ML20106E254
| ML20106E254 | |
| Person / Time | |
|---|---|
| Site: | Arkansas Nuclear, Waterford, 05000000 |
| Issue date: | 10/24/1984 |
| From: | LOUISIANA POWER & LIGHT CO. |
| To: | |
| Shared Package | |
| ML19269A686 | List: |
| References | |
| MSS-NA3, NUDOCS 8410290129 | |
| Download: ML20106E254 (51) | |
Text
_ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
MSS-NA3 4
VERIFICATION OF CECOR COEFFICIENT METHODOLOGY FOR APPLICATION TO PRESSURIZED WATER REACTORS OF THE MIDDLE SOUTH UTILITIES SYSTEM i
Reviewed by: kl'Date
/E4 Manager, Reactor Phys 7cs AnalysisSection I
Approved by: I. rt ?lik1C Director Nuclear Engi ing Department Date 8410290129 841024 PDR ADOCK 05000382 A PDR
L l
ABSTRACT i
The purpose of this report is to demonstrate Middle South Services, Inc.
capability to provide updates to the CECOR program for Arkansas Nuclear One -
Unit 2 and Waterford - Unit 3. CECOR is a computer program for synthesizing t
three dimensional power distributions from incore detector readings that was purchased from Combustion Engineering by Arkansas Power & Light and Louisiana Power & Light. This report documents the MSS methodology for generating cycle dependent CECOR data library updates and quantifies the power distribution reliability factors for Fxy, Fr and Fq to be used with the MSS libraries. The reliability factors insure that there is a 951 probability that at least 95%
of the true Fxy, Fr and Fq will be less than the Fxy, Fr and Fq measured by CECOR plus 6.92, 5.69 and 7.711, respectively. The benchmark database included data from 4 cycles of 177 and 217 fuel assembly CE reactors.
PROPRIETARY DATA CLAUSE ,
This document is the property of Middle South Services Inc. and contains Proprietary information developed and owned by Middle South Services, Inc.
and is transmitted in confidence and trust. Appendices C and D are prc-Prietary. Other proprietary information is identified by .
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TABLE OF CONTENTS Page CHAPTER 1-1
- 1. INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . .
- 2. IN-CORE INSTRUMENTATION . . . . . . . . . . . . . . . . . . . 2-1
- 3. CECOR POWER DISTRIBUTION CALCULATION. . . . . . . . . . . . . 3-1
- 4. CECOR LIBRARY GENERATION. . . . . . . . . . . . . . . . . . . 4-1
- 5. DETERMINATION OF MSS CECOR LIBRARY UNCERTAINTIES. . . . . . . 5-1
- 6. REFERENCES. . . . . . . . . . . . . . . . . . . . . . . . . .
6-1 APPENDICES A-1 APPENDIX A - DEFINITIONS OF TERMS. . . ...........
B-1 APPENDIX B - POOLING METHODOLOGY. . . . . . . . . . . . . . .
APPENDIX C - COUPLING / MEASUREMENT ERRORS FOR 177 AND 217 FUEL ASSEMBLY PLANTS . . . . . . . . . . . . . . C-1 APPENDIX D - ASSEMBLY AXIAL SYNTHESIS ERRORS FOR 177 AND 217 FUEL ASSEMBLY PLANTS . . . . . . . . . . . . . . D-1 11
LIST OF TABLES TABLE TITLE PAG 5 5.2.1 AND-2 CYCLE 1 CECOR STATEPOINTS. . . . . . . . . . . . . . 5-8 5.2.2 AN0L2 CYCLE 2 CECOR STATEPOINTS. . . . . . . . . . . . . . 5-9 5.2.3 AND-2 CYCf.E 3 CECOR STATEPOINTS. . . . . . . . . . . . . . 5-10 l
5.2.4 217 FA CYCLE 1 CECOR STATEPOINTS . . . . . . . . . . . . . 5-11 5.2.5 ANO-2 CYCLE 1 CEC OR STATISTICS . . . . . . . . . . . . . . 5-12 5.2.6 AN OL2 CYCLE 2 CECOR STATISTICS . . . . . . . . . . . . . . 5-13 5.2.7 AND-2 CYCLE 3 CECOR STATISTICS . . . . . . . . . . . . . . 5-14 5.2.8 217 FA CYCLE 1 CECOR STATISTICS. . . . . . . . . . . . . . 5-15 5.3.1 ASSEMBLY AXIAL _YNTHESIS UNCERTAINTY . . . . . . . . . . . 5-16 5.6.1
SUMMARY
OF UNCERTAINTY COMPONENTS FOR CECOR PEAKING FACTORS. . . . . . . . . . . . . . . . . . . . . . . . . . 5-25 5.6.2 COMBINED 95%/95% PROBA8ILITY CONFIDENCE LOWER TOLERANCE LIMITS FOR CORE PEAKING FACTORS MEASURED BY CECOR . . . . 5-26 iii
