NLS2007032, SSP-07/405-C, Rev. 1, Gardel BWR - Power Distribution Uncertainties, Enclosure 5

SSP-07/405-C, Rev. 1, Gardel BWR - Power Distribution Uncertainties, Enclosure 5

ML072280318
Person / Time
Site:	Cooper
Issue date:	05/11/2007
From:	Tarves S Studsvik Scandpower
To:	Office of Nuclear Reactor Regulation
References
NLS2007032 SSP-07/405-C, Rev. 1
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NLS2007032 Page 1 of 29 ENCLOSURE 5 Studsvik Scandpower Report "GARDEL BWR - Cooper Nuclear Station Power Distribution Uncertainties" (Report No. SSP-07/405-C, Rev. 1)

Non-Proprietary Version Cooper Nuclear Station NRC Docket 50-298, License DPR-46

StudsvikmScandpower Report: SSP-071/405-C Rev. 1 NON-PROPRIETARY GARDEL BWR - Cooper Nuclear Station Power Distribution Uncertainties Shaun Tarves I / 2007.05.11

/ 09:03:41 -04'00' Prepared by:

Shaun Tarves Date Digitally signed by David Dean Date: 2007.05.11 03:47:29

-04'00' Reviewed by:

David Dean Date

/2 Jerry Umbarger 2007.05.11 11:16:15 -04'00' Approved by: ~,

Jerry Umbarger Date

SSP-07/405-C Rev I GARDEL BWR - Cooper Nuclear Station Non-Proprietary Power Distribution Uncertainties Revision History Revision Number Description Date 0 Original February 2007 Mark proprietary information with double brackets May 2007 ii StudsvikVScand---ower

GARDEL BWR - Cooper Nuclear Station SSP-07/405-C Rev I Power Distribution Uncertainties Non-Proprietary Abstract This document describes the methodology used to evaluate the uncertainties in the adaptive relative power distribution within GARDEL. These uncertainties are dependent on the quality of the simulation model employed, as well as on the reactor's instrumentation uncertainties.

By utilizing the symmetric TIP positions in Cooper Nuclear Station (CNS), the measurement uncertainties, and indirectly, the calculational uncertainties, can be obtained.

The adapted power is based on calculated power adjusted with observed differences between calculated and measured TIP response. By regarding the adapted power as a weighted average of measured and calculated power, a basis for evaluating the overall uncertainty is established.

The power distribution uncertainties are explored using a variety of perturbed simulation cases to emulate modeling errors. The first method requires a set of idealized cases, in which the calculated TIP values are fed back into SIMULATE to demonstrate the ability of the adaption model to reduce bundle power uncertainty. The second method uses the plant-measured TIP values to power-adapt perturbed and unperturbed cases to more realistically assess he adaption model. The decrease in difference between the adapted power for the perturbed and unperturbed cases drives the overall uncertainty reduction.

Finally, because TIP+LPRM-adaption is used in online monitoring, the additional uncertainty contribution from LPRM drift and the impact of basing the adaption on the prior TIP calibration is determined.

Uncertainties when all TIP machines are in service:

Gnodal = []

adia= []

Uncertainties with one out-of-service TIP machine:

Snoda, = (( ))

Cyradial [ ]

Studsvik-Scandpower

SSP-07/405-C Rev I GARDEL BWR - Cooper Nuclear Station Non-Proprietary Power Distribution Uncertainties Table of Contents Abstract ...................................................................................................................................... iii

1. Purpose and Scope .......................................................................................................... 1-1

2. Norm al Distribution Statistics ......................................................................................... 2-1

3. Measurement and Calculation Uncertainties ................................................................. 3-1

4. TIP-Adapted Power Uncertainties ................................................................................... 4-1 4.1 The Perturbation Method ......................................................................................... 4-2 4.2 Method 1: Calculated TIP Responses Used for Adaption .................................... 4-5 4.3 Method 2: Measured TIP Responses Used for Adaption ...................................... 4-6

