ML18054B061

Rev 1 to Cpco Full Core Pidal Sys Uncertainty Analysis

ML18054B061
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Site:	Palisades
Issue date:	10/18/1989
From:	Baustian G CONSUMERS ENERGY CO. (FORMERLY CONSUMERS POWER CO.)
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THE CPCO Fl.JU. CORE PIDAL SYSTEM UNCERTAINTY.ANALYSIS G.A. Baustian Reactor Engineering Palisades REV O~June 05, 1~8~ P*PID*8~00Z REV 1--0Ctober 18, 1~8~ P*PID*8~00Z Rev 1 ABSTRACT This report provides an uncertaint~ analysis for the Palisades Incore Detector Algorithm, PIDAL. A detailed description of the individual uncertainties associated with using the PIDAL methodolo~ for determining the power distribution within the Palisades reactor is presented.

,' 8911010085 891023 1

PDR ADOCK 05000255 1

P PNU

TSP0889-0181-NL04 ATTACHMENT 4 Consumers Power Company Palisades Plant Docket 50-255 FULL CORE PIDAL SYSTEM UNCERTAINTY ANALYSIS October 23, 1989 50 Pages

1'HE CPCO FULL CORE P IDAL SYSTEM 1-INTRODUCTION Uncertainty Analysis REV l TABLE OF CONTENTS 2-DESCRIPTION of the STATISTICAL MODEL 2.1 Description of Uncertainty Components 2.2 F(s) Uncertainty Component 2.3 F(sa) Uncertainty Component 2.4 F(r) Uncertainty Component 2.5 F(z) Uncertainty Component 2.6 F(l) Uncertainty Component 3-CALCULATION of the UNCERTAINTIES 3.1 Methodolo~y/Data Base 3.2 Effects of Failed Detectors on Uncertainties 3.3 Results of Statistical Combinations 4-TABLES 5-FIGURES 6-LIST of REFERENCES

?- GLOSSARY

S.ection 1 Pl Rev 0 INTRODUCTION This report provides ~~ analysis documentin~ U1e uncertainties associated with using the Palisades Incore Detector ALgori thm, PIDAL, for measuring the full core three dimensional power distribution within the Palisades reactor core (reference #1).

The PID *.\\L methodolo~ was developed over the course of two years bl:/ the Palisades staff with the intention of having the full core PIDAL eventualll:I replace U1e original Palisades one ei~hth core INCA.model.

Initially, the full core PIDAL solution method was oased on a combination of the existin~ Palisades INCA methodoloffit and other full core measurement schemes. over the course of development, shortcomings in the previous meti1ods were identified, particularill:I in the w~ the full core radial power distributions a~d tilts were constructed. Several new techniques were employed w.'1ich resulted in an improved methodoloffit as compared to the previous systems.

In order to determine the uncertainty associated with using the PIDAL system for monitorin~ the Palisades power distribution, it was again decided to draw on previous industry experience. A copy of the INPAX-II monitoring s~stem uncertainty analysis, developed bl:/ Advanced Nuclear Fuels Corporation (formerll:I Exxon Nuclear) was obtained with the permission of ANF. After preliminarl:I work, the statistical methods used bl:/ ANF were deemed adequate, with a few variations, and the uncertainties associated with PIDAL were determined as described bl:/ the remainder of this report

• Section Z PZ Rev 0 DESCRIPTION of the STATISTICAL MODEL Section Z.l Description of Uncertaintv Components As mentioned in the previous section, the desire herein was to determine an uncertaintv associated with using the Palisades full core incore analvsis model for measuring reactor core power distributions. Therefore, the uncertainties were determined for three different measurement quantities:

F(q), core total peaking factor. Ratio of the peak local pin power to the core average local pin power. For Palisades this value is frequentl~ written in terms of peak linear heat generation rate.

F(Jlh), integrated pin peaking factor. Ratio of the peak in~rated pin.power to the core average assembl~ power.

F(Ar), assemblv radial peaking factor. Ratio of the peak assemblV power to the core average assemblV power.

For each of the parameters defined above, three separate components of the uncertainties associated with the peaking factor calculations are defined. For our purposes these are box measurement, nodal ~Ul.esis and pin-to-box uncertainties.

The box measurement component is the uncertaintv associated with measuring segment powers in the instrumented detector locationso The nodal ~thesis component is the uncertaintv associated with using the radial and axial power distribution svnthesis techniques emplo~ed bV the PIDAL full core model to calculate a nodal power. Specificallv, the uncertainties associated with the radial coupling to uninstrumented locations and the axial curve fitting used to obtain an axial power shape from five discrete detector powers.

The pin-to-box uncertaint~ is the error associated with using the local peaking factors supplied in the vendors phvsics data libracy to represent the pin power distribution within each assemblv.

With the three uncertaintv components defined above, 1 t was necessarv to mathematical lv re-define each of the peaking factors in terms of these components. This was accornpl ished bV utilizing forms for the peaking factors developed bV Advanced Nuclear Fuels Corporation (ANF, formerl~ EXXON Nuclear) for an uncertaintv anal~sis performed on the St. Lucie Unit 1 incore analvsis routine, INPAX-II. This analvsis is documented bv ANF in proprietarv report XN-NF-83-0l (p) (Reference #Z) used bv Palisades personnel with the permission of ANF

• J

Section Z P3 Rev 0 DESCRIPTION of the STATISTICAL MODEL The peaking factors, for purposes of statistical analysis, were written in the following forms:

F(q) = F(s)F(r)F(z)F(L)

F~h)

F(sa)F(r)F(L)

F(Ar)

F(sa)F(r) where:

F(s) =Relative power associated with a single incore detector measurement.

(1)

(2)

(3)

F (sa) = Re 1 at i ve power associated w i th the average of the de tee tor measurements within a single assembly.

F(r)

Ratio of the assembly relative power to the relative power of the detector measurements within the assemblyo F(z) = Ratio of the peak planar power in an assembly to the assembly average power.

F(L) =Peak local pin power within an assembly relative to the assembly average power.

An important point to be drawn from these definitions for the peaking factors is that the F(r) value is equal to the ratio of the assembly relative power to the F(s) or F(sa) value. Thus it should be apparent that the F(s) and F(sa) terms would drop out in a mathematical sense. The F(s) and F(sa) values were retained for the statistical analysis because their respective uncertainties could be calculated directl~ and used to quantif~

the box measurement uncertainty. It can be shown that the F(s) or F(sa) terms (denominator) disappear from the F(r) statistical uncertainty term.

See section Z.4.

Given the above representations for the three peaking factors of interest, the problem was to develop a method for determining the variance or standard deviation using a combination of the separate uncertaint~ components. For example, the uncertainty component for F(Ar) is as follows.

The peaking factor, F(Ar), is defined in equation 3 above. Using the general form of the error propagation formula given in Reference #5 Pl3l, (4)

(5)

Section Z DESCRIPTIO.~ of tl1e STATISTICAL MCXJEL From equation 3 tl1e partial differentials are computed as:

d-F(Ar) d F(sa) d F(Ar) 6 F(r)

= F(r) and F(sa)

Substitution of tl1e partials back into (5) gives:

2.

z

'Z.

z

~

sffA~) = F(r) sFrs....r F(sa) sffs)

P4 Rev 0 (6)

(7)

(8) 2 2

Dividing botl1 sides of equation 8 b~ F(Ar)

, which is equivalent to (F(sa)F(r))

gave an equation for tl1e relative variance for F(Ar) as:

(-:;~ f t.::~)

+ ( F:;~'0

( ')

It is now necess~ to find a more convienient form of equation ' to use for tl1e relative variance of F(Ar). This is done b~ using tl1e error propagation formula and implementing a simple variable transformation as follows:

let ~ = ln(x) d~

--=--

dX 1

and note ilia t x

Substituting into tl1e error propagation formula, l

Sy (10)

Note tl1at tl1e form of equation 10 is the same as the form of the individual components of equation'* Therefore, it is possible to substitute the natural logarithms in the individual variance (or standard deviation) for the actual independent variables. i.e. substitute ln(F(s)) for F(s) in equation Zl

• Section Z P5 Rev 0 DESCRIPTION of the STATISTICAL MODEL From the results of equations ' and 10, the followinJ;;l formulae for the

. relative sample variances of F(q), F(Ah) and F(Ar) can be written:

(11) z "Z.

2.-

sf(4\\.,.) = s,,,s... ) + Snr) + sf<t..>

(lZ)

(13)

It should be noted that equations 11, lZ and 13 are val id onl~ b~ assumi~

that the individual uncertainW components which make up the overall variance for the peaking factors are independent.

After determini~ the sample variance for each peaking factor, it is neces~ to construct sample tolerance intervals for each estimate. The J;;leneral form for the tolerance limits is given in Reference #3 page ZZl, as:

(14) where x = the estimated sample bias K = tolerance factor, based on interval size and number of observations S = estimated sample standard deviation For our purposes, it is necessacy to define onl~ a one-sided tolerance limit. This is because we are ~ing to quantif~ how ~

peaking factor measurements mey be below a given limit. In addition, if it can be shown that the overall variance (or standard deviation) for each peaking factor component is made up of normall~ distributed individual deviations, then the bias term becomes zero. Realizing these two points, equation 14 can be used to construct the following upper tolerance limits for each peaki~ factor:

+f¥r'b~SFr'%\\

Upper tolerance limit for F(Q)

+KF'fA~)SrtA~)

Upper tolerance limit for F~h)

+KrtAr)SF(Ar">

Upper tolerance limit for F(Ar)

(15)

(16)

(17)

For this anal~sis, a '5/'5 tolerance limit is used and appropriate K factors are used to determine the respective one-sided '5/'5 tolerance limits.