LIST OF FIGURES FIGURE TITLE FAGE 2.1 INSTRUMENT PATTERW, ARKANSAS NUCLEAR ONE - UNIT 2. . . . . 2-3 2.2 INSTRUMENT PATTERN, WATERFORD - UNIT 3 . . . . . . . . . . 2-4 2.3 TYPICAL NEUTRON DETECTOR AND DETECTOR ASSEMBLY . . . . . . 2-5 2.4 RHODIUM EMITTER DECAY SCHEME. . . . . . . . . . . . . . . 2-6 2.5 IN-CORE INSTRUMENTATION WIRING DI AGRAM . . . . . . . . . . 2-7 4.1 SCHEMATIC OF CECOR LIBRARY GENERATION. . . . . . . . . . . 4-2 4.2 ASSEMBLY 15 COUPLING COEFFICIENT COMPARISON. . . . . . . . 4-3 5.3.1 Fxy ASSEMBLY AXIAL SYNTHESIS ERROR. . . . . . . . . . . . 5-19 5.3.2 Fr ASSEMBLY AXIAL SYNTHESIS ERROR . . . . . . . . . . . . 5-20 5.3.3 Fq ASSEMBLY AXIAL SYNTHESIS ERROR , . . . . . . . . . . . 5-21
~
5.4.1 ANO-2 CYCLE 2 BOC COMPARISON OF ]
PDQ PEAK PIN TO ASSEMBLY AVERAGL" PIN POWER, ARO . . . . . 5-22 5.4.2 ANO-2 CYCLE 2 80C COMPARISON OF[ ]
PDQ PEAK PIN TO ASSEMBLY AVERAGE PIN POWER, BK6 INSERTED. 5-23 5.4.3 PIN PEAKING SYNTHESIS ERROR. . . . . . . . .*. . . . . . . 5-24 iv
L 4
1.0 INTRODUCTION
The CECOR program (Reference 1) is an off-line computer program which synthesizes - detailed three-dimensional assembly and peak pin power distributions from fixed incore detector signals. The -purpose of this report is to descrit.e the methodology used by Middle South Services (MSS) to generate input data libraries for the CECOR program and to quantify the CECOR power distribution uncertainty which results from the use of this methodology.
l The CECOR uncertainty documented herein, supercedes those uncertainties estimated in the MSS Physics Topical (Reference 2) relating to core monitoring. Section two of this report describes the incore instrumentation
- for Arkansas Nuclear One - Unit 2 ( ANO-2) and Waterford - Unit 3 (W-3).
Section three descr.ibes the algorithms used by CECOR to synthesize the ,
i three-dimensional power distribution from the incore detector readings and the coefficient library. A precalculated library of coefficients is used in the l power synthesis. Chapter four describes the generation of the coefficient l libraries from data generated from the MSS reactor physics methods described in Reference 2. Section five provides a quantification of CECOR uncertainties using MSS generated libraries.
1 l
f 1-1
- _ _ _ ~ _ . _ . . _ _ _ _ _ . _ . _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . . . _ _ _ _ _ _ . _ _ _ _
I 2.0 IN-CORE INSTRUMENTATION The incore instrumentation at Arkansas Nuclear One
- Unit 2 and Waterford Unit 3 consists of fixed self-powered rhodium detector strings, movable self-powered rhodium detectors and background detectors. Figures 2.1 and 2.2 give the layout of incore instrumentation for ANO-2 and W-3. Each fixed incore detector string consists of five detactors equally spaced axially over the active fuel height. Each detector string is centered in the large center water hole of an assembly.
THE CECOR power distribution is based only on the fixed incore detector readings. The movable detectors are used for detector cross calibration and the background detectors are used periodically to detemine a background correction for the fixed self-powered rhodium detectors.
2.1 Fixed Rhodium Detectors A typical rhodium detector consists of a rhodium emitter, insulation, a collector sheath and signal lead wire as shown in Figure 2.3. The emitter consists of 99.9% rhodium-103 which is surrounded by a A1 023 insulator which is enclosed in an Inconel sheath.
The detectors are 40cm in length and are centered at 10, 30, 50, 70, and 90%
of active core height.
When the rhodium-103 in the detector absorbs a neutron, rhodium-104 is produced which decays through beta emission. The complete rhodium decay scheme is shown in Figure 2.4. The escape of beta particles from the emitter produces a low-level current. A measuring resistor is utilized to produce a measurable voltage as shown 2-1
t in Figure 2.5. The voltage is amplified, then digitized by an analog to digital converter for use by the plant computer.
2.2 Fixed Detector Signal Reliability The concerns of detector signal repeatibility, signal-to-power linearity and background signal effects were evaluated in Reference 3 by Combustion Engineering, and will not be repeated here.
