ML19310A227

Statistical Combination of Uncertainties Methodology,Part 1:C-E Calculated Local Power Density & Thermal Margin/Low Pressure LSSS for St Lucie Unit 1, Nonproprietary Version

ML19310A227
Person / Time
Site:	Saint Lucie
Issue date:	12/31/1979
From:	ABB COMBUSTION ENGINEERING NUCLEAR FUEL (FORMERLY
To:
Shared Package
ML17208A685	List: ML17208A684 ML19310A224 ML19310A226 ML19310A227 ML19310A231 ML19310A233
References
CEN-123(F)-NP, CEN-123(F)-NP-PT01, CEN-123(F)-NP-PT1, NUDOCS 8006060321
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CEN-123(F) NP i

4 8% s STATISTICAL COMBINATION OF UNCERTAINTIES PART 1 DECEMBER,1979 E POWER SYSTEMS COMBUSDON ENGINEERING, INC.

80060603 \

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LEGAL NOTICE THIS REPORT WAS PREPARED AS AN ACCOUNT OF WORK SPONSORED BY COMBUSTION ENGINEERING, INC. NEITHER COrv1BUSTION ENGINEERING l 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, l COMPLETENESS, OR USEFULNESS OF THE INFORMATION CONTAINED IN THIS j REPORT, OR THAT THE USE OF ANY INFORMATION, APPARATUS, METHOD,  ;

OR PROCESS DISCLOSED IN THIS REPORT MAY NOT INFRINGE PRIVATELY 1 OWNED RIGHTS;OR B. ASSUMES ANY LIABILITIES WITH RESPECT TO THE USE OF, OR FOR DAMAGES RESULTING FROM THE USE OF, ANY INFORMATION, APPARATUS, l METHOD OR PROCESS DISCLOSED IN THIS REPORT.

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CEN-123(F)-i1P STATISTICAL COMDIt1AT10:; 0F UliCERTAI!! TIES METHODOLOGY PART 1: C-E CALCULATED LOCAL POWER DEtiSITY AliD THERfiAL iMRGITULGU PRESSURE LSSS FOR ST. LUCIE Ui!IT 1 de 6

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Af;STP.ACT This report describes the methods used to statistically combine uncertainties f or the C-E calculated Local Power Density (LPD) LSSS and Thennal ibrgin/ Low Pressure (TM/LP) LSSS for St. Lucie Unit I. A detailed description of the unce. tainty probability distributions and the stochastic simulation techniques used is prdsented.

- The total uncertainties presented in this report are ex-pressed in percent overpower (I'fdn' fdl) units, assigned to the LPD LSSS and the TM/LP LSSS at the 95/95 probability / confidence limit.

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IABIE Of C0tiTEfils Chapter Page 1.0 Introduction 1.1 Purpose

. 1-1

1.2 Background

1-2 1.3 Report Scope 1-3 1.4 Sum. mary of Results 1-4 1.5 Reierences for Section 1.0 1-4 2.0 Analysis 2.1 General 2-1 2.2 Objective of Analysis 2-1

2. 3 Analytical Techniques 2-1 2.3.1 General Strategy 2-1 2.3.2 TM/LP Stochastic Simulatit.o 2-3 2.3.3 Local Pcwer Density Stochastic Simulction 2-4 2.4 Analyses Performed 2-5 2.4.1 lii/LP LSSS Analysis 2-5 2.4.2 Local Power Density ;SSS Anaijsis 2-11

2. 5 P.cferences for Section 2.0 2-13

3. 0 Results and Conclusions 3.1 Results of Analyses 3-1 3.2 Impact on llargin to SAFDL 3-3 l 3.3 References for Section 3.0 3-4 i

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_TABlI 0F C0!!TE;iTS (Continued)

@pendix Page A.

Basis for Uncertainties Used in Statistical A-1 Combination of Uncertainties Progran Al Axial Shape Index Uncertainties A-2 A2 ficasurement Uncertainties

' A-25 A3 Trip Syt, tem Processing Uncertainties A-29 B.

Summary of Previous llethods for Combining Uncertainties 8-1

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LISI Of I A!!L f 5 T,'l e l-1 Pfl" USSS P.irameters Af fec ting fuel Design L ir.ii ts 1-5 3-1 Uncertainties Associated with the Local Power Density LSSS and the IM/LP tSSS 3-2 3-5 In pac t of Sta t is tical Co'..bina t. ion o f lincertaint ies on liargin to SAFDL 3-6 LIST Of FIGURES Fioure 2-1 Pag Stochastic Simulation ?*ethodology 2-2 2-14 Stochastic Sin;ulation of the D:3 Linits 2-3 2-15 Stochastic Simulatior, of the LPD Limits 2-4 2-16 Thermal Margin Uncertainty Analysis 2-5 2-17 Linear Heat Rate Untertainty Analysis 2-18 D

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DLiINITION OF ACRONYMS AND ABBREVIATIONS ACU Axial shape index calibration uncertainty A00 Anticipated Operational Occurrence (s)

, APU,TPU Processing uncertainty ARD All rods out ASI LSSS Axial shape index after application of uncertainties

ASi ggg Axial shape index after inclusion of the DNB LSSS uncertainties LSSS ASi gg Axial shape index after inclusion of LHR LSSS Uncertainties B

Unless specifically defined in context as representing AT Power, B is used interchangeably with Q, core power.

B DNB fdn aRer applicadon of uncertaindes fdl fler application of uncertainties B P LHR B[gg LHR overpower including uncertainties B

Power limit for UR LSSS B

gE Available overpower margin B

opmo Reference B opm for calculating the constants in the 1M/LP trip equation LSSS OdNB P wer level after inclusion of DMB LS$$ uncertainties and allowances.

LSSS il LHR P wer 1 vel after inclusion of linear heat rate LSSS uncertainties aid al1owances.

B opmk (h) kth (hth) simulated value of overpovier margin, AB k (h ) value of sampled overpower uncertainty due to axial UP*k(h) shape index uncertainties i

BMU Power measurement uncertainty BMUk @) V lue of the pcuer measurement uncertainty sampled by SIGMA in trial k(h).

! BDC Beginning of Cycle 1

CEA Control Element Assembly l

l CECOR Computer code used to monitor core power distributions CETOP Computer code used to determine the overpower limits due to

• thermal-hydraulic conditions .

i CE-1 DNBR DNB Ratio calculated by the 10RC/CE-1 correlation I

l v l

i 2-- - 1

i DDE Design Basic Event (s)

Di Value of simulation point i DN3 Departure f rc:a tiucleate Boiling DMP,R Departure from Nucleate Boiling Ratio EOC End of Cycle F

Primary coolant flow rate f Number of degrees of freedom U

F "U Cooiant flow used in the generation of (P rdered pairs fdn' p) of data I

F g' Engineering factor on local heat flux i

F,, F" Synthesized three-dimensional core power peak i

4 4 P

F Planar radial peaking factor F

g Integrated radial peaking factor H

~

Height of core Core average axial shape index i Ig Fxternal shape index l 1 5 Axial shape index for the ith a s s e,T.b ly 1

p Peripheral axial shape index

-Q l

QUlX-calculated core average axial shape index 0

1 P QUlX calculated I p i

1 (RSF) QUlX calculated value of I p using the rod shadowing factor cethod

-n

! 1 R

ROCS-calculated core average axial shape index I

P ROCS calculated I p R

1p(AWF) ROCS power distribution based values of I using the assembly

! p weighting factor method R

I P(RSF) ROCS power distribution based values of I using the rod shadowing p

l factor method C

Ip I calculated by CECOR p

I .I calculated by CECOR L

Power in iower half of-core LC0 Limiting Condition (s)-for Operation LHS Latin Hypercube Sampling i LilR - Linear ficat Rate

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i LPD Local Power Density l

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s-F i.5SS i

I:0NBR Limiting Sately System Setting (s) 1 liininum Ord!R

I f10C itiddle of Cycle t

fist liegawatt(s) thernial tilC il ttoderator Ten;perature Coefficient t #

Sample size llSSS I

P Nuclear Steam Supply System (s) i .