The tolerance factors (K), as a function of dewees of freedom, were taken from Reference #4

• Section Z P6 Rev O DESCRIPTION of the STATISTICAL MODE:L As mentioned previously, it is necessary to determine U1e appropriate number of degrees of freedom for each sample standard deviation in order to obtain tolerance factors. This is accomplished by using Satterthwai teTs formula which was also used in Reference #Z. This formula is given below:

For a variance defined as:

"'2-

+ *** 0

+ a _s I( r.:

The de~rees of freedom are given by:

+

s'f 0

(18)

(1~)

Section Z Pf' Rev 0 DESCRIPTION of the STATISTICAL MODEL Section Z.2 F(s) Uncertainty Component The standard deviation Srts) is defined as the relative uncertainty in the individual detector segment powers inferred by the full core model.

Inferred detector powers are those calculated for uninstrumented assemblies by the full core radial synthesis routine as opposed to detector powers derived directly from the detector signals in instrumented a.Ssemblies *

. The standard deviation Stts') can be obtained by comparin~ equivalent inferred detector powers to powers from already measured, instrumented locations. First, a full core power distribution is obtained based on the full core methodology described in Reference #1. Then, one detector string (consisting of five separate axial operable detectors) is assumed to be failed and the full core radial synthesis routine is repeated. Since the detector locations of the.. failed.. string are inoperable, the synthesis routine will treat these locations as uninstrumented and independent inferred powers for the once operable string will be obtained.

At this point, the.. failed.. string is ~ain made operable by using the original detector signals. A second string of five operable detectors is then failed and the solution step repeated. This scheme of failing and replacing operable detector strings is repeated until independent inferred segment powers have been calctilated for all operable strings in the reactor.

From this scheme, five deviation data points can be obtained for each fully operable string in the core. The whole process is then repeated for roughly fifteen separate power distribution cases from each of Palisades fuel cycles 5, 6 and?

• The eqllation for determining the standard deviation of all of the individual segment inferred/measured deviations is as follows:

where:

(ZO)

N.s = total number of inferred/measured segment power deviations J:

I'\\

= lnCFs*

) - lnCFs. )

c.

Ds =arithmetic mean of the individual Ds~

I"\\

Fs. = radially normalized measured detector s~ent power for detector 1 *

'J:.

F5. =radially normalized inferred detector segment power for L

detector 1 *

(Zl)

Section Z P8

• Rev 0 D~SCRIPTION of the STATISTICAL MODEL Section 2.2 F(s) Uncertainty Component It should be noted that there is an underlyin1;5 assumption made in usinf6 equation 20 to determine uie individual detector seement power standard deviation. It is assumed that the uncertainty associated with inferring powers in the uninstrurnented re15ions is greater than the uncertainty of the measured de tee tor se~1en t powers from instrumented 1 oca ti ons. This assu:np ti on is supported by the fact that the inferred detector powers, by design, are infiuenced by the theoretical solution via the assembly aver~e coupling coefficients. (Section 2.4, Reference #1) Therefore, the inferred detector powers will contain errors induced by ~~e theoretical nodal model.

Initially, this method m~ appear to not consider any uncertainty components brought about by detector measurement errors and errors in converting the measured detector signals to seement powers. However, the deviations between inferred and measured will in fact contain the measurement uncertainty because the relative difference between measurement and inferred detector seement power represents an estimate of the combined measl.Jred and calculational error

• Section Z P?

Rev 0 DESCRIPTION of the STATISTICAL MODSL Section Z.3 F(sa) Uncertainty Component The standard deviation Sfts.~)is defined as the relative uncertainty in t.~e aver~e of tl1e five inferred detector segment powers within an assembly. The inferred and measured detector segment power data used for tl1is co~.ponent comes from the same individual segment power data used for the Sfls) analysis.

The equation used for determining the standard deviation of the string-average detector segment inferred/measured deviations is:

where:

1 N5 "' = total number of inferred/measured average segment power deviations.

r DSc... = ln(F~Q* ) - ln(Fr_* )

~

~

--~

= ari tl1metic mean of the individual D~~

(ZZ)

(23)

= average of the radially normalized measured detector segment powers for detector strin~ 1.

~

Fs~* =average of the radially normalized interred detector segment powers for detector strin~ 1 o

Section Z PlO Rev 0 DESCRIPTION of the STATISTICAL MODEL Section Z.4 F(r) Uncertainty Component The standard deviation s;,... ) is defined as the relative uncertainty associated with the radial eysthesis from instrumented assembly powers to assembly powers for uninstrumented assemblies. This component assumes that the radial coupling methods employed are valid and accurate for inferring detector powers in uninstrumented assemblies, and that the resultant integrated assembly powers are similar to known values.

The data for this component is obtained by starting with a theoretical XTG quarter core power distribution and obtaining from this equivalent detector powers. Note that these theoretical detector powers are alrea~

calculated in the ful 1 core model for other uses. TI1ese detector powers can then be used as the detector data input to the correspondi~ full core case. The PIDAL model will then calculate a full core power distribution based on the XTG detector powers. The resultant integerated assembly powers are then compared with the original radial power distribution supplied by XTG. The difference will represent the error in the radial synthesis method.

The equation used for calculating the S t'Cr) standard deviation is:

i LD~ - Ne D~ ""l SFCr) =

N<' -

l where:

N, = total number of PIDAL/XTG assembly powers compared

s:

Dr* = lnCF.r* ) - ln(F.. * )

~

'I.

0'4"'

= arithmetic mean of the individual Dr~

(Z4)

(Z5)

F:.

= core normalized PIDAL F(r) peaki~ factor calculated b}I the full core modei for assembly 1 F(. = core normalized (original) XTG F(r) peaking factor for

~

assembly i As mentioned in section Z.l, the F(r) uncertainty term is mathematically the ratio of assembly relative power to the power of the detector measurements in an assembly. From equation Z5, it can be shown that the detector measurement term (either F(s) or F(sa)) drops out of the formulation. This is because the difference in the natural logarithms is identically equal to the natural logarithm of the inferred F(r) term divided by the measured F(r) term. Thus the denominators of each term would cancel out

• Section Z Pll Rev 0 I\\

DESCRIPTIO~ of the STATISTICAL MODEL

\\

Section Z.5 F(z) Uncertainty Component The standard deviation Sf(l:) is defined as the relative uncertainty associated with the axial systhesis from five detector segment powers to twenty-five axial nodal powers. This is the uncertainty associated with the axial curve fitting technique, including calculation of axial boundary conditions, employed by the Palisades full core model.

The data for this component is obtained by swting with a theoretical XTG quarter core power distribution and detector powers as discussed for the F(r) component. The XTG detector powers were again used as the detector data input to a corresponding full core case. The PIDAL model then calculates a full core power distribution based on the XTG detector powers. Tile resultant assembly normalized axial peaking factors obtained by PIDAL are then compared with the original XTG axial peaking factors for each quarter core location.

The equation used for calculating the SFli.) standard deviation is:

l~-z.

""")

1 L._Det -

N~ Dc-S:c =

Ne-l where:

Ne = total number of inferred/XTG F(z). axial peaks compared r

D1:..:. =

ln(F~\\. ) - ln(F ~' )

De- = arithmetic mean of the individual D~c:

(26)

(27)

r F.:c.:. = assembly normalized F(z) peakini.;i factor calculated by the full core model for assembly i I""

F~L = assembly normalized (original) XTG F(z) peaking factor for assembly 1

• .I

~-*

• Section Z PlZ Rev 0 DESCRIPTION of the STATISTICAL MODEL Section Z.6 F(l) Uncertainty Component The standard deviation s,11.) is defined as the uncertainty associated with pin-to-box factors supplied to PIDAL in the fuel vendors cycle dependent data library. This factor is the ratio of assembly peak pin power to average power for that assembly. These factors are supplied by the fuel vendor (Advanced Nuclear Fuels Corporation) and come from quarter core PDQ models used by ANF in the Palisades reload design process.

The value of Sft1.> can be obtained from ANF. The value currently used by ANF, as determined for Westinghouse PWR*s, and Combustion Engineering PWR*s with 14Xl4 assemblies is.0135.

Because Palisades has cruciform control rods and thus there are wide-wide, narrow-wide, and narrow-narrow water gaps surrounding the Palisades assemblies, there is some concern that the same value for SF,.. ) can be used.

It was determined however, that the previously derived ANF pin-to-box uncertainty component could be used herein for the following two reasons.

The ANF cycle dependent pin-to-box fac~r are generated using PDQ methods that are consistent with other reactors for which ANF supplies physics data.

Therefore, it is expected that the error in pin powers calculated by ANF for Palisades will be similar to the error that ANF has derived for other PWR~s.

Secondly, concern over the abi 1 i ty of a two-group PDQ model to accurately describe the local power distributions in the regions of the differing water gaps prompted an agreement between the NRC, CPCo and ANF to have ANF use a four group PDQ model for Palisades design work. It is reasonable to assume that a four group PDQ model for Palisades wi 11 be at least as accurate as a two-group model for other PWR*s. Therefore, the ANF value of sF,.. ) =.0131;;

will be used for this analysis.