2-2
1 Figure 2.1 '
INSTRUMENT PATTERN ARKANSAS NUCLEAR ONE - UNIT 2 ,
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i 3.0 CECOR POWER DISTRIBUTION CALCULATION 3.1 General The CECOR program synthesizes 3-D power distributions from fixed incore detector readings. The first step in the process is to convert the signals from the five axially spaced detectors in a string to powers. Coupling coefficients are next used to calculate pseudo-l detector powers in uninstrtmented assemblies or assemblies with failed detectors. A five term Fourier fit is used to construct assembly axial shapes based on the five detector powers. Calculation of the maximum 1-pin and 4-pin assembly peaks are done using 1-pin and 4-pin peaking library coefficients. Libraries are a function of burnup and control rod position. The following sections present the MSS methodology for determining the flux-to-power conversion library, coupling coefficient library and 1-pin peaking factor libraries.
3.2 Flux-to-Power Conversion The flux-to-power conversion factors are used to convert from
- depletion corrected instrument flux to assembly power integrated over detector length. The equation used is
Pni
- I in IF in 3.2.1 Where iP n is the power for assembly i at detector level n and Ijn is the background and depletion corrected incore
( detector flux reading, and IFi n is the flux-to-power conversion facter.
f The flux-to-power factors (IF in) are updated for each reload and are defined as the assembly power integrated over detector length divided by the rhodium reaction rate per rhodium atom.
3-1 l
A 2-0,1/4 core PDQ depletion calculation is used to obtain both the assembly power and flux in the detector region used in IFi n-The PDQ model is that described in Reference 2 and is a two energy group model with each fuel pin modeled explicitly. All exterior regions which ,
affect the power distribution are modeled including core baffle and reflector.
Effective rhodium absorption cross sections for use with PDQ fluxes are obtained by matching rhodium reaction rates from a PDQ assembly calculation to a detailed two-dimensional transport theory calculation with the CPM code (Reference 2). The transport theory calculation is an assembly depletion with the rhodium incore detector modeled explicitly. The rhodium is allowed to deplete. Two-group rhodium absorption cross sections for use with PDQ fluxes edited over the instrument cell are fit as a function of detector burnup.
Fast and Mixed Number Density (MND) thermal rhodium cross sections are combined with fast neutron flux and thermal neutron densities edited over instrument cells from the quarter core PDQ calculations to obtain rhodium reaction rates per atom. The assembly edits of power fraction are divided by rhodium reaction rates per atom to obtain the IF as shown in equation 3.2.2.
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IFin "
(oh* $ dr dE R 3.2.2
)( )
E V The IFi n coefficients are fit by cubic expressions in assembly cycle burnup.
3-2 -
3.3 Coupling Coefficients Coupling coefficients relate the detector powers in instrumented assemblies to pseudo-detector powers in uninstrumented assemblies.
Coupling coefficients are obtained from the 2-0 1/4 PDQ depletion calculations or from a 3-D nodal calculation. The coupling calculation is done prior to the axial synthesis described in Section 3.4. The coupling coefficient for assembly j is defined as:
NJ CCj = Pi/(Nj
- Pj) 3.3.1 i=1 i
Where Nj is the number of assemblies neighboring asembly j Pi are the powers in the neighboring assemblies at a I specific detector level, and i
Pj is the power in assembly j at the same detector level.
Coupling coefficients are generated for both rodded and unrodded core l-configurations and are fit by cubic expression versus assembly burnup.
> 3.4 Axial Power Synthesis The axial power distribution synthesis converts the five incore l detector level readings into a 51 node axial power shape using a Fourier l fit as described in Reference 1. The choice of the input variable (wave l
. nimber B) is the only required calculation. MSS uses a location and 1
l burnup dependent value of B based on 3-D nodal calculations.
l 3-3
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3.5 One Pin Peaking Factor The one pin peaking factor is defined as the ratio of the maxi. mum pin power in an assembly to the average pin power in the assedly. One pin peaking factors are obtained from a 1/4 ccre PDQ full power depletion model. The one pin peaking factors are input to CECOR as cubic fits as a function of assedly burnup for each assembly and rod configuration.
3.6 4-Pin Peaking Factor The 4-pin peaking factor is defined as the ratio of the maximum channel power in an asse21y to the average power in the asse21y.
CECOR used to use the results of the 4-pin peaking calculation to pass to another program to calculate DNBR. Currently however, the one-pin peaking information is used for this purpose. MSS, therefore, supplies dussy data for the 4-pin peaking factor. If in the future the 4-pin peaking data is needed, the methpdology will be identical to that for the 1-pin factors as described in Section 3.5.
3-4
4.0 CECOR LIBRARY GENERATION Most of tile infomation necessary to generate the CECOR data library comes from two dimensional, quarter core, full power, PDQ7 depletion calculations or 3-D nodal calculations. Both control rod out ( ARO) and rods inserted calculations are perfomed.
