ML18057B004

Consumer Power Co Full Core Pidal Sys Uncertainty Analysis

ML18057B004
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Site:	Palisades
Issue date:	06/25/1991
From:	Baustian G CONSUMERS ENERGY CO. (FORMERLY CONSUMERS POWER CO.)
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ATTACHMENT 1 Consumers Power Company Palisades Plant Docket 50-255 THE CPCo FULL CORE PIDAL SYSTEM UNCERTAINTY ANALYSIS June 25, 1991 50 Pages

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THE CPCO FULL CORE PIDAL SYSTEM UNCERTAINTY ANALYSIS G.A. Baustian Reactor Engineering Palisades REV 0--June REV 1--0ctober REV 2--August 05, 1989 P*PID*89002 18, 1989 P*PID*89002 Rev 1 15, 1990*gAB*90*06 ABSTRACT This report provides an uncertainty analysis for ~he Palisades Incore Detector Algorithm, PIDAL. A detailed description of the individual uncertainties associated with using the PIDAL methodology for determining the power distribution within the Palisades reactor is presented.

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7-THE CPCO FULL CORE PIDAL SYSTEM Uncertainty Analysis REV 2 TABLE OF CONTENTS INTRODUCTION 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 CALCULATION of the UNCERTAINTIES 3.1 Methodology/Data Base 3.2 Effects of Failed Detectors on Uncertainties 3.3 Effects of Radial Power Tilts on Uncertainties 3.4 Results of Statistical Combinations TABLES FIGURES LIST of REFERENCES GLOSSARY

__J

Section l Pl REV 2 INTRODUCTION This report provides c.n analysis documentin~ the uncertainties assosiated with usin~ the Palisades Incore Detector ALgorithm, PIDAL, for measuring the full core three dimensional power distribution within the Palisades reactor core (reference #1).

The P IDAL me thodo 1 o~ was deve 1 oped over the course of two years by t11e Palisades staff with the intention of havin~ the full core PIOAL eventually replace t11e original Palisades one eighth core INCA. model.

Initially, the full core PIDAL solution method was based on a combination of the existin~ Palisades INCA methodolo~ and other full core measurement schemes. Over the course of development, short.comings in the previous met11ods were identified, particularily in the w~ the full core radial power distributions and tilts were constructed. Several new techniques were employed which resulted in an improved methodology as compared to the previous systems.

In order to determine the uncertainty associated with usin~ t11e PIO.<\\L system for monitoring the Palisades power distribution, it was ~ain decided to draw on previous industry experience. A copy of llie INPAX-II moni torin~

S'dstem uncertainty analysis, developed by Advanced Nuclear Fuels Corporation (formerly Exxon Nuclear) was obtained willi the permission of ANF. After preliminary work, the statistical melliods used by ANF were deemed adequate, with a few variations, and llie uncertainties associated willi PIDAL were determined as described by the :remainder of this report

• Sectioo Z PZ..

REV 2 DESCRIPTION of the STATISTICAL l10DEL Section Z.l Description of Uncertaint~ Components As mentioned in the previous section, the desire herein was to determine an uncertaint~ associated with using the Palisades full core incore anal~sis model for measurinQ reactor core power distributions. Therefore, the uncertainties were detemined for three different measurement quantities:

F(q),

core total peaking factor. Ratio of the peak local pin power to the core aver~e local pin power. For Palisades this value is frequentl~ written in tenns of peak linear heat li,!eneration rate.

FV;lh), inte~rated pin peaking factor. Ratio of the peak in~rated pin.power to the core aver~e assembl~ power.

F(Ar), assembl~ radial peaking factor. Ratio of the peak assembl~

power to the core ave~e assembl~ power.

For each of the parameters defined above, three separate components of the uncertainties associated with the peaking factor calculat_ions are defined. For our purposes these are box measurement, nodal S}ll1thesis and pin-to-box uncertainties.

The box measurement component is the uncertaiQ.'t.V associated with measuring segment powers in the instrumented detector locations *.

The nodal ~thesis component is the uncertaintv associated with using the radial and axial power distribution S}ll1t,hesis techniques emplo~ed bV the PIDAL full core model to calculate a nodal power. Specificall~, 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 uncertaintv is the error associated with using the local peaking factors supplied in the vendors phvsics data l ibr~ to represent the pin power distribution within each assemblv.

With the three uncertaintv components defined above, it was necess~ to mathematicall~ re-define each of the peaking factors in terns of these components. This was accomplished bv utilizing forms for the peaking factors developed bv Advanced Nuclear Fuels Corporation (ANF, formerlv EXXON Nuclear) for an uncertaint~ analvsis performed on the St*. Lucie Unit l incore anal~is routine, INPAX-II. Ulis analvsis is documented bv ANF in proprie~ report XN-NF-83-01 (p) (Reference llZ.) used bV Pal i$ades personnel with the permission of ANF

• Section Z P3_

REV 2 DESCRIPTION of the STATISTICAL MODEL The peaking factors, for Purposes of statistical analysis, were written in the fol lowing forms:

F(q)

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

F(Ah) = F(sa)F(r)F(L)

F(Ar) = F(sa)F(r) where:

F(s) =Relative power associated with a sin~le incore detector measurement.

(l)

(2)

(3)

F(sa) =Relative power associated with the ave~e of the detector measurements within a single assembly.

F(r)

= Ratio of U1e assembly relative power to the relative power of the detector measurements within the assembly.

F(:z)

= Ratio of the peak planar power in an assembl~ to the assembl~

average power.

F(L)

= Peak local pin power within a,n assemb~~ relative to the assembl~ average power

• AA 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 assembl~

relative power to the F(s) o:r 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 anal~sis because their

respective uncertainties could be calculated di:rectl~ and used to quantif~

the box measurement uncertaint~. It can be shown that the F(s) or F(sa) terms (denominator) disappear from the F(r) statistical unce:rtaint~ 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 uncertaint~ component for F(Ar) is as follows.

The peaking factor, F(Ar), *is defined in equation 3 above. Using the

~ene:ral form of the error prop~ation formula.given in Reference #5 Pl31,

+ ***

(4) z s =----

fc.v'I (5)

Section Z DESCRIPTION of the STATISTICAL MODEL F:rom equation 3 the pa:rtial dif~e:rentials a:re computed as:

a. F(A:r)

).. F(sa) d F(A

r) d F(:r)

= F(:r) and

= F(sa)

Substitution of the pa:rtials back into (5) gives:

Plf.

REV 2 (6)

(7)

(8) 2

~

Dividing both sides of equation 8 by F(A:r)

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

~ave an equation fo:r the :relative va:riance fo:r F(A:r) as:

(

-SF !!:!_'I_\\-,_= l_~f_JSA.) \\ + (-~:~~

\\

F(Ar))

~F(sa) J F(:r). J

( 51)

It is now necess~ to find a mo:re convienient fo:rm of equation 51 to use for the :relative va:riance of F(A:r). This is done by using the e:r:ro:r p:ropagation fo:rmula and implementing a simple va:ri2ble transformation as follows:

let ~ = ln(x) and note that -- = ---

Substituting into the e:rro:r propagation formula,

'2.

Sy (10)

Note that the form of equation 1 O is the same as the form of the individual components of equation 51. 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 2

. DESCRIPTION of the STATISTICAL MODEL Frpm the results of equations ") and 10, the following formulae for the

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

(ll).

z

-z.

a.

'2..

sf(A..,_) = SFts... ) + Ste*) + st"Ct..)

(lZ) 1.....

~

-z....

SffM) = Sf(s..._) + SF-fr)

(13)

It should be noted that equations ll,lZ and 13 are valid onl~ b~ assuming

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

After determining the sample variance for each peaking factor, it is necessar~ to construct sample tolerance intervals for each estimate. TI1e

~eneral 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 necessa.11{ to define onl~ a one-sided tolerance limit. This is because we are tcy'inQ to quanti f~ how m~ 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 peaking factor:

+f<i:-r"b )SFri \\

Upper tolerance limit for F(q)

+K,..r61..)S F'fA"-)

Upper tolerance limit for F(6.h)

+K;!Ar~f'(Ar)

Upper tolerance limit for F(Ar)

(15)

(16)

(17)

For this anal~is, a "J5/"J5 tolerance limit is used and appropriate K factors are used to determine the respective one-sided "J5/"J5 tolerance limits.

