY UITH 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-0PM modeling uncertainty, a [ ] program is employed. [

1. ;;.: E, " ,.

Sk/h .);js 3:: .; .a.1

} ._ p. p,w -

4:.\ ". '

By comparing the reactor core simulator calculated DNB-0PM with the CPC f calculated DNB-0PM for each case, the DNB-OPM modeling error is obtained.

The mean of the DNB-0PM modeling error is represented by:

%[,=

Q'.:;.

il r ;]((

if.2'7i ,

(2-19)

[ ] < p:$ J h.iy$:;

e, .:

h-/

-p g4

?

Y #.i

[' g

,y l

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

2-14

?.4.2.2 DYNAMIC PRESSURE UNCFRTAINTY Core inlet temperature, primary system pressure, and primary coolant flow rate affect the calculation of DNB-0PM. Errors associated with the static temper-ature, pressure, and flow measurements must be accounted for in the calculation of the net CPC DNB-0PM uncertainty. These errors are .

implicitly included in the modeling uncertainty via the SCU program. h$h kk.Nh For the CPC DNBR calculation during a transient, the pressurizer pressure sensed by the precision pressure transducer is adjusted to get the RCS hk pressure by considering dynamic pressure compensation offset. In order to - #,W:;a]

e,n . .:

take account for RCS pressure change during a transient, an additional .

!W.,

uncertainty in the DNB-OPM overall uncertainty analysis is considered. ' E3

.pp Y$ $ 5 The uncertainty for the dynamic pressure may be represented by: .. .

[ ] (2-20) .- g

- -=

where

[ ] .

]

By using the CETOP-D code, the calculation of DNB-OPM is carried out over the E

parameter range of plant operation presented in Table 2-2. Wide ranges of l radial peak and ASI are also considered in this analysis. [

]

[ ] (2-21)

[  :

]

2-15

l l

The dynamic pressure compensation offset (aP D

) is defined as the pressure difference between sensor measured pressure and the RCS pressure during a transient. In order to calculate AP , the RCS pressure change rate during the D

worst transient (such as a pressurizer spray valve malfunction) is calculated.

Next, the dynamic pressure compensation is obtained by multiplying the pres-sure change rate by the dynamic pressure compensation offset. [

3 ..

2.4.2.3 OTHER UN. 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 en the CPC DNBR calculations. The computer processing uncertainty is represented by the tenn (ka)CP and is part of the DNB-0PM composite modeling uncertainty (kaDT). This computer processing uncertainty (kaCP) is calculated by using the following equation:

[ ] (2-22)

[

]

[ ] (2-23)

Startup Test Acceptance Band Uncertainty The startup test acceptance band uncertainty for DNB-0PM is detennined 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-0PM are determined by the method described in Section 2.4.1.4.

2-16

V

-System-Parameter Uncertainties L

In order to determine the minimum DN8R (MONBR) limit, C-E thermal margin

_ =meth6ds utilize the detailed TORC code with the CE-1 DN8 correlationThe .

(15) l@NBR 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 MDN8R limit:

1. Inlet flow di.stribution uncertainties

?. 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 MDN8R limit provides, at a 95/95 probability and confidence level, e 'that the' limiting fuel pin will avoia DNB. Since the SCU MDN8R limit includes system parameter ur. certainties as described in Part I of this report, these uncertainties are not considered in the determination of the CPC DN8-OPM

'overall uncertainty factor. ,

2.4.2.4 OVERALL DNBR LSSS UNCERTAINTY FACTOR The off-line overall CPC uncertainty factor for DN8-OPM (BERRI) 's detennined

-by combining all one-sided (upper) 95/95 probability / confidence tolerance limits of the error components. This overall uncertainty factor includes a DN8-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 DN8-OPM uncertainty factor, s

l 'A composite DN8-0PM modeling uncertainty is obtained by following a similar strategy to that used for the Fq uncertainty analysis. The CECOR Fxy 2-17

(

. measurement uncertainty is calculated in terms of DNS-0PM units using the sensitivity of DNB-OPM to Fxy { a(%DNB-0PM)/a(%Fxy) }. The mean of the CECOR Fxy error is given by:

m

[ ] (2-24a)

[. ] (2-24b)

The composite mean error.for the composite DNB-OPM modeling uncertainty can th:n be calculated as: ,

• (2-25)

IDT

• DM + IDC + DM DC)

