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PALISADES INCORE DETECTOR ALGORITHM (PIDAL) |I

ANALYSIS OF QUADRANT POWER TILT UNCERTAINTIES!

G.A. BaustianConsumers i>cwer Company

August 14,1990

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CONTENTS

1: Objective

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2: Summary of Results

3: Assumptions

4: Analysis Methodology

S: Analysis Results

6: Palisades Core Map

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Objective

The purpose of the work described by this analysis was to determine the accuracy ofthe full core PIDAL power distribution calculations when the true core power distributionis radially tilted. This is in response to comments made by the USNRC while reviewing thePIDAL methodology and uncertainty analysis.

In particular, the NRC requested the following:

1- A comparison of the tilt measured by PIDALwith the true or theoretical tilt.

2- Verification that the PIDAL code programmingwas correct by supplying theoretical detectorinput and comparing the resulting PIDALsolution with the original theoretical powerdistribution solution.

3- Determination of the Srm uncertainty componentfor radially perturbed or tilted powei distributionsup to the full power Technical Specification limitof 5% quadrant power tilt.

4- An explanation of what assumptions are made inthe Palisades Safety Analysis to cover radialpeaking factor increases caused by quadrantpower tilts.

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Summary and Conclusions

Comparisons Laeen the quadrant power tilts determined by the PIDAL model w eremade to corresponding theoretical values. It was found that in all cases PIDAL eitheraccurately measured the quadrant power tilt, or in some instances conservatively measuredthe tilts to be greater than truth.

The Srci) uncertainty component as defined in the PIDAL uncertainty analysis wasrecalculated for radially tilted cores, it was found that in all cases the Sr(i> value for tiltedcores was bounded by the value used in the PIDAL uncertainty analysis for cores .zithquadrant power tilts up to 2.8%. It was also found that the value of the Srci) uncertaintycomponent depended strongly on the direction and magnitude of the oscillation causing thepower tilt. For cores oscillating about the diagonal core axis, the assumed PIDALmeasurement uncertainty is valid for tilts up to 5%.

For the ascillation about the core major axis, the Sr(s) uncertainty component ceasesto be bounded by the value assumed in the PIDAL uncertainty analysis for quadrant powertilts greater than 2.8%. Since the Palisades Technical Specifications allow for full poweroperation with quadrant power tilts of up to 5%, and it was clear that the current PIDALuncertainties were only valid for tilts up to 2.8%, it was necessary to derive newuncertainties to allow use of PIDAL for tilts abcVe 2.8%. An analysis was performed, asdescribed in Sections 3 and 4 of this report in order to determine the uncertainties in F9,F4" and F^ at the 5% quadrant power tilt threshold. These uncertainties may be found inTable #3 of Section 5 of this report.

It was shown that the coding in the PIDAL program is correct by reproducing atheoretically flat power distribution when given the appropriate theoretical incore detectorvalues. This is in agreement with results previously obtained as part of the PIDALUncertainty Analysis.

Finally, it was found that quadrant power tilt is not an input to the Safety Analysisand that the increase in local or radial peaking resulting from a tilted core scenario isimplied by the peaking factor or LHOR used in the analysis. There is no tilt multiplicationfactor applied to the peaking factors. ..

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Assump: ions

The Palisades FSAR specifically talks about three types of instabilities within thereactor core: radial, azimuthal and axial. This analysis is only concerned with the first twomodes. It is assumed that the use of the word " radial"in the FSAR refers to an oscillationwhich moves from the center of the core outward to the periphery and then back. Anoscillation of this type could be depicted by the top of a single spired circus tent beingraised and lowered. It is assumed that the word " azimuthal" refers to an oscillation whichtraverses the entire width or the core before returning back to the point of origination. Inthe rigorous sense of the word, this type of oscillation could hypothetically traversecircumferentially around the core as well, much like a pie tin would rotate if it were notperfectly balanced on a central point.