The tolerance factors (K), as a function of degrees of freedom, were taken from Reference IP+

• Section Z P6 REV 2 DESCRIPTION of the STATISTICAL MODEL As mentioned previously, it is necessary to determine U1e appropriate number of degrees of freedom for. each sample stand.ard deviation in order to obtain tolerance factors. This is accomplished by using Satterthwaite*s formula which was also used in Reference #Z. This formula is given below:

For a variance defined as:

The degrees of f~eedom are given by:

s'f 0

+

(18)

(151)

Section Z Pr-REV 2 DESCRIPTION of the STATISTICAL MODEL Section Z.Z F(s) Uncertainty Component The standard deviation Sf/s) is defined as the relative uncertainty in the individual detector segment powers inferred by the full core model.

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

The standard deviation Sns)can be obtained by comparing equivalent inferred detect.or 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 a.Ssumed 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 U1is point, the "failed" string is again made operable by using the original detect.or signals. A second string cf 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 se~ent powers have been calculated for all operable strings in the reactor.

From this scheme, five deviation data points can b~*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 7.

The equation for determining the standard deviation of all of the individual se~ent inferred/measured deviations is as follows:

where:

(ZO)

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

r r'\\

lnCFs.

) - lnCFs. )

~

~

arithmetic mean of the individual 05 *

~

radial!~ normalized measured detector segment power for detector 1.

radial!~ normalized inferred detector segment power for detector 1 *

(Zl)

Section Z P8_

REV 2 D~SCRIPTION of the STATISTICAL NOOEL

, Section 2.2 F(s) Uncertainty Component

---

~--------------------------

It should be noted ~1at there is an underlying assumption made in using equation 20 to determine uie individual detector segment power standard deviation. It is assumed that the uncertainty associated with inferring powers in the uninstrumented regions is greater than the uncertainty of the measured detector segment powers from instrumented locations. This assumption is supported by the fact that the inferred detector powers, by design, are influenced by the theoretical solution via the assembly average coupling coefficients. (Section Z.4, Reference #1) Therefore, the inferred detector powers will contain errors induced by ~~e theoretical nodal model.

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

• Section Z P~

REV 2 DESCRIPTION of the STATISTICAL MODEL Section Z.3 F(s<?.) Uncertainty Compor.ent The standard deviation Sfts.,.,) is defined as the relative uncertainty in the averaf!e of the five inferred detector segment powers within an assembly. TI1e inferred and measured detector se~ment power data used for this component comes from the same individual se~ent power data used for the Sf(s) analysis.

TI1e equation used for determinin~ the standard deviation of the strin~

aver~e detector se@Tlent inferred/measured deviations is:

where:

Ns.._

total nunber of inferred/measured aver~e segment power deviations *

.i:

\\'\\

ln(F~.. - ) - ln(F5. )

L Q. l ari tbrnetic mean of the individual D~~

(ZZ)

(23)

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

average of the radially normalized inferred detector segment powers for detector string 1

• Section 2 Pl O REV 2 DESCRIPTIOr."l of the STATISTICAL MODEL Section 2. t+ F' (r) Unc'er ta in ty Component The standard deviation Sf(.. ) is defined as the relative uncertainty associated with the radial systhesis from instrumented assembly powers to assembly powers for uninstrurnented assemblies. This component assumes that the radial coupling methods employed are valid and accurate for inferring de tee tor powers in uni ns trumen ted assemb 1 i es, and that the resu 1 tan t 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 alreac:W calculated in the ful 1 core model for other uses. These detector powers can U1en be used as the detector data input to the corresponding ful 1 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 calculatin~ the S flr) standard deviation is:

(24) total number of PIDALIXTG assembly powers compared (25)

D.r = arithmetic mean of the individual Dr~

core normalized PIDAL F(r) peaking factor calculated by the full core model for assembly 1 l"'I F,. =core normalized (original) XTG F(r) peaking factor for 1..

assemb 1 y 1 As mentioned in section 2.1, 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 25, i t can be shown that the de tee tor measvremen t term (either F(s) or F(sa)) drops out of the formulation. TI1is 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 PlJ.;

REV 2 DESCRIPTION of the STATISTICAL MODEL.

Section Z.5 F(z) Uncertainty Component The standard deviation Sf<?:.) is defined as the relative t.incertainty 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 starting 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 i"nput to a correspondinll!! full core case. The PIDAL model then calculates a full core power distribution.based on the XTG detector powers. The resultant assembly normalized axial pea.king factors obtained by PIDAL are then compared with the original XTG axial pea.king factors for each quarter core location.

The equation used for calculating the SfCi) standard deviation is:

S:r =

where:

N~

D~.:. =

De-

.J::

F~.:.

I"'

F~i:: =

N -

l c

total number of inferred/XTG F(z) axial peaks compared i:'

M ln(F~~ ) - ln(F ti )

arithmetic mean of the individual D-ec:

assembly normalized F(z) pea.kinll!! factor calculated by full core model for assembly i (26)

(27) the assembly normalized (original) XTG F(z) pea.king factor for assembly i

,I

Section Z PlZ REV 2 DESCRIPTION of. the STATISTICAL MODEL Section Z.6 F(l) Uncertainty Component The standard deviation SftL-) 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 avera~e 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 tl1e Palisades reload desi~n process.

The value of Si:11.> 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 factor are ~enerated 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.

Second! y, concern over the ab i 1 i ty of a two-group PDQ model to accurate 1 y describe the local power distributions in the re~ions of the differing water gaps prompted an ~reement 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 ~roup PDQ model for Palisades will be at least as accurate as a two-group model for other PWR*s. Therefore, the ANF value of s,,,1.. ) =.0135 will be used for this analysis

• Section 3 Pl3 Rev 2 CALCULATION of the UNCERTAINTIES Section 3.1 Methodology/Data Base

---

~----------

Four steps were taken in order to determine the uncertainties associated with the PIDAL full core monitoring model. The first step consisted of defining an appropriate statistical model. This was done as described by Section 2.

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

Finally, it was necessary to take the results of the computer cases and combine them in order to determine the overall uncertainties as defined by the statistical model. Included in this step was a study of the effects of failing large numbers of incore detectors, as well as an investigation into the effect of radial power tilts on the PIDAL methodology.

The results of this step are discussed i~ Sections 3.2 through 3.4.

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

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

The PIDAL program was described in detail by Reference #l.

The BDSTAT program was used to calculate the F(s), F(sa) and F(r) uncertainty 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) uncertainty component. This program reads output from the PIDAL exposure data file and calculates F(z) deviations and statistics between the stored PIDAL 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 PIDAL cases, equally distributed over the three cycles, were run. The cases used were selected from Reference #7. Since Reference #7 contained twice as many cases as were statistically necessary, it was decided to use use only half of the cases so only every other case was selected. Tables #1, #2 and #3 list the cases which were run using the PIDAL statistical analysis option for cycles 5, 6 and 7, respectively.

Section 3 Pl4 Rev 2 CALCULATION of the UNCERTAINTIES Section 3.1 Methodology/Data.Base Three separate cycle 7 BDSTAT statistical runs were performed. The first considered the entire compliment of detector data, including fresh and reused incores; and the original cycle 7 INCA Y' signal-to-box power conversion library. This library was revised by ANF which resulted in a second set of statistical data. A third cycle 7 set was then generated which omitted the reused detectors from the cycle 7 data. Note that the statistics from the first cycle 7 BDSTAT run are for information only.

A total of 22 PIDAL cases were run in order to generate data for the PIDAL F(z) uncertainty component. Of these 22 cases, 11 were selected from the cycle 7 INCA run log. These 11 cases were selected at approximately equal intervals over the fuel cycle. Also part of the total 22 cases were 11 cases run from a hypothetical EOC 7 Xenon oscillation. These cases were selected in order to include off-normal axial power shapes in the uncertainty analysis.