Reactor coolant system pressure s I'(J) {

j Average power in axial node J t' ;

Axially integrated power of assembly i f'fdl j P fdl h Power Y I""

to the fuel design liait on fuel centerline IE e c lt i

fdl IIU" SI""I#'i "h i DN3 P

Pressure used in calculating the (P  ;

P fdn Power to ONBR SAFDL fdn' Ip) rdered pairs of data  !

P fdn Overpower f rom CETOP for the sampled e ers input param t in simulation k '

P var Variable low pressure trip limit DNB P

var PLSSS'ON8 Variable pressure to achieve DNB at the LSSS limit q

ygp P0ll Variable pressure to achieve DNB at the m LSSS li it Power Dependent CEA Group Insertion Limit including uncertainties ,

PliU PU Pressure lieasurement Uncertainty j Uncertainty limit in predicting local core power at th e fuel design

! P(x) Normt j Q ized power level at core height x QUIX Core power, auctioneered higher of flux power power or AT Computer code used to solve the 1 dimension 11 neut equation ron diffusion RCS Reactor Coolant Systui ROT Pressure equivalent of the total trip unit and proc essing delay time on DNCR for the DBE exhibiting the most rapid appr oach to the SAFDL 1

ROCS RPS Coarse mesh code for calculating power distributions Reactor Protection System j RSU '

Per.ipheral shape index uncertainty .

a Vii

. , 4- , , ,n. , - - . . , ,- - - _ . - , , -

l 4

H(x) Rod shadowing factor at. core height x '

5 Sample standard deviation SAfDL 5pecified Acceptable fuel Cesign Limit (s)

{ SAU i

Shape annealing factor uncertainty SC Approved credit in lieu of statistical combination of uncertainties SCU Statistical Cabination of Uncertainties SIG!!A 1 Stochastic Simuhtion Code

afiL5 Statistically cc

nbined uncertainties applicable to the Local

!' Power density LSSS T

g7 Azinothal tilt allowance l ,I j i

ReaClor coolbot Cold leg, inlet temperature Df;B

$ l jg Inlet Coolant ter perature used in the Calculation of (P ordered pairs of data fdn* p}

{ T n Final inlet coolant temperature for LSSS calculation T

h React r c lant hot leg temperature i TMLL Thermal Iiargin Limit Line(s)

Til/LP Thernal Margin / Low Pressure litu Temperature measurement uncertainty TORC /CE-l Thermal hydraulic calculational model including CE-1 critical

{ heat flux correlation l TPD Allowance for Transient Power Decalibration TPU i

Trip processing uncertainty j U Power in upper half of core VilPT Variable High Power Trip W Core average linear heat rate V!

cim Peak generated linear heat rate limit corresponding to the SAFDL on fuel centerline melt Wi Weighting factor of assembly i x Axial position

. X Sample mean 2 i O

5 value of a normally distributed randem variable with zero j- mean and unit standard deviation i

i a Shape annealing factor e

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r , .,,. s , nr s , ,,mr.. iy ey t- '-e

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I (4t),(p), a (Y) Coef f icients in use P lI1, equation U

f C Population mean 0 Population standard deviation i li Axial shape index correction term i

is (r) [ ,

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. C l' [  :

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18s [ ]

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'A f Chi-squared deviate with f degrees of freedom f

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1.0 Illf R00tfC I ION -_

l .1 PURPOSE The purpose of this report is to describe a rethod for statistically n ng combi i the uncertainties involved in the analog protection and monitoring setpoints. n syste The following uncertainties are considered:

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Uncertainty in predicting integrated radial pin power i

t' t 2.

1 Uncertainty in predicting local core pc.ver density i

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! Power measurement uncertainty l

4 Shape annealing factor uncertainty S.

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Shape index separability oncertainty

! 6.

i Axi.I shape index calibration uncertainty t

7.

Processing uncertainty-

8. ,

Pressure equivalent of the total trip unit and processing delay time for the DBE exhibiting the most rapid approach to the SAFDL on DNBR 9.

Flow measurement uncertainty 10.

Pressure measurement uncertainty I

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Temperature measureraent uncertainty

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1.2 CACV4ROUND

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1.2.1 Pro'tection and f'onitoring Sy". ten The analog protection and monitorinq systems in operation on the Combustion Engineering Muclear Steam Supply Systems h3ve been designed to assure safe operation of the reactor in accordance with the criteria established in 10 k CFR 50, Appendix A.

This is demonstrated in the Final Safety Analy',is j- Report (FSAR) and subsequent reload licensing amendments.

This is achieved by specifying:

1.

Limiting Safety System Settings (LSSS) in terms of paraneters directly monitored by the Reactor Protection System (RPS); and 2.

Limiting Conditions for Operation (LCO) for reactor system parameters.

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3. LCOs for equipment performance The LSSS, combined with the LCO, establish the thresholds for automatic pro-tection system action to assure that the specified acceptable fuel design linits (SAfDL) are not exceeded for the design basis events categorized as i

Anticipated Operational Occurrences (A00s). The SAFDL's addressed by the RPS are:

1.

Th.e reactor fuel shall not experience centerline melt; and

2. The departure from nucleate boiling ratio shall have a minimum allowable linit correspondina to a 95% probability at a 95%

l confidence level that DUB will not occur.

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The RPS trips jointly provide protection for all A00s. The RPS providing l

primary protection from centerline melt is the Local Power Density (LPD) LSSS.

The RPS providing primary DNB protection is the Thermal 1:argin/ Low Pressure (Til/LP) _ LSSS.

l The design of the RPS requires that correlations including uncertainties be j applied to express the LSSS in_ terms of functions of monitored parameters.

! l-2 w, I

l' These functions are the trip limits which are then set into the RPS. A

, list of parameters which af fect the calculation of limits for linear heat  !

i rate and Ofl0 protection is shown in Table 1-1. A nore detailed discussion of C-E setpoint methodology may be found in Reference 1-1. i

1. 2. 2 Previ_ous Uncertainty Evaluation Procedure The nethods previously in use for the application of uncertainties to the subject limits are presented in Reference 1-1 and summarized in Appendix 8.

As noted in Reference 1-1 these methods assume that'all applicable uncertainties occur simultaneously in the most adverse direction even though not.all of the uncertainties are systematic; some are randoc and some contain both i

systematic and random characteristics. This assumption is extremely conser-vative. As described in References 1-2, partial credit has been j allowed in view of the existence of this conservatism. This report documents the raethodology used to statistically ccTbine uncertainties explicitly in lieu of the credit previously used.

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1.3 REPORT SCOPE '

l The scope of this report encompasses the following objectives:

1. To define the methods used to statistically combine uncertainties applicable to the Thermal l'.argin/ Low Pressure (Til/LP) and Local Power Density (LPD) LSSS;

2. To evaluate the aggregate uncertainties as they are applied in the 6: termination of the TI1/LP and LPD LSSS.

l To achieve these objectives it is necessary to define the probability l-distributions associated with the uncertainties defined in Section 1.1.

The acvelopment of these distributions is discussed in Appendix A.

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The methods presented in this report are applicable to the following C-E reactor:

i St. Lucie Unit I (Florida Power & Light Coropany)

I* 1.4

SUMMARY

OF RESULTS The analytical methods presented in Section 2.0 are used to show that a i

stochastic simulation of uncertainties associated with the LPD LSSS and IM/LP LSSS results in aggregate uncertaint ies of [

4 ], reapectively, at a 95/95 probability / confidence lim t.

1 The total uncertainties previously applied to the LPD LSSS and the TM/LP LSSS are approximately [

I

], respectively. Therefore the use of the statistical cc:tbination of uncertaint ies provic'es a reduction in conservatism in the raargin to SAFnt of approxin.ately [ ],

i respectively.

1.5 REFERENCES

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l-1 CEt1PD-199-P, "C-E Setpoint Methodology," April, 1976.

i i 1-2 Docket flo. 50-335, " Safety Evaluation by the Office of fluclear Reactor Regulation," St. Lucie Unit I Cycle 3, 4

j May 27, 1979.