The composite (ko) is made up of uncertainties fer DNB-OPM modeling algorithm (koDM), CECOR Fxy (koDC), r d and poison bow penalties (kapp, kopp), DNBR computer processing (koCP), and a reactor core simulator modeling error (koFR). Using[ ),thiscomposite(ko)DT is calculated as:

[ ](2-26)

The upper 95/95 composite modeling tolerance limit for DNB-0PM (TL D

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

(2-27)

TLD"IDT+(ko)DT The composite DNB-OPM modeling penalty factor (PM D

) can then be determined as:

(2-28)

PMD = 1 + TLD I

2-18

i In order to determine an overall DNB-0PM uncertainty, the composite DNB-OPM modeling penalty factor (PM ) is [ ] combined with the dynamic D

pressure penalty (PPD ) and the startup acceptance band uncertainty (PSD)*

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

, PPD , and PS D

[ .

] (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 " ACTUAL" DNB-OPM will be larger than the CPC DNB-0PM:

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

Therefore, the use of the overall uncertainty factor (BERRl) [ ,

]

on the on-line CPC hot pin heat flux distribution used in the DNBR calculation assures at least a 95% probability, at a 95% confidence level, that the CPC calculated DNBR < actual core minimum DNBR:

CPC calculated hot pin DNBR corrected with (BERRI)95/95 < actual core minimum DNBR (2-31) 2-19 l-

TABLE 2-1 STATISTICALLY MODELED VARIABLES NEUTRONICS CEA Positions Ex-Core Detector Signals ,

THERMAL-HYORAULICS RCS Pressure Core Inlet Temperature Core Flow f

2-20

r : -- ..

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

~

~

CEA Positions (in)

Ex-Core Detector (% power)

Signals Core Inlet Coolant ('F)

Temperature Primary Coolant (PSIA)

Pressure Primary Coolant (GPM)

Flow Rate .

f 2-21

FIGURE 2-1 CPC SIMULATION FOR Fq l

l - -

2-22

p._. ._. -.

FIGURE 2-2 CPC SIMULATION OF DNB-0PM 4 . ,

2-23

FIGURE 2-3 FLOW CHART FOR CPC OVERALL UNCEkTAINTIES FOR LHR AND DNB-0PM 3

~ Suui 2-24

l l

t i

4 i FIGURE 2-4 CALCULATIONAL PROCEDURE FOR PENALTY FACTORS DUE TO RSF, SAM, AND BPPCC UNCERTAINTY

• *I REACTOR CORE SIMULATOR F 0N84PM, AND EX CORE DETECk,OR SIGNALS FOR 1288 CASES i

CPC CPC . i RUN WITH SASE RUN WITH l PARAMETERS R'"

PARAMETERS R' ,

t  ?

i CPC F ON84PM CPC F ON84PM FOR 1h CASES FOR 1h CASES WITH SASE VALUE(R)

WITH R' f t

L 17 1 f e COMPARE CPC RESULTS e COMPARE CPC RESULTS i WITH THOSE OF REACTOR WITH THOSE OF REACTOR '

CORE SIMULATOR CORE SIMULATOR  !

e CALCULATE ERROR e CALCULATE ERROR e ANALYZE ERROR l e ANALYZE ERROR OISTRituTION OltTRIBUTION k k TOLERANCE LIMIT ,

l TOLERANCE LIMIT

! (TLO)

(TL) .

I I

PENALTY FACTOR r

NOMINALVALUE(R)

CHANGEDVALUE(R+aR) 2-25

3.0l RESULTS AND CONCLUSIONS

~

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

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

. t I

3.1 LHR LSSS t Following the analysis techniques described in Section 2.4.1. CPC synthesized

, Fqmodelingerrors.weretabulated(Table 3-1)forthethreetimesincorelife .

~(80C,MOC,andE0C). All time-in-life dependent Fq modeling uncertainties f were considered in evaluating the overall Fq penalty. However, the I time-in-life that led to the most non-conservative modeling uncertainty was .

used to determine the overall Fq uncertainty factor. The individual f 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 [ ']ata95/95 probability / confidence  ;

level. This overall uncertainty factor of [. -),whenappliedtotheCPC c 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 DN8R LSSS 4