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 by fuel

. assembly spacer grids. It is reasonable to assume that axial peaking uncertainties caused by these types of flux disturbances would be small, compared to the off-normal axial shapes bei~g investigated, and therefore these fluxuations were_ ignored by this analysis.

A total of 18 PIDAL cases were run in order to determine the measurement uncertainties for radially tilted cores. All of these PIDAL cases used theoretical detector powers from two full core XTG dropped rod induced transient scenarios. One of these (used for the first six PIDAL cases) was induced by dropping a group 4 control rod, while the other (used for the second six PIDAL cases) used a group 3-outer rod as initiator.

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. Concentration on tilts between 0% and -5% was greater because it is over this range that the operator 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.

There were two reasons for using the two different transient scenarios as suppliers of the theoretical detector powers.

First, the dropped group 3-outer rod scenario did not result in quadrant power tilts greater than 5% during the oscillatory period. Therefore, it was necessary to use cases from the dropped group 4 rod scenario in order to get results on tilts up to 10%. Secondly, the oscillations between the two scenarios were quite different. The dropped group 3-outer rod oscillated about the major symmetric axis while the dropped group 4 rod scenario oscillated about the diagonal axis.

Consideration of both is important because the majority of the symmetric incore detector locations are rotationally symmetric (arid not generally symmetric about either major axis or diagonal). and therefore oscillations about differing axis' could have differing effects on the accuracy of the PIDAL quadrant power tilt algorithm.

Section 3 P14a Rev 2 CALCULATION of the UNCERTAINTIES Section 3.1 Methodology/Data Base Expanding on this last statement, it was decided to further investigate the effects of tilt location on the PIDAL solution.

In the case of the dropped group 4 rod induced transient, 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 if the power distribution was the same, just rotated 90, 180 or 270 degrees?

Since the incore detectors are not equally distributed over the quadrants, it is not expected that the power distributions as measured by PIDAL would be the same for the rotated cases.

The same questions can be asked for the group 3-outer rod induced transient as well.

Six additional PIDAL cases were then run.

Three of the cases were for -the 5% tilted group 4 rod induced oscillation at rotations of 90, 180 and 270 degrees clockwise from the original power distribution.

The other three cases were for the 5% tilted group 3-outer rod induced transient at rotations of 90, 180 and 270 degrees.

Section 3 Pl5 REV 2 CALCULATION of the UNCERTAINTIES Section 3.Z Effects of Failed Detectors on Uncertainties Current Palisades Technical Specifications require that 507o 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 system operable. A look at current Combustion Engineering standard tectmical specifications revealed that the current standard is for 757o 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 methodology becomes production. In order to make this change, the study described by this section was necessary in order to justify the 757o operability value which will be used.

In Refer-ence #Z, ANF came to the conclusion that the accuracy of an incore monitoring SdStem or methodology depended more on which instruments were operable than on the total n:s.nber 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 measured/inferred power distribution. These conclusions are valid because,* for random detector failures, there is an equal probability 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 r:Nery possible combination of failed detectors for a lar15e set of power distributions.

From a computational standpoint, this would not be practical. Therefore, two tests were devised in order to verify that incore failures resulting in only 757o detector operablility would produce accurate measurements.

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

This failure rate, 25.6~ of 215, was chosen because of its consistency with current standard technical specifications. Cl{cle 6 PIDAL case 115 was chosen as the base case to this test. The Sfrs...> and Sfrs>component uncertainties for this case were found to be 0.0134 and a.oz~~' respectively. See Table #6.

Five sets of elr:Nen failed incore strings were then chosen using a random number generator and input to PIDAL. The statistical analysis was repeated for each of tile five failed sets. The resultant S,-(So.)and Sf(s)components were found to be 0.017l_and 0.0328, respectively. Statistical peaking factor uncertainties were then determined based on the base case: and Z5Z failure rate case. From these calculations, penalty factors accountin~ for the apparent measurement de~radation based on detector failures were derived.

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

• Section 3 Pl6 REV 2 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 c~*cle ?

• The base case uncertainty components for this case were Sf~~)= 0.0812 and SRs)= 0.0'.755. Five new random sets of 11 incore strings to be failed were generated and the statistics calculations repeated. The resultant Sffs.o.) and s,.h)were O.lZ'.73 and 0.136'.7, respectively. From these results,, it is clear that PIDAL does not handle large local perturbations such as a dropped rod with a high def:ree of certainty.

There are two reasons why the dropped rod case resulted in higher measurement uncertainties. The W data used by P IDAL, and most other mon i tori ng syste.11S as wel 1, comes from stea~ state PDQ (or similar) calculations.

Therefore, the detector signal-to-power conversion is not very accurate for this type of case. Secondly, end more importantly,, t...'1e CO'wpl ing coefficients used by PIDAL are inferred based on one-quarter core measured and

~~eoretical detector powers. These couplin~ coefficients have no way of compensating for gross full core c:.ssymetries such as a dropped control rod.

Palisades plant procedures cuT:rently state that the incore monitoring S'JStem can not be used for verifying core peaking factors in the event of a dropped or misali~ned control rod. At this time, there is no intention of revising these procedures to the contra111 until a full core coupling coefficient methodoloffi!, capable of accounting for* !~e local reactivity perturbations has been added to PIDAL.. Work is underwey to develop such a me t11odo logy

• A second test was devised in order to further stucy the effects of gross incore failures on the PIDAL. methodology. This test consisted of fail in~ lar2e qJantities of incores on an indidual basis (not by strin~) and quantifying the resultant effects on the 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 ~enerated using a random number generator. The PIDAL power dist-ribution was then re-calculated for each of the five sets of failures, with the resu 1 tan t in te~ra ted assemb 1 y powers compared back to the base case.

This test was then repeated for failure thresholds of 507o and ?5h failed incores.

Aver~e assembly power deviations were found to be 0.60;?, l.107o and l.5?7o for the Z5~, 50Z and ?57o failed incore detector* cases respectively. From these results it is clear-that as additional incore detectors are failed, the power distribution as measured by PIDAL. tends to depart from the base case. From the individual cases, it is also apparent that the dei.!1ree of ~reement between the test cases and base case depends strongly on which incore detectors are operable. An example of this is the spread between the ave~e deviations for the five 25/? cases which had a hieh case aver~e of 0.717o 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 i ncore men i tor in~ system operab 1 e w i th up to 25~ of i t

• s 215 i ncore de tee tor considered failed. It is also apparent that detector failure rates greater than 25fo have an adverse effect on PIDAL *s abi 1 i ty to determine the measured power distribution.

<r*

Section 3 Pl6a Rev 2 CALCULATION of the UNCERTAINTIES Section 3.3 Effects of Radial Power Tilts on Uncertainties This section is a summary of work performed as documented in Reference #8, which should be consulted if further detail is required.

The purpose of the work described by Reference #8 was to determine the F(s) uncertainty component for radially perturbed or tilted power distributions up to the full power Technical Specification Limit of 5% quadrant power tilt.

The F(s) uncertainty component was recalculated for radially tilted cores.

It was found that in all cases the F(s) uncertainty component for tilted cores was bounded by the value assumed for the whole data base (0.0277) for quadrant power tilts up to 2.8%.

It was also found that the value of the F(s) uncertainty component depended strongly on the direction and magnitude of the oscillation causing the power tilt. For cores oscillating about the diagonal core axis, the 0.0277 value is valid for tilts up to 5%.

For oscillations about the major core axis, the F(s) uncertainty component ceases to be bounded by the 0.0277 value for quadrant power tilts greater than 2.8%.

Since the Palisades Technical Specifications allow for full power oper-ation with quadrant power tilts of up to 5%, and it was clear that the overall PIDAL uncertainties were only valid for tilts up to 2.8%, it was necessary to derive new uncertainties to allow use of PIDAL for tilts above 2.8%. The new uncertainties were derived and the results may be found in Table #12.

en Section 3 Pl7 Rev 2 CALCULATION of the UNCERTAINTIES Section 3.4 Results of Statistical Combinations Tables #5 through #9 contain the results of the F(s), F(sa) and F(r) statistical calculations for fuel cycles 5,6 and 7. Table #8 shows the original cycle 7 results assuming reused incore detectors. Table #9 shows analogous cycle 7 data with the reused incore data omitted. Table #10 shows a summary totaling all of the F(s), F(sa) and F(r) data for all three fuel cycles assuming no reused incore detectors.