Section 3 Pl3 Rev 0 CALCULATION of the UNCERTAINTIES Section 3.1 Methoclo 1 om; /Data Base Four steps were taken in order to determine the uncertainties associated with the PIDAL full core moni taring model. The first step consisted of defining an appropriate statistical model. This was done as described by Section Z.

The second and third steps consisted of generating the computer software necessa.I1{ for implementing the statistical model and running the necess~ computer cases. These steps are described in this section.

Finally, it was neces~ to take the results of the computer cases and combine them in order to determine the overall uncertainties as defined b~ ~~e statistical model. Included in this step was an investigation of the effects of fa i l i ng 1 arge numbers of i ncore detectors on the P IDAL methodolo~. The results of this step are discussed in Sections 3.Z and 3.3.

Three computer codes were used for the statistical analysis work performed. The following brief discriptions apply.

The PIO.~ main program was used to determine the measured and inferred full core detector powers and power distributions required.

The PIO.Ar.. program was described in detail b~ Reference #1.

The B!JSTAT program was used to calculate the F(s), F(sa) and F(r) uncertainW components. This program reads output files generated by the PIDAL program statistical analysis routines and calculates the deviations, means and standard deviations required by this analysis. BDSTAT also sets up histogram data files for figure plotting.*

The STATFZ program was used to calculate the F(z) uncertaint~

component. This program reads output from the PIDAL exposure data.

file and calculates F(z) deviations and statistics between the stored PIO.Ar.. and XTG values. STATFZ also sets up a histogram data file for plotting.

The data base used for this analysis was generated using measured and predicted power distributions for Palisades cycles 5, 6 and 7. For the F(s),

F(sa) and F(r) uncertainty components a total of 54 PIO.Ar.. cases, equally distributed over the three cycles, were run. The cases used were selected from Reference #'1. Since Reference #'1 contained twice as many cases as were statistical!~ necessacy, it was decided to use use only half of the cases so only everv other case was selected. Tables #1, #Zand #3 list the cases which were run using the PIDAL statistical analysis option for cycles 5, 6 and 7, respectively.

• ~-.:

Section 3 Pl4 Rev 0 CALCULATION of the UNCERTAINTIES Section 3. l Me thodo l om1 /Data Base Three separate C¥cle 7 BDSTAT statistical runs were performed. The first considered the entire compliment of detector data, includin~ fresh and reused incores, and the original cycle 7 INCA WT signal-to-box power conversion libr~. This libra.r,/ was revised b¥ ANF which resulted in a second set of statistical data. A thj ::-d cycle 7 set was then generated which omitted the reused detectors from t.-ie cycle 7 data. Note that the statistics from the first C¥cle 7 BDSTAT run are fo~ information onl¥.

A total of ZZ PIDAL cases were run in order to generate data for the PIDAL F(z) uncertaint¥*component. Of these 22 cases, 11 were selected from the cycle 7 INCA run log. These 11 cases were selected at app;oximatel¥ equal intervals over the fuel cycle. Also part of the total ZZ cases were 11 cases run from a h~othetical EOC 7 Xenon oscillation. These cases were selected in order to include off-normal axial power shapes in the uncertaint¥ anal¥sis.

Table #4 lists the cases used for the F(z) uncertainty component.

One concern was the fact that the.. known.. axial power shapes which were to be reconstructed using PIDAL came from XTG solutions. This was a problem because XTG does not account for slight flux depressions caused b~ fuel assembl¥ spacer grids. It is reasonable to assume that axial peaking uncertainties caused b~ these t~es of flux disturbances would be smal 1, compared to the off-normal axial shapes being investigated, and therefore these fluxuations were ignored b~ this anal~sis

• Section 3 Pl5 Rev 0 CALCULATION of the UNCERTAINTIES Section 3.2 Effects of Failed Detectors on Uncertainties Current Palisades Technical Specifications require that 50~ of all possible incore detector locations, with a minimum of two incore detectors per core level per quadrant be working in order to declare the incore monitoring ~stem operable. A look at current Combustion Engineering standard technical specifications revealed that the current standard is for 75% of the possible incore locations be operable. It is assumed that the CE standard is referring to plants which. incorporate the standard CE full core moni taring methodologies.

It is anticipated that the Palisades technical specifications will be revised to reflect the current CE standard once the PIDAL methodolomt becomes production. In order to make this change, the st.u~ described bV this section was necessa.I11 in order to justif~ the 75~ operabilit~ value which will be used.

In Reference #Z, ANF came to the conclusion that the accuracy of an incore monitoring ~stem or methodolomv depended more on which iru:itruments were operable than on the total number operable. ANF also concluded that it was best to use all available data points in determining the individual uncertainties and therefore did not go into great detail investigating the effects of large numbers of incore failures on the r;nea.sured/inferred power distribution. These conclusions are valid because, for random detector failures, there is an equal probabilit~ that the well behaved detectors and the non-well behaved detectors would fail.

In order to prove these conclusions it would be necessary to test evecy possible combination of failed detectors for a large set of power distributions.

From a computational standpoint, this would not be practical. Therefore, two tests were devised in order to verif~ that incore failures resulting in onl~

75% detector operabl il it~ would produce accurate measurements.

The first test consisted of verif~ing the F(sa) and F(s) uncertainW components for measurements with 11 incore strings (55 total detectors) failed.

This failure rate, Z5.6% of Zl5, was chosen because of its consistency with current standard technical specifications. ~cle 6 PIDAL case #5 was chosen as the base case to this test. The Sfts...> and Sfrs>comp1;ment uncertainties for this case were found to be 0.013~ and 0.02',, respectivel~. See Table #6.

Five sets of eleven failed incore strings were then chosen using a random number generator and input.to PIDAL. The statistical anal~is was repeated for each of the five failed sets. The resul tan t s,.., ~) and Sr< s) components were found to be 0.0171 and 0.0328, respectivel~. Statistical peaking factor uncertainties were then determined based on the base case and 25;t failure rate case. From these calculations, penalt~ factors accounting for the apparent measurement degradation based on detector failures were derived.

These penalt~ factors were then applied to the uncertainties derived from the full data base

• Section 3 Pl6 Rev 0 CALCULATION of the UNCERTAINTIES Section 3.2 Effects of Failed Detectors on Uncertainties The first test was then repeated for an off-normal power distribution case.

The PIDAL base case was a dropped rod measurement from cycle 7. The base case uncertainty components fo:r this case were Sffso..) = O. 081Z and Sf(s)= 0. 0~55. Five new random sets of 11 inco:re strings to be failed we:re generated and the statistics calculations repeated. The resultant Sffs.o..) and Srt.s)Were 0.1~3 and 0.136~, respectively. F:rom these results, it is clear that PIDAL does not handle lar~e local perturbations such as a dropped :rod with a high degree of certainty.

There are two reasons why the dropped rod case resulted in higher measurement uncertainties. The w* data used by PIDAL, and most other moni taring cyste.11S as well, comes from steacy state PDQ (or similar) calculations.

Therefore, the detector signal-to-power conversion is not very accurate fo:r this type of case. Secondly, and more importantly, the coupling coefficients used by PIDAL are inferred based on one-quarter core measured and theoretical detector powers. These coupling coefficients have no wey of compensating for gross full core assymetries such as a dropped control rod.

Palisades plant procedures currently state that the incore monitoring cyst.em can not be used fo:r verifying core peakinQ factors in the event of a dropped or misaliQned control rod. At this time, there is no intention of revising Ulese procedures to the contrary t.mtil a full core coup! ing coefficient metilodolomt, capable of accounting for l~e local reactivity perturbations has been added to PIDAL. Work is underwey to develop such a meU1odolow.

A second test was devised in order to further stucy the effects of g:ross incore failures on the PIDAL methodology. TI1is test consisted of.failing large quantities of incores on an indidual basis (not by string) and quantifying the resultant effects on tile PIDAL measurements.

The base case for this test consisted of a typical run from cycle 8 in which 206 of 215 possible inc6res were operable. Five sets of 54 (25~) failed incores were generated using a random number generator. The PIDAL power dist-ribution was then re-calculated for each of the five sets of failures, with the resultant integrated assembly powers compared back to the base case.

This test was then repeated for failure thresholds of 50~ and 75~ failed incores.

Average assembly powe:r deviations were found to be 0.60~,.1.10% and 1.57~

for the Z5%, 50:l and 75% failed incore detector cases respectively. From these results it is clear that as additional inco:re detectors are failed 5 the powe:r distribution as measured by PIDAL tends to depart* from the base case. From the individual cases, it is also apparent that the degree of agreement between the test cases and base case depends strongly on which incore detectors are operable. An example of this is the spread between thC!3 average deviations for the five Z5~ cases which had a high case average of 0.71% and a low of 0.45~.

Based on these results, it is safe to assume that the uncertainties associated with the PIDAL system documented by this report are val id for an incore monitoring cyst.em operable with up to Z5~ of it*s Zl5 incore detector considered failed. It is also apparent that detector failure rates greater than Z5% have an adverse ef feet on PIDAL

• s ability to determine the measured power distribution.

~*.