5. LPRM+TIP-Adapted Power Uncertainties ....................................................................... 5-1 5.1 LPRM Handling During TIP/LPRM Calibrations ..................................................... 5-1 5.2 LPRM Handling Between TIPILPRM Calibrations ................................................. 5-2 5.3 LPRM+TIP-Adapted Power Distribution Uncertainties ......................................... 5-3

6. Overall Uncertainty ........................................................................................................... 6-1

7. References ......................................................................................................................... 7-1 iv ivStudsvik-Scand---ower

GARDEL BWR - Cooper Nuclear Station SSP-071405-C Rev 1 Power Distribution Uncertainties Non-Proprietary

1. Purpose and Scope This document describes the methodology used to evaluate the uncertainties in the adaptive relative power distribution within GARDEL. These uncertainties are dependent on the quality of the simulation model employed, as well as on the reactor's instrumentation uncertainties.

The adapted power is based on calculated power adjusted with observed differences between calculated and measured TIP response. By regarding the adapted power as a weighted average of measured and calculated power, a basis for evaluating the overall uncertainty is established in section 2.

By utilizing the symmetric TIP positions in CNS, the measurement uncertainties, and indirectly, the calculational uncertainties, are obtained in section 3.

The power distribution uncertainties through adaption are assessed in section 4 using a variety of perturbed simulation cases to emulate modeling errors. The first method requires a set of idealized "baseline" cases, in which the calculated TIP values are fed back into SIMULATE as measured data to illustrate how well the adaption can recover from a known perturbation. The advantage of this method is that the "true" values are available and the ability to recover can be studied.

The second method uses the plant-measured TIP values to power-adapt perturbed and unperturbed cases. The decrease in difference between the adapted power for the perturbed and unperturbed cases drives the overall uncertainty reduction. Both methods can be utilized to assess the impact of one TIP machine being out of service.

In online monitoring, TIP+LPRM-adaption is used. Therefore, the additional uncertainty contribution from LPRM drift and the impact of basing the adaption on the prior TIP calibration is determined in section 5 by developing a TIP-calibration uncertainty to account for the LPRM-to-Studsvik-Scandpower

SSP-07/405-C Rev I GARDEL BWR - Cooper Nuclear Station Non-Proprietary Power Distribution Uncertainties TIP correction that GARDEL-BWR regularly performs. There are two effects that have to be considered; the drift of the LPRM detectors, and the fact that the shape of the TIP deviations from the last TIP calibration is employed in the time between TIP calibrations. By using the recorded GARDEL data, a good estimate of the total impact of these two effects can be obtained by comparing the adapted power immediately before a TIP calibration with the adapted power immediately after a TIP calibration.

Finally, all uncertainty pieces are combined to obtain the overall uncertainty in section 6.

The methodology employed is based on the observed differences in the TIP measurements and was applied to analyze Cooper Nuclear Station cycle 21-23 data.

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GARDEL BWR - Cooper Nuclear Station SSP-07/405-C Rev 1 Power Distribution Uncertainties Non-Proprietary

2. Normal Distribution Statistics Total bundle power uncertainty is comprised of a calculational uncertainty piece and a measurement uncertainty piece, which are assumed to be independent of each other. To develop a methodology for combining these uncertainties, we use the following definitions:

X, = true parameter XM = measured parameter X, = calculated parameter X,. - X,

• = measurement error X, - X, c = -, calculationerror X -

C.* = X observed difference The unbiased estimator for the variance of a normal-distributed variable is given by

~ N-1j where 2 _- )2

Thus, N

Z(X 1 ,i= (2.1)

N-I Using the definitions prescribed above, the expected value of the respective errors, Y, for N independent measurements of c, is given by 2-1 Studsvik"Scandpower

SSP-07/405-C Rev I GARDEL BWR - Cooper Nuclear Station Non-Proprietary Power Distribution Uncertainties N

N As c,. and c, were assumed to be independent, the following relationship exists and will serve as the basis for total bundle uncertainty calculations, 2 2 2 a., = o"m + o- (2.2)

Assumption 1: The adapted power can be considered to be a weighted average of measured and calculated values The value of adapted power in any location can be expressed as a weighted average of measured power and calculated power:

A'0 = (I - S)X+ SX (2.3)

Equation (2.3) cannot be applied immediately, since we do not have direct access to the measured nodal and bundle powers. Moreover, the values of Sm and 1- S, will vary by core location. To distinguish these local values from the core-wide average, we use S= I--Sm to denote core-average values.