A schematic of the CECOR library generation methodology is shown in Figure 4.1. Inputs are generated by the PDQ (Reference 4) and 3-0 nodal simulator programs. The outputs include the CECOR cycle dependent data libraries as well as files used for quality assurance of the library. Output also includes graphs of the evaluated polynomial fits of the coefficients.
Figure 4.2 is an example of the coupling coefficient for assembly #15 for designates the data points to be fitted and "A" ANO-2, Cycle 1. "B" "B"
designates the points calculated using the polynomial fit based on the input points. These graphs serve to verify a smooth, well behaved fit between the input points.
i l
4-1
FIGURE 4.1 SCHEMATIC 0F CECOR LIBRARY GENERATION l l
INPUTS OUTPUTS Assembly Burnup Distribution '
CECOR 3-Dimensional
- LIBRARY Data Assembly Power GENERATION N EXPOSURE FILE
, Distribution y FOR QA e -
2-Dimensional W Assembly Burnup N FLUX-TO-POWER Data Distribution -
CONVERSION COEFFICIENTS Assembly Power IASSEMBLY Distribution -
COUPLING COEFFICIENTS Local Pin Power > 1-PIN ]
Peaking g COEFFICIENTS :
Flux in Instrumented Locations ;
Geometric Core > TEST SIGNALS Description ; FOR QA Rhodius Cross > GE04ETRY Sections -
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l 5.0 DETERMINATION OF CECOR UNCERTAINTIES 5.1 General The CECOR power distribution uncertainty relating to Fxy, Fr and Fq dich are defined in Appendix A of this report is composed of four components which are discussed in detail in the following sect'fons. The four are identified as the Coupling /Measurment Uncertainty, Assembly Axial Synthesis Uncertainty, Pin Peaking Synthesis Uncertainty and Pin Peaking Calculational Uncertainty.
5.2 Coupling / Measurement Uncertainty The Coupling /Measurment Uncertainty is the uncertainty associated with the wasurement of power at the five detector levels. It includes uncertainties in the measured power in instroented levels and the uncertainties in extrapolating to uninstroented assemblies.
l l
l
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l The variable X is defined differently for Fq, Fr, and Fxy. For the purpose of quantifying Fq uncertainty, the variable X is defined as the power in any instroented segment. For Fr the variable X is defined as the sum of five detector segments in any assembly. For Fxy the l
5-1 l
l
___ , mm._ e
r variable X is the pocer at any instrenented segment aithin a core level.
~
Data from two different size plants was included, three cycles of data for a 177 FA plant and one cycle of data for a 217 FA plant. The 217 fuel assembly plant is San Onofre Unit 2 which has the same reactor core as Waterford-3. Tables 5.2.1 - 5.2.'4 are a list of the CECOR cases run to calculate the Coupling / Measurement Uncertainty. Tables 5.2.5 through 5.2.8 provide a summary of the statistics from the fou cycles of comparisons.
The resultant map-by-map and cycle-by-cycle statistics were pooled. A poolability test was performed before pooling. In the event the data did not pass the poolability test, a conservative measure was taken as described in Appendix B.
5.3 Assembly Axial Synthesis Uncertainty The axial synthesis of the detailed three dimensional assembly power distribution is done in the CECOR program using a Fourier series l
expansion. Three dimensional nominal cycle nodal code depletions as well as rodded cases are performed and the nodal power distributions obtained are used to generate CECOR input detector signal s. The accuracy of the CECOR axial synthesis (Fourier fit) is then determined by comparing the Fourier fit to the original nodal code calculation.
5-2
l After normalization of the CECOR total core power to the r.odal core p3wer, three different errors are calculated from the nodal and fit power distribution compariwns:
- 1. The relative difference between the nodal code and Fourier fit values of integrated power for each assembly.
- 2. The relative difference between the nodal code and fit values of assembly axial peak to core average power density for each i assembly.
l
- 3. The relative difference between the nodal code and fit values of the maximum assembly planar power to the plane average power for each plane.
These quantities are used in the calculation of the Fr Fq and Fxy uncertainties, respectively. Appendix D gives a comparison of synthesized power distributions in the assembly containing the peak Fq vs. the -nodal input powers for both reactors at several points in each cycle. Comparisons are performed for all assemblies in the calculation of the Fr and Fq uncertainties and for all nodal planes used in the calculation of the Fxy. Table 5.3-1 gives a list of the cases used in the development of the assembly axial synthesis uncertainty and the resulting standard deviation and mean error. The Fq and Fr statistics comprise 177 (217 for W-3) comparisons per case and Fxy comprises 12 comparisons per case. All statepoints are at one hundred percent (100%)
full power. Since the errors were found to be non-normal, a non parametric, one sided tolerance limit was calculated and a 55/95 value 5-3
I was then obtained from Reference 7 for the nisber of samples available.