The Palisades FSAR states that a radial oscillation in the reactor is highly unlikelyand stable if it does occur. To this end, there are times when the word " radial" is usedloomly, meaning either a truly radial oscillation, or sometimes meaning "about the radialplane". It is hoped that the context of the usage will clearly dictate the meaning.

There is one fundamental difference between the uncertainties derived from thisanalysis and the original values derived in the PIDAL Uncertainty Analysis which wasbrought on by the nature in which this analysis had to be performed. In the original PIDAL

uncertainty components contained bothuncertainty analysis, it was assumed that the Snothe measured and inferred components of the box power synthesis uncertainty. For this

uncertainties calculated do not contain the same component because theanalysis, the Sngdetector powers supplied to PIDAL are based on theory. Since no data for significantlytilted cores exists for the Palisadet reactor, it must be assumed that recalculating theuncertainty components based purely on theoretical detector powers is valid.

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Analpis Methodology

in order to answer the questions posed by the NRC. it was necessary to supplyPIDAL with incore detector signals from a variety of radially tilted configurations. It wasdesired to investigate the effects of quadrant power tilts on the order of 0% to 50, as wellas more severely tilted cases on the order of 10G.

The 0% to 5% tilt range was chosen because this covered the range over which thePalisades reactor can operate at greater than 25G power while remaining within thequadrant power tilt guidelines set forth in Palisades Technical Specification 3.23.3. At thepresent time, power operation with quadrant power tilts greater than 5% is not anticipatedsince tilts of this magnitude are highly unlikely unless a dropped control tod or otherwisesevere localized power anomaly occurs. Nevertheless,it was deemed necessary to investigatehow well PIDAL performed when more severe tilts were present.

Since Palisades rarely operates with measured quadrant power tilts greater than 10,and measured incore detector signals for radially tilted cores were not available, it wasnecessary to find an alternate method for providing PIDAL with the required tilted incoredetector data, it was decided to use detector powers derived from full core XTG sc.lutionsas input to PIDAL This required that XTG cases be run which modelled rr. dial orazimuthal imbalances in the reactor core.

A total of four XTG cases were run in order to model a variety of azimuthal andradial Xenon oscillation scenarios. Three of the four XTG runs started from a restartcorresponding to roughly 3/4 total cycle length. The fourth case was run at BOC. These fourcases all started the transient by dropping a single control rod into the core and then leavingthe rod fully inserted for a period of 72 hours after which time the rod was rapidly pulledout. The ensuing transient was then followed for a period of 36 hours. The only differencesbetween the four transient cases run were which control rod was dropped and thereforewhich direction the oscillation took across the core.

The first two of the transient cases were run by dropping group 3 control rods intothe core. The first case dropped in a group 3 outer rod (rod 3 34) while the second casedropped in the central control rod (rod 3 33). The object of the case which dropped in the3 outer rod was to induce an azimuthal oscillation. The object of dropping the central rodwa io see if a radial oscillation could be induced.

The second two cases run both used a group 4 control rod as the transient initiator.The object of these two cases was to initiate an azimuthal oscillation which started off ofthe major axis (on a diagonal). Both of the two cases which used a dropped group 4 controlrod as transient initiator were identical with the exception being tbt the first case was runat 3/4 cycle length while the second case was run at BOC.

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Analysis Methodology-

After the XTG cases were run,it was necessary to infer theoreticalincore detectorpowers from the resultant three dimensional XTG power distributions. This wasaccomplished by writing a small utility program, XTGDET, which used the powerdistribution from the XTG punch file as input.

The purpose of the XTGDET program was to read in a 3 D power distributionpunch file created by XTG and convert the nodal powers into equivalent incore detectorpowers. Subroutine EXPAND is the meat of the XTGDET program. Based on the 3 Dnodal power distribution determined by XTG, it calculates the theoretical detector powers.EXPAND uses the same methodology as subroutine EXPAND of PlDAL and Section 2.2.1of the PIDAL Methodology Report should be consulted if further reference is required.