Section 3 Pl7 Rev 0 CALCULATION of the UNCERTAINTIES Section 3.3 Results of Statistical Combinations Tables #? throueh If'} contain the results of the F(s), F(sa) and F(r) statistical calculations for fuel qycles 5,6 and 7. Table if8 shows the original cycle 7 results assuming reused incore detectors. Table#'} shows analogous cycle 7 data with the reused incore data omitted. Table #10 shows a Sl.Jil'.marv totaling all of the F(s), F(sa) and F(r) data for all three fuel cycles assuming no reused incore detectors.

Fi~es #1 throueh #15 are deviation histoerams corresponding to the data used for the F(s), F(sa) and F(r) standard deviations. From the histograms and means presented, it is apparent that the data is normal and unbiased. One interesting point to note is that the F(r) data is not biased as ANF had found it to be. They explained their bias as being induced by using data sets that were not normalized. The PIDAL data used was radially normalized so the P IDAL resul t seems to support the ANF assumption.

Table #11 contains the results of the F(z) statistical calculations using cycle 7 data. The first 11 elements of Table #11 were taken from the simulated Xenon oscillation data. The last 11 elements correspond to "typical**

data equally spread out through cycle 7. Note that element ZO was from a Cl'opped rod transient. Figure #16 shows a histogram for the F(z) deviation data. From this histogram, the data appears generally.normal but the mean deviation indicates a bias of O.,~. Since thi~ bias is positive, the PIDAL model is over-predictiing the peak and is therefore conservative. This is similar to the result obtained by ANF.

Two sets of tolerance 1 imi ts were determined for F(q), F(Ah) and F(Ar)

• The first set is based entirely on cycle 7 data and is valid only for reload cores which contain fresh and once-burned incore detectors. The second set of tolerance limits is based on data from all three cycles, excluding the qycle 7 reused detector data, and is valid only for reload cores with all fresh incore detectors.

Table #lZ contains a sum.111arv of all of the statistical uncertainty values obtained. From this table, the one-sided '5/515 tolerance limits associated with Palisades PIOAL model were found to be: 0.0623 for F(q), 0.0455 for F(.6h) and 0.0401 for F(Ar).for cores with all fresh incore detectors. For cores using a mixture of fresh and once-burned incore de.teeters, the '5/515 tolerance limits for F(q),°F(Ah) and F(Ar) were found to be 0.0664, 0.05Z6 and 0.04'0 respectively

• Section 4 Pl8 Rev 0 TABLES PIDAL Run Exposure Rx. Power Number MWD/MT 11Wth l

o.o 16?4 z

2Z4.5 241?

3 5ZO.Z Z300 4

5!44.?

2321 5

1504.6 24?4 6

2287.7 2515 7

3007'.?

2514 8

4235.7' 2505'

?

5338.Z 245'6 10 6424.l 245'5' 11 7248.3 2524 lZ 805'?.?

2518 13

?187'.Z 2504 14 10068.5 2525 15 10860.l 24?7' 16 11721.?

2480 17 12127'.l 22Z7 18 12487'.6 1845' Table #l~C~cle 5 PIDAL case exposures and powers for F(s)3 F(sa) and F(r) uncertaint~ components

• Section 4 Pl' Rev 0 TABLES PIDAL Run Exposure Rx. Power Number MWD/MT MW th 1,

0.0 1160 20 135.,

15ln 21 370.6 254Z 22 1051.6 2464 23 1840.3 2456 24 2845.5 2456 Z5 3527.1 2460 Z6 4180.8 Z477 Z7 4533.1 Z460 Z8 5618.,

Z468 z'

648,.7' Z457' 30 6881.Z Z468 31 7'63.,

2455 32 8Z8Z.6 ZZ40 33

,080.0 Z467' 34 51832.7' 2483 35 10300.Z Z464 Table #Z~C~cle 6 PIDAL case e><posures and powers for F(s),

F(sa) and F(r) uncertaint~ components

• PIDAL Run Number 36 37' 38 3,

40 41 42 43 44 45 46 47' 48 4, 50 51 52 53 54 Section 4 TABLES Exposure h"WIJ/MT 85,.8 125'3.7' o.o 143.0 265.8 51,.3 155'6.7' Z310.7' 25'7'4. l 35'5'4.4" 5Zl5'.7' 6615.5 7'386.0 8226.8 85'Z2.5' 5'837'.4 10468.8 1110568 11556.4 Rx. Power MW th Z47'5 2:453 7'8Z Z406 2462 1341 185'2 Z514 Z535 Z525' 2357' 2527' 2531 2537' 2526 2525' 2528 2405' 2406 Table #3~C~le 7 PIDAL case exposures and powers for F(s),

F(sa) and F(r) uncertaint~ components

• PZO Rev 0

Section 4 PZl Rev 0 TABLF.S PIDAL Run

• Exposure Rx. Power

% Axial Number MWD/11T MW th Offset l

l7Z.,

23,,-

- l.8 z

1075.7 2476

- 0.7 3

1437.3 251Z Ool 4

1807.Z Z476

- O.l 5

~74.l 2530 1.4 6

35'?4.4 25~

Z.5 7

5?30.l 2518 3.8 8

7386.0 Z5Z5 4.0 8683.3 ll4Z

-18.3 10

?364.5 Z5Z6 3.5 ll 10468.8 25Z8 3.2 12 10510.7" 25Z8

-40.0 13 10513.3 Z5Z8

-3Z.7' 14 10514.6 2528

-27".6 15 10515.?

Z5Z8

-Zl.4 16 l 0517".3 Z5Z8

-13.,

17" 10518.6 25Z8

- 5.1 18 1051?.,

Z5Z8 4.5 1,

10521.Z Z5Z8 14.4 zo 1052Z.5 Z5Z8 23.4 21 10523.,

Z5Z8 30.5 Z2 l05Z7".8 Z5Z8 35'.. Z Table.#4--C~cle 7" PIDAL runs used for F(z) uncert.aint~ components *

~

~

SUMMARY

EDIT FOR ALL CASES THIS RUN CASE AVERAGE SEGMENT RMS SEGMENT FCS)

FCS)

FCSA)

FCSA)

FCR)

FCR)

DEVIATION

'Yo DEVIATION ST. DEV.

OBSERV.

ST. DEV.

OBSERV.

ST. DEV.

OBSERV.

1 0.44 3.30 0.0324 195.

0.0216 39 0.0021

51.

2 0.38 2.61 0.0259 190.

0.0200 38 0.0021

51.

3 0.33 2.56 0.0254 195.

0.0199 39 0.0018

51.

4 0.32 2.66 0.0264 190.

. 0. 0208 38 0.0018

51.

5 0.22 3.60 0.0356 169.

0.0256 33 0.0023

51.

6 0.24 2.81 0.0282 165.

0.0210 33 0.0024

51.

7 0.19 3.09 0.0314 164.

0.0253 32 0.0024

51.

8 0.19 2.67 0.0266 177.

0.0227 35 0.0024

51.

9 0.21 2.94 0.0295 177.

0.0258 35 0.0023

51.

10 0.11 2.66 0.0268 177.

0.0229 35 0.0025

51.

11 0.11

2. 74 0.0271 177.

0.0227 35 0.0026

51.

12 0.14 2.93 0.0293 167.

0.0251 33 0.0026

51.

13 0.24 2.76

0. 0275 158.

0.0228 31 0.0026

51.

14 0.17 3.23

0. 0311 152.

0.0251 30 0.0024

51.

15

-0.05 3.26 0.0324 148.

0.0270 29 0.0023

51.

16

-0.01 2.80 0.0280 160.

0.0239 32 0.0022

51.

17

-0.05 3.41 0.0341 172.

0.0280 34 0.0021

51.

18

-0.01 2.94 0.0291 161.

0.0255 32 0.0021

51.

FCS)

STANDARD DEVIATION ALL CASES = 0.0293 /MEAN = 0. 0014,,- DEGREES OF FREEDOM = 3094./

0. 0233 /MEAN

~

FREEDOM 619.-'

FCSA) STANDARD DEVIATION ALL CASES =

= 0.0014 DEGREES OF

=

FCR)

STANDARD DEVIATION ALL CASES = 0. 0023 /MEAN = 0. 0000 J DEGREES OF FREEDOM =

918../

TA6U s-C'(CL.E s f(s)) f(.s... ) "".i f(r)

Pc..~o.

r

~

~

SUMMARY

EDIT FOR ALL CASES THIS RUN CASE AVERAGE SEGMENT RMS SEGMENT FCS)

FCS)

FCSA>

FCSA)

FCR)

FCR)

DEVIATION

%DEVIATION ST. DEV.

OBSERV.

ST. DEV.

OBSERV.

ST. DEV.

OBSERV.

1 0.04 3.29 0.0336 152.

0.0182 30 0.0017

51.

2 0.01 3.09 0.0314 163.

0.0149 32 0.0018

51.

3 0.00 2.90 0.0294 168.

0. 0130 33 0.0015

51.

4

-0.03 3.06 0.0314 175.

0.0136 35 0.0016

51.

5

-0.01 2.94 0.0299 175.

0.0134 35 0.0020

51.

--- 6-- -

- 0.-o 8 ----- -- --

---2-.-67-- -

0.0267 170.

0.0114 -

34 0.0022

51.

7

-0.15 2.38 0.0238 155.

0. 0114 31 0.0022

51.

8

-0.15 2.37 0.0236 160.

0.0110 32 0.0023

51.

9

-0.10 2.42 0.0242 160.

0. 0114 32 0.0023

51.

10

-0.14 2.29 0.0228 16 0.