If the uncertainties in the measurement are independent of the uncertainties in the calculation, the variance of X., 7, can be expressed as:

2x 2~ 2

~

1 f (2.4)

We will determine the variance of the TIP adapted power by evaluating I - S, (section 4) and conservatively assume that Sm = I 2-2 Studsvik-Scandpower

GARDEL BWR - Cooper Nuclear Station SSP-07/405-C Rev 1 Power Distribution Uncertainties Non-Proprietary Assumption 2: The predicted-to-measured TIP response ratio provides a measure of the deviation in the predicted power from the true power The adaption model in GARDEL/SIMULATE assumes that the measured-to-calculated TIP ratio, TIPRA T, provides an accurate measure of the relative deviation in calculated power in the surrounding bundles:

APOW1 TIPMEA Oc - =TIPRAT POWC TIPCAL where APOW1 = TIP-adapted power (also denoted as POWM)

POWC = Predicted (calculated) power TIPMEA = Plant-measured detector response TIPCAL = Predicted (calculated) detector response This is reiterated in a more formal fashion in equation (4.1) in section 4, the TIP-adapted power equation.

The calculation of uncertainties for the adaptive method relies on the assumption that the TIP deviations provide a measure of the nodal power deviations. This is a reasonable assumption, since, in principle, the calculation of the flux can be made with the same accuracy throughout the core. The uncertainty on the calculation of the reaction rates in the instrument tubes is of the same magnitude as that on the calculation of the flux, and hence the power, in the fuel pins.

The uncertainty for calculating the average power in a node is smaller than in the pins, since the pin-power calculations are summed over all the pins in the node. This means that the estimate of o7, for the predicted (calculated) TIP response, as derived in chapter 3, constitutes a conservative estimate of the uncertainty of the calculated nodal power.

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SSP-07/405-C Rev I GARDEL BWR - Cooper Nuclear Station Non-Proprietary Power Distribution Uncertainties Since each measurement location in the core may have a unique value of Sm that can satisfy equation (2.4), estimating the effective value of the core-wide distributions, (--S-) and Sm-, will be crucial.

We will assess the effective value of (1---) by using the adaption model in two variations of a perturbation method:

1. The calculated TIP values from a "baseline" case will be used to power-adapt a series of perturbed cases to illustrate the capabilities and limitations of the adaption model. A measure of the effectiveness of this adaption will be used to define the distribution, (1-SI).

2. The actual plant-measured TIP values will be used to power-adapt a set of base cases and a series of corresponding perturbed cases to establish the ability of the adaption model to recover the expected result. A measure of the effectiveness of this adaption will be used to define the distribution, (I - S2).

For the strategy outlined above, it is straightforward to estimate the impact of one out-of-service TIP machine.

Note that when we analyze equation (2.4) for the purpose of determining the uncertainty, (1- m) and Sm will be treated like two variables A and B, and conservative estimates for the two variables will be generated so (I--- ) + S,, = A + B >1. A conservative estimate of 1.0 for S,,, the weighting of the measurement uncertainty, will be used.

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GARDEL BWR - Cooper Nuclear Station SSP-071405-C Rev I Power Distribution Uncertainties Non-Proprietary

3. Measurement and Calculation Uncertainties A central part of the uncertainty analysis is determining o7m and a-,, the uncertainties associated with the measurement and the calculation. As shown in Figure 3-1, the core design and detector layout in CNS is quite advantageous. The large number (13) of symmetric or close-to-symmetric instrument locations provides a good statistical basis for the estimation of the measurement uncertainties.