Figures #l through #15 are.deviation histograms 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 PIDAL result seems to support the ANF assumption.

Table #ll contains the results of the F(z) statistical calculations using cycle 7 data. The first 11 elements of Table #ll were taken from the simulated Xenon oscillation data. The last 11 elements correspond to "typical" data equally spread out through cycle 7. ~ote that element 20 was from a dropped 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 0.9%. Since tais bias is positive, the PIDAL model is over-predictiing the peak and is therefore conservative. This is similar to the result obtained by ANF.

Three sets of tolerance limits were determined for F(q), F( h) and F(Ar).

The first set is based on theoretical data and is valid when quadrant power tilt, as measured by PIDAL, exceeds 2.8%. The second set is based entirely on cycle 7 data and is valid only for reload cores which contain fresh and once-burned incore detectors. The third set of tolerance limits is based on data from all three cycles, excluding the cycle 7 reused detector data, and is valid only for reload cores with all fresh incore detectors.

Table #12 contains a summary of all of the statistical uncertainty values obtained. From this table, the one-sided 95/95 tolerance limits associated with Palisades PIDAL model were found to be: 0.0623 for F(q), 0.0455 for F( h) and 0.0401 for F(Ar) for un-tilted cores with all fresh incore detectors. For cores using a mixture of fresh and once-burned incore detectors, the 95/95 tolerance limits for F(q), F( h) and F(Ar) were found to be 0.0664, 0.0526 and 0.0490 respectively. Finally, for measurements. when quadrant power tilt as measured by PIDAL exceeds 2.8%, the 95/95 tolerance limits for F(q), F( h) and F(Ar) were found to be -0.0795, 0.0722 and.0.0695, respectively.

. l

Section 4 TABLES PIDAL Run Exposure Rx. Power Number MWD/11T NW th 1

o.o 16'74 z

ZZ4.5 241'7 3

520.Z 2300 4

'744.'7 23Zl 5

1504.6 24'74 6

ZZ87.7 2515 7

3007.'7 2514 8

4235.7' 2505' SI 5338.2 24'76 10 6424.1 24'75' 11 7248.3 2524 12 80'7'7. '7 2518 13

'7187'.2 2504 14 10068.5 2525 15 10860.1 24'77 16 11721.'7 2480 17' 12127.1 2227 18 1248?.6 184~

Table #l~Cycle 5 PIDAL case exposures and powers for F(s),

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

Pl8 REV 2

PIDAL Run Number 1,

20 21 22 23 24 25 26 27 28 2, 30 31 32'.

33 34 35 Section 4 TABLES Exposure Rx. Power NWD/MT NW th o.o 135.,

370.6 1051.6 1840.3 2845.5 3527.l 4180.8 4533.l 5618.,

648,.7' 6881.Z 7'763.,

8282.6

'7080.0

'7832.7' 10300.2 1160 l '7'72 2542 2464 2456 2456 2460 2477 2460 2468 2457 2468 2455 2240 2467 2483 2464 Table F,'Z~C~cle 6 PIO.AL case exposures and powers for F(s),

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

• Pl5' REV 2

Section 4 TABLES PIO.Al. Rlm Exposure Rx. Power Number liWD/I11' MW th 36 855'.8 2475 37 125'3.7 2453 38 0.0 782 35' 143.0 2406 40 265.8 2462 41 515'.3 1341 42 15'.76.7 18'.72 43 2310.7 2514 44 2~74. l 2535 45 3'.7~4.4 252~

46 521~.7 2357 47 6615.5 2527 48 7386.0 2531 45' 8226.8 2537 50 85'22.~

2526 51 5'837.4 252~

52 10468.8 2528 53 11105.8 2405' 54 11556.4 2406 Table #3-Cycle 7 PIO.Al. case exposures and powers for F(s),

• F(sa) and F(r) uncertaint~ component.$

• PZO REV 2

Section 4 PZl REV 2 TABLF.S PIDAL Run

• Exposure Rx. Power

~ Axial Number l1WD/MT MW th Offset l

172.~

23~

- 1.8 z

1075.7 Z476

- 0.7 3

1437.3 Z51Z 0.1 4

1807.Z Z476

- 0.1 5

25174.l Z530 1.4 6

351514.4 25~

Z.5 7

55130.l 2518 3.8 8

7386.0 2525

4. 0 51 8683.3 114Z

-18.3 10 51364.5 2526 3.5 11 10468.8 2528 3.2 lZ 10510.7 2528

-40.0 13 10513.3 2528

-3Z.7 14 10514.6 25Z8

-27.6 15 10515.51 2528

-21.4 16 10517.3 2528

-13.51 17 10518.6 2528

- 5.1 18 10517.7 2528

1.

c:

"To/

151 10521.2 2528 14.4 20 10522.5 2528 23.4 21 10523.51 Z5Z8 30.5 22 10527.8 2528

• 351.Z Table #4--C~cle 7 PIDAL runs used for F(z) uncertainty components

• __J

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

• ~*-

~

P2.2.

REV 2

~

SUMMARY

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

FCS)

FCSA>

FCSA)

FCRl FCRJ DEVIATION

"*DEVIATION ST. DEV.

OBSERV.

ST. DEV.

OBSERV.

ST. DEV.

OBS ERV l

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. 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

-a.as 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.

FCSA) STANDARD DEVIATION ALL CASES = 0.0233 MEAN = O.OOi4 DEGREES OF FREEDOM =

619..

• FCR)

STANDARD DEVIATION ALL CASES = 0.0023 MEAN = 0.0000 DEGREES OF FREEDOM =

918.

T"-6Lf s-c'(c1..e-s f{s)) f'(.s... ) o"'.t F lr) Oo..\\'\\

~

P23 REV 2

~

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.

l 0.04 3.29 0.0336 152.

0.0182 30 0.0017

51.

2 0.01 3.09 0.0314 163.

0.0149 32 0.0013

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

-o.os*

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

-o.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 160.

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

-0.06 3.13 0.0318 140.

0. 0130 28 0.0028

51.

15

-o.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 =

5.38.

FCR)

STANDARD DEVIATION ALL CASES = 0.0023. MEAN = -.0001 DEGREES OF FREEDOM =

867.

T l'ri3 i..-r.

~-

C'<CLi: b f(~)) r <.s") It"" f(.-) D ~.-\\ '\\

l

~

P24

~

REV 2

SUMMARY

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

FCS>

FCSA)

FCSA>

FCRJ FCRl DEVIATION

%DEVIATION ST. DEV.

OBSERV.

ST. DEV.

OBSERV.

ST. DEV.

OBS ERV l

0.30 3.14 0.0310 180.

0.0245 36 0.0014

51.

2 0.49

3. 6 0 0.0350 185.

0.0269 37 0.0015

51.

3 0.41 3.88 0.0382 17 5.

0.0225 35 0.0018

51.

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

o. 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 0.0325 185.

0.0297 37 0.0026

51.

16 0.31 3.21 0.0318 185.

0.0292 37 0.0026

51.

17 0.28 3.25 0.0322 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.

FCSJ STANDARD DEVIATION ALL CASES = 0. 0331 ~ MEAN = 0.0027 *DEGREES OF FREEDOM = 3415.

FCSA> STANDARD DEVIATION ALL CASES = 0. 0272 - MEAN = 0. 0027 - DEGREES OF FREEDOM =

683.

FCR)

STANDARD DEVIATION ALL CASES = 0.0021 MEAN = 0. 0000 ""DEGREES OF FREEDOM =

969.

TAi3i...f: 1- -

C.'(CL.E 1-F(.s) > f (.!.q ') """".L f ( ~) (:)... ~~.or:~:<\\... ~ l....l' ) R e "".s l'.R. D e -+ ec. "'t " r.s '1-c 11-4~ eJ..

~

~

P25'

§ii REV 2

SUMMARY

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

FCS)

FCSA)

FCSA)

FCR)

FCR. J DEVIATION

%DEVIATION ST. DEV.