I A standard deviation was then calculated to conserve the one-sided tolerance limit. Figures 5.3.1-3 give comparisons of the samp1e error ,
distributions and the normal distributions with the calculated standard deviations. As can be seen in the figures, the normal distribution tolerance limit bounds the sample error distributions except for very small percents shown in the figures, indicating that the normal assumption is conservative.
5.4 Pin Peaking Synthesis Uncertainty CECOR pin peaking libraries are generated from a PDQ model which MSS models a slice through the reactor core at one particular level.
uses an " average" power plane. The Pin Peaking Synthesis Uncertainty is the uncertainty associated with the pin peaking at axial heights other than this " average" power plane. MSS estimates the pin peaking synthesis error from a comparison of PDQ results[ .
] The deviations in the calculated pin Tcorrespond to the maxistad overall peaking between these [
deviations within the instrumented portion of core height. Figures 5.4-1 through 5.4-2 give the comparisons of the PDQ power distributions
[ ]forroddedandunroddedcases.'
M l
l .
5-4
l l
l l
t' 5.5 Pin Peaking Calculational Uncertainty
- Since the local pin power cannot be measured directly in the ;
I operating reactor, the pin power synthesis process must rely on calculated values of pin-to-box factors. The pin peaking calculational t' uncertainty is the uncertainty associated with the PDQ calculation of pin-to-box peaking factors. The MSS pin peaking calculational uncertainties were based on PDQ comparisons to CPM calculations which P
were compared to critical experiments. The MSS pin peaking calcula-tional uncertainties were doctmented in the physics methodology report (Reference 2). The pin factor uncertainty established in Reference 2 was[
]
5.6 Combination of Uncertainties In order to determine a lower tolerance limit for the random error in pin peaking factors Fq, Fr, and Fxy as measured by CECOR, it is necessary to statistically combine the uncertainty factors due to Coupling / Measurement (C/M), Assembly Axial Synthesis (AAS), Pin Peaking Synthesis (PPS) and Pin Peaking Calculations (PPC). Since the error components are due to entirely different and unrelated factors, they are independent and uncorrelated random variables, and one may write:
5-5
U "
"C/M + UAAS + UPPS + UPPC 5.6.1 and o2 . a2 ,a 2 +a 2 +g 2 5.6.2 C/M AAS PPS PPC Using the sample means and variances from Sections 5.2 -
5.5 as estimates of the true bias and variance, one can write:
u = E=EC/M + AAS + PPS + PPC 5.6.3 and o'. 2 32.SC/M+SbS*8PPS + 8PPC 5.6.4 The sample statistics Oand S from equations 5.6.3 and 5.6.4 are estimates of the true parameters u and o and are therefore subject to a random distribution of their own. The one sided lower tolerance limit can be calculated such that the uncertainty in the CECOR power can be estimated on a 95%/95% probability / confidence level.
Table 5.6.1 lists the estimates of I) and S and the ntaber of degrees of freedom of the four camponents of CECOR pin power uncertain-ty. If one expressa the sample variance as being proportional to a x2distribution, one may write:
S2 . X2 ,2 5.6.5 f
or substituting in equation 5.6.4, one can write:
x7 22
. x4,,.xq,,.x4,,.xe,c 2 2 2 22 s.e.e f
c/M AAS PPS PPC and taking the variance of both sides 2fo4 = .6.7 2fC/M 'C/M
( f2 f2 f2 f2 f2
e . q ,,. q ,, . o;,, . o;,c s.6.s I f I I
! 5-6
-- . -..,..,...n.,_. ,-we., . , , , , , - -, -- - ---n-, ,.,~.,..,,,,.n _ _ , , , . . - , - . - - - - - - , , - - - - - - - _
,-.m ,, - -
l Using the sample variances as approximations for the true variances, one can write:
S" 5.6.9 I +
Sb/M Ob + SPPS + SfPC f f f f C/M AAS PPS PPC where all measured variances are known. The number of degrees of freedom is used to determine the lower one-sided tolerance limit for the 95%/95% probability / confidence interval. The results for Fq, Fxy and Fr are given in Table 5.6.2. These tolerance limits insure that there is a 95% probability that at least 95% of the true Fxy, Fr and Fq will be less than the Fxy, Fr and Fq measured by CECOR plus 6.92, 5.69, and 7.71% respectively.