01:*03 05 '0_7* 09 1Z13 *15 17*19. 21* 23 25 27 9 31' 37>i39: 41 43.. 45 4j.!49: '

_J_

_Ij _ -L _ -I- _1 -I l- "

.261 I I I_1_ -

- EDI l_ I_-

_ L+IJJ I I l + -- +

i II

• I. I I " I i I

ýL _J_

I I- I I JI

_J_--i--

17 f I

_jF _jI-04_ _J_ IL "U_

I I~ I~~

02 -L _J_ _jI

06;

_L _J_

I I Figure 3-1. Cooper Nuclear Station Core Layout 3-1 Studsvik'Scandpower

SSP-07/405-C Rev 1 GARDEL BWR - Cooper Nuclear Station Non-Proprietary Power Distribution Uncertainties The uncertainty in the measured TIP response is assessed using a method that takes advantage of the symmetric detector locations in the core. Assuming that TIPs x and x' are symmetric, then

= sd I~mmfn T~s(TIP~fAE4 - TIPME<')- (TIPCAL; - TIPCAL( )1 o-ý stdJiE$

-... tric TIPA N (3.1)

V2 where N = Total number of symmetric TIPs in the core In the above method, the term (TIPCALý - TIPCALý') accounts for slight asymmetries that exist during operation.

When cym is determined from the measurements, oc can be determined from equation (2.2).

Results of this calculation are presented in Table 3-1 for 44 TIP measurements in CNS cycles 21-23.

3-D 2-D

,-,.______ [_[I )) (( ))_________

Table 3-1. Uncertainties on Measured and Calculated Detector Response The calculational uncertainty, o-c, is the calculational uncertainty of the predicted (calculated)

TIP response. As noted in chapter 2, this provides an estimate of the uncertainty of the calculated pin powers and a conservative estimate of the calculated nodal power.

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GARDEL BWR - Cooper Nuclear Station SSP-071405-C Rev I Power Distribution Uncertainties Non-Proprietary

4. TIP-Adapted Power Uncertainties The adaption model in GARDEL/SIMULATE assumes that the measured-to-calculated TIP-signal ratio, TIPRA T, provides an accurate measure of the relative deviation in calculated power in the surrounding bundles. TIPRA T is expanded to non-instrumented locations by radially weighting the instruments up to five fuel assemblies away from the current bundle.

TIPRAT is then applied to POWC to calculate APOWI , the TIP-adapted, relative nodal power distribution as follows, c.f. Reference 1:

Z TIPRA T7'w APOW = POWCk. M (4.1)

I=1 where APOW] = TIP-adapted power (also denoted as POWM)

POWC = SIMULATE-3-predicted (calculated) power TIPRAT = Ratio of measured-to-predicted relative reaction rate in the detector location k = Node index n = Bundle index w = Weighting factor for the 1 th TIP surrounding bundle n GARDEL uses a weighting-factor array based on the following equation:

4-1 Studsvik'Scandpower

SSP-071405-C Rev I GARDEL BWR - Cooper Nuclear Station Non-Proprietary Power Distribution Uncertainties The adaption model will take into account bundles up to five positions away from the instrument, yielding the weighting-factor matrix shown below.

))

TIPRAT remains constant between TIP measurements and GARDEL's adaptive post-processor calculates APOWI after each SIMULATE core supervision calculation (typically once per hour at stable reactor conditions). The purpose of the APOWI calculation is to eliminate deviations in the calculated power distribution observed in the latest TIP comparison.

One limitation to this method is that deviations in non-instrumented assemblies will only partially affect TIPRAT. The relative gamma or thermal neutron flux in an instrumented location is affected by the contributions from the four neighboring fuel assemblies. The power deviation in a particular node will be the result of the node's intrinsic deviation plus the contribution from the deviations in its neighboring nodes. It is apparent that the detectors cannot supervise any local deviation that may take place in the non-instrumented assemblies; however, the supervision system is strong in detecting global deviations.