OBSERV.

ST. DEV.

OBSERV.

ST. DEV.

OBSERV.

l 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

-a.as 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 0.0026

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 = 0.0000 DEGREES OF FREEDOM =

969.

TASLE

~-

C'(Cc.E "T f(s) l F(s...)) tef") bQ.~"* Ne..J i.v' > \\le4.s.e ~ Ce ~et~ o's r "C.14.( e.Q.

• \\"*

\\.-

~

~

P2G.

REV 2

SUMMARY

EDIT F0R ALL CASES THIS RUN CASE AVERAGE SEGMENT RMS SEGMENT FCS)

FCS)

FCSA)

FCSA)

FCR) f(q)

DEVIATION

'to DEVIATION ST. DEV.

OllSERV.

ST. DEV.

OBSE~V.

ST. DEV.

GB SER'/.

l 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 5 l.

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 16 a.

0.0200 32 0.0017

51.

7 0.73 2.83 0.0267 155.

0.0194 31

0. 0 0.13

51.

8 0.68 2.82

0. 026 9 165.

0.0208

.)3 0.0021

51.

9 0.88 2.80 0.0261 155.

0. 0211 31 0.3021

51.

10 0.95 2.95

0. 0274 150.

0.0219 30 0.0022

51.

11 0.75 2.86 0.0270 150.

0.0212 30 0.0023

51.

12 0.39 2.24 0.0219 140.

0.0161 23 a.on:;

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 0.00<6

51.

17 0.69 2.61 0.0248 165.

0.0217 33 0.CG25

51.

18 0.72 2.68 0.0254 165.

0.0223 33 0.0025

51.

19 0.72 2.74

0. 026 0 16 0.

0.0228 32 0.0024

51.

FCS)

STANDARD DEVIATION ALL CASES = 0. 0259, MEAN = 0.0061-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.

TA!3LE.,,_ C< C L.E 1-f{s); F(.~Q.) a.,..J. f(.-)

Da.~o.. o"":+ie~ [2.e~r.e..i l:le~..-c.~orS.J Ne.w LJ I

~- _... *-

• ,*~~

~

~

P2.I REV 2

~

SUMMARY

EDIT

~.~ ALL CASES THIS RUN CASE AVERAGE SEGMENT RMS "SEGMENT FCSl FCSl FCSAJ FCSAJ FCRJ FCRJ DEVIATION

% DEVIATION ST. DEV.

OBSERV.

ST. DEV.

OBSERV.

ST. DEV.

OBSERV.

l 0.44 3.30 0.0324 195.

0.0216 39 0.0021

51.

2 0.38 2.61 0.0259 19 0.

0.0200 38 o.on1

51.

3 0.33 2.56 0.0254 195.

0.0199 39 0.0018

51.

4 0.32

2. 66

0. 026 4 190.

0.0208 38 0.0D18

51.

5 0.22 3.60 0.0356 16 9.

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 16 7.

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 16 0.

D.0239 32 0.0022

51.

17

-0.05 3.41 0.0341 172.

0.0280 34 C.O:J21

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 16 3.

0.0149 32 0.0018

51.

21 a.co 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

-0.15 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 16 0.

0.0114 32 0.0023

51.

28

-0.14 2.29 0.0228 16 o.

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 16 0.

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 0.0017

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 16 0.

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 0.0260 160.

0.0228 32 D.0024

51.

~

~

DEVIATION ALL CASES D. 0277 ~ MEAN

0. 0022 ""'DEGREES OF FREEDOM 8768../

FCS)

STANDARD

=

=

=

FCSA) STANDARD DEVIATION ALL CASES = D. 0194 ~MEAN = 0.0022" DEGREES OF FREEDOM = 1754.......

FCR>*

STANDARD DEVIATION ALL CASES = D. 0022../MEAN = 0. ODDO VDEGREES OF FREEDOM = 2754.....

lAl!>t..C. IO -

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SUMMARY

EDIT FOR ALL CASES-THIS RUN

,CASE FCZ)

FCZ)

BLOCK COMPUTER POWER ST. DEV.

OBSERV.

RUN DATE SPLIT 1

0.0168

51.

173 890331 120151200

-0.3997 2

0.0169

51.

17 5 890331 120713400

-0.3265 3

0.0162

51.

17-6 890331 122518910

-0.2758 4

0.0150

51.

177 890331 122839300

-0.2140 5

0.0140

51.

178 890331 123233500

-o.1386 6

0. 0135

51.

179 890331 123541400

-0.0514 7

0.0117

51.

180 890331 123903800

.0.0452 8

0.0150

51.

181 890331 124307900 0.1435 9

0.0119

51.

182 890331 124540200 0.2341 10 0.0131

51.

183 890331 124901700 0.3047 11

o. 0137

51.

186 890331 130048600 0.3921 12 0.0023

51.

5 890403 111937710

-0.0181 13 0.0016

51.

21 890403 113038680

-0.0071 14 0.0020

51.

26 890403 113746680 0.0011 15 0.0038

51.

34 890403 114504490

-0.0006 16

0. 0 06 0

51.

50 890403 122824420 0.0144 17 0.0108

51.

67 890403 123356290 0.0250 18 0.0144

51.

97 890403 123929710 0.0377 19 0.0167

51.

120 890403 124447390 0.0399 20 0.0178

51.

139 890403 125013590

-0.1834 21 0.0174

51.

149 890403 130227920 0.0346 22 0.0149

51.

162 890403 131014030 0.0319 FCZ)

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

/

Tf"t~L-E(/-

C.Y'C.LE -=t f (~.) t> o.-\\ C\\

-_j C*

Section 4 TABLES Statistical Standard Degrees of Tolerance Variable Deviation Freedom Factor P29 Rev 2 Tolerance Limit F(s) #

F(sa)#

F(r) #

F(s)

• F(sa)*

F(r)

• F(s)

F(sa)

F(r)

F(z)

F(L)

F(q) #

F~h)#

F(Ar)#

F(q)

• F~h)*

F(Ar)*

F(q)

F(Ah)

F(Ar) 0.0393 0.0351 0.0026 0.0306 0.0241 0.0021

-0.0211.

0.0194 0.0022 0.0151 0.0135 0.0433 0.0383 0.0352 0.0368

0. 0277 0.0242 0.0344 0.0237 0.0195 1800 360 408 3415 683 969 8768 1754 2754 1122 188 2487 1.703 0.0795 489 1.766

0. 0722 364

1. 785 0.0695 3822

1. 692 0.0664 877

1. 73.3 0.0526 694 *

1. 746 0.0490 4826

1. 692 0.0623 1225

1. 727 0.0455

. 1790

• i. 712 0.0401

1. --values for cores when quadrant power tilt exceeds 2.8%

but is less than or equal to 5%.

• --values for cores with once-burned reused incore detectors For the final tolerance limits, penalty factors of.0041,.0046 and.0067 for F(q), F(Ah) and F(Ar) repectively were included to account for up to 25% incore detector failures.

Table #12--Summary of statistical component uncertainties.

1000 900 800 700 600 500 400 JOO 200 100 0

-25

-20 G.A. BAUSTJAN

-15

-10

-5 0

DEVIATIO..

5 10 15 20 25 26APR89

t;'

300 270 240 210

.. 180 150 120 90 60 30 0

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10 15

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xi t'1 26APR89

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CYCLE 5 FULL CORE F Cr). SY-NTHES!S-/. DEVfATIONS 500 450 400 350 300 250 200 150 100 50 0

-2.5

• A* BAUSTIAN

-2.0

-1.5

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FU((- CO-RE F Cr1 -SYNTHESTSY.-DE 500 450 400 350 300 250 200 150 100 50 0

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.A *. BAUST1AH fi~uRe.. ~0

~

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vi IS'

xi t'1 N

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1000 800 700 500 400 200 100 0

-L;:::;;:::;:::;:::::;;:::;::::;::::;;:::;:::::;:::;:::;:::;=;::::;::::....~-------_..,.--..l-. __

.._...-r-._....---~;:::;:::;:::;:::::;::::;=::;:::;::::;:=;:::::;::::::;=;~::;::=j r

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DEVIATION 10 15 20 25 4APU9

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t<l r-->

--300-.....,?,_F..... U

.... [....... [___,C....,O...... R

.... E_..,F_,.(_s _e...... ) -s,..,...v--N..... T-A"'POE_S_I s-'Yo_D_E....,v-1---A r--1 """"o..... N-s,_.)_1_N_C L-*'1..-D-,...I-,-::> _(L_£_'-\\._~_E..._.P_()_E.._i_E_c.:_::i:,_o(Z..._S ___ __,I 210 240 210 180 ISO 120 80 IO 0

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• A* llAUSTlAll

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-15

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DEVtATlOll 10 15 20 r

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500 400 250 200 150 100 so.