J f
l t
l.
i l
5-7
TABLE 5.2.1 AN02 CYCLE 1 CECOR STATEPOINTS CASE # EXPOSURE (MWD /MT) POWER CONTROL ROD BANK (% INSERTED) 5 6 PLR 1 2544 99.5 0 0 0 2 3208 99.9 0 0 0 3 4385 89.0 0 0 0 4 5916 100.0 0 0 0 5 6750 100.0 0 0 0 6 8012 100.0 0 0 0 5-8 j
TABLE 5.2.2 AN02 CYCLE 2 CECOR STATEPOINTS CASE # EXPOSURE (MWD /MT) POWER CONTROL ROD BANK (1 INSERTED) 5 6 PLR 1 7975 50.7 0 6 0 2 8242 72.2 0 0 0 3 8859 96.8 0 6 0 4 9282 95.3 0 0 0 5 9505 97.3 0 7.5 0
'6 10013 99.7 0 0 0 7 10140 77.6 0 6 0 l 8 11589 100.0 0 0 0 9 12394 99.6 0 0 0 10 13986 100.0 0 0 0 11 14276 99.6 0 4.5 0 12 14745 89.7 0 0 0 13 15932 99.9 0 0 0 14 18200 99.3 0 3.4 0 15 18646 84.4 0 3.2 0 16 18971 76.1 0 0 0 17 7975 49.9 0 96.5 0 18 7975 49.6 68.6 %.5 0 19 7975 50.4 67.9 96.9 0 20 7975 49.7 0 96.9 73.2 21 7975 50.2 0 0 73.2 1
5-9
TABLE 5.2.3 AN02 CYCLE 3 CECOR STATEP01N15 CASE f EXPOSURE (MWD /MT) POWER CONTROL ROD BANK (% INSERT 50) 5 6 PLR 1 11183 50.1 0 0 0 2 11243 49.6 0 0 0 11601 80.1 0 0 0 3
4 12537 99.7 0 0 0 14026 92.8 0 0 0 5
6 14965 99.8 0 0 0 15152 100.0 0 0 0 7
8 11183 50.4 97.4 97.4 0 9 11183 49.7 97.4 97.4 74.6 10 11183 50.3 0 97 74.6 11183 50.7 0 97 0 11 5-10
, m -.r.- . - - _ , . . _ _ _ , - - - - - - - - - , - - - , ,-
TABLE 5.2.4 217 FA CYCLE 1 CECOR STATEPOINTS CASE # EXPOSURE (MWD /MT) POWER CONTROL ROD BANK (% INSERTED) 5 6 PLR 1 979 80.4 0 0 0 2 1599 91.1 0 0 0 3 1884 96.0 0 0 0 e
5-11 l
TABLE 5.2.5 ANO-2 CYCLE 1 CECOR STATISTICS l .
l _ FXY LEVEL *1 _ FXY LEVEL =2 _ FXY LEVEL =3 _ FXY LEVELS 4 CASE O(%) $(%) N 0(%) S(%) N O C%) $(%) N 0(%) $(%) N q
1 42 42 42 40 2 42 42 43 41 3 43 42 43 42 4 43 43 1 42 42 42 43 42 42 5
44 ,3, 4 42 42 6 , _ ,
_FXY LEVEL =5 _
FR _
FC CASE D(%) S(%) N 0(%) $(%) h 0(%) S(X) N 1 41 36 207 2 42 38 210 3 43 39 213 4 43 39 213 5 43 38 212 6 43 39 214 l
5-12
TABLE 5.2.6 ANO-2 CYCLE 2 CEC 04 STATISTICS
_ PXY LEV 5L=1 _ FXY LEVEL =2 _ FXY LEVP.L=3 FXY LEVEL =4 CASE O(X) $(X) N C(%) $(%) N D(X) SC%) N 3(2) $(%) N
~ ~ ~ ~ ~ ~ ~
1 43 44 44 44 2 43 44 44 44 3 44 44 44 42 4 44 44 44 42 5 44 44 44 42 6 44 44 44 42 7 44 44 44 42 8 42 43 43 42 9 42 43 43 42 10 42 43 43 42 11 42 43 43 42 12 43 43 43 42 13 ' 42 43 43 42 14 42 42 43 42 15 41 4C 41 41
! 16 40 4C 39 42 17 42 42 42 42 1E 42 42 42 42 19 41 42 42 42 20 41 42 42 42 l 21 41 42 42 42 l .