I 1-4 p- _ _ _ . _

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. . __ _ _ _ . . . _ _ _ _ .._ _____ . ~. _

4 T ABl.L' l- 1 t

NSSS PARAMETERS AFFECilMG FUEL DESIG!i 1.IMITS i

t DNBR l

1. CORE POWER

, 2. AXIAL POWER DISTRIBUTION j 3. RADIAL POWER DISTRIBUTION i

4. AZIMUitML TILI MAGNITUDE 1 5. CORE CO3LANl it LET TEMPERATURE 2

4 i

6. PRIMARY COCLAMT PRESSURE '

! 7. '

PRIMARY CGOLAMT MAS 5 FLOW b

i j Lit! EAR HEAT RATE l

i i 1. CORE POWER 1

j 2. AX1AL POWER DISTRIBUTION 4

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3. RADIAL POWER 0151RIBUTION r

4. AZIMUTiiAL TILT MAGt:ITUDE e

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2. 0 AfJALYSIS 2.1 GENERAL The following sections provide a description of the analyses rmed to perfo i - statistically combine uncertainties associated with the DNS LSSS and the LPD LSSS.

The technique involves use of the camp. iter code SIGM (Reference

~

2-1) to select calculations. data for the stochastic simulation of the TM/LP Apperidix A. The bases for the individual uncertainties are presented in The stochastic simulation techniqces'are described below.

2.2 OBJECTIVES OF ANALYSIS The objectives of the analyses presented in this section are:

1.

To document the stochastic simulation techniques for combining the uncertainties associated with the TM/LP LSSS and the LPD L ,

2.

To determine the 95/95 probability / confidence limit uncertainty i factor to be applied in calculating the TM/LP LSSS and LPD LSSS and ,

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To demonstrate that a simplified algorithm, derived from the detailed stochastic simulation techniques, is valid for combination of the uncertainties defined in Section 1.

2.3 ANALYTICAL TECHNIQUES l 2.3.1 General Strate g

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1-The stochastic simulation code used for the statistical combinat I

uncertainties associated with the TM/LP LSSS and the LPD LSSS is corrput er code SIGMA.

i

s 2-1

~ - _ .

p

• F M t  ? m'F M P- W-

• W

" T

g ,.& " _-, . - .- -

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!. pig A produces the dependent variable probability histogram for a number independent variables. Each oi the independent variables has a specified

' probability distribution associated with it. This is illustroted in Fit;ure 2-1.

k 4

The thecretical bases upon which this code depends are those' e involv Monte-Carlo and Stratified Sampling Techniques.

{' between the dependent variable and the independent variablese depends o The functional relationship 3

safety system under consideration.

l' For each independent variable a set of data points is generated corresponding to the probability distrib u on ti associated with that independent variable.

with each independent variable is then randomized.The resulting data set Finally the tirst data

{

point in each data set is selected a id all are combined accorning to the appropriate functional relationship.

) Combining these randomized independent variables in accordance with the appropriate functional relationship results in a calculated value of a dependent variable .

This process is i

continued until all data in each data set have been used and dependant variable probability histogram nas been generated .

The ratio of the mean value of the dependent variable to the lower 95/95 a prob bili ty/

confidence limit value is the quantity of interest for a lower limit.

The analyses considered in excess of two thousand (2000) r u ons power dist ib i

approximately equally distributed at three times in life (BOC , MOC, EOC) for a typichl reload cycle depletion.

These power distributions were used in the determination factors. _of the 95/95 probability / confidence e a nty limit unc rt i Power distributions were generated using xenon distributions and CEA configurations that could occur during steady state operation , load i

maneuvers that used for determination and uncontrolled of trip setpoints. axial xenon oscillations o in a man:

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y ~ .

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

I . . . ..

._ , _ _ _ _ , . .- . . . . . _ _ . , . . . . . _ - . . _ _ . , - _ - =

2.3.2 _TM/LP Stocha stic Simula tinn i

for the TM/LP LSSS, Du3 cverpower (Pfdn) is the dependent variable of in-terest. The core coolant inlet temperature, reactor coolant system pressure, RCS coolant flow rate, peripheral axial shape index and integrated radial peakirg factor are the independent variable of interest. CETOP (Reference 2-7),

which is based on TORC /CE-i (References 2-2, 2-3), is the model used to deter-mine the functienal relationship between the dependent variable and the inde-pendent variables. The probability distributions of uncertainties associated j with the independent variable are discussed in Appendix A.

Figure 2-2 is a flow chart represcnting the stochastic simulation of the DNB

! limits. The independent variables and their uncertainties are input to SIG"A.

Each data set ger.erated by Sire.A is evaluated with CETOP until a Pfdn prob-a bili ty distribution is generated.

The ratio of the mean value of Pfdn to the lor:er 95/95 value of P fdn is the quantity of interest for evaluating a lower limit.

The core coolant inlet temperature range of interest for the DNB LSSS stochastic sinJ1ation is bounded by the loci of the core power and core coolant inlet temp-

eratures corresponding to

1. the temperature at which the secondary safety valves open; and

2. the temperature at which the low secondary pressure trip occurs.

The reactor coolant system pressure rance of interest for the DMB LSSS stochastic simulatica is bounded by j l.

the value of the high pressurizer pressure trip setpoint; and

!. 2. the lower pressure limit of the thermal nargin/ low pressure trip.

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Ihe details of the specific ~TM/LP stoch.n, tic simulations performed are presented in Section 2.4.

2.3.3 Loca_1 Poser Censity Stochastic Simulation for the LPD LSSS, the power to fuel design limit on linear heat rate (P is the dependent variable of interest. fdl) i The peripheral axial shape index and 3-D peak are the independent variables of interest.

}

The functional relationship between the dependent variable and the independent variables is (Reference 2-4):

(Wclo) (1001

{ "fdl

• IFq) (Wavii) (2-1) where:

Wcin -

peak generated linear heat rate limit representing centerline i

fuel celt L' avg -

core average generated linear heat rate at rated power Fq -

synthesized core power peak.

j 9

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The probability distributions of each of the uncertainties associated with the independent variables are discussed in Appendix A. )

Figure 2-3 is a flow chart representing the stochastic sinulation of the LPD LSSS.

The independent variables and their uncertainties are input to l

_S I GM A .-

Each data set generated by SIGMA is input to the functional relation-  ;

1 ship defined above until a P fdl pr bability distribution is generated. The-ratio of the mean value of P fdl t the lower 95/95 value of P IS U quantity of interest. fdl t

l

- The details of the specific LPD LSSS stochastic simulation performed are i

presented in section 2.4. '

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2.4 ANALYSES PERf0hMEl1 2.4.1 Thermal Margin / Low Pressure LSSS Uncertaintv Analysis i i I In order to combine the uncertainties as shown in Figure 2-2 th -

simulation sequence shown in Figure 2-4 was used. ~

e stochastic j Distributions of the i following parameter uncertainties are input to the SIGMA _

sampling r;odule:

i.

t i

]

t I

i

.w ,

L 1

j Al each selected value of per ipheral axial shape index (1 ) the r epresentative p

I

' axial power distribution is read from the data file. ,

A series of siculation trials (500-1000) is run at this I . ,

value f rom each parameter dis tribution.Each si nulation trial uses 'ene sample 2.4.1.1 Sampling Module SIGMA i The values of input parameters selected for simulation trials are represen-tative of the actual distribution of parameter values.

The SIGMA sampling module (Reference 2-5) perforns this data selection using Latin liypercube Sampling (LliS .

LHS is a stratified sampling scheme that covers the range of the independent variables with a miniraum of simulation data points.

teristics are input to SIGMA [ Distributional charac-

].

is divided into equal probability intervals.In tilS the range _ of paraa.eter

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In each interval a' point'is

-selected at randon from the distribution, k .

2-5

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'P'

_ _ . _ - - . - - - - ,,,,w-.,-ww'w '

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

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Tile specific scmpling procedure used in this analysis is discussed.