~

I

'Following the analysis techniques presented in_Section 2.4.2, the CPC synthesized DN8-OPM modeling errors were calculated and are sunmarized 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 DN8-OPM r

uncertainty. The individual uncertainty components of the overall DN8-OPM l

uncertainty factor are presented in Table 3-2. Combining the uncertainties associatedwiththeON8RLS$$givesanoveralluncertaintyfactorof[ ] at a 95/95 probability / confidence level. This overall uncertainty factor, when

l. applied to the heat flux input to the on-line CPC DN8R calculation, will assure that the CPC DN8R will be smaller than the actual DNBR at a 95/95 probability / confidence level at all times during the fuel cycle, f l I

! 3-1 1

TABLE 3-1 CPC SYNTHESIZED Fq MDDELINEi ERROR III ANALYSIS ,

95/95 TIME IN INMBER OF MEAN ERROR TOLERANCE (2),(3)

CORE LIFE DATA POINTS (N) (Y),,% LIMIT (TL)pg v1

. MOC EOC 3%3 1

i i

i l

(1) ERROR = ( 7q -1) i (2) See References 12 and 13. Most conservative of normal or non-parametric values presented. l i  :

(3) If the error distribution is determined to be non-parametric, the value for (ka)g is calculated as -

(ko)g =-(TL)g +Ygg 1

l I  !

1 i

l i

1

y, _ _ _ . _

r TABLE 3-2 CONTRIBUTION OF INDIVIDUAL UNCERTAINTIES TO LSSS OVERALL UNCERTAINTY FACTORS r UNCERTAINTY I' LHR LSSS DNBR LSSS

.: ! Modeling Error (Y)py,(Y)DM ,

~

[T (ko)pg,(ko)DM CECOR Fxy (T)FC,

)DC (ko)FC,(ko)DC Engineering Factor (ko)FE cual Rod Bow (ko)pp Poison Rod Bow (ko)pp Computer Processing (ko)CP Reactor' Core Simulator (ko)pg

'Modeling

,4 Axial Densification PA

' ' L_c

' " Rod Shadowing P y

Shape Annealing Matrix P 2

Boundary PoinC ?ower P 3

Dynamic Pressure PP D ,

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

..CEA position error, a,.

~

(2) includes [

))inadditiontoerrorsof(1).

l i

3-3

TABLE 3-3 CPC SYNTHESIZED DNB-0PM MODELING ERROR (1) ANR YSIS 95/95 TIME IN NUMBER OF MEAN ERROR TOLERANCE (2),(3)

CORE LIFE DATA POINTS (N) (Y) , .

LIMIT (TL)DM

~ ~

B0C M0C 3

a E0C w

k SYN" DN8-0PM (1) ERROR = ("" ACTUAL" DNB-OPM ~ I )

(2) See References 12 and 13. Most conservative of the nonnal or non-parametric values presented.

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

(ko)DM = (TL)DM ~ DM

REFERENCES

1. Combustion Engineering Inc., " Assessment of the Accuracy of PWR Safety System Actuation as Performed by the Core Protection Calculators", CENPD-170-P and Supplement, July, 1975.

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

January, 1984.

3. Combustion Engineering, Inc., "COLSS, Assessment of the Accuracy of PWR Operating Limits as Determined by the Core Operating Limit Supervisory System", CENPD-169-P, July, 1975.

4. Combustion Engineering, Inc., " Statistical. Combination of Uncertainties Methodology", Parts I and III, CEN-124(8)-P, 1980.

5. Docket No. 50-317, i' Safety Evaluation by the Office of Nuclear Regulation for Calvert Cliffs Unit 1, Cycle 3", June 30,1978.

6. Combustion Engineering, Inc., " Response to Questions on Documents Supporting the ANO-2 Cycle 2 Licensing Submittal", CEN-157(A)-P, Amendment 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", 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 Thermal Margin analysis for System 80", Enclosure 1-P to LO-83-037, April, 1983.

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

10. American National Standard Assessment of the Assumption of Normality, ASI-N15-15, 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 Manual", Dover Publications, Inc., New York, 1978.

13. R. E. Walpole and R. H. Myers, " Probability and Statistics for Engineers and Scientists 2ed", 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",

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

R-1

~

15. Combustion Eng1neering, Inc., "CETOP-D Code Structure and Modeling

- Methods for San Onofre Nuclear Generating Station Units 2 and 3",

CEN-160(S)-P, May,1981.

16. Combustion Engineering, Inc., " Functional Design Specification for a Core Protection Calculator", CEN-147(S)-P, January 1981.

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

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., " 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", CEN-281(s)-P, June, 1984.

6 f

l i.

l l

R-2

l 1

l 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 [ .