4.1 The Perturbation Method To estimate the weighting of the calculational uncertainty in the adaption model, (I -S-ý ) a number of cases have been simulated for which input parameters have been perturbed to emulate errors in the calculation scheme. All of these cases have been evaluated for two different scenarios:

1. The calculated TIP responses from the baseline case have been used as "measured" signals for the adaption that is performed on the perturbed case.

2. The actual measured TIP responses have been used for the adaption that is performed on the perturbed case.

4-2 Studsvik-Scandpower

GARDEL BWR - Cooper Nuclear Station SSP-07/405-C Rev 1 Power Distribution Uncertainties Non-Proprietary Each method will assess the ability of the adaption model to compensate for a perturbation in an effort to characterize the calculational component of the overall uncertainty. The following "global" parameters have been disturbed: ((

Method 1 Original case ....... Perturbed case PPowC, A I Calculated TIP Adapted case response APO WC +AAPO WI Uncertainty components:

POWC, = Calculated power, unperturbed baseline case, i.e. "true power" APOWCp = Difference between calculated power in the perturbed case and POWC, AAPOWIp = Difference between TIP-adapted power in the perturbed case and POWC, By first idealizing the cases using the calculated TIP values and assuming the plant has measured the TIP values perfectly, the experiment becomes more controllable. All deviation from the original case is due to the perturbation and the TIP response calculation. That is, the assessment of the adaption model compensation is directly proportional to the deviation of APOWCp + AAPOWIP from zero. In this way, the individual mechanisms of the adaption model can be understood without having to account for errors introduced by plant measurements.

.eL..

.. ... -... 1.-'_ _. 4-3 ItUUsviK .)Cd!1powIZ

SSP-07/405-C Rev I GARDEL BWR - Cooper Nuclear Station Non-Proprietary Power Distribution Uncertainties Method 2 AAPOW1 + ATIPMEA I Plant-measured POWCVC + AAOI +A I TIP response Adapted case I S,'owccase !

Perturbed O AAPOWI °1+ri

+ATIPME .

Uncertainty components:

POWC = Calculated power, unperturbed case AAPOWI = Difference between TIP-adapted power in the unperturbed case and POWC, APOWCP = Difference between calculated power in the perturbed case and POWC, AAPOWlp = Difference between TIP-adapted power in the perturbed case and POWCp ATIPMEA = Uncertainty introduced by plant-measured detector response The second method more realistically models the ability of the core to adjust for a perturbation.

The additional uncertainty introduced by using the plant-measured TIP response means that less of the total overall uncertainty can be compensated for by the adaption model. In areas of low power, the plant-measured TIP response to the perturbation will not be as strong as in areas of higher power. Because the adaption model is based on measured TIP values, this has the net effect of lowering the ability of the adaption model to correct for perturbations. In the case of method two, the recovery capability is directly proportional to the deviation of APOWCp + AAPOWIp from AAPOWIU.

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GARDEL BWR - Cooper Nuclear Station SSP-071405-C Rev 1 Power Distribution Uncertainties Non-Proprietary 4.2 Method 1: Calculated TIP Responses Used for Adaption After adaption, the average remaining error (1 - S) is estimated by:

) = std(APOW1P -POWC,)

(4.2) std(POWCp - POWC,)

where APOWIp = TIP-adapted power, perturbed case (adapted using calculated response from baseline case)

POWC, = Calculated power, unperturbed baseline case, i.e. "true power' POWCp = Calculated power, perturbed case Table 4-1 shows the average and standard deviation of (I -- S1) for a variety of perturbations on all available cases (38 TIP-calibrations over 3 cycles).

All TIP Machines in Service One TIP Machine Out of Service Perturbationcase avg(FS1 ) sid (1-S1 ) avg (I-S 1 ) sid (1-S1 )

I [ [ 11 [ 11 [ 11 Table[41 ((es II [ I values.

(( 1 ((I I] ((I 1](( 1[ II Table 4-1. (l - S1 ) for various perturbed cases, adapted with calculated TIP values.