0.0108 32 0.0024

51.

11

-0.17 2.28 0.0226 155.

0.0107 31 0.0023

51.

12

-0.15 2.22 0.0221 155.

0.0106 31 0.0026

51.

13

-0.23 2.79 0.0283 145.

0.0123 29 0.0026

51.

14

-o. 06 3.13 0.0318 140.

0.0130 28 0.0028

51.

15

-0.15 2.97 0.0306 152.

0.0132 30 0.0028

51.

16

-0.18 2.34 0.0241 152.

0.0124 30 0.0025

51.

17

-0.23 2.37 0.0244 152.

0.0126 30 0.0026

51.

FCS)

STANDARD DEVIATION ALL CASES = 0. 0272/ MEAN = -.0013 /DEGREES OF FREEDOM =

2689"

/

/

FCSA) STANDARD DEVIATION ALL CASES = 0.0125 MEAN = -.0014 DEGREES OF FREEDOM =

538.

/

FCR)

STANDARD DEVIATION ALL CASES = 0. 0023, MEAN = -.0001 /DEGREES OF FREEDOM =

867.

Tl"ri31.-f. G:,-

C'<CLE f(!>)) F(.so..)

~.... ~ f{r) Do.."\\o,.

~

~

SUMMARY

EDIT FOR ALL CASES THIS RUN CASE AVERAGE SEGMENT RMS SEGMENT FCS)

FCS)

FCSA)

FCSA)

FCR)

FCR)

DEVIATION Oj.,DEVIATION ST. DEV.

OBSERV.

ST. DEV.

OBSERV.

ST. DEV.

OBSERV.

l 0.30 3.14 0.0310 180.

0.0245 36 0.0014

51.

2 0.49 3.60 0.0350 185.

0.0269 37 0.0015

51.

3 0.41 3.88 0.0382 175.

0.0225 35 0.0018

51. I 4

0.36 3.61 0.0354 180.

0.0244 36 0.0017

51.

5 0.46 3.26 0.0318 180.

0.0246 36 0.0017

51.

6 0.51 3.62 0.0353 185.

0.0267 37 0.0017

51.

7 0.45 3.49 0.0341 180.

0.0266 36 0.0018

51.

8 0.27 3.39 0.0337 190.

0.0284 38 0.0021

51.

9 0.39 3.35 0.0331 180.

0.0292 36 0.0021

51.

10 0.43 3.52 0.0347 175.

0.0306 35 0.0022

51.

11 0.40 3.39 0.0334 170.

0.0287 34 0.0023

51.

12 0.07 3.00 0.0300 160.

0.0259 32 0.0025

51.

13 0.09 2.91 0.0291 175.

0.0257 35 0.0026

51.

14 0.15 2.97 0.0297 180.

0.0267 36 0.0025

51.

15 0.35 3.29 D.0325 185.

0.0297 37 0.0026

51.

16 D.31 3.21 0.0318 185.

0.0292 37 0.0026

51.

17 0.28 3.25 D.0322 185.

0.0297 37 0.0025

51.

18 0.30 3.31 0.0329 185.

0.0303 37 0.0025

51.

19 0.25 3.41 0.0339 180.

0.0314 36 0.0024

51.

FCS)

STANDARD DEVIATION ALL CASES = 0. 0331.,..- MEAN = 0. 0027 _,DEGREES OF FREEDOM = 3415.--

FCSA> STANDARD DEVIATION ALL CASES = 0. 0212-MEAN = 0. 0 027._,,DEGREES OF FREEDOM =

683 *...---

FCR)

STANDARD DEVIATION ALL CASES = 0. 0021.....-MEAN = 0. DODO J DEGREES OF FREEDOM

_ _../

=

969.

iA6t...f: t -

C.'(Ct..£ l f(.s~ > r C.s..r..) """'.( f(r-) \\'.:).... -4.CI., 0('\\~:o\\... \\

l..l1 )

R.e'4.SE'~ t>e~ec."\\:""5 "L-ci I.(,{ E'~ *

,/ *

/

I

~

~

SUMMARY

EDIT FOR ALL CASES THIS RUN CASE AVERAGE SEGMENT RMS SEGMENT FCS)

FCS)

FCSA>

FCSA)

FCR)

FCR)

DEVIATION cr:,DEVIA TI ON ST. DEV.

OBSERV.

ST. DEV.

OBSERV.

ST. DEV.

OBSERV.

1 0.18 2.89 0.0286 180.

0.0213 36 0.0014

51.

2 0.38 3.39 0.0332 185.

0.0242 37 0.0015

51.

3 0.28 3.61 0.0357 175.

0.0175 35 0.0018

51.

4 0.23 3.37 0.0332 180.

0.0208 36

0. 0017

51.

5 0.33 3.00 0.0294 180.

0.0213 36 0.0017

51.

6 0.40 3.43 0.0335 185.

0.0240 37 0.0017

51.

7 0.33 3.25 0.0318 180.

0.0234 36 0.0018

51.

8 0.16 3.15 0.0315 190.

0.0257 38 0.0021

51.

9 0.28 3.11 0.0309 180.

0.0266 36 0.0021

51.

10 0.30 3.27 0.0324 175.

0. 0279 35 0.0022

51.

11 0.28 3.14

0. 0311 170.

0.0259 34 0.0023

51.

12

-0.07 2.64 0.0266 160.

0.0217 32 0.0025

51.

13

-0.05 2.55 0.0256 175.

0.0215 35 0.0026

51.

14 0.04 2.65 0.0266 180.

0.0232 36 0.0025

51.

15 0.24 3.01 0.0299 185.

0.0268 37 0.0026

51.

16 0.20 2.92 0.0291 185.

0. 0262 37

0. 0 026

51.

17 0.17 2.95 0.0295 185.

0.0266 37 0.0025

51.

18 0.18 3.02 0.0301 185.

0.0273 37 0.0025

51.

19 0.13 3.12 0.0312 180.

0.0284 36 0.0024

51.

FCS)

STANDARD DEVIATION ALL CASES = 0.0306/MEAN = 0. 0016.....- DEGREES OF FREEDOM = 3415.'

FCSA) STANDARD DEVIATION ALL CASES = 0. 0241 /MEAN = 0. 0016 /DEGREES OF FREEDOM =

683. /

FCR)

STANDARD DEVIATION ALL CASES = 0.0021 /MEAN = 0. DODD /DEGREES OF FREEDOM =

969. -

TASt..f i-('(CLE,.. FCs)) F(~.j) f"(.r) bA+q_. Ne..i 1.,/>. Rel.{f.E'~ Ce ~t> t~ ors r "'C.11..4.J e.Q.

~

~

SUMMARY

EDIT FuR ALL CASES THIS RUN CASE AVERAGE SEGMENT RMS SEGMENT FCS)

FCS)

FCSA)

FCSA)

FCR)

FCR)

DEVIATION

%DEVIATION ST. DEV.

OBSERV.

ST. DEV.

OBSERV.

ST. DEV.

OBSERV.

1 0.53 2.33 0.0225 155.

0.0164 31 0.0014

51.

2 0.79 3.02 0.0285 160.

0.0202 32 0.0015

51.

3 0.34 3.31 0.0329 150.

0.0158 30 0.0018

51.

4 0.42 2.98

0. 0292 155.

0.0169 31 0.0017

51.

5 0.60 2.48 0.0237 155.

0.0169 31 0.0017

51.

6 0.77 3.05 0.0288 160.

0.0200 32 0.0017

51.

7 0.73 2.83 0.0267 155.

0.0194 31 0.0013

51.

8 0.68 2.82 0.0269 165.

0.0208 33 0.0021

51.

9 0.88 2.80 0.0261 155.

0.0211 31 0.0021

51.

10 0.95

2. 95 0.0274 150.

0.0219 30 0.0022

51.

11

0. 7 5 2.86 0.0270 150.

0.0212 30 0.0023

51.

12 0.39 2.24 0.0219 140.

0.0161 28 0.007.5

51.

13 0.39 2.14 0.0208 155.

0.0162 31 0.0026

51.

14 0.50 2.25 0.0216 16 0.

0.0178 32 0.0025

51.

15 0.74 2.69 0.0253 165.

0.0220 33

0. 0025

51.

16 0.70 2.58 0.0245 165.

0.0213 33 0.0025

51.

17 0.69 2.61 0.0248 165.

0.0217 33 0.0025

51.

18 0.72 2.68 0.0254 165.

0. *0223 33 0.0025

51.

19 0.72 2.74 0.0260 160.

0.0228 32 0.0024

51.

FCS)

STANDARD DEVIATION ALL CASES = 0. 0259 / MEAN

0. 0061.r DEGREES

=

OF FREEDOM = 2985.

/

FCSA) STANDARD DEVIATION ALL CASES = 0.0195~MEAN = 0.0062 DEGREES OF FREEDOM =

597.

FCR)

STANDARD DEVIATION ALL CASES = 0. 0021./MEAN = 0. 0000/

/

DEGREES OF FREEDOM =

969.

TAl3L.f "'-

C.'( (. L..E ':f-

.* f (s); F(~o.) av-J.. f (*) Co.-lio.. Q,..,; -He~ R.e"l.s.e.i

'De~ec.~or s. > New w'

~

~

SUMMARY

EDIT r-K ALL CASES THIS RUN CASE AVERAGE SEGMENT RMS SEGMENT FCS>

FCS>

FCSA>

FCSA)

FCR>

FCR)

DEVIATION o/o DEVIATION ST. DEV.