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• • -. --, -- '-w a D. -e s=89m--- y--- w - 4%+ww' 6 9 w, ag wewq ,, y % gge-e.--ye ,9v t%- , , --.tv,v-,ie- - v g- --r +y-,-p-y*,e--ewre----e +- -- - e-n-e

' The specific sa:tpling peccedure used in this analysis is discussed.

The sampled values f or ecich interval are stored in an array. To generate set.s of input values, SIQ'A selects intervals at random from each variable using each interval only once in a simulation.

2-7

.-,,_-m=-- . _ . _ , . _ . _ - - -

\ 2.4.1.2 Axial Shape Index: Calculation i

I The a>.ial shade seen.by t.he excore detectors is related to the core avera axial shape provided by Ou!F. (Reference 2-6) by several factors. These f actors are obtained by calculation or rueasurec.cnt and are subject to some uncertainty. .

A 20-node core average axial shape is selected from [

.]. The core average axial shape index, i, from this shape. is calculated I L-U 20 "L+U i U= ^

E(J)

J=11 (2-9) 4 1 e (2-10) 10 7

L= j.. ) E(J) (2-11) lo relate this to the peripheral shape index inferred by the excores , the

, following relation is used:

M66 i

(2-12) i.

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(.

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' 2 !

l l

.% -.--- *- y.y- '~ _ _ . .. . - . - - -

1

[

] have uncertaint~ies associated with them. These uncertainties were used in SIGMA to generate representative values of [ ]. Using these values, corresponding values of Ip are cemputed to obtain a distribution of lp.

i - Uncertainties in Ip affect the nargin calculation by affecting the trip point selected by the on-line calculators. To account for this, the q,

standard deviation of the distribution of Ip is converted to overpower units using a conservative value of the sensitivity of overpower to Ip, Thus the standard deviation in overpower, o(B ) is (2-13)

This uncertainty in overpower due to shape index uncertainties is combined 4 with other f actors as detail.ed under Combination of Uncertainties (2.4.1.5).

2. 4.1. 3 Processing Uncertainties The Thermal Margin / Low Pressure (lM/LP) trip calculator receives inputs of i

hot and cold leg ten'peratures and Ip. It uses these values and the precal-culated setpoint relacion to produce a low pressure trip point. [

] methodology is used to estimate the uncertainty due to electronic processing in this result.

This estimated standard deviation in the low pressure trip point is calculated for mean values of hot and cold leg temperatures and Ip.

To produce the pressure equivalent of the processing uncertainty, pressure values are sampled from [ .

] the processing uncertainty for the low pressure trip. '

2.4.1.4 Overpower Calculation with Respect to DNBR i -

l l

i Overpower limits due to reactor thennal-hydraulic condit ions are determined l

by the code CETOP (Reference 2-7), which uses the 10RC/CE-1 correlation. . i t

l 2-9 i f- -,-.-.i--e- , - , * , - ~ . . , . , . , . . , - - . ,er ~ - - -

CflCP accepts values of pres'sure, inlet leaperature, axial shape , core coolant flow, and radial peaking factor, and ret. urns an overpower limit In the .

simulation sequence, the input arra:/ produced by SICf1A containing values o CE10it input pararceters is modified by adding an adjustment toe the pressur value. ['

' ]. The c.odified pressure value, along with the other parameter values, are input to CETOP, and the resultant overpower value is available for con. bit,ation with other overpower modifiers.

2.4.1.5 Combination of Uncertainties i

1 buring each simulation trial k, the value of D.'iB overpower produced by C_ Ell is nodified by additional u, certainty values to produce a final overpower value.

The final value is given by l

l Af for ter all simulation trials are run a distribution in overpower is produced each specific axial power distribution under study, incorporatinq all uncertainties under consideration.

I

\ 2-10

• l

2. 4. 2 - 1ocal Power Density t555 lincertainly Analvr.is 1 The stochastic simulation procedure shown in Figure 2.5 was used to implement i

the calculational sequence outlined in figure 2.3. The following distributions of parameter uncertainties are input to SIGMA:

l The SIGIM sampling module is cescribed in Section 2.4.1.1.

2.4.2J1 Overpower Calculation with Respect to Linear Heat Rate For. this calculation, ordered pairs of P and i values are input to the fdl code.

These are obtained from the lower bound of all the " flyspeck" points of the QUIX calculation. [

simulation run, fdl , is h

1 1

I (2-15).

The value of [ ] is obtained from SIGMA for each simulation trial.

2.4.2.2 ASI Calculational and Processing Uncertainties I*

• The I used in the linear heat rate simulation is converted to a peripheral

, shape index Ip as outlined in Section 2.4.l. If this Ip were generated from the excore detector signals, it would be subject to electronic processing uncertainties.

The uncertainty in the simulated value of Ip is 2-11

y _ _. .___ __ , _ _

i I ev.sluated by a [ ] methodology to estic: ate the uncertainty due i

to processing. Values of Ip and mean hot and cold leg temperatures are evaluated to produce a one standard deviation value in Ip due to processing uncertainties.

1 4

l t

k 4

This calculation froa i to ta g, is perforn:ed once for each simulation

trial.

l 2.4.2.3 Combination of Uncertainties For each simulation trial, [

I P

i ] the modified overpower value fdl . Thus, the LHR overpower including uncertainties, GLiiR ' IS h

4

! (2-16) 1 Over many simulation trials, the required distribution on overpower is i

built up for each value of ASI inccrporating the uncertainties under consideration, l

il 3

I i

l I

~

i i

)

h t 2-12 i

A

") , y 9y +94 -TT--T-"*-w' ' #~

I 2.5 RLIERi31CLS 2-1 F. J. Berte,'"The Application of Monte Carlo and Bayesian

\

Probability Techniques to Flow Prediction and Determination,"

T15-5122, Februa ry , 1977.

2-2 " TORC Code: A Computer Code for Determining the Thermal Margin of a Reactor Core", CEfiPD-161-P, July, 1975.  ;

i 2-3 "10RC Code: Verification and Simplified Modeling Methods",

l CENPD-2CG-P, January, 1977 j

i 2-4 CEf!PD-199-P, "C-E Setpoint Methodology," April, 1976. f j

r 2-5 McKay, M. D., et al., " Report on the Application of Statistical Techniques to the Analysis of Co.mputer Codes," LA-flUREG-6526-MS, Los Alar..os Scientific Laboratory, October,1976.

2-6 System 80 PSAR, CESSAR, Volume 1, Appendix 4A, Amendment No.

3, June 3, 1974.

.i i

1 2- 7 C. Chiu, J. F. Church, "Three Dimensional Lumped Subchannel

(

fladel and Prediction-Correction Numerical Method for Thermal  !

l Margin Analysis of PWR Cores," TIS-6191, June, 1979.

l

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d I

l l

l l

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POWER & LIGHT CO. ~

see Lucie mn, LINEAR HEAT RATE UNCERTAINTY ANALYSIS 25-Uni, i i

3.0 RESUI I5 A!y) CD!CLlf5fl0:1S i

4 3.1 RESULTS OF AriALYSES The analytical methods presented in Section 2 have been used to l

, show that a stochastic simulation of uncertainties associated with the

, Local Power Density LSSS and the T 1/LP LSSS results in aggregate uncertainties

. of [ ], respectively, at a 95/95 probability / confidence limit.

a j

Table 3-1 shows the values of the individual uncertainties which were statistically co:rbined to yield the above aggregates. Appendix A contains a

a further discussion of the bases for these individual uncertainties.

The aggregate uncertainties are in units of percent overpower (P and fdl Pfdn) and are applied in the generation of the LPD and TM/LP LSSS.as I

discussed below.