The XTGDET program was compiled and link edited four times. The program wasidentical for each compilation except for the incore detector location array, DETLOC. Forthe first compile DETLOC defined the actuallocations of the detector strings in the reactorcore (i.e. DETLOC was defined just like it was in the PIDAL block data section). For thesecond compilation the incore detectors spatial orientation to each other was not changed,but the entire core was rotated 90 clockwise underneath them. The third and fourthcompiles rotated the core 180* and 270* clockwise respectively from its true orientation tothe incore c'etector strings. The reason for wanting to rotate the core about the incoredetector locations will be discussed shortly.

Once the theoretical detector powers were obtained for the radially tilted conditions,they were input to PIDAL The core power distributions calculated by PIDAL were thetcompated back to the original XTG solution. For each of the PIDAL cases run, thestatistical analysis option was chosen in order to determine the uncertainties associated withthe PIDAL calculations for the tilted conditions.

Prior to discussing the actual PIDAL cases which were run, it is appropriate todescribe the temporary modifications which were made to the cycle 7 PIDAL model inorder to overlay the measured incore detector signals with the full core theoretical valuessupplied by XTG via XTGDET, In the main program, immediately after the call toSubroutine BXPWR (which calculates the detector powers based on measured millivoltsignals and the Wprimes), temporary coding was added which reads in the theoreticaldetector powers and detector level normalization factors produced by XTGDET. This readwas activated by the IXPOW f'ag which is normally used to tell PIDAL to use theoreticaldetector powers from the 1/4 core XTG model that runs concurrently with each PIDALcase. Following the input of the ful! core theoretical detector powers, the IXPOW flag wasturned off so that the normal 1/4 core theoretical detector power logic in PIDAL would nottake effect. Note that the measured detector powers are actually overlaid by the new codingand that PIDAL assumes the full core theoretical values to be measured from this point on.

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Analysis Methodology

A total of 19 PIDAL cases were run for this analysis. The irst case was a non tiltedf

base case which corresponds to the core conditions at 3/4 EOC. The XTG case used tosupply the full core theoretical detector powers was the second step of the 3/4 EOC group4 rod drop scenario. The base case is important because it serves to verify that the entiresystem is working as designed for this analysis. The following checks were made:

- Verifiertion that the full core XTG model forcycle 7 is working properly by comparing the fullcore XTG run with the 1/4 core XTG powerdistribution of PIDAL

- Verification that the XTGDET program isworking properly by comparing the full core XTGpower distribution with the XTGDET collapsed2 D radial power distribution.

- Verification that the XTGDET program isworking properly by comparing the XTGDETtheoretical detector powers with those previouslycalculated by the 1/4 XTG which is part ofPIDAL.

Verification that the full core detector signalsare getting input to PIDAL correctly fromXTGDET and that the PIDAL solutica is correctby comparing the PIDAL solution with theoriginal XTG solution.

With description of the base case out of the way, discussion on the remaining 18PIDAL cases is appropriate. The PIDAL cases run used theoretical detector powers fromtwo of the XTG dropped rod induced transient scenarios. The first 6 PIDAL cases usedpowers from the 3/4 EOC group 4 rod induced transient while the second 6 used powersfrom the group 3-outer rod induced XTG case.

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The first six PIDAL cases run corresponded to peak quadrant power tilts of 10%,7.6%, 5.6%, 2.9%,1.6% and 0.3% respectively. These cases were selected because they

| covered the spectrum of tilted cores for a tilt range of no tilt up to 10% tilt. Concentrationon tilts between 0% and ~5% was greater because it is over this range that the reactor may'

| be operated without reducing power or correcting the tilt. The second six PIDAL cases all; lie within the no tilt and ~5% quadrant power tilt range.