0 *t;::::;:=;:::;;:::;:::;::=;:::::::;:=;:::;;::::::;::::;:::::::;:::;::::;:::;;::::::;:=;:::::;:::::._ ___._..,_.. __ _j_ __ _.............:::::::::::;::::;:::::,;;:::::::;,=:;::=;::=;:::::::;=:;:::;=:;::=;:::::;::::;:::;;:::;:::;::~

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009 OOl 008 008 OOOl

7 FOLL CORE F Csa) SYNTHESIS 2 DEVlATIONS, No Rcl.\\SE.t> ot.recro\\t..5 300 270 240 210 180 150 120 80 60 30

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-20

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5 10 15 20 25 DEVIATION

xi t<l

• A* BAUSTIAN 211Af'R89 N

F'i~~ ~,,

CYC E 500 450 400 350 300 250 200 150 100 so

.A. BAUSTJAH

-o.s o.o DEVIATION 1.0 2.0 2.5 26APR89

2500 2000 1500 1000 500 0

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• "-* BAUSTIAll

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DEVIATION

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10 15 20 25 l:'I 26APRB9 l'..J

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800 800 400 200 0

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• CORE Cr) 1000 800 800 400 200

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2.0 2.5

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.----.ULL CORE F Czl 500 450 400 350 300 250 200 150 100 50 0

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• A* BAUSTIAll SYNTHESIS r. DEVIAT....... IO

...... NT'"JIS~------------ ----i

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-to Saeed on C~ole 7 Data

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to I

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Number 1

2 3

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6 7

8 Section 6 P47 REV 2 List of References Title P*PID*89001, The Palisades Full Core PIDAL System Methodology and Programmers Manual by GA Baustian, Consumers Power Company, Palisades Reactor Engineering XN-NF-83-0l(P), Exxon Nulcear Analysis of Power Distribution Measurement Uncertainty for St. Lucie Unit l, January 1983.

Probability and Statistics for Engineers and Scientists, 2 Ed.,

RE Walpole and RH Myers, Macmillan Publishing Co, 1978.

Factors for One-Sided Tolerance Limits and for Variable Sampling Plans, D.B. Owen, Sandia Corporation Monograph, SCR-607, March 1963.

Radiation Detection and Measurement, Glenn F. Knoll, Wiley Publishing Co, 1979.

CALCULATIONAL VERIFICATION OF THE COMBUSTION ENGINEERING FULL CORE INSTRUMENTATION ANALYSIS SYSTEM CECOR, W.B. TERNEY et al, Combustion Engineering, p,resented at International Conference On World Nuclear Power, Washington D.C., November 19, 1976.

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

EA*GAB*90*06,- PIDAL Quadrant Power Tilt Uncertainty, by GA Baustian, Consumers Power Company, Palisades Reactor Engineering.

INCA PIO.AL XTG PDQ CECOR Wprime Normal Section 7 P4-8 REV 2 GLOSSARY An incore analysis pro~ram developed by Combustion Engineerin~

to determine (measure) the power distribution within the Palisades reactor assumin~ one-eighth or octant core symmetry.

- An incore analysis pro~ram developed by Consumers Power Company to determine (measure) the power distribution within the Palisades on a full core basis.

- A g:-ou;J and one-half nodal diffusion theory code developed by Advanced Nuclear Fuels Corporation (formerly Exxon Nuclear) for general predictive modelin~ of pre~surized water reactors.

A m:..i 1 ti -~roup diffusion theory code, run pr i mar i 1 y in two dimensions, capable of modelin~ each fuel pin in the reactor explicitly.

- An incore analysis pro~ram developed by Combustion En~ineeri~

to determine (meas.._rre) the power distribution within a pressurized water reactor on a full core basis.

- Factor used in conversion of measured incore detector millivolt signals to detector seement powers. Data sur;ipl ied by ANF *

- Refers to a statistically **normal** or Gaussian distribution of data.

~5/~5 Tolerance Limit - this limit ensures that there is a ~5 percent probabi 1 i ty that at least ~5 percent of the true peaking values will be less than the PIO.AL measured/inferred peaking values plus the associated tolerance limit

• ATTACHMENT 2 Consumers Power Company Pali sades Pl ant Docket 50-255 PIDAL ANALYSIS OF QUADRANT POWER TILT UNCERTAINTIES June 25, 1991 15 Pages

PALISADES INCORE DETECTOR ALGORITHM (PIDAL)

ANALYSIS OF QUADRANT POWER TILT UNCERTAINTIES G.A. Baustian Consumers Power Company August 14,1990 1

(

9107020012 9:1.0~?!?

\\

PDR ADOCK 05000~55 p

PDR

l: Objective 2: Summary of Results 3: Assumptions 4: Analysis Methodology 5: Analysis Results 6: Palisades Core Map CONTENTS 2

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

In particular, the NRC requested the following:

1 -

A comparison of the tilt measured by PIDAL with the true or theoretical tilt.

2 -

Verification that the PIDAL code programming was correct by supplying theoretical detector input and comparing the resulting PIDAL solution with the original theoretical power distribution solution.

3 -

Determination of the SF(s) uncertainty component for radially perturbed or tilted power distributions up to the full power Technical Specification limit of 5% quadrant power tilt.

4 -

An explanation of what assumptions are made in the Palisades Safety Analysis to cover radial peaking factor increases caused by quadrant power tilts.

3

Summary and Conclusions Comparisons between the quadrant power tilts determined by the PIDAL model were made to corresponding theoretical values. It was found that in all cases PIDAL either accurately measured the quadrant power tilt, or in some instances conservatively measured the tilts to be greater than truth.

The SF(s) uncertainty component as defined in the PIDAL uncertainty analysis was recalculated for radially tilted cores. It was found that in all cases the SF(s) value for tilted cores was bounded by the value used in the PIDAL uncertainty analysis for cores with quadrant power tilts up to 2.8%. It was also found that the value of the SF(s) uncertainty component depended strongly on the direction and magnitude of the oscillation causing the power tilt. For cores oscillating about the diagonal core axis, the assumed PIDAL measurement uncertainty is valid for tilts up to 5%.

For the oscillation about the core major axis, the SF(s) uncertainty component ceases to be bounded by the value assumed in the PIDAL uncertainty analysis for quadrant power tilts greater than 2.8%. Since the Palisades Technical Specifications allow for full power operation with quadrant power tilts of up to 5%, and it was clear that the current PIDAL uncertainties were only valid for tilts up to 2.8%, *it was necessary to derive new uncertainties to allow use of PIDAL for tilts above 2.8%. An analysis was performed, as described in Sections 3 and 4 of this report in order to determine the uncertainties in Fl,

~hand F~ at the 5% quadrant power tilt threshold. These uncertainties may be found in Table #3 of Section 5 of this report.

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

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

4

Assumptions The Palisades FSAR specifically talks about three types of instabilities within the reactor core: radial, azimuthal and axial. This analysis is only concerned with the first two modes. It is assumed that the use of the word "radial" in the FSAR refers to an oscillation which moves from the center of the core outward to the periphery and then back. An oscillation of this type could be depicted by the top of a single spired circus tent being raised and lowered~ It is assumed that the word "azimuthal" refers to an oscillation which traverses the entire width or the core before returning back to the point of origination. In the rigorous sense of the word, this type of oscillation could hypothetically traverse circumferentially around the core as well, much like a pie tin would rotate if it were not perfectly balanced on a central point.