l
_ FXY LEVEL =5 _
PR _
PC CASE 0(X) SC%) N 0(%) SC%) N D(%) $(%) N l - - ,
1 42 41 217 2 42 41 217 l 3 42 42 216
! 4 42 42 216 l 5 42 42 216
! 6 42 42 216 l 7 42 42 216 8 42 41 212 9 42 41 212
, 10 42 41 212 l 11 42 41 212 1 12 42 42 213 j 13 42 41 212 14 42 4C 211 15 41 38 204 16 39 36 200 17 42 42 210 l 18 42 42 210 19 42 41 209 20 42 41 209 21 42 41 209 5-13 L
TA8LE 5.2.7 AND-2 CYCLE 3 CECOR STATISTICS
_ FXY LEVEL =1 _ FXY LEVELS 2 _ FXY LEVEL =3 _ FXY LEVELS 4 CASE 0(%) $(X) N 0(%) S(%) k D(%) $(%) N 0(%) S(%) N
~
1 4'O 3'8 33 38 2 40 38 33 38 3 40 38 33 38 4 40 37 33 38 5 40 37 33 38 6 40 37 33 38 7 40 37 33 38 8 39 37 32 37 9 39 37 32 37 10 39 37 32 37 11 ,
,39, ,
,3 7 _ ,
32 , ,
37
_ FXY LEVELS! _
FR _ FC CASE D(%) S(%) N OC%) S(%) h 0(%) S(%) N
~ ~ ~ ~ ~ ~
1 38 31 187 2 38 31 187 3 37 3C 186 4 37 3C 185 5 36 3C 184 6 38 . 31 186 7 37 31 185 8 37 3C 182 9 37 3C 182 10 37 3C 182 11 37 30 182 l
1 5-14
TA8LE 5.2.8 217 FA CYCLE 1 CECOR STATISTICS
_ FXY LEVELui _ FXY LEVELS 2 _ FXY LEVEL *3 FXY LEVELS 4 CASE O(X) S(%) N 0(%) $(%) h D(%) S(%) N 0(3) $(%) N
- . - .- ~ ~ " ~~
56 55 56 2 56 56 55 56 3 , _56, ,56, ,56_ ,
55
_FXY LEVEL =5 FR _
FQ CASE O(X) S(%) . N _0(%) 5(%) h 0(%) $(2) N
~ ~ ~ ~ ~ ~
1 56' 55 279 2 56 55 279 3
56 55 - -
279 l
l I
l l
! 5-15 l
l l
TABLE 5.3.1 ASSEMBLY AXIAL SYNTHESIS UNCERTAINTY FXY FR EXPOSURE R005 Fa
.S 15 %S 25 %S ll%5 -
! mwd /MT AN02C2 0 ARO AN02C2 500 ARO AN02C2 1000 AR0 !
AN02C2 2000 ARO (
AN02C2 3000 AR0 l AN02C2 4000 ARC AN02C2 5000 ARO AN02C2 6000 ARO '
- u. AN02C2 7000 ARO 4 AN02C2 8000 ARC
- AN02C2 9000 ARC AN02C2 10000 AA0 AN02C2 11000 AEC AN02C2 0 6 AN02C2 1352 o AN02C2 47C5 o l AN02C2 7513 6 AN02C2 10500 6 AN02C2 0 e>5 ANC2C2 1252 eiS AN02C2 4705 oL5 AN02C2 7528 o65 AN02C2 10500 6&S AN02C2 0 P .
AN02C2 13c 2 P AN02C2 4705 P ANO2C2 75LS P AN02C2 10$00 P
TABLE 5.3.1 ASSEMBLY AXIAL SYNTHESIS UNCERTAINTY PAGE FXY FA ,
EXPOSURE RODS FQ 30 %S 2C %S '%D MhD/MT S ANO202 0 P&6 AN02C2 13c2 Pt6 AN02C2 4705 PS6 ANO2C2 7528 Ps6 AN02C2 10500 P&O ANo2C2 C P,625 AN02C2 1952 PicE5 AN02C2 4705 P,6&5 I AN02C2 7528 Pisi5 U AN02C2 10500 Pr615 AN02C3 0 AAG AN02C3 300 ARC AN02C3 1000 ARO l
AN02C3 2000 ARO AN02C3 3000 ARO l
- AN02C3 4000 ARO I AN02C3 5360 Anc AN02C3 o0LG ARC AN02C3 7006 AAC AN02C3 0000 Ako
' AN02C3 9000 ARC AN02C3 1000C Ako AN02C3 11000 ARG e
0
TABLt 5.3.1 ASSEMBLY AXIAL SYNTHESIS UNCERTAINTY
~
PAGE EXPOSURE RODS 50 FXY FR ',
MhD/MT t! 25 %S 20 %S 10 AN02C3 0 6 Ah02C3 1962 o Ah02C3 4705 6 .
Ah02C3 752S e Ah02C3 10500 e AN02C3 0 6s5 AN02C3 1962 685 Y' Ah02C3 4705 615 E AN02C3 7523 615 Ah02C3 105u0 655 Ah02C3 0 P AN02C3 1662 P AN02C3 4705 P Ah02C3 7525 P Ah02C3 10500 P Ah02C3 0 p e.e AN02C3 1?t2 cce Ah02C3 47u5 Plc AN02C3 7522 Pee AN02C3 10500 Pse45 ,
AN02C3 0 P,655 AN02C3 18c2 Pict5 Ah02C3 *705 P,6ES AN02C3 75;$ Pro &5 Ah02C3 10500 Psci5 v3C1 12.5 ARO
s e
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y e x h t
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-- - 1 ..- ,
. g. , ,
f x Y
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Figure 5,323';fq Assembiy exial' Synthesis Error ,
4
/g A x i a l Synt hes i s .Et,y or , W Nsimal Distribution .,
f 4
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e# q
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_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ - . _ _ . _ _ _ - - . __ _ _ I
Figure 5.4.1 ANO-2 Cycle 2 BOC Comparisonof[ ]PDQ Peak Pin to Assembly Average Pin Power, ARO
> - *umma e
5-22
7-1 i
l l- Figure 5.4.2 ANO-2 Cycle 2 BOC Comparisonof(, ]PDQPeakPintoAssembly Average Pin Power, BK6 Inserted I
l-l l
l l
I l
l l
l r
mummes 5-23 L
n o
i t
u b
i r
t s
i d
r l o a r m r r E o n
s l -
i s
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t n r y o S r r
g e i
n g k n a i e k P a e
i n p
_ P i
n
_ p
_ 3 4
5 g
E R
U G
I F
W 8
^ ; .