I 3.1.1 local Power Density LSSS l

The fuel design limit on lirear heat rate corresponding-to fuel centerline melting is represented by the ordered pairs (P b A lown bound is fdl' p drawn under the " flyspeck" data such that all the core power distributions

analyzed are accommodated. This lower bound is reduced by the applicable f uncertainties and allowances to generate the LSSS as follows

l (3-1)

[

(3-2) where:

B LS$$ -

LHR Power limit for LHR L5SS e

f I

l 3-1 i

(

E__ = _ _

LMLS - Statistically Combined Uncertaintie f.pplicable to the Local Power Density L5SS TPD -

Allowance for l eans ient Power Deca l ibrat. ion ASIL" 5 -

Axial sha;1e index associated with [i 3.1. 2 1M/LP LSSS -

~

The fuel design limit on GNBR for the TM/LP LSSS is represented by a curbinalien of the ordered pairs (P lines. fdn' p} "" '" 0 "f*l '#9 " I I A lower bound is drawn under the " flyspeck" data such that all the core power distribut.iens analyzed are acccatodated.

This lower bcund is reduced by 6pplicable uncertainties as follows:

(3-3)

(3-4) where:

Bopm -

Available overpower margin S(10$

- Statistically Combined Uncertainties Applicable to the IM/LP LSSS ASI ONB - Axial shape index associated with Bg , .

Both components of the TM/LP LSSS can be represented by the followinq eauations:

.memel (3-5)

(3-6)

(3-7)

N N

e 3-2

'~

. . ~ ..- . - -

7- ..

(3-8) where:

! o,p,y- Coefficients B

ONB Core power, % of rated power LSSS'DNB P

var -Variable pressure to achieve DNS at the LS' S Limit including uncertaintie; i

i RDT - Pressure Equivalent of the Total Trip Unit Processing Delay Time for the DBE Exhibiting the Most Rapid Approach to the 1 SAFDL on DhBR.

1

~

LSSS B

ONB -

P wer level after inclusion of DNS LSSS uncertainties and allowances.

i TPD - Allowance for Transient Power Decalibration

- L T.SSS,0NB-Core -

inlet temperature associated with P LS$5,0NS in var i

DNB -

j T in '

Inlet coolant temperature used in the calculation of (Pfdn' IP) "

ordered pairs of data.

I l

t 3.2 IMPACT ON MARGIN TO SAFDL The motivation for using a statistical combination of uncertainties is to l improve USSS performance throu0h a reduction in the analytical conservatism i in the margin to the SAFDL. This section contains a discussion of the i margin obtciinable through a reduction in this conservatism.

Table 3-2 lists the uncertainty values previously used on the plants included in this analysis. The approximate uorth of each of these uncertainties in terms =of percent overpower margin (P fdl' fdo) s s shown. -

3-3 i

t

! Ihe total uncertainties previously applied t i the local Power Density LSSS ,

t and the TM/LP LSSS are approximately [ ], respectively. The l .

uncertainties resulting f rom the a;] plication of the statistical combination of uncertainties program are approxir.iately [ ]. The use of the statistical corabination of uncertainties provides a reduction in conservatism in the margin to SAfDL of approximately [ ], respectively.

i j,

1 Although the conservatism in the margin to SAFDL has been reduced, a high j degree of assurance remains that the SAFDL 'till not be violated.

I ,

i  !

3.3 REF E ret:CES 1 l t

4 3-1 "IORC Lode: A Co:aputer Code for Determining the Theraal Margin of a i

1 Reactor Core", CENPD-161-P, July, 1975.

i 1

3-2 " TORC Code: Verification and Simplified t*.odeling Methods", CENED-206-j , P, January, 1977.

2 1

1 3-3 CEf1PD-199-P, "C-E Setpoint Methodology,' April, 1976.

3 .

I .

1 l

e 4

3-4

_ _ . .____ . _ _ . _ . . . a _ __ . . . _...______,._,______.,..,,._._._.___m._._._..

. - . . - . _ - .-- .. _ ~ . . _ _ - . _ - . ._

l ABLt F1 U!iCERTAliHil.S ASSOCI Ali D Willi lHE LOCAL PCi!ER DEilSI T ( LSSS A:;D liiE IM/Li' LSSS Uncertainty *' LPD 1.555 0:18 LSS5

, Core power (% of rated power) + 2% + 2%

Primary coolant mass flow (% design) liA ^^

Primary coolant pressure (psid)  !!A "

i Core coolant inlet ten:perature ( F) NA  ;**

__ a l Power distribution (peaking factor) TA, 0%

I

) 1. Separability (asiu) See Table 1 of Appendix Al

2. Calibration (asiu) [

i 3. Shape Annealing (asiu) 4 fionitoring system processing ((asiu)

L_ _

i i

j tiotes: *For complete description of these uncertainties, see Appendix A.

1

[ ] values D

Y I

i 1 .

. 1 i

e

<a 3 ;

s~ ,_

~m m. -

sw ' -

6 --- -

em e @p +-d- g- -4, e r?y -- ---e g '4N--rP7** w-F *- + y-+v--Pwye- t- + + * = * -*-9--t-a w

i I -

1Antt 3-?

3 -

l

)

_IliPACT OF ST ATISIICAL CO.*4BitiATIOff UF  ;

l Ut:CERTAltiTIES CN '~tRGIti TO SAfDL l

1 i

! Approxinate Values of

.i. Equivalent Operpower flargin (%)

l DNB LPD Uncertainty Value LSSS LSSS Pcwer 2% of rated Core coolant inlet

Temperature 2 F 1

j lteactor coolant system l Pressure 22 psid a

Axial shape index

i Separability [ ]

i Shape Annealing [ ]

l Calibration [ ]

i I!eactor coolant s:/ stem j Flow ( ]

l Perking factors 6% DNB, 7% LPD

{ Equiptr.ent processing:

Dt,'B LSSS

~

[ ]

LPD LS55 [ ]

Total Less credit for statistics Total Uncertainty Applied Previously Total Uncertainty Statistically Combined t!et flargin Gain e

3-6 '

. - -- _....------ - - - . . . ----s.

- - - + ,,-n-..m ,-,nnrw.--,,.c -, , , . . _ , - . ,.n, . , . , . .,,--,,_in-n-_...n.....,.., ..w.a.-.,.,--,. <.wwn.,--,-m.,-,-,..-,-,,~-,-,,,-.

i.

j.

I i

i 4

i

a 1

i i

l APPENDIX A l

Basis for Uncertainties Used in l

! Statistical Cctbination of Uncertainties I

e 4

6 l -

,l-I i

A-1 t

1

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

W--% m , ,

MT 9 -""P**- t-*' m~fW < 7YT **9+ **W@wm -@ -eq e-

• WrrzMw 's-Rl f M r9 T' pCW"r'-7 '"

• 4e- --Wg r yew 9y -

d,-p y y---wy- g o.-emw9-* t--N-T

I t

t i-i r

t t

l 4

i e

i i

I t

,i Al i

Axial Shape Index Uncertaint.ies t

t I

a t

k e i

4 f

' 1 1

1 i

(

3 A-2 r 1- wa-%'%%%',. ,

-.m-.-,+, .~ y ,, .-----.- ,, ,w -+-,-,ve,. e.,we-+,,- , ,w. . . . - . . . , -, 12eg. . . . , ~~1 rvir nom ,+amr-- m or - w-rw--+=v-w-e.1 m e nve-- e e r - e -wwe re

LIST Of 1A3tES

1. Uncertainty [ ] components for the Evaluation of the peripheral shape index.

2. [ ]

3. [ ]  !

4. fleasured Values of Shape Annealing factors.

5. [ ] Standard Deviation of the Shape Annealing Factor f or Each Channel.

I LIST if f IGURES i

! l 4 t

1. [ L 3

fiillstone 11, Cycle 1.  :

[

2. [ ]

. 't.

. Lucie I Cycle 2.

3. [ 3 Calvert Cliffs I Cycle 3. l t

l L

e l

A-3 '

- - - w - - ---- ~~~

i g ndix Al f

Al.1 Objectives of this Analysiss The four peripheral shape index uncertaint,ies which are incorporated into

, the setpoint analyses are: 1) the Separability Uncertainty,

2) the Calibra-Lion Uncertainty, 3) the Shape Annealing factor Uncertainty, and 4) the

{. Processing Uncertainty (uncertainties in the electronic processing of I

excore detector signals). Prior to the development of the methodology to co:.-bine thet-e uncertainties statistically, they were.ccit.bined additively 4

to yield a net uncertainty (Reference Al-1). The purpose of this part of the SCU progran is to develop the dat6 base necessary to support a pro-(

cedure for statistically co:: tining these four cox.ponents of the axial shape index uncertainty.