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

There is one fundamental difference between the uncertainties derived from this analysis and the original values derived in the PIDAL Uncertainty Analysis which was brought on by the nature in which this analysis had to be performed. In the original PIDAL uncertainty analysis, it was assumed that the SF(s) uncertainty components contained both the measured and inferred components of the box power synthesis uncertainty. For this analysis, the SF(s) uncertainties calculated do not contain the same component because the detector powers supplied to PIDAL are based on theory. Since no data for significantly tilted cores exists for the Palisades reactor, it must be assumed that recalculating the uncertainty components based purely on theoretical detector powers is valid.

5

Analysis Methodology In order to answer the questions posed by the NRC, it was necessary to supply PIDAL with incore detector signals from a variety of radially tilted configurations. It was desired to investigate the effects of quadrant power tilts on the order of 0% to 5%, as well as more severely tilted cases on the order of 10%.

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

Since Palisades rarely operates with measured quadrant power tilts greater than 1 %,

and measured incore detector signals for radially tilted cores were not available, it was necessary to find an alternate method for providing PIDAL with the required tilted incore detector data. It was decided to use detector powers derived from full core XTG solutions as input to PIDAL. This required that XTG cases be run which modelled radial or azimuthal imbalances in the reactor core.

A total of four XTG cases were run in order to model a variety of azimuthal and radial Xenon oscillation scenarios. Three of the four XTG runs started from a restart corresponding to roughly 3 / 4 total cycle length. The fourth case was run at BOC. These four cases all started the transient by dropping a single control rod into the core and then leaving the rod fully inserted for a period of 72 hours8.333333e-4 days <br />0.02 hours <br />1.190476e-4 weeks <br />2.7396e-5 months <br /> after which time the rod was rapidly pulled out. The ensuing transient was then followed for a period of 36 hours4.166667e-4 days <br />0.01 hours <br />5.952381e-5 weeks <br />1.3698e-5 months <br />. The only differences between the four transient cases run were which control rod was dropped and therefore which direction the oscillation took across the core.

The first two of the transient cases were run by dropping group 3 control rods into the core. The first case dropped in a group 3-outer rod (rod 3-34) while the second case dropped in the central control rod (rod 3-33). The object of the case which dropped in the 3-outer rod was to induce an azimuthal oscillation. The object of dropping the central rod was to 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 of the major axis (on a diagonal). Both of the two cases which used a dropped group 4 control rod as transient initiator were identical with the exception being that the first case was run at 3 I 4 cycle length while the second case was run at BOC.

6

. I Analysis Methodology After the XTG cases were run, it was necessary to infer theoretical incore detector powers _ from the resultant* three-dimensional XTG power *distributions. This was accomplished by writing a small utility program, XTGDET, which used the power distribution from the XTG punch file as input.

The purpose of the XTGDET program was to read in a 3-D power distribution punch file created by XTG and convert the nodal powers into equivalent incore detector powers. Subroutine EXP AND is the meat of the XTGDET program. Based on the 3-D nodal power distribution determined by XTG, it calculates the theoretical detector powers.

EXP AND uses the same methodology as subroutine EXP AND of PIDAL and Section 2.2.1

• of the PIDAL Methodology Report should be consulted if further reference is required.

The XTGDET program was compiled and link edited four times. The program was identical for each compilation except for the incore detector location array, DETLOC. For the first compile DETLOC defined the actual locations of the detector strings in the reactor core (i.e. DETLOC was defined just like it was in the PIDAL block data section). For the second 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 fourth compiles rotated the core 180° and 270° clockwise respectively from its true orientation to the incore detector strings. The reason for wanting to rotate the core about the incore detector 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 then compared back to the original XTG solution. For each of the PIDAL cases run, the statistical analysis option was chosen in order to determine the uncertainties associated with the PIDAL calculations for the tilted conditions.

Prior to discussing the actual PIDAL cases which were run, it is appropriate to describe the temporary modifications which were made to the cycle 7 PIDAL model in order to overlay the measured incore detector signals with the full core theoretical values supplied by XTG via XTGDET. In the main program, immediately after the call to Subroutine BXPWR (which calculates the detector powers based on measured millivolt signals and the Wprimes), temporary coding wa8 added which reads in the theoretical detector powers arid detector level normalization factors produced by XTGDET. This read was activated by the IXPOW flag which is normally used to tell PIDAL to use theoretical

. detector powers from the 1/4 core XTG model that runs concurrently with each PIDAL case. Following the input of the full core theoretical detector powers, the IXPOW flag was turned off so that the normal 1/ 4 core theoretical detector power logic in PIDAL would not

• take effect. Nate that the measured detector powers are actually overlaid by the new coding and that PIDAL assumes the full core theoretical values to be measured from this point on.

7

Analysis Methodology A total of 19 PIDAL cases were run for this analysis. The first case was a non-tilted base case which corresponds to the core conditions at 3/4 EOC. The XTG case used to supply the full core theoretical detector powers was the second step of the 3 / 4 EOC group 4 rod drop scenario. The base case is important because it serves to verify that the entire system is working as designed for this analysis. The following checks were made:

- Verification that the full core XTG model for cycle 7 is working properly by comparing the full core XTG run with the 1/4 core XTG power distribution of PIDAL.

- Verification that the XTGDET program is working properly by comparing the full core XTG power distribution with the XTGDET collapsed 2-D radial power distribution.

- Verification that the XTGDET program is working properly by comparing the XTGDET theoretical detector powers with those previously calculated by the 1/ 4

• XTG which is part of PIDAL.

- Verification that the full core detector signals are getting input to PIDAL correctly from XTGDET and that the PIDAL solution is correct by comparing the PIDAL solution with the original XTG solution.

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

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. Concentration on 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.

8

.r-Analysis Methodology There were two reasons for using the two different transient scenarios as suppliers of the theoretical detector powers. First, the dropped group 3-outer rod scenario did not result in quadrant power tilts greater than 5% during the oscillatory period. Therefore, it was necessary to use cases from the dropped group 4 rod scenario in order to get results on tilts up to 10%. Secondly, the oscillations between the two scenarios were quite different.

The dropped group 3-outer rod oscillated about the major symmetric axis while the dropped group 4 rod scenario oscillated about the diagonal axis. Consideration of both is important because the majority of the symmetric incore detector locations are rotationally symmetric (and not generally symmetric about either major axis or diagonal) and therefore oscillations about differing axis' could have differing effects on the accuracy of the PIDAL quadrant power tilt algorithm.

Expanding on this last statement, it was decided to further investigate the effects of tilt location on the PIDAL solution. In the case of the dropped group 4 rod induced transient, 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 if the power distribution was the same, just rotated 90°, 180° or 270°? Since the incore detectors are not equally distributed over the quadrants, it is not expected that the power distributions as measured by PIDAL would be the same for the rotated cases. The same questions 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 four

• possible symmetric oscillations induced by individually dropped group 4 rods. In a similar fashion, the existing group-3 outer dropped rod XTG case could be used for three additional symmetric transient scenarios.

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

9

Analysis Results The results of the three transient cases which caused azimuthal xenon transients are summarized in Table #1. From this table it is apparent that the core is less stable at beginning of cycle than at EOC azimuthally. This is in agreement of Section 3.3.2.8 of the Palisades FSAR which states that it appears that the azimuthal mode is the most easily excited 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 the group 4 rod drop is more 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 is symmetric along the quadrant lines, and therefore the peak tilt is actually distributed over two adjacent quadrants. In the case of the dropped group 4 rod transient, the power peaking 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 data that will be used to answer the questions asked by the NRC. The first NRC request was for comparison of the tilt measured by PIDAL with the true or theoretical tiit. For the dropped group 4 rod case, the agreement between the PIDAL solution and the original XTG quadrant power tilt was very good: For the true tilts between 0% and 10%, the error was on the order of 0.72% or less.

For the dropped group 3-outer rod induced transient, the quadrant power tilt was not as accurately measured, however it was measured conservatively in each case. For true quadrant 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 reached 1.23%. Again it should be noted that the PIDAL tilt for these cases was always higher than the true tilt and therefore conservative.