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SSP-07/405-C Rev 1 GARDEL BWR - Cooper Nuclear Station Non-Proprietary Power Distribution Uncertainties 4.3 Method 2: Measured TIP Responses Used for Adaption After adaption, the average remaining error (--s 2) is estimated by:

(_ = std(APOWI1 - APOWWI) (4 std(POWCp -POWC.) .3) where APOWIP = TIP-adapted power, perturbed case (adapted using measured response)

APOW1 = TIP-adapted power, unperturbed case (adapted using measured response)

POWCP = Calculated power, perturbed case POWC. = Calculated power, unperturbed case Table 4-2 shows the average and standard deviation of (i -- 2) for a variety of perturbations on all available cases (38 TIP-calibrations over 3 cycles).

All TIP Machines in Service One TIP Machine Out of Service Perturbationcase avg (I-S 2 ) std(-) av(-) sd(S)

(( )) ((i ]((I )) ((11[ I1

((1 [ ]1 (( 11 (( 11 (( ]

((I] (( ] (( )) (( I] (( ))

[ )) (( )) (( (( ]2) (( I]

Table 4-2. (1- $2) for various perturbed cases, adapted with calculated TIP values.

Both methods produce consistent results. Method 2 was used to evaluate (i -- ) , since it provides a more realistic description of the real situation in the plant. In order to obtain a conservative estimate, 2a is added to the estimate of ( I - S)* ).

4-6 Studsvik-Scandpower

GARDEL BWR - Cooper Nuclear Station SSP-07/405-C Rev 1 Power Distribution Uncertainties Non-Proprietary avg (avg (I -S.)) 2sid(avg (1- S.)

where avg((I-s-) =The average of (1--S-) over all TIP calibrations Results are given in equations (4.4) and (4.5) below, cf Table 4-2:

All TIP machines in operation:

(1--- )m) overall = [ I] (4.4)

One TIP machine out of service:

-- m ) .. .

a -- [ I] (4.5) 4-7 Studsvik-Scandpower

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5. LPRM+TIP-Adapted Power Uncertainties GARDEL continuously uses the incoming LPRM detector signals with following purposes:

1. Apply an LPRM correction to the power distribution in order to evaluate APOW2, the LPRM+TIP-adapted power distribution.

2. Perform a verification of the applicability of the LPRM depletion modeling by comparing the incoming LPRM signals versus the deviations observed during the latest TIP calibration.

In addition, GARDEL includes a detector depletion model to account for sensitivity changes between TIP/LPRM calibrations.

5.1 LPRM Handling During TIPILPRM Calibrations Immediately after a TIP/LPRM calibration was accepted, GARDEL will evaluate the LPRM-to-TIP reference ratio, PRMREF, as PRMREF - LPRMCAL LPRMMEA where LPRMCAL = Predicted LPRM signal computed using an LPRM-type detector LPRMMEA =Predicted LPRM signal computed using a TIP-type detector PRMREF is a snapshot of the expected calculation-to-measurement deviations in the LPRM positions at the TIP calibration times. At the axial locations of the LPRMs, LPRMMEA is equal to TIPMEA.

GARDEL also maintains PRMSCF, the LPRM calibration factors, so that PRMSCF = TIP- A PRM where 5-1 Studsvik-Scandpower

SSP-07/405-C Rev I GARDEL BWR - Cooper Nuclear Station Non-Proprietary Power Distribution Uncertainties PRM = Un-calibrated, plant-measured LPRM signals This calculation is an attempt-to capture the drift in LPRM signal since it was last calibrated to match the TIP signal. If an LPRM spans a node boundary, an average of the measured TIP values in the two nodes containing the detector is taken.

GARDEL also resets all depletion calibration factors, PRMDCF, to 1.0 and begins updating them again after the calibration.