l!/
I TABLE 5.6.1 SUl0ERY OF UNCERTAINTY C0WONENTS FOR CECOR PEAKING FACT 0P.S PARAMETER UNCERTAINTY D S D-kS C0WONENT (1) (%) n k
~ ~
Fxy Coupling / Measurement Assembly Axial Synthesis Pin Power Synthesis Pin Power Calculational Fr Coupling Measurement Assembly Axial Synthesis Pin Power Synthesis Pin Power Calculational
.Fq Coupling Measurement j Assembly Axial Synthesis Pin Power Synthesis 1 Pin Power Calculctional l
~
l l
l i
I
)
1 l 5-25
\
L i
TABLE 5.6.2 COMINED 955/95% PROBABILITY / CONFIDENCE LOWER TOLERANCE LIMITS FOR CORE PEAKING FACTORS EASURED BY CECOR l
D S f k D-kS PARAMETER
% 5 %
~
~
pxy
-6.92
-5.69 Fr
-7*71 Fq _
1 e
5-26
,y.
l
6.0 REFERENCES
- 1. CECOR 2.0 General Descri) tion, Methods and Algorithms, NPSD-103-P, l Combustion Engineering, i/80.
- 2. Qualification of Reactor Physics Methods for Application to Pres-surized Water Reactors of the Middle South Utilities System, MSS-NAl-P , 8/4/B0. )
- 3. INCA /CECOR Power Peaking Uncertainty, CENPD-153-P Revision 1-P-A, 1 Combustion Engineering, 5/80.
l I
- 4. B. M. Rothleder, PDQ7/ HARMONY User's Manual, EPRI 8/1/79.
- 5. American National Standard Assessment of the Assumption of Normality, ANSI N15.15 - 1974.
- 6. W. J. Conover, Practical Non-Parametric Statistics, John Wiley and Sons, New York,1980.
- 7. R. E. Odeh and D. B. Owen, Tables for Normal Tolerance Limits, Sampling Plans, and Screening, Marcel Dekker, Inc., New York,1980.
- i l
6-1 1
l
APPENDIX A DEFINITION OF TERMS 1.0 Fq: The maximum 3-D power. One value for the core; i.e., the maximum for a nodal power (i.e, the maximum of any of (177/AN0-2, 217/W,3)
XY assembly power values on any of the 51 I planes) times the appropriate pin to assembly factor.
2.0 Fxy: Calculated for each axial plane as follows:
Let there be 51 axial nodes (i = 1, 51)
Let there be 177 assemblies (j = 1,177) (W-3 = 217 assemblies) a) Search for maximum Pj within that plane i Pjmax = Max of [P1, P2, P3 . . . P17731 b) Find the average power for that plane i 177
- E ji ji .
j=1 c) Increase Pjmax as defined in a) by the pin to assembly ratio to account for local peaking, i.e.
Pjmax Local Peaked = Pjmax * (pin to assembly ratio) d) Then, define Fxy for that plane i p ,
Pjmax Local Peaked xy1 ,
p),1 3.0 Fr: Defined for any assembly as follows:
51 F
rj
=
Pji i=1 where Pji is maximum pin power in assembly j at level i A-1
= l APPENDIX B POOLING ETH000 LOGY D
W e
e e
t i
0 k
= m
, , . . - , a.-------,------,------- , - ~ , . - - - - - , - , - - , - - - - , - --. ,.--n. , -. - - - - -, - - - - - -. - .
- 7.
l 1
i I
i 1
J I
APPENDIX C .
COUPLING /E ASUREMENT ERRORS FOR 177 and 217 FUEL ASSEMBLY PLANTS Figures C.1 - C-45 PROPRIETARY
~
G
l i
APPENDIX D ,
~
ASSEMBLY AXIAL SYN 1HESIS ERRORS FOR 177 AND 217 FUEL ASSEMBLY PLANTS Figures D.1 - D.11 PROPRIETARY 4
- - , , . . . - . .. . , - - - - . - . - . . . .. . . . . - . . - - . - . - . . . . . - - , . . - . . . . . . - - - - . - - - .