OBSERV.

ST. DEV.

OBSERV.

ST. DEV.

OBSERV.

1 0.44 3.30 0.0324 195.

0.0216 39 0.0021

51.

2 0.38 2.61 0.0259 190.

0.0200 38 0.0021

51.

3 0.33

2. 56 0.0254 195.

0.0199 39 0.0018

51.

4 0.32 2.66 0.0264 190.

0.0208 38 0.0018

51.

5 0.22 3.60 0.0356 169.

0.0256 33 0.0023

51.

6 0.24 2.81 0.0282 165.

0.0210 33 0.0024

51.

7 0.19 3.09 0.0314 164.

0.0253 32 0.0024

51.

8 0.19 2.67 0.0266 177.

0.0227 35 0.0024

51.

9 0.21 2.94 0.0295 177.

0.0258 35 0.0023

51.

10 0.11 2.66 0.0268 177.

0.0229 35 0.0025

51.

11 0.11

2. 74

0. 0271 177.

0. 0227 35 0.0026

51.

12 0.14 2.93 0.0293 167.

0.0251 33 0.0026

51.

13 0.24

2. 76

o. 027 5 158.

0.0228 31 0.0026

51.

14 0.17 3.23

0. 0311 152.

0.0251 30 0.0024

51.

15

-0.05 3.26 0.0324 148.

0.0270 29 0.0023

51.

16

-0.01 2.80 0.0280 160.

0.0239 32 0.0022

51.

17

-0.05 3.41 0.0341 172.

0.0280 34 0.0021

51.

18

-0.01 2.94 0.0291 161.

0.0255 32 0.0021

51.

19 0.04 3.29 0.0336 152.

0.0182 30 0.0017

51.

20

0. 01 3.09 0.0314 163.

0.0149 32 0.0018

51.

21 0.00 2.90 0.0294 168.

0.0130 33 0.0015

51.

22

-0.03 3.06 0.0314 175.

0.0136 35 0.0016

51.

23

-0.01

2. 94 0.0299 175.

0.0134 35 0.0020

51.

24

-0.08 2.67 0.0267 170.

0.0114 34 0.0022

51.

25

-o.15 2.38 0.0238 155.

0.0114 31 0.0022

51.

26

-0.15 2.37 0.0236 16 0.

0.0110 32 0.0023

51.

27

-0.10 2.42 0.0242 160.

0.0114 32 0.0023

51.

28

-0.14 2.29 0.0228 160.

0.0108 32 0.0024

51.

29

-0.17 2.28 0.0226 155.

0.0107 31 0.0023

51.

30

-0.15 2.22 0.0221 155.

0.0106 31 0.0026

51.

31

-0.23 2.79 0.0283 145.

0.0123 29 0.0026

51.

32

-0.06 3.13 0.0318 140.

0.0130 28 0.0028

51.

33

-0.15 2.97 0.0306 152.

0.0132 30 0.0028

51.

34

-0.18 2.34 0.0241 152.

0.0124 30 0.0025

51.

35

-0.23 2.37 0.0244 152.

0.0126 30 0.0026

51.

36 0.53 2.33 0.0225 155.

0.0164 31 0.0014

51.

37 0.79 3.02 0.0285 160.

0.0202 32 0.0015

51.

38 0.34 3.31 0.0329 150.

0.0158 30 0.0018

51.

39 0.42 2.98 0.0292 155.

0.0169 31 0.0017

51.

40 0.60 2.48 0.0237 155.

0.0169 31

o. 0017

51.

41 0.77 3.05 0.0288 160.

0.0200 32

0. 0017

51.

42 0.73 2.83 0.0267 155.

0.0194 31 0.0018

51.

43 0.68 2.82 0.0269 165.

0.0208 33 0.0021

51.

44 0.88 2.80 0.0261 155.

o. 0211 31 0.0021

51.

45 0.95 2.95 0.0274 150.

0.0219 30 0.0022

51.

46 0.75 2.86 0.0270 150.

0.0212 30 0.0023

51.

47 0.39 2.24 0.0219 140.

0.0161 28 0.0025

51.

48 0.39 2.14 0.0208 155.

0.0162 31 0.0026

51.

49 0.50 2.25 0.0216 160.

0.0178 32 0.0025

51.

50 0.74 2.69 0.0253 165.

0.0220 33 0.0026

51.

51 0.70 2.58 0.0245 165.

0.0213 33 0.0026

51.

52 0.69 2.61 0.0248 165.

0.0217 33 0.0025

51.

53 0.72 2.68 0.0254 165.

0.0223 33 0.0025

51.

54 0.72

2. 74

0. 026 0 160.

0.0228 32 0.0024

51.

ls:

~

0. 0 022.,, DEGREES FREEDOM 8768./

FCS)

STANDARD DEVIATION ALL CASES = 0. 0277 ~ MEAN =

OF

=

FCSA) STANDARD DEVIATION ALL CASES = 0.0194 ~MEAN = 0. 0 0 22"' DEGREES OF FREEDOM = 1754..../

FCR).

STANDARD DEVIATION ALL CASES = 0. 0022 _,,MEAN = 0. 0000 vDEGREES OF FREEDOM =

2754. v

I I

~

~

SUMMARY

EDIT FOR ALL CASES THIS RUN CASE FCZ)

FCZ)

BLOCK COMPUTER POHER ST. DEV.

OBSERV.

RUN DATE SPLIT l

0.0168

51.

173 890331 120151200

-0.3997 2

0.0169 SI.

17S 890331 120713400

-0.326S 3

0.0162

51.

176 890331 122Sl8910

-0.27S8 4

O.OlSO SI.

177 890331 122839300

-0.2140 s

0.0140 SI.

178 890331 123233SOO

-0.1386 6

0. 013S

51.

179 890331 123541400

-0.0514 7

0.0117 SI.

180 890331 123903800 0.04S2 8

0.0150

51.

181 890331 124307900 0.1435 9

0. 0119

51.

182 890331 124S40200 0.2341 10 0.0131

51.

183 890331 124901700 0.3047 11 0.0137 SL 186 890331 130048600

0. 3921 12 0.0023 Sl.

s 890403 111937710

-0.0181 13 0.0016 Sl.

21 890403 113038680

-0.0071 14 0.0020 Sl.

26 890403 113746680

0. 0011 15 0.0038 SI.

34 890403 114504490

-0.0006 16 0.0060

51.

50 890403 122824420 0.0144 17 0.0108 SL 67 890403 1233S6290 0.02SO 18 0.0144 SI.

97 890403 123929710 0.0377 19 0.0167 SI.

120 890403 124447390 0.0399 20 0.0178 Sl.

139 890403 125013S90

-0.1834 21 0.0174 SI.

149 890403 130227920 0.0346 22 0.0149 Sl.

162 890403 131014030 0.0319 FCZ)

STANDARD DEVIATION ALL CASES = 0.0151 MEAN = 0.0086 DEGREES OF FREEDOM = 1122.

v' Tf't i!.L-f. fl -

C,'((LE i-f(=l) t> °" "'* '\\

/

Section 4 PZ' Rev 1 TABLES Statistical Standard Degrees of Tolerance Tolerance Variable Deviation Freedom Factor Limit F(s)

• 0.0306 3415 F(sa)*

0.0241 683 F(r)

• O.OOZl

,6, F(s)

O.OZ77 8768 F(sa) 0.01,4 1754 F(r) o.oozz 2754 F(z) 0.0151 llZZ F(L) 0.0135 188 F(q)

• 0.0368 38ZZ 1.6,Z 0.0664 F(Ah)*

O.OZ77 877 1.733 0.05Z6 F(Ar)*

O.OZ4Z 6~4 1.746 0.04,0 F(q)

-0.0344 4826 1.6,Z 0.06Z3-F(A.h)

O.OZ37 1ZZ5 l.7Z7 0.0455 F(Ar) 0.01,5 17~0 l.71Z 0.0401

-values for cores with once-burned reused incore detectors For the final tolerance limits, penalt~ factors of.0041,.0046 and.0067 for F(q), F(A.h) and F(Ar) repectivel~ were included to account for up to Z57o incore detector failures

• Table #lZ-Summ~ of statistical component uncertainties

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Section 6 P47

~'"V 0 List of References Title P*PID*~OOl, The Palisades Full Core PIDAL System MeUlodolo~ and Pro~rammers Manual by GA Baustian, Consumers Power Company, Palisades Reactor En~ineering Z

XN-NF-83-01 (P), Exxon Nulcear Analysis of Power Distribution Measurement Uncertainty for St. Lucie Unit l, January 1~83.

3 Probability and Statistics for En~ineers and Scientists, Z Ed.,

RE Walpole and RH Myers, Macmillan Publishing Co, 1~78o 4

Factors for One-Sided Tolerance Limits and for Variable Sampling Plans, D.B. Owen, Sandia Corporation Monograph, SCR-607, March 1~63.

5 Radiation Detection and Measurement, Glenn F. Knoll, Wiley Publishing Co, l~,.

6 CALCULATIONAL VERIFICATION or THE C0.'1BUSTION ENGINEERING FULL CORE INSTRUMENTATION ANALYSIS SYSTEM CECOR, W.B. TERNEY et al, Combustion Engineeri~, presented at International Conference On World Nuclear Power, Washington D.C., November l~, 1~6.