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

A.2 State Parameter Measurement Uncertainties The on-line DNB algorithm (A-1) used for CPC requires primary system pressure, core inlet temperature, core power, primary coolant flow rate, and L 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. [

i

] 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-0PM overall uncertainty. Therefore, uncertainties with respect to temperature, pressure, and flow are implicitly accounted ~for in the DNB-0PM modeling uncertainty.

A-1

A.3 DNB-OPM Algorithm Uncertainties Ideally, the DNB-OPM overall uncertainty calculation would use three distinct thennal-hydraulic algorithms:

The off-line design T-H algorithm (CETOP-D) )

represents the base-line DNB-OPM calculation. CETOP-1(A-2) and CETOP-2(A-1 are simplified versions of CETOP-D, and perform the on-line thermal-hydraulic calculations for the plant monitoring and protection systems, respectiv-4 g jy(A-3) {. + ,

4

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

CETOP-D is a. fast running, accurate, core thennal-hydraulics calculator. It

-is used as the setpoint DNB-Overpower Margin calculator for all CPC/COLS5 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.

[

-m A-2

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-D. 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 was 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. [

.]

[ _ - .

3 A4 Reactor-Core Simulator Modeling Error The reactor core simulator uses the FLARE neutronic model to predict represen-tative power distributions. -The FLARE model is tuned to a more accurate and rigorous ROCS neutronic simulator code. The reactor core simulator modeling A-3

error accounts for the effect of the reactor core simulator modeling l

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

l 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 Trunsport Coefficient Model and Prediction-Correction Numerical Method for Thernal Margin Analys.is of PWR Cores", Nuclear Eng. and Design, P103-115, 64,, March,1981.

A-3 Combustion Ertgineering, Inc., " Response to.NRC Questions on CESSAR-F Statistical Combination of Uncertainties in Thermal Margin analysis for System 80", Enclosu're .1-P to LD-83-037, April,1983.

A-4 Combustion Engineering, Inc., "CETOP-D Code Structure and Modeling Methods for San Onofre Nuclear Generating Station Units 2 and 3", Docket No. 50-361, 50-362, CEN 160(S)-P, Rev.1-P, September 1981.

A-5 Combustion Engineering, Inc., "CETOP-D Code Structure and Modeling Methods for Arkansas Nuclear One - Unit 2," CEN-214(A)-P, July 1982.

A-6 Combustion Engineering, Inc., "CPC/CEAC Software Modifications for I Arkansas Nuclear One - Unit 2," CEN-143(A)-P, Rev.1-P, September 1981.

A-7 Combustion Engineering, Inc., " Response to Questions on Documents Supporting the ANO-2 Cycle 2 License Submittal", 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", Hafner Publishing Company, New York, 1961, p. 457.

l-l A-4

- a & -

% , h 1

i FIGURE A-1 DNB-0PM A!.GORITHMS ensus M

A-5 t

-_ - . - . , . , . - - - - - . . , - . , , , - - - - - - - - - - - - - -~-- ~ - - ~ - - + - - ~ ~ - - - - - - - ~ - - - - - * - ' - ' ' ~ ~ - ^ ' ~ ' ' ~ ~ ' ' ' ' ' ~ ' ' ~ ~ ' ' ~

APPENDIX B Core Power Level Measurement Uncertainty B.1 Uncertainty. Components w

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 allowance. .

. S_econdary 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, I based on the above uncertainty components and secondary instrument accuracies, is provided in Figure B-1. Verification of the secondary calorimetric power l

. error -is performed during startup testing.

l-I L B-1

^

The secondary calorimetric power measurement 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 -

l_

The thermal power transient offsets on CPC DNBR and LHR calculations are

~

evaluated to assure that the CPC Design Basis Events (DBEs) are adequately modeled. 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 (XTD)wasdeterminedas[ ] which covers the maximum non-conservatism involved. The DNBR thermal power transient offset is used in the l

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.

I B-2

The limiting DBE for the thermal power transient offset on CPC LHR calculation u  ;(XTF) is the single CEA withdrawal. This event gives the most non-conserva-tive' power for the CPC calculation of LHR. The thermal power transient offset

cn the CPC L!m calculation was determined as [ .], which covers the maximum n:n-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 i 1200 cases at-each time-in-life. The most non-conservative value of the one-  !