5.2 LPRM Handling Between TIP/LPRM Calibrations Although the LPRMs are calibrated to produce the same signal as the TIPs independent of detector type, they cannot be directly compared to predicted (calculated) LPRM signals. The LPRM signal must first be corrected for possible mis-calibration, depletion effects, and computed reaction rate if the detector types are different.

GARDEL evaluates a pseudo-LPRM signal, LPRMP, as LPRMP = PRM x PRMREF x PRMSCF PRMDCF where PRM = Un-calibrated, plant-measured LPRM signals PRMREF = LPRM-to-TIP reference ratio PRMSCF = LPRM signal calibration factors PRMIDCF = LPRM depletion calibration factors The pseudo-LPRM signal can now be compared to the calculated LPRM signal to define PRMRAT, the LPRM adaption distribution PRMRAT LPRMP PRMCAL where LPRMP = Measured LPRM signal, corrected PRMCAL = Calculated LPRM signal 5-2 Studsvik'Scandpower

GARDEL BWR - Cooper Nuclear Station SSP-07/405-C Rev I Power Distribution Uncertainties Non-Proprietary 5.3 LPRM+TIP-Adapted Power Distribution Uncertainties To evaluate the LPRM+TIP-adapted relative power distribution, PRMRAT is used to evaluate an LPRM-based TIPRAT distribution, TIPRATpRM, as TIPRA TPRg (z) = TIPRA T(z) x PRMRA T(z) where z = Axial node index PRMARA T(z) values are evaluated by linear interpolation in between the four LPRM levels TIPRATpR~ is applied in the same way as TIPRAT to obtain APOW2, the LPRM+TIP-adapted relative power distribution APOW2 = TIPRATPRM x POWC

= PRMRATxTIPRATxPOWC

= PRMRATx APOWI Note that immediately after a TIP/LPRM calibration, TIPRATpRA I TIPRAT and APOW1I APOW2. This makes the additional uncertainty in going from APOW1 to APOW2 easy to assess from data. Immediately after a TIP calibration, the additional uncertainty is small and it grows continuously until the next calibration. A good estimate of the maximum additional uncertainty due to the transition from APOWI to APOW2 can be obtained by calculating the standard deviation of the difference in APOW2 immediately before and after the TIP calibration UryT = std[(APOW2 - APOW2 )- (POWC- - POWC+)] (5.1) where CD-*T is the uncertainty immediately before a TIP calibration due to LPRM drift and the fact that TIPRA T used for the adaption is from the last calibration APOW2- = APOW2 immediately before a TIP calibration APOW2' = APOW2 immediately after a TIP calibration Studsvik-Scandpower

SSP-07/405-C Rev I GARDEL BWR - Cooper Nuclear Station Non-Proprietary Power Distribution Uncertainties POWC- = POWC immediately before a TIP calibration POWC+ = POWC immediately after a TIP calibration For practical reasons, the real time between "immediately before" and "immediately after" the TIP calibration is up to twenty-four hours. The term (POWC- -POWC+) is included to account for the changes in core conditions during this time. For the available data, daD (( 1] (5.2) where oda is the expected additional nodal uncertainty due to LPRMIU drift and variation in TIPRA T Correspondingly, the additional bundle uncertainty is, bundle =[

O'DT (5.3) 1]

where bundle (rDT is the expected additional bundle uncertainty due to LPRM drift and variation in TIPRAT 5-4 Studsvik-Scandpower 5-4

GARDEL BWR - Cooper Nuclear Station SSP-07/405-C Rev 1 Power Distribution Uncertainties Non-Proprietary

6. Overall Uncertainty The overall uncertainty for LPRM+TIP-adapted power immediately before a TIP calibration is determined by the following equation:

~AP~l I _J1S.)2 2+ S2c I DT (6.1)

Nodal Bundle Equation

- [ )) 1] (3.1)

-c7 (( )) 1[)) (2.2) o-.odIf[ (( )) (5.1)

Table 6-1. Summary of uncertainties Combining the results from Table 6-1, equations (4.4), (4.5) and equation (6.1), the overall uncertainties for the LPRM+TIP-adapted nodal and bundle power, with all TIP machines in service and one TIP machine out of service are given below:

All TIP Machines in Service One TIP Machine Out of Service Nodal Bundle Nodal Bundle

[)) (( ))

Table 6-2. Overall LPRM+TIP-adapted power uncertainties 6-1 Studsvik-Scandp-ower

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7. References

1. "SIMULATE-3 Adaptive Model for BWR On-Line Core Monitoring", STUDSVIK/SOA-96/19 (1996).