Palisades Reactor Engineeri~ Dept. Benchmarking Calculation File For Fuel Cycles 5,6 and 7

• INCA PID.a\\L XTG PDQ CECOR Wprime Nonnal Section 7 P48 REV 0 GLOSSARY

- An incore anal~sis pro~ram developed by Combustion Engineer:!.~

to determine (measure) the power distribution within the Palisades reactor assumi~ one-eiQhth or octant core ~~.

- An incore anal~sis program developed by Consumers Power Compan~

to determine (measure) the power distribution within the Palisades on a full core basis.

- A ~oup and one-half nodal diffusion theocy code developed b~

Advanced Nuclear Fuels Corporation (formerl~ Exxon Nuclear) for ~eneral predictive modelin~*of pre~surized water reactorso

- A mul ti--woup diffusion theocy code 3 n.m primaril~ in two dimensions 3 capable of modelinQ each fuel pin in the react.or expl ici tl~.

- An incore anal~sis program developed b~ Combustion Engineeri~

to det.emine (measure) the power distribution within a pressurized water react.or on a full core basis.

- Fact.or used in conversion of measured incore detector mill ivo.1 t signals to detector segment powers. Data supplied b~ ANFo

- Refers to a statistical l~ "normal.. or Gaussian distribution of data.

J5/!;J5 Tolerance Limit - this limit ensures that there is a '5 percent probabil it~ that at least !;J5 percent of the true peakin~ values will be less than the PIDAL measured/inferred peakinQ values plus the associated tolerance limit

• TSP0889-0181-NL04 ATTACID1ENT 5 Consumers Power Company Palisades Plant Docket 50-255 PROPOSED FSAR PAGE CHANGES October 23, 1989 9 Pages

described in the analysis of the boron dilution incident (Section 14.3).

Section 14.3 also shows that the reactor operator has sufficient time to recognize and to take corrective action to compensate for the maximum reactivity addition due to xenon decay and cooldown.

3.3.2.5 Power Distribution The power distribution in the core, especially the peak power density, is of major importance in determining core thermal margin.

Enrichment zoning within fuel bundles is used to reduce local power peaking.

Since dissolved boron is used to control long-term reactivity changes such as burnup, the control blades do not.need to be used to a great extent, Typically, at hot full power, only Group 4 blades are in the reactor about 10% or less.

This is not enough to upset t.he global power distr.ibution.

Several power distribution limits have been established to protect against fuel failures.

A limit on the linear heat generation rate that is a function of the axial location of the peak power in the pin protects

• against departure from nucleate boiling and from overheating during an LOCA.

The LHGR limits are given in Section 3.23.1, Linear Heat Rate, of the Technical Specifications

• There are additional limits on the.axially averaged radial peaking factors that also protect against fuel failures.

These limits ensure that the margin to DNB and the linear heat generation rates are not violated during normal or transient conditions and that the thermal margin/low-pressure trip and the high-power trip set points remain valid during normal opera-tions.

The peaking factors are given in Section 3.23.2, Radial Peaking Factors, of the Technical Specifications.

The peaking factor definitions are:

• A Assembly Radial Peaking Factor - F r The assembly radial peaking factor is the maximum ratio of individual fuel assembly power to core average assembly power integrated over the total core height, including tilt, 8H Total Interior Rod Radial Peaking Factor - Fr The maximum product of the ratio of individual assembly power to core average assembly power times the highest interior local peaking factor integrated over the total core height including tilt.

The LHGR and peaking factor limits shown in Tables 3.23-1 and 3.23-2 of the Technical Specifications must be reduced by several factors before all necessary conservatisms are accounted for.

To account for calculational uncertainties in the incore monitoring system, the limits are reduced by dividing them by the appropriate uncertainties (Reference 32) given in FS0789-0365C-TMI3~TMII 3.3-7 Draft

Table 3-12.

In addition, to account for the change of dimensions from den-sification (due to resintering) and thermal expansion, the LHGR limits are reduced by dividing them by 1.03.

To account for uncertainty in the re-actor thermal power, the LHGR limits are reduced by dividing them by 1.02.

3.3.2.6 Neutron Fluence on Pressure Vessel At the end of Cycle 2, after 2.26 effective full-power years of operation, a capsule containing reactor vessel construction specimens was removed from the reactor vessel for evaluation (see Reference 17).

The capsule was located at 240 degrees, just outside of the core barrel.

The neutron fluence of the specimens within the capsule was deduced from the neutron induced activity of several iron wires from the capsule.

The neutron fluence for*neutron energies gre~ter than 1 MeV was determined to be 4.4 x 10 19 nvt.

The fluence at the capsule location is then adjusted by a lead factor, which is the ratio of the fast flux at the capsule location to the maximum fast flux at the vessel wall.

The DOT-3 computer code (see Reference 19) was used to compute a value of 17.5 for this factor (see References 17 and 18).

The corresponding peak vessel fluence was determined to be 2.5 x 10 18 nvt.

A vessel wall capsule at 290 degrees location was pulled out at the end of Cycle 5 at 11.67 calend~r ¥ears of operation.

Measured fluence levels at the capsule were 1.1 x 10 1 nvt corresponding to 5.20 effective full power years (see References 28.and 29).

A lead factor of 1.28 (see Reference 28) was established to compute the peak vessel wall fluence of 8.6 x 10 18 nvt.

Recently for the Cycle 8 operation, a fluence reduction program was initi-

• ated.

A low-leakage fuel management scheme with partial stainless steel shielding assemblies near the critical axial weld locations was employed to reduce the vessel wall flux.

DOT calculations have been performed to compute the flux levels during the Cycle 8 operation (see Reference 30).

By this new core loading pattern, it is possible to reduce the vessel wall flux in the range 14%-51%, compared to previous cycles (see Reference 31).

Assuming 75% capacity factor for the remainder of the Plant's 40-year operational life and flux levels similar to Cycle 8 o~eration, the maximum fast fluence the vessel wall will receive is 3.9 x 10 9 nvt.

Ho~ever, PTS screening criteria and Regulatory Guide 1.99, Revision 2 restrict the fluence levels to 1.6 x 10 19 nvt at the vessel axial weld locations (see Reference 31), which corresponds to seek vessel fluence of 2.8 x 10 19 nvt.

Further, a supplemental dosimetry program has been established.

A set of dosimeters outside the vessel have been installed during the end of Cycle 7 refueling outage.

These dosimeters would undergo irradiation during the entire Cycle 8 operation.

At the end of Cycle 8, these dosimeters would be removed and replaced with a new set of dosimeters for Cycle 9 operation

• Irradiated.dosimeters would be analyzed, and measured flux values will be determined.

These measured flux values would be used for benchmarking the vessel flux/fluence calculations on a cycle-by-cycle basis.

FS0789-0365C-TM13-TM11 3.3-8 Draft

31.

Attachment to letter of R W Smedley (CPCo) to NRC (dated April 3, 1989).

"Docket-50-255 - License DPR Palisades Plant - Compli-ance with Pressurized Thermal Shock Rule 10 CFR 50.61 and Regulatory Guide 1.99, Revision 2 - Fluence Reduction Status (Tac No 59970)".

32.

The CPCo Full Core PIDAL System Uncertainty Analysis, Revision 0, June 5, 1989, G A Baustian, Palisades Reactor Engineering

• FS0789-0365D-TM13-TM11 3-3 Draft

TABLE 3-12 POWER DISTRIBUTION MEASUREMENT UNCERTAINTIES Measurement Measurement LHGR/Peaking Factor Uncertainty Uncertainty Parameter (a)

(b)

LHGR 0.0623 0.0664

~

0.0401 0.0490 F~H 0.0455 0.0526 (a)Measurement uncertainty based on the PIDAL calculational methodology for reload cores using all fresh incore detectors.

(b)Measurement uncertainty based on the PIDAL calculational methodology for reload cores using a mixture of fresh and once-burned incore detectors

• FS0789-0319A-TM13-TM11 Draft

The thermocouples are of Inconel sheathed, Chromel-Alumel construction and are located at the top end of each incore detector assembly so that the primary coolant outlet temperatures may be measured.

The neutron detectors in the assemblies are short rhodium detectors equally spaced.

These units with their cabling are contained inside a 0.311-inch nominal diameter stainless steel sheath.

Sixteen of the detectors are provided with envi-ronmentally qualified electrical connectors and cabling inside containment to provide increased reliability of the thermocouple readout for monitoring the potential approach to inadequate core cooling conditions.

Assemblies are inserted into the core through eight instrumentation ports in the reactor vessel head.

Each assembly is guided into position in an empty fuel tube in the center of the fuel assembly via a fixed stainless steel guide tube.

The seal plug forms a pressure boundary for each as-sembly at the reactor vessel head.

The neutron detectors produce a current proportional to neutron flux by a neutron-beta reaction in the detector wire.

The emitter, which is the central conductor in the coaxial detector, is made of rhodium and has a high thermal neutron capture cross section.

The rhodium detectors are 40 cm long and are provided to measure flux at several axial locations in fuel assemblies.

Useful life of the rhodium detectors is expected to be about three years at full power, after which the detector assemblies will be replaced by new units.

The data from the thermocouples and detectors are read out by the PIP data processor which scans all assemblies and, periodically or on demand, prints out the data.

The data processor continually computes integrated flux at each detector to update detector sensitivity factors to compensate for detector burnout.