The second NRC comment asked that the PIDAL code programming be verified correct by supplying theoretical detector input and comparing the resulting PIDAL solution with the original theoretical power distribution solution. In actuality, this comment had already been addressed by the. PIDAL Uncertain~ Analysis.

The.sF(r) uncertainty component represents the error m the PIDAL solution when PIDAL is given detector powers from a known power distribution solution. For the entire data base, the SF(r uncertainty component was 0.0022. This value is in excellent agreement with the individual case SF(r) uncertainty components found on the statistical summary edit following each of the PIDAL runs performed for this analysis.

10

Analysis Results The third comment made by the NRC requested that a determination of the SF(s) uncertainty component for tilted cores be made. To this end, the PIDAL statistical analysis routines, which calculate the individual case uncertainty components, were activated for each of the eighteen tilted core PIDAL runs made. The individual results are presented in Table

1. 2. When looking at these values,. the reader should keep in mind the overall SF(s) uncertainty component of 0.0277 for the entire data base arrived at in PIDAL Uncertainty Analysis.

Based on the results presented in Table #2 it can be concluded that the uncertainty component SF(s) bounds core measurements up to quadrant power tilts of 2.8%

(linear interpolation between cases 9 and 10). Furthermore, depending on the direction of the oscillation, the PIDAL measurements are bounded to above the current 5% quadrant power tilt Technical Specification limit.

For the oscillation symmetric about the core diagonal, the PIDAL measurement uncertainty previously determined is valid for tilts up to 5%. For the oscillation about the.

core major axis, the SF(s) uncertainty component ceases to bound the value assumed in the PIDAL uncertainty analysis for quadrant power tilts greater than 2.8%. This means that the uncertainties derived in the PIDAL Uncertainty Analysis are not valid for all cases when quarter core tilts are greater than 2.8%.

Because it was shown that the current uncertainties do not bound all tilted cases, it was necessary to find new uncertainties which take power distributions with tilts greater than 2.8% into account. This was done by utilizing the PIDAL statistical processor program, to combine the data from PIDAL cases 13 through 18. The PIDAL statistical program, which was developed and documented as recorded in the PIDAL UncertaintY Analysis, can take statistical data output by individual PIDAL cases and combine it to represent an entire population. Cases 13 through 18 were used as the basis for the new tilted core uncertainty because 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 3.23.3 allows for full power operation of the reactor for quadrant power tilts up to 5%, without any compensatory action.

The results of the statistical combination for the tilted cases may be found in Table

1. 3. The non-tilted data presented is taken from the previous PIDAL Uncertainty Analysis.

The Fl, ~

h and f~ data presented in Table #3 is the basis f9r the revised Technical Specification Table 3.23.3.

In response to the fourth NRC comment, a discussion on how quadrant power tilt effected the Palisades Safety Analysis took place with members of the Palisades Transient Analysis Group. It was learned that quadrant power tilt is not an input to the Safety Analysis and that the increase in local or radial peaking resulting from a tilted core scenario is implied by the peaking factor or LHGR used in the analysis.

There is no tilt multiplication factor applied to the peaking factors.

11

• .(,

• Step Hours from drop 1

0 2

0 3

72 4

73 5

74 6

75 7

76 8

77 9

78 10 79 11 80 12 81 13 82 14 83 15 84 16 85 17 86 18 87 19 88 20 89 21 90 22 91 23 92 24 93 25 94 26 95 27 96 28 97 29 98 Analysis Results Table #1 Group 3-0uter 3/4 EOC TILT 1.0000 1.0627 1.0488 1.0191 1.0329 1.0424 1.0483 1.0510 1.0511 1.0495 1.0459 1.04.16 1.0369 1.0318 1.0266 1.0217 1.0171 1.0129 1.0092 1.0060 1.0033 1.0011 1.0006 1.0018 1.0027 1.0033 1.0036 1.0038 1.0037 Group 4 3/4 EOC TILT 1.0000 1.0708 1.0542 1.0410 1.0697 1.0892 1.1007 1.1057 1.1054 1.1013 1.0941 1.0854 1.0757 1.0657 1.0558 1.0463 1.0374 1.0294 1.0222 1.0160 1.0108 1.0065 1.0030 1.0036 1.0045 1.0051 1.0054 1.0054 1.0053 Group 4 BOC TILT 1.0000 1.0708 1.0505 1.0458 1.0777 1.1011 1.1162 1.1238 1.1251 1.1212 1.1133 1.1025 1.0898 1.0761 1.0621 1.0484 1.0354 1.0236 1.0132 1.0043 1.0104 1.0145 1.0173 1.0189 1.0194 1.0190 1.0177 1.0159 1.0136 Table #1 - Peak quadrant power tilts for three scenarios each initiated by dropping a control rod, leaving it inserted for 72 hours8.333333e-4 days <br />0.02 hours <br />1.190476e-4 weeks <br />2.7396e-5 months <br /> and then rapidly withdrawing it. Values predicted by Palisades cycle 7 full core XTG model.

12

Analysis Results Table #2 Case Initiating XTG PIDAL

% Tilt SF(s)

SF(sa)

Rod Tilt Tilt Error BASE 1.0000 1.0000 0.0000 0.0010 0.0008 1

4 1.1013 1.0959

-0.54 0.0376 0.0321 2

4 1.0757 1.0721

-0.36 0.0280 0.0242 3

4 1.0558 1.0533

-0.25 0.0198 0.0180 4

4 1.0294 1.0284

-0.10 0.0101

.0.0102 5

4 1.0160 1.0158

-0.02 0.0077 0.0066 6

4 1.0030 1.0037 0.07 0.0089 0.0044 7

3-0uter 1.0511 1.0634 1.23 0.0495 0.0445 8

3-0uter 1.0416 1.0520 1.04 0.0409 0.0367 9

3-0uter 1.0318 1.0403 0.85 0.0313 0.0289 10 3-0uter 1.0217 1.0282 0.65 0.0219 0.0211 11 3-0uter 1.0092 1.0132 0.40 0.0112 0.0112 12 3-0uter 1.0006 1.0014 0.08 0.0083

. 0.0035 13 4

1.0558 1.0486

. -0.72 0.0239 0.0217 14 3-0uter 1.0511 1.0606 0.95 0.0529 0.0476 15 4

1.0558 1.0533

-0.25 0.0207 0.0188 16 3-0uter 1.0511 1.0634 i.23*

0.0490 0.0439 17 4

1.0558 1.0486

-0.72 0.0228 0.0205 18 3-0uter 1.0511 1.0606 0.95 0.0533 0.0480 Table #2 - Quadrant power tilts and detector power uncertainty components for for PIDAL for radially tilted cores.

Note: For all scenarios, PIDAL correctly identified the quadrant in which the maximum 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.

13

Analysis Results Table #3 Statistical Standard Degrees of Tolerance Tolerance Variable Deviation Freedom

• Factor -

Limit F(s)* #

0.0393 1800 F(sa) #

0.0351 360 F(r) #

0.0026 408 F(s)

• 0.0306 3415 F(sa)

• 0.0241 683 F(r)

• 0.0021 969 F(s) 0.0277 8768 F(sa) 0.0194 1754 F(r) 0.0022 2754 F(z) 0.0151 1122 F(L) 0.0135 188 Fl #

0.0443 2487

. 1.703 0.0795

~h #

0.0383 489 1.766 0.0722 pA 0.0352 364 1.785 0.0695 r

Fl

• 0.0368 3822 1.692 0.0664 P-h

• 0.0277 877 1.733 0.0526 p.\\

• 0.0242 694 1.746 0.0490 r

Fl 0.0344 4826 1.692 0.0623 ph 0.0237 1225 1.727 0.0455 pA 0.0195 1790 1.712 0.0401 r.

Table #3 - Summary of PIDAL Statistical Component Uncertainties.

1. -- values to be used when quadrant power tilt exceeds 2.8%

but is less than or equal to 5%.

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

Note: For the final tolerance limits, penalty factors of.0041,.0046 and.0067 for Fl, ~

h and F~ respectively were included to account for up to

/

25% incore detector failures.

14

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Form from EGAD 13 revision 0 IS