2. "ADPS3B Program Description", SSP-04/430, rev. 1 (2006).

3. "Qualification of Reactor Physics Methods for Application to Monticello," (NSPNAD-8609 Rev. 2).

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NLS2007032 Page 1 of 3 ENCLOSURE 6 10 CFR 2.390 Affidavit from Studsvik Scandpower, Incorporated Cooper Nuclear Station NRC Docket 50-298, License DPR-46

Affidavit I, Thomas Smed, state as follows:

1. I am President of Studsvik Scandpower, Inc. (SSP) and have reviewed the information described in paragraph 2 which is sought to be withheld.

2. The information sought to be withheld is contained in the attachment, "GARDEL BWR-Cooper Nuclear Station Power Distribution Uncertainties," dated May 11, 2007. SSP proprietary information is indicated by enclosing it in double brackets.

The basis for proprietary determination is provided in paragraph 3.

3. In making this application for withholding of proprietary information of which it is the owner, SSP relies on the exemption from disclosure set forth in the Freedom of Information Act ("FOIA"), 5 USC Sec. 552(b)(4), and the Trade Secrets Act, 18 USC Sec. 1905, and NRC regulations 10CFR 9.17(a)(4) and 2.390(a)(4) for "trade secrets and commercial or financial information obtained from a person and privileged or confidential" (Exemption 4). The material for which exemption from disclosure is here sought is all "confidential commercial information".

4. The information sought to be withheld is considered to be proprietary for the following reasons:

" Information that discloses a process, method and supporting data and analyses, where prevention of its use by SSP's competitors without license from SSP constitutes a competitive economic advantage over other companies;

" Information which, if used by a competitor, would reduce his expenditure of resources or improve his competitive position in the design, manufacture, shipment, installation, assurance of quality, or licensing of a similar product.

5. To address the 10 CFR 2.390 (b) (4), the information sought to be withheld is being submitted to NRC in confidence. The information is of a sort customarily held in confidence by SSP, and is in fact so held. The information sought to be withheld has, to the best of my knowledge and belief, consistently been held in confidence by SSP, no public disclosure has been made, and it is not available in public sources. All disclosures to third parties including any required transmittals to NRC, have been made, or must be made, pursuant to regulatory provisions or proprietary agreements which provide for maintenance of the information in confidence.

6. The information identified in paragraph 2 is classified as proprietary because it contains details of SSP's power distribution uncertainties methodology. The development of the methods used in these analyses was achieved at a significant cost to SSP.

7. Public disclosure of the information sought to be withheld is likely to cause substantial harm to SSP's competitive position and foreclose or reduce the availability of profit-making opportunities. The power distribution uncertainties methodology is a part of SSP's GARDEL core monitoring system, and its commercial value extends beyond the original development cost.

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The precise value of the expertise to devise an evaluation process and apply the correct analytical methodology is difficult to quantify, but it clearly is substantial.

SSP's competitive advantage will be lost if its competitors are able to use the results of the SSP's experience.

The value of this information to SSP would be lost if the information were disclosed to the public. Making such information available to competitors without their having been required to undertake a similar expenditure of resources would unfairly provide competitors with a windfall, and deprive SSP of the opportunity to exercise its competitive advantage to seek an adequate return on its investment.

I declare under penalty of perjury that the foregoing affidavit and the matters stated therein are true and correct to the best of my knowledge, information and belief.

Executed at Newton, Massachusetts, this 1 th day of May 2007.

Thomas Smed Studsvik Scandpower, Inc.

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