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Analysis Methodology

There were two reasons for using the two different transient scenarios as suppliersof the theoretical detector powers. First, the dropped group 3 outer rod scenario did notresult in quadrant power tilts greater than 5% Juring the oscillatory period. Therefore, itwas necessary to use cases from the dropped group 4 rod secuario in order to get results ontilts up to 10E Secondly, the oscillations between the two scenarios were quite different.The dropped group 3 outer rod oscillated about the major symmetric axis while the droppedgroup 4 rod scenario oscillated about the diagonal axis. Consideration of both is importantbecause the majority of the symmetric incore detector locations are rotationally symmetric(and not generally symmetric about either major axis or diagonal) and therefore oscillationsabout differing axis' could have differing effects on the accuracy of the PIDAL quadrantpower tilt algorithm.

Expanding on this last statement, it was decided to further investigate the effects oftilt location on the PIDAL solution. In the case of the dropped group 4 rod inducedtransient, the power peak used for the PIDAL cases 1 through 6 occurred in quadrant 2.What if the power peak was in one of the other three quadrants? In other words, what ifthe power distribution was the same, just rotated 90*,180* or 270 ? Since the incore

- detectors are not equally distributed over ine quadrants, it is not expected that the powerdistributions as measured by PIDAL would be the same for the rotated cas:s. The samequestions can be asked for the group 3-outer rod induced transient as well.

The XTGDET program allowed for use of the same XTG case for each of the fourpossible symmetric oscillations induced by individually dropped group 4 rods. In a similar,

l fashion, the existing group 3 outer dropped rod XTG case could be used for three additionalsymmetric transient scenarios.

Six additional PIDAL cases were then run. Three of the cases were for the 5% tiltedgroup 4 rod induced oscillation at rotations of 90,180 and 270* clockwise from the originalpower distribution. The other three cases were for the 5% tilted group 3 outer rod induced

i transient at rotations of 90,180* at d 270*.

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Analysis Results

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The results of the three transient cases which caused azimuthal xenon transients aresummarized in Table #1. From this table it is apparent that the core is less stable atbeginning of cycle than at EOC azimuthally. This is in agreement of Section 3.3.2.8 of thePalisades FSAR which states that it appears that the azimuthal mode is the most easilyexcited at beginning of life even though the axial mode becomes the most unstable later.From Table #1 it is also clear that the oscillation resulting from tne group 4 rod drop ismore severe from a quadrant power tilt standpoint than for the group 3 outer rod drop.The reason for this is that in the group 3 outer induced transient, the power peaking issymmetric along the quadrant lines, and therefore the peak tilt is actually distributed overtwo adjacent quadrants. in the case of the dropped group 4 rod transient, the powerpeaking is symmetric about the diagonal which lies within a single quadrant.

Table #2 presents the results of the PIDAL cases which were run and it is this datathat will be used to answer the questions asked by the NRC. The first NRC request wasfor comparison of the tilt measured by PIDAL with the true or theoretical tilt. For thedropped group 4 rod case, the agreement be: ween the PIDAL solution and the originalXTG quadrant power tilt was very good. For the true tilts between 0% and 10%, the errorwas on the order of 0.72% or less.

For the dropped group 3 outer rod induced transient, the quadrant power tilt was notas accurately measured, however it was measured conservatively in each case. For truequadrant power tilts of ~4% or less, the PIDAL tilt was still within 1% of the original XTG.When the true tilt rose to greater than 5% the error in the PIDAL tilt calculation reached1.23%. Again it should be noted that the PIDAL tilt fer these cases was always higher thanthe true tilt and therefore conservative.

j The second NRC comment asked that the PIDAL code programming be verifiedcorrect by supplying theoretical detector input and comparing the resulting PIDAL solutionwith the original theoretical power distribution solution. In actuality, this comment hadalready been addressed by the PIDAL Uncertainty Analysis. The S ,y uncertaintyg

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component represents the error in the PIDAL solution when PIDAL is given detector| powers from a known power distribution solution. For the entire data base, the Sr

uncertainty component was 0.0022. This value is in excellent agreement with the individualcase S ,) uncertainty components found on the statistical summary edit following each ofnthe PIDAL runs performed for this analysis.