Table I shows the values of the uncertainties developed in this program.

A1. 2 General Strateg.:

E Each of the components of the axial shape index uncertainty is investigated i

in this Appendix in order to justify their statistical combination.

1

The Separability Uncertainty accounts for the difference between the core averaDe axial shape ir.dex and the peripheral axial shape index. This uncertainty has four ccaponents

l 1. [ ]

2. [ ]

3. [ ]

4. '[ ]

f The Calibration Uncertainly accounts for errors introducted into the protection systen when the excure detector system is periodically adjusted to match measured parameters of the core's power distributon.

h

-A-4

,-.:,==

lhe Shape Annealing Factor Uncertainty accounts fc+ the error in the

, "casure: rent of the shape annealing factor.

4 The Processing Uncertainty accounts for the uncertainty in Ip calculated by the protection system. This uncertainty is taken into account by its explicit representation in the stochastic sinulation prccedure used to statistically combine all the uncertainties.

Al.3 Specific Uncertainty Fvaluations A1.3.1 Sonarabilit" Uncertainty i

The Separability Uncertainty is a calculational uncertainty. It is the 1 uncertainty associated with inferring a peripheral shape index, Ip, from a given known core average shape index i. The one dimensional shape analysis used in the developT.ent of setpoints correlates the power to centerline trelt (Pfdl) and the power to DNB, (Pfdn) t e core average adal shape. ,

Since the exccre detectors respond only to the power distribution nea" the i

periphery of the core, a calculated relationship is needed between } and Ip.

This relationship, represented in the setpoint development by incorporation of the rod shadowing factors in QU_lX (Reference Al-2), is

' currently calculated by means of the three dimensional code ROCS (Reference i

I Al-3). The uncertainty in this calculation is the Separability Uncertainty.

The Separability Uncertainty consists of four components: [

.] The components of the Separability Uncertainty are discussed in detail below.

Al.3.1.1 [ ]

Definition of the first component of the separability uncertainty.

l ^4 A-5

., n. ,~e i _ . - t _

mM 5

) -

! Rod Shadowing factor Method l

ll The peripheral axial shape index, Ip, is defined in the following manner:

i U

~g

-D g I =

p DL+DU (Al-1)

If _

1 where DU = f dx R(x) P (x) (Al-2)

H/2 t

i H/2 Og = f dx R(x) P (x) (Al-3) 1 0 l

1 4

where D,D g are g the powers at the periphery of the upper and lower j

', half of the core, respectively.

i P (x) is the core average power distribution R(x) is the rod shadowing factor for the rod configuration inserted at position x.

H is the height of the core.

The rod shadowing factors are derived from the product of redded and unrodded 20 power distributions-and the assembly weighting factors, which account for the contribution of each assembly to the excore detector response to a 9 i ven power distribution.

k A-6

_. m_____

l l

t.

1 h

Assenbly Weighting _ Factor ik thod i

lhe Assembly Weighting Factor (AWF) method consists of the following l calculat. ion of Ip:

i*i i i 1 = 1W P (Al-4) l 9 i i i i

i where 3 P. '

e I is the axially integrated power of fuel assembly i '

i Ij is the axial shape index of asser61y i [

l W

9 is the weighting f actor of asserably i The W 5 values are computed f or those core edge asserablies which are the principal source of the excore detector's response.

h The result of this procedure is [

3 h

6 O

h I

i I

A-7 L...._,.'-,----

_ . _ _ __ _. . _ . _ _ _ _ _ _ . . _ . ~ _ _ _. _. . _ _ _ _ _ _

u An ilyt.es have tieteruined thi-s uncri tainty .ind h,ive .la>wa it to be essentially L

] This component of the separability uncertainty i i

is as shown in Table 1 along with the other components, j A1.3.1.2 [ ]

l e

i.

Definition of the second coaponent of the '

j separability uncertainty. ,

.i  !

j -

i S

[

l ] A review of previous cycles shows a

i that [' ] 1p is 1

i dependent on rod bank insertion. The [

. ] is rod bank insertion dependent. A[ ] fit of the calculated data was performed to determine the mean which is shown in Table 2. An error analysis perforraed on the dif ference between the calculated i

data and the mean shows that [

i

.] (see Table 1).

J I

A1.3.1.3 [ ]

The third component in the Separability Uncertainty consists of [

). The AWF method is described in section A1.3.1.1.

i

{

4 2

4 i ,

A-8

___ . . - _ . _ . . _ _ . _ , = _ . _ _ _ _ _ _ _ _ _ . . . . ~ . - . . _ . _ _ . . - _ . . _ _ . _ - . _ . , ._, _.. ._ -._. _. _. ..._ ____

Definition of the third corponent of the separability uncertainty.

1 A1.3.1.4 [ ]

The fourth component of the Separability Uncertainty consists of the [

] the uncertainty in the calculated power distribution also results in a component of the 5eparability Uncertainty.

Definition of the forth component of the separability uncertainty.

e 4

l A-9 g ..._... .. _ , .,_.m_.o.._.,_ _.

4 5

4 t .

[

t 1

-] . The result is as follows:

(Al-5) i Since the above result also [ i f 3 1

A1. 3. 2 Uncertainty on In e

l Calibration of the excore detectors relative to the axial shape index as measured by [

] The components of this measurement uncertainty consist of the uncertainty in [

i 1

i

] modeling the reactor power distribution.

The calibration is perfor:ned [

] This calibration is done near an ASI of zero so i that accuracy of the shape annealing factor has ninimal impact. on the calibration result. ,

f A-10

'he mNsuroment uncertainty on i is analyzed heroin by (

) Differences between I [

] were

{ studied to determine uncertainties statistically.

The mean and standard I

j deviation of the respective differences for each cycle wer e calculated, aftercould data which the data were exa".ined to determine whether be pooled. ce the'cyle by i

i L

i Description of data used. i' i

Results of analysis, i b l I  !

} . l Table 3 shows '

the standard deviations of the [ .

l The pooled cycles which formed th -

un rtainty data is

! also indicated in Table 3.

Al.3.. ,

Shape Annnalina Factor Uncertainty _

The shape annealing factor, o, t i

relates the external axial shape index Iis an experimentally measured v .

index. g to the peripheral axial shape  !

Ip = uI e

(Al-6)

This factor accounts for the f act that the excore detectors n o the respo d t .

power in beth the upper and the lower portion of the core.

. This signal mixing yields shape annealing tactors which are larger for.vhich detectors are far from the periphery than for detectors which are near e ry. the periph The theoretical lower limit of a is unity. [

o A-11

_ ,.,w,-M1 **""*# _ wwwwC***'* _ _ _ _ _ --

1 i The shape annealing f actor is raeasured { lbyinducinga

, xenon oscillation in the core and measuring the external shape index of the j S excore channel (I U

5) along with the internal axial shape index I as measured i

by the CECOR system using incore instruments. The [ ]

slope of I versus I g is the shape annealing factor. At the beginning of l'

1 lifeiisassum.edtobeequaltoI.[ p i

l-1

] as discussed above.

1 4

Measured values of the shcpe annealing factor are shown in fable I, for various C-E operat:ng reactors.

4 i

j An orror analysis was performed on this data to determine the deviation of each value of a from the average values for a given plint and a given

channel. The error analysis was performed on [

1 4

] The data is presented in Table 5 for all plants except for CC&E Unit 2. For BG2.E Unit 2 only one test has been performed and therefore a specific deviation from an average cannot be I

defined.