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 POWER TH = Adjusted thermal power POWERNF = Adjusted neutron flux power B = Calculated thermal power DT-B = Calculated neutron flux power NF BERRO = Thermal power measurement uncertainty factor for the CPC DNBR calculation BERR2- = Neutron flux power measurement uncertainty factor for the CPC DNBR calculation X = power level dependent core power measurement error SC B-3

l i

The; thermal power measurement uncertainty constant for the CPC DNBR calculation (BERRO) is determined by selecting the maximum value of the thermal power measurement errors (XCA+XTD) f r the core power range (0-100%

full power). ['

~3 The' neutron flux. power measurement uncertainty constant for the CPC DNBR calculation (BERR2) is determined by selecting the maximum neutron flux power measurementerror(XCA+Xue) at each power level for the core power range 1(0-130% full power).. ['-

3  ;

3 For the DNBR calculation", the CPC selects the larger of the thermal power

'(POWERTH) r the neutron flux power (POWERgy).

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

' POWER = power level input to the LHR calculation corrected for LHR power measurement uncertainties power level calculated from thermal or neutron flux power

'POWERCALC =

measurements (B DT or BNF,whicheverisgreater)

-BERR4 = core power measurement uncertainty factor for the LHR calculation X .= p wer level dependent core power measurement error SC f

B-4

.- - - - , - . . - . . . . , - ,,_-,,,,s.c ,#-.__,, . . , . , _ , ,,,,____,,,,y,,,, , , , _ - _ , _ , . , , , ., ,_ . ,,.__.,___.,_,.__,j _

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+ NF TF) ver the core power range from 0-130% full. power. [

]

The CPC power measurement errors for SONGS Unit 2 cycle 2 are given in Table B-2 as a function of power.

e i

B-5 l

7 TABLE B-1 CORE POWER SYNTHESIS. ERROR ANALYSIS II)

TIME-IN-- NUMBER OF MEAN LOWER 95/95 I2)

LIFE DATA POINTS ERROR . TOLERANCE LIMIT

~

BOC ,

M0C E0C , _

ca En (1) Power Synthesis Error = (SIMULATOR POWERCPC NEUTRON FLUX POWER - SIMULATOR POWER) -

(2) See References 12 and 13. Most conservative of the nonnal or non-parametric values presented.

t

- 0 0 ,

1 i 0 9

i 0 8

. 0 7

e R

O R

R .

R E 0 E 6 W R O E P W

O D P E T

1 C A

- I . 0 R B R 5 T N

, E E G R M I U I S G R E

- I O D F L

_ A F C i 0 O 4

Y  %

, R A

D N

O C

E i 0 S 3

- c i

0 2

i 0

1

- _ - - - 0 5 4 3 2 1 8Eaa g=o' 44

==

4 ' 1 1

.I* . .  !1j-1! :11 [! l1! i- l l,

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:

P -P '

ASI = p .p (C-1) where P and P are, respectively, power in the lower half and the upper half L U 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.

h-C-1

TABLE B-2 POWER MEASUREMENT UNCERTAINTY AS A FUNCTION OF POWER FOR DNBR FOR LHR SECONDARY TRUE .

CALORIMETRIC THERMAL POWER ** NEUTRON FLUX POWER ERROR *** ,

l POWER (%) ERROR (%) ERROR (%) POWER ERROR (%) (%)

0 l

! 20 40 60 co

, 4 80 100 130 _j l

(XSC) (XCA + XTD) (XCA + XNF) -

max CA XCA + Xgp 4

4 1

l

• Largest value installed in the CPCs.

! ** Power error for Thermal Power includes a transient power offset of [ ].

l ***[ -

1 ]

TABLE'C-1

~

HOT-PIN ASI ERROR III ANALYSIS 4

NUMBER OF MEAN LOWER 95/95(2) UPPER 95/95(2)

BURNUP DATA POINTS . ERROR LIMIT . LIMIT

~ ~

B0C

M0C 4

E0C n

k 1

4 l

1 l (1) ASI ERROR = (CPC ASI - SIMULATOR ASI)

(2) See References 12 and 13. Most conservative of normal or non-parametric values presented.

4

TABLE C-2 y CORE AVERAGE ASI ERROR III MRYSIS NUMBER OF MEAN LOWER 95/95(2) UPPER 95/95(2)

BURNUP DATA POINTS ERROR LIMIT LIMIT-

~ ~

BE MOC E0C _

n L>

(1) ASI ERROR = (CPC ASI - SIMULATOR ASI)

(2) 'See References 12 and 13. Most conservative of normal or non-parametric values presented,

COMBUSTION ENGINEERING, INC.

m O

be