Temperature indication from the 16 qualified core exit thermocouples is also displayed on strip chart recorders in.the control room and is available to be read out from the CFMS computer.

The incore instrumentation is also used for measurement of reactor core radial peaking factors and quadrant power tilt and for annunciating linear heat rate.

The incore alarm system provides these last functions on a continuo~s.basis using the Plant information processor described in Subsec-tion 7.6.2.3, annunciating in the control room.

Verification of incore channel readings and identification of inoperable detectors are done by correlation between readings and with computed power shapes using an off-line computer program.

Quadrant power tilt and linear heat rate can be determined from the excore nuclear instrumentation (Sub-section 7.6.2.2), provided they are calibrated against the incore readings as required by the Technical Specifications.

Quadrant power tilt calibra-tion of the excore readings is performed based on measured incore quadrant power tilt. Incore quadrant power tilt is calculated using a computer pro-gram which determines tilts based on symmetric incore detectors and/or the integral power in each quadrant of the core (Reference 12).

Linear heat rate calibration of the excore readings involves two intermediary parame-ters, axial offset and allowable power level, which can be determined by FS0789-0565G-TM13-TM11 7.6-16 Draft

the incore readings.

The Technical Specifications give limits on these parameters above a certain reactor power level to ensure that the core linear heat rate limits are maintained while using the excore instruments.

The incore alarm system function is verified by the Plant information processor program out-of-sequence alarm and channel check feature.

7.6.2.5 Plant Data Logger System Layout - The hardware portion of the Plant data logger system (DLS) consists of one central control station (CCS), two field remote stations (FRSs), one command print station (CPS), one remote print station and in-terconnecting cables.

The DLS is a minicomputer-based distributed monitor-ing system located in the CCS which communicates with one microprocessor controller located in each FRS.

Identification of the DLS components and their relationship to interfaced systems is shown in Figure 7-64.

The power supply includes a 125 volt de subsystem (one battery, two char-gers and one distribution panel) and a dc-to-ac conversion subsystem (two inverters, one static switch) with a bypass transformer.

Power is taken from the 480-volt engineered safeguards MCCs 1 and 2.

The power supply subsystem, the CCS and FRS 1 (located in the.cable spread-ing room) have been qualified as Seismic Category I components (Sec-tion 5.7).

The battery enclosure in the cable spreading room meets IEEE 484-1975 and Regulatory Guide 1.128 for fire prevention.

The software part of the system includes a CPS/remote print station switch-over such that the remote print station in the feedwater purity building can take over the function of the CPS in the main control room if the CPS is nonfunctional.

Analog inputs and digital inputs/outputs are provided at the FRSs.

An analog status/events program is available as well as a digital (sequence) events program.

A pre/post-event program also allows recording in the main control room of significant event history.

Finally, alarm, status, analog and diagnostic summaries are provided.

Printouts are directly readable to the operator via an English language program.

Interfaces - Interfaces with the Reactor Protective System are both analog and digital.

Refer to Subsection 7.2.9.2 for details.

Interfaces with the engineered safeguards controls.and the Class lE electrical distribution system are exclusively digital.

They are provided via relay contact inputs from these controls, thus ensuring adequate electrical isolation as re-quired by IEEE 384-1977 and 10 CFR 50, Appendix A, GDC24.

Interfaces with the reactor shutdown control, fluid systems protection (PORVs) and auxil-iary feedwater controls are also exclusively digital via relay contacts.

Interfaces with nonsafety-related systems (regulating controls, primary and secondary plant process and Nonclass IE electrical distribution) are.both digital and analog.

They do not require any special isolation means.

FS0789-0565G-TM13-TM11 7.6-17 Rev 3

System Evaluation - The data logging system provides the operator with a readily available printout of the Plant parameters as well as pre/post-event sequences which help him diagnose the Plant condition.

The system is made out of a reliable electronic gear fed from an uninterruptible type of power supply, which power can be available from the emergency generators.

Being a Nonclass lE system, all safety systems interfaces have isolation means in accordance with IEEE 384-1977 and GDC24 either via relay coil-contact isolation or qualified electronic isolators. Its components, located in the CP Co Design Class 1 portion of the auxiliary building, have been qualified as Seismic Category I and the system battery enclosure in the cable spreading room meets IEEE 484-1975 and Regulatory Guide 1.128.

7.6.2.6 Critical Functions Monitor The Critical Functions Monitor System (CFMS) is a Nonclass lE computer system which provides the data processing requirements for the Safety Parameter Display System (SPDS), the Technical Support Center (TSC) and the Emergency Operations Facility (EOF).

The CFMS consists of remote signal termination/multiplexers located in the control room, a mainframe computer and associated peripherals located on the turbine deck, and cathode ray tubes (CRT) and keyboards located in the control room, TSC, EOF and at the Company General Offices.

A block diagram of the CFMS hardware configura-tion is shown in Figure 7-65

• The signal termination/multiplexer cabinets provide for termination of signal inputs and provide for data scanning independent of the mainframe computer.

The use of multiplexe~s off-loads the data scanning function from the mainframe computer allowing more time for the computer to perform data manipulation.

The three input cabinets also provide for separation and isolation between nonsafety and safety inputs and between inputs from redundant divisions of the safety channels.

After conversion to digital form by the multiplexers, the data is trans-mitted to the mainframe computer.

The mainframe computer converts the data to engineering units, performs various data checking (ie, validity, alarms, etc) and further processes the data for display on the various CRTs.

Power to the CFMS computer hardware located at the Plant site, necessary for the system to perform its function, is provided from a Nonclass lE battery-backed source.

The principal software function of the CFMS is to provide concise displays of Plant data, provide for trending of input data and to provide for historical data storage and retrieval.

This information is available to system users at each of the various CRTs.

Access to the information is provided through keyboards located at_each CRT location which allows the user to request the required information.

The CFMS provides a hierarchy of CRT displays showing the status of the Plant's critical safety functions.

The hierarchy starts'with a top-level display showing individual bo~es that give an indication of the status of each critical safety function.

Lower-level displays give system overviews FS0789-0565G-TM13-TM11 7.6-18 Rev 3

with current values of important process variables and more detailed mimic diagrams showing system line-up and indicating variables that are in alarm state by use of color and flashing of component symbols or variable values.

A chronological listing of all alarms of CFMS input variables also can be displayed.

The CFMS provides trends of input variables and historical data on the input variables.

Trends are displayed in strip chart form and are updated in real time at a rate selected by the operator. Historical data on each input parameter can also be displayed in strip chart form.

Additional information on the Critical Functions Monitoring System is.

provided in References 8 and 9

• FS0789-0565G-TM13-TM11 7.6-19 Rev 3

REFERENCES

1.

Consumers Power Company, "Palisades Plant Reactor Protection System Common Mode Failure Analysis," Docket 50-255, License DPR-20, March 1975.

2.

Consumers Power Company, Response to NUREG-0737, December 19, 1980 (Item II.E.4.2 - Special Test of April 15, 1980),

3.

Gwinn, D V, and Trenholme, WM, "A Log-N Period Amplifier Utilizing Statical Fluctuation Signals From a Neutron Detector," IEEE Trans Nucl Science, NS-10(2), 1-9, April 1963.

4.

Failure Mode and Effect Analysis:

Auxiliary Feedwater System, Bechtel Job 12447-039, dated January 14, 1980, Letter 80-12447/039-10, File 0275, dated March 25, 1980 to Consumers Power Company's B Harshe (Consumers Power Company FC 468-3 File).

5.

VandeWalle, David J, Director, Nuclear Licensing, CP Co, to Director, Nuclear Reactor Regulation, USNRC, "Proposed Technical Specification Change Request - Auxiliary Feedwater System," September 17, 1984 *

6.

Zwolinski, John A, Chief, Operating Reactors Branch 5, USNRC, to David J VandeWalle, Director, Nuclear Licensing, CP Co, "Amendment No 91 -

Deletion of Technical Specification 4.13, Reactor Internals Vibration Monitoring," September 5, 1985.

7.

Johnson, B D, Consumers Power Company, to Director Nuclear Reactor Regulation, Attention Mr Dennis M Crutchfield, "Seismic Qualification of Auxiliary Feedwater System," August 19, 1981.

8.

Vandewalle, David J, Director, Nuclear Licensing, CP Co, to Director, Nuclear Reactor Regulation, USNRC, "Supplement 1 to NUREG-0737, Safety Parameter Display System, Revised Preliminary Safety Analysis Report,"

August 21, 1985,

9.

Berry, Kenneth W, Director, Nuclear Licensing, CP Co, to Director, Nuclear Reactor Regulation, USNRC, "Response to Request for Additional Information, Safety Parameter Display System," May 19, 1986.

10.

Kuemin, James L, Staff Licensing Engineer, CP Co, to Director, Nuclear Reactor Regulation, USNRC, "Generic Letter 83-28, Salem ATWS Event, Item 1.2, Control Rod Position," May 5, 1986.

11.

Thadani, Ashok C, Director, Nuclear Regulatory Commission, to Kenneth.W Berry, Director, Nuclear Licensing, CP Co, "NUREG-0737, Item II.F.2, Inadequate Core Cooling Instrumentation," January 19, 1987.

12.

The CPCo Full Core PIDAL System Software Description, Revision 4, June 5, 1989, G A Baustian, Palisades Reactor Engineering.

FS0789-0565J-TM13-TM11 7-1 Draft