1 i

i l This data was analyzed for pooling using the Bartlett test, and for nor-

• I mality using the W test. It was found that the pooled standard deviation

[ ] and that the corresponding Bartlett statistic [

] This is to be compared with a theoretical Bartlett statistic at the upper 5% significance level equal to[ ]. This means that the above data is consistent with the assumption that all are samples from the same parent population. [

4

.[

l J i

A-12 L _

. . _ . _ , - _ . . . - - = -- -- --

l Since the adsumption of poolin!) nas been shown to be warranted, [

]

tolerance limit. can be evaluated. Results show that [

il i

i -

t 1- ] This K factor Lines the above standard deviation yielas a 95/95 tolerance limit 1

i I

[ 3 1

k l Al.3.4 Processing !!ncertainty

{

a The Processing Uncertainty is discussed in Appendix A2. I 1

Al.4 [ _ _ _ ) of the Peripheral Shape Index (Jncertainties 3

1

{

The folloeing [ ] have been identified in the develop: cent of l 3 peripheral shape index uncertainties.

[~ _

l t

i t i

t Discussion of the components of the i peripheral shape index uncertainties.  ;

i  !

l i

I f

l

. I

\

I g

k -. .

~

I  ?

I.

I j A- ~t3 i

i

l

' - Discussion of the coinpenents of the peripheral shape index uncertainties.

f The first equation is an identit '* T' n

~

f 11c'as from the assumption that [

.].

Equation 3 and the results su:r.:narized in Tabl

' 1 simulator described in Section 2.4 of this report 1

i O

D a

b 4

A-14

-.-~...--_-_.._._____

-L-___.:.._'_ *-

l 4 '

i AI 5 References *  !

j I I

Al-1 "C-E Setpoint,ftethodology," CENPD-199-P, April, 1976.  !

l l j Al-2 System 80 PSAR, CESSAR, Volume 1, Appendix 4A, Amendmern No. 3, June 3, 1974.

l- Al-3 BGEE Application for Cycle 4 Reload, AE Lundvall (BG&E) to j R. W. Reid (NRC), February 23, 1979.

i

\ '

l Al-4 " INCA, Method of Analyzing In-Core Detector Data in Power 1

l j

Reactors," CENPD-145-P, April, 1975. 1 1

Al-5 " Evaluation of Uncertainty in the Nuclear Form Factor t lleasured by Self-Powered Fixed In-Core Detector Systems,"

l CENPD-153, August, 1974.

i r f t l

I I

(

W O

4

.4-15

n. _ ;- - - - .;. . _::i .:uine = _. _; :, , _ c_ - . .v. 2 ,. .__,--..,__..._.._..___________.,.:._.__.._?

1 lable 1 4

, Uncertainty L ] Co.mponents for t! Evaluation of +he Peripheral Shape Index(l)

Ko 95/95 j

(asiu) K(f)(2) LJ

1. Separability Uncertainty s

i j

II. Calibration Uncertainty (0)

III. Shape Annealing Uncertainty (")

i 1

IV. Processing Uncertainty (n) l l r l flotes On Table 1 (1) All components of tne peripheral shape index have been tested for normality, [

]

, (2) f = degrees of freedom.

(3) [ ]

i 1

4 i.

i 1.

A-16 mr.. -

..._.i _ m- 27 ~ ~ ~

~~C.~~~, ,~T'~~J-~~.__,.. -~~~~.--

i

~

Table 2 1

1 Rod Bank Insert.!an

[ Generic OUIX Bias, asiu]

_- q All Rods Out. (ARO) 4

) Reg Bank 1 (20%)

Reg Bank 1 (40%)

Reg Bank 1 (60%)

Reg Bank 1 (80%), Reg Bank 2 (20%)

Reg Bank 1 (100%), Reg i ,. 2 (40%)

Reg Bank 1 (100%), Reg Bank 2 (60%)

Reg Bank 1 (100%), Reg Bank 2 (80%), Reg Bank 3 (20%)

j Reg Bank 1 (100%), Reg Bank 2 (100's), Reg Bank 3 (40%)

Reg Bank 1 (100%), Reg Bank 2 (100%), Reg Bank 3 (60%)

i t

e l

4 e

f A-17

.-_ $. __ _.7_-~ _

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

i I

l l

1 l

Table 3~~

I i

i i.

i.

l Mean Standard flun.ber o f Value, Deviation, i fjegctor Data Points asiu asiu

~

.\ ~

j l. St. Lucie I Cycle i i

2. St. Lucie I Cycle 2

3. Calvert Cliffs 1 Cycle 1

4. Calvert Cliffs 1 Cycle 2 f 5. ' Calvert Cliffs I Cycle 3

6. Calvert Cliffs II Cycle 1

7. Cahert Cliffs 11 Cycle 2.

8. Millstone 11 Cycle 1

9. Millsto'ne 11 Cycle 2

[

]

4 p 4 l

[

A-18

pp le 1 Measured Vaiues of Shape Annealing factors St. Lucie 1

- Cycle 1 Cycle 1A Cycle 2 Cycle 3*

June 1976 Jan 1977 June 1978 June 20, 1979 Channel 50% Puwe: 50?; Power 80% Power 80% Power l

3 he eI

• flote that a ne. streaming shield was placed in St. Lucie I at EOC2.

This ne.i streaming shield ch3nged the shape annealing factors.

Calvert Cliffs Unit 1 Cycle 1 Cycle 2

, Feb 1975 April 7, 1977 Channel 80Y Po.ter 50% Pc.,er 1

l l '

i I

3 e

e A-19 1

L _ ._.______ _ - . . _ . . _ _ _ _ _ _ _ _ . . _ -- -

. = - _ _ . _ . . _ - - _ - - . - - ._- . - ..- - _

l l

i iglh'4 i (Con t_ i nued)

Calvert. Cliffs Unit 2 i

Cycle 1 Dec 27, 1976 Chantiel 50% Power

..m.

j f'  !

i  !

l I

I l

f I.

l 1

i fiillstone Point 2 i I

Cycle 1 Cycle 1 Feb G-9, 1976  !

Channel March ll, 1976 50% Power 80% Power

_ l g b i

3 i

I l

hebusinium i

4 i

s i -f i .

i i . 6 I

1 ,

f 4

i

• A-20 '

= . _ _ _ _ _ . _ _ . - - --. _ _ - .

. I ab l e> b

[ ]

1 Standard Deviation of the Shape .

Annealing Factor for Each Channel

{

i i

f i

[ ] l j Plant & Number of Standard Deviation  !

j Channel Degrees of freedo:n per Channel I 1

i l i

I f . _

l j -.

1 .

! St. Lucie 1 '

I a ,

f t t

1 I

3 i

i i t i t Calvert Clif fs 1 i

Millstone Point 2 m

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4 j A-21

-- e e s e ,w. eme-> ~c. ----s--, - .-..--wn.--.,s-,--e.= _ . . . - , . _ - _ _ _ - . _ en- eren- reece

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t I 1 I o m N H r -t N m o .

o .

o o o o o O o o o o oi o i

(II - I-

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POWER & l.lGHT CO. fi O "r" St. l.ucie Plant '

Unit I Al--1

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1 5T I D

W G

P 4 U N

R U

S

- -' 3 2

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0 0 0 0 0 . . .

0 0 0 0 0 - - -

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r i

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4 A2 i

fleasurement Uncertainties i

G 9

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8 n-25

.._yc_....: -- > . : ~ ~ ~ ' -~ ~ ~~ ' ~ ~

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i

/gglix A2 1

A2.1 Basis for flow Uncertainty i

i t

The flow rate was determined by an evaluation of calorimetric data taken i ,

f rom the Glvert Clif fs fiuclear Power Plant at approximately 100% reactor f'

t power. ,

Uncertainty in that flow rate was evaluated by examining the uncertainties in each input parameter used in the flow determination. The l

inputs include hot and cold leg P.TD temperatures, systen pressure, and core i I thermal power.  !

The core thermal power is based on a secondary side calorimetric

, measurement.  ;

Each component uncertainty was first evaluated and then the i

j net effeet of all instrumentation inaccuracies on calculated ficw rate was determined [ t

]. The resulting overall [ ] uncertainty was found to be

[ ] of the design flow rate.

i i

! A2.2 4 Monitored Thermal-Hydraulic Paraneter Uncer tainty Distributions 1

The unc.ertainty distributions pretiously used to characterize the inputs to the safety analyses and setpoint theraal-hydraulics modules were based on j

. highly conservative assumptions.