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Analysis Results'

The third comment made by the NRC requested that a determination of the S ,,guncertainty component for tilted cores be made. To this end, the PIDAL statistical analysisroutines, which calculate the individual case uncertainty components, were activated for eachof the eighteen tilted core PIDAL runs made.The individual results are presented in Table# 2. When looking at these values, the reader should keep in mind the overall S nguncertainty component of 0.0277 for the entire data base arrived at in PIDAL UncertaintyAnalysis. Based on the results presented in Table #2 it can be concluded that theuncertainty component S ,) bounds core measurements up to quadrant power tilts of 2.8%n(linear interpolation between cases 9 and 10). Furthermore, depending on the direction ofthe oscillation, the PIDAL measurements are bounded to above the current 5% quadrantpower tilt Technical Specification limit.

For the oscillation symmetric about the core -diagonal, the PIDAL measurementuncertainty previously determined is valid for tilts up to 5%. For the oscillation about thecore major axis, the S ,) uncertainty cornponent ceases to bound the value assumed in thenPIDAL uncertainty analysis for quadrant power tilts greater than 2.8% This means that theuncertainties derived in the PIDAL Uncertainty Analysis are not valid for all cases whenquarter core tilts are greater than 2.8%. *

Because it was shown that the current uncertainties do not bound all tilted cases, itwas namary to find new uncertainties which take power distributions with tilts greater than2.8% into ac:ount. This was done by utilizing the PIDAL statistical processor program, tocombine the data from PIDAL cases 13 through 18. The PIDAL statistical program, whichwas developed and documented as recorded in the PIDAL Uncertainty Analysis, can takestatistical data output by individual PIDAL cases and combine it to represent an entirepopulation. Cases 13 through 18 were used as the basis for the new tilted core uncertaintybecause they all were based on theoretical tilts of roughly 5% (actually 5.58% and 5.11%).The 5% quadrant power tilt cut off was specified because Technical Specification 3.23.3allows for full power operation of the reactor for quadrant power tilts up to 5%, without anycompensatory action.

The results of the statistical combination for the tilted cases may be found in Table#3. The non tilted data presented is taken from the previous PIDAL Uncertainty Analysis.The F9, Fa h and F^ data presented in Table #3 is the basis for the revised TechnicalSpecification Table 3.23.3.

L In response to the fourth NRC comment, a diccussion on how quadrant power tilteffected the Palisades Safety Analysis took place with members of the Palisades TransientAnalysis Group. It was learned that quadrant power tilt is not an input to the SafetyAnalysis and that the increas t in local or radial peaking resulting from a tilted core scenariois implied by the peaking factor or LHGR used in the analysis. There is no tilt

| multiplication factor applied to the peaking factors.Ll

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Analysis Results*|

Intile.# 1

Step Hours Group 3 Outer Group 4 Group 4hom dron 3/4 EOC TILT 3/4 EOC TILT BOC TILT

1 0 1.0000 1.0000 1.0000

2 0 1.0627 1.0708 1.0708

3 72 1.0488 1.0542 1.0505

4 73 1.0191 1.0410 1.0458

5 74 1.0329 1.0697 1.0777

6 75 1.0424 1.0892 1.1011

7 76 1.0483 1.1007 1.1162

8 77 1.0510 1.1057 1.1238

9 78 1.0511 1.1054 1.1251

10 79 1.0495 1.1013 1.1212

11 80 1.0459 1.0941 1.1133

12 81 1.0416 1.0854 1.1025

13 82 1.0369 1.0757 1.0898

14 83 1.0318 1.0657 1.0761

15 84 1.0266 1.0558 1.0621

16 85 1.0217 1.0463 1.0484

17 86 1.0171 1.0374 1.0354

18 87 1.0129 1.0294 1.0236

19 88 1.0092 1.0222 1.0132

20 89 1.0060 1.0160 1.0043

21 90 1.0033 1.0108 1.0104

22 91 1.0011 1.0065 1.0145

23 92 1.0006 1.0030 1.0173

24 93 1.0018 1.0036 1.0189

25 94 1.0027 1.0045 1.0194

26 95 1.0033 1.0051 1.0190

27 96 1.0036 1.0054 1.0177

28 97 1.0038 1.0054 1,0159

29 98 1.0037 1.0053 1.0136

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Table #1 Peak quadrant power tilts for three scenarios each initiated by droppinga control rod, leaving it inserted for 72 hours and then rapidly withdrawing it. Values

| predicted by Palisades cycle 7 full core XTG model.,

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Analysis Results

TaNe *2

Case initiating XTG PIDAL % Tilt Srm S%,Rod Tilt Tilt Error

1.0000 1.0000 0.0000 0.0010 0.0008BASE - - - -1 4 1.1013 1.0959 0.54 0.0376 0.03212 4 1.0757 1.0721 -0.36 0.0280 0.02423 4 1.0558 1.0533 0.25 0.0198 0.01804 4 1.0294 1.0284 -0.10 0.0101 0.01025 4 1.0160 1.0158 0.02 0.0077 0.00666 4 1.0030 1.0037 0.07 0.0089 0.00447 3 Outer 1.0511 1.0634 1.23 0.0495 0.04458 3 Outer 1.0416 1.0520 1.04 0.0409 0.03679 3-Outer 1.0318 1.0403 0.85 0.0313 0.02S910 3 Outer 1.0217 1.0282 0.65 0.0219 0.021111 3 Outer 1.0092 1.0132 0.40 0.0112 0.011212 3 Outer 1.0006 1.0014 0.08 0.0083 0.0035

13 4 1.0558 1.0486 0.72 0.0239 0.0217'

14 3-Outer 1.0511 1.0606 0.95 0.0529 0.047615 4 1.0558 1.0533 -0.25 0.0207 0.018816 3-Outer 1.0511 1.0634 1.23 0.0490 0.043917 4 1.0558 1.0486 0.72 0.0228 0.020518 3 Outer 1.0511 1.0606 0.95 0.0533 0.0480

Table #2 - Quadrant power tilts and detector power uncertainty components forfor PIDAL for radially tilted cores.

Note: For all scenarios, PIDAL correctly identified the quadrant in which themaximum quadrant tilt occurred.

Cases 13 and 14 were for a core rotated 90* CW under the incores.

Cases 15 and 16 were for a core rotated 180* CW under the incores..

Cases 17 and 18 were for a core rotated 270* CW under the incores.

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Analysis Results.

Table #3

Statistical Standard Degrees of Tolerance Tolerance_ Variable Deviation Freedom Factor LimitF(s) # 0.0393 1800 --F(sa)# 0.0351 360

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F(r) # 0.0026 408---

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F(s) * 0.0306 3415 ---F(sa)' O.0241 683

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F(r) * 0.0021 969--

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F(s) 0.0277 8768 -F(sa) 0.0194 1754

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F(r) 0.0022 2754-

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F(z) 0.0151 1122-

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F(L) 0.0135 188---

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P # 0.0443 2487 1.703 0.0795Fo" # 0.0383 489 1.766 0.0722.

Ff # 0.0352 364 1.785 0.0695P * 0.0368 3822 1.692 0.0664F*" * 0.0277 877 1.733 0.0526Ff * 0.0242 694 1.74 6 0.04 )P 0.0344 4826 1.692 0.06234Fh 0.0237 1225 1.727 0.0455Ff 0.0195 1790 1.712 0.0401

Table #3 Summary of PIDAL Statistical Component Uncertainties.

# - values to be used when quadrant power tilt exceeds 2.8?c'but is less than or equal to 59c.

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- values for cores with once-burnt reused incore detectors.

Note: For the final tolerance limits, penalty factors of .0041, .0046 and .0067for P, P)" and F^ respectively were included to account for up to25% incore detector failures.

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