Table 1 outlines these distributions.

j j

lt is now possible to refine these distributions using more detailed system analysis and observed plant data.

Updated distributions representing more detailed system analysis and measured data from the Calvert Cliffs ttuclear Power Plant have been examined to define specific contributors to the total

{ uncertainty and dependencies between parameters. The uncertainty distributions shown in Table 2 represent the results of this detailed-systems analysis.

9 e

A-26

l Measurenent of these parameters' uncertainties shu.s l'oth ranJora and '!

nonrandom components which are so small that their nest adverse contrib-utions are fully covered by the uncertainties of Table 2. The degree of

{

i dependency found is so sinall that, in conjunction with the size of the l

i evaluated uncertainties, the assumption of independence amoung the 1

'rameters of Table 2 is justified. Therefore, for the purposes of the '

statistical contribution of uncertainties evaluation reported herein, the i uncertainties of Table 2 can be used in the stochastic simulation nodel.

A.2.3 Power Peaking Factor Uncertainties I The 30 Power Peaking Factor Uncertainty (F q

) and the Integrated Radial Power  !

Peaking Factor Uncertainty (Fg ) are currently being re evaluated in response to fiRC questions regarding C-E's uncertainty topical report (Reference A2-1).

Pending resolution of these questions and approval of the topical report, C-E will continue to use the values listed in Table 3. These values are used f in the stochastic simulator described in this report. I i

i j References j

A2-1 " Evaluation of Uncertainty in the !!uclear Form Factor Measured by i.

Self-Powered Fixed In-Core Detector Systeins" CEtiPD-153, August 1974.

I l  !

l 1 l a

f

}  !

{* i 1

[ A-27 1

{-

4

p. .,

.:-.-.._--.-a... .; ~ . .: ..

La,-.n_.._._._._-___-___-__.-,___-. . _ _ _ . . - -

. .. . , . ..n. a

I Allt i 1 Previously Assumed Uncertainty Distributions on f tonitnred Thernal/ Hydraulic Parameters Parameter Distribution Note:

[ ]

TABLE 2 Results of Detailed Systems Analysis of Monitored Thermal / Hydraulic Parameters Parameter

. _ _ _ Distribution l

~

Note:

[ ]

TABLE 3 Peaking Factor Uncertainties Peaking factor Uncertainty (% of Power)

F R 6.0

.- f q 7.0 e

t A-28

. . _ - _. _.1... . .___ _ . . - . . . . - - - - - - - - - -- - --

__p,_ _ _ _ . .-.----- --

I 1.

~

l I

a i

t I

(

A3 Trip System Processing tincertaint,ies o

O i

A-29

-mw, _

[qipendix A3 i.

1 j A3 Trip System Processing Uncertainties lwo types of instrt. ment errors are considered in this analysis. First are those errors that are random in nature. The basic accuracy of an instrument or component falls into this category as it is dependent upon such factors t-as manufacturing tolerances, etc. Second are those errors that are Meter-ministic and present in approximately the same degree in any equipnent built to a given design. Examples of this type of error are changen due to j ter.'perature, changes under force loads etc.

1 The reason for considering two types of errors is that the mathematical techniques for combining errors frcm several sources differs for each type of error. The deterministic errors are combined using the governing equations and the techniques of ordinary algebra, while the random errors are best combined using probabilistic methods.

The method of determining the random error of an instrumentation loop is b ned upon two approximations. The first approximation is that the errors of the various pieces of equipment are independent. The second approx-

, imation that is used in the analysis is that the equations which define the relationshi~s p between the variables in the instrumentation loop can be approximated by the linear terms of a Taylor series expansion. This is a good approximation because the errors are very small in relation to the overall range of the quantities in question and cause only small perturba-tions about the norninal value.

The procedure followed in calculating the variance consists of obtaining

. . the partial derivatives of the syst.em or instrument equation with respect to each of the variables and evaluating them at the nominal values. These partial derivatives are then used to calculate the variance.

A-30 D 1 i

lhis method of determining the variance of a function of several variables was arrived at without placing any restrictions on the probability distri-butions of the variables involved, hence the method is generally applicable.

Having obtained the variance, its significance can only be interpreted in terms of the distribution to which it applies. The probability distribution of a function that is dependent upon several variables is dependent upon the distribution of those variables. However as the number of variables increases (such as that obtained by using the previously_ described method),

the resulting distribution tends to a normal curve (this is the Central Limit Theorem).

If the probability densities of the variables are reasonably concentrated

_.__near the nomin ) values [

d The instrument errors are calculated in the stochastic simulation procedure.

In this computerized error analysis, a subprogram is used for each type of module (i.e. , power supply, multiplier / divider, adder /subtracter, etc.)

Each subprogram accepts the input voltages and errors (in volts) for its module and determines the outputs of the module and their associated errors.

The simulation then goes through the calculator, module by module. As each module is reached, -the appropriate subprogram is called. The module inputs are obtained f rom the outputs of the modules which feed it.

h 9

e me e

A-31

.m._ _ -._ --_ _-

APPEt: DIX B Sum: nary of Previous Methods for Combining Uncertaint.ies 8

4 B-1

t l

l 0LE'l'J i x B i ^

The methods previously used for the application of uncertainties to the LSSS ,

aie presented in Reference B-1 and are summarized in this Appendix.

B.1 Limiting Saf ety Systen Setting on Linear Heat Rate (LPD 1555) l l, The fuel design limit on linear heat rate at fuel centerline melt is represented by the ordered pairs (P p}' ^ "" "" U" "" ""

fdl' this " flyspeck" data such that all the core power distributions analyzed are accommodated. Using the previous methodology this lower bouna was j reduced by the applicable uncertainties and allowances to./janerate the

{ Local Power Density LSSS as follevs:

1 L _

i (B-1) l (B-2) i -

i j where:

l i

I j T AZ

- Azimuthol Tilt Allowance i

PU - Uncertainty in predicting local core power at the fuel design limit s EMU - Power measurement uncertainty SAU - Shape annealing factor uncertainty RSV - Shape index separability uncertainty I

ACU - Axial shape index calibration uncertainty

.APU - Processing uncertainty

! B.2 Limiting Sately System Setting on DNBR (IM/LP L5SS) i.

I f*

+

The fuel design limit for the TM/LP trip on DNBR is represented by a certination of the ordered pairs (P 1 fdn' l p) and the DNB TMLL. A lower . I bound is drawn under the " flyspeck" data such that all the core pm.ter 1

k l

1 1

l j r2 j

p._.. _ . . _ _ _ . . . . _ _ . . . - . - . - - - -

. _ . . _ . . . . - . _ . . . . _ _ . _ _ __.-_.___.._______.t _ _ . _ . . . _ . . _ . _ _ _ .

,c..____ -.

l i

distributions analy.:ed are accor.imadated. Using the previous r;ethodology l this lower bound was reduced by a;)plicable uncertainties and allowances as 1

follows:

1 l

l l- (B-3)

(B-4) ubere:

SC - approved partia' credit for conservatism in uncertainty application.

Both components of the CPB LSSS were then represented by the following equations:

(B-5)-

(B-6)

(B-7)

(B-8) where:

RDT - Pressure equivalent of the total trip unit and processing delay time for the DBE exhibiting the most rapid approach to

, the SAFDL on DNBR PMU - Pressure measurement uncertainly TPU - Processing uncertainty j

i B-3 J

Bl4U - Power measurement uncertainty TMU - lemperature :neasurement. uncertainty REFEREf;CE

. B-1 CEf1PD-199-P, "C-E Setpoint liethodology," April, i976 l

i 4

i 4

k I

i 1  :

1

\

9 4

B-4 j

j f

• -w..- - . - - . .- . , , . . _ . , , , , , , . , , , _ . _

$ ,q +

sm -s w4 a em e---e < >- w -% -w --m w - s -w m- sv- F y vv+ .-.y.