ML070790394
| ML070790394 | |
| Person / Time | |
|---|---|
| Site: | LaSalle  |
| Issue date: | 03/22/2007 |
| From: | Exelon Generation Co |
| To: | Office of Nuclear Reactor Regulation |
| Sands S,NRR/DORL, 415-3154 | |
| Shared Package | |
| ML070790219 | List: |
| References | |
| TAC MD0336, TAC MD0337 | |
| Download: ML070790394 (5) | |
Text
MD0336 1 7 LaSalle UHS LaSalle UHS Temperature Limit Modification Request -- TAC MD0336 / 7 Measurement uncertainty review and alternative calculation
- Uncertainties are presented in units of degrees Fahrenheit unless otherwise noted.
- Uncertainties are stored as elements of vectors named for the physical component to which they apply. Vector element numbers are related to the names of the various uncertainties. Element zero is not used.
- "Calculation" refers to licensee calculation L-003230 revision 000, transmitted via letter RS-06-106, (August 4, 2006)
- Prefixes "c" and "a" indicate licensee and alternative values, respectively
" Suffixes "r" and "n" indicate random and non-random uncertainties, respectively.
- If the calculation assigns a value of zero to an uncertainty and the alternative calculation does not assign a different value, then the uncertainty may not be explicitly presented below.
" The symbol ":=" indicates definition: x := 2 assigns the value of"2" to the variable "x."
- The symbol "." reports the value of a variable or computation: 10 e x = 20.0000 SRSS function definition: SRSS(x) := "x must be a vector; element zero is ignored" u2 <- 0 demonstration of the function:
for r e 1.. rows(x) 1 u2 +- u2 + (xr) 2 SRSS LL 1.00000000000000000 RTD Errors (Module 1) random errors:
Elements: Values: Alternative Values:
RAl := 1 cRTDrRA 1 := 0.1 aRTDr := 0.2 arbitrary factor of 1/2 is removed in the alternative calculation.
CALl := 2 cRTDr cAL= 0 aRTDrcAL1 0 ST1 := 3 cRTDrsT1 0 aRTDrs = 0 Olin := 4 cRTDr al := 0 aRTDrli := 0 D1 := 5 The calculation applies SRSS to time-based drift. This is not valid, since drift is not random over time and the interval over which drift is assumed is arbitrary. Nevertheless, the alternative calculation accepts the SRSS assertion pending a more complete justification from the licensee.
0 The alternativecalculationis therefore nonconservative in this regard The calculation also applies an arbitrary factor of 1/2, which is omitted in the alternative calculation.
The drift rate is presented in the calculation as 0.1 F per year.
cRTDr := 0.112 aRTDrDl := 2
- cRTDrDl aRTDrDl = 0.2240 c_ol := SRSS(cRTDr) c_ol = 0.1501 a_ol := SRSS(aRTDr) a_ol = 0.3003 non-random errors elRl := 1 cRTDnelR1 := 0 aRTDn elRl~ := 0 eRD1 :__-2 cRTDneRD1 := 0 aRTDneRD1 := 0 eT1 := 3 cRTDneT1 0 aRTDn eT= 0 elin := 4 cRTDn elin= 0 aRTDn elin= 0 cYel := ZcRTDn clel = 0.0000 a~el := I aRTDn a~el = 0.0000 8 812006 3:50 PH LaSalleUHS-AtCalcxmcd Da-e 105 1
MD0336 / 7 LaSalle UHS TransmitterErrors(Module 2) random errors:
Elements: Values: Alternative Values:
RA2 := 1 The calculation applies a divisor of 3 based upon an assumption that the vendor data are based upon 3o, and uses SRSS to accommodate time-based drift. The alternative calculation again accepts the SRSS assertion pending a more complete justification from the licensee, and applies the extention only to the estimated drift portion of the overall accuracy specification. The basis for the 3a assumption and the factor of 1/3 do not seem reasonable, and these are omitted in the alternative calculation.
vendorRA:= 0.54 vendorRA includes conventional RA, 0. IF resolution error, and drift.
Assume 2-yr drift and conventional RA are equal, and that all are combined via SRSS: then (2-yr drift)2 + RA 2 + 0.12 = vendorRA 2.
vendorRA - 0.12 RA 2 RA = 0.3752 2 2 2 drfR yr RA + RA + 0.1 = 0.5400 2yr drift = 0.5933 cXMTRrRA2 := 0.285 aXMTRr := 4 RA2 + drift2 + 0.12 aXMTRrRA2 = 0.7091 CAL2 := 2
- The calculation includes meter and calibration standard errors as random effects. The calculation indicates that alternate channels are calibrated using different equipment, but there are only two meters and there are four channels of which two are credited in the ultimate UHS temperature measurement. The alternative calculation therefore addresses meter error as a non-random uncertainty.
- In addition, the same standard would be used to calibrate both meters and is therefore common to all four channels. The calculation asserts that the calibration standard is sufficiently accurate to be ignored, but also indicates that it may be better than the meters themselves by no more than 4:1, which does not appear to be inconsequential. The alternative calculation includes the calibration standard error as a non-random uncertainty.
- Finally, the calculation makes an unsupported assumption that the calibration setting tolerance is a 3-sigma value rather than the more conventional 2-sigma, and applies an incorrect factor of 1/3 (rather than 2/3) to make the conversion. The alternative calculation accepts the stated value as 2-sigma.
" The alternative calculation retains only the setting tolerance as calibration uncertainty.
cXMTRrcAL2 := 0.29 aXMTRrcAL2 := 0.54 cYT2 := 3 " The calculation makes an unsupported assumption that the ambient temperature effect is a 3-sigma value rather than the more conventional 2-sigma, and applies an incorrect factor of 1/3 (rather than 2/3) to make the conversion. The alternative calculation accepts the stated value as 2-sigma. The effect is 0.1% of range per 10 degrees C.
- The calculation is based upon a minimum ambient temperature is 75F. This seems unreasonably high for the indicated location. The alternative calculation does not alter this assumption, since no alternative value is available.
- The alternative calculation corrects a numerical error in the temperature unit conversion factor.
The calculation uses a value of 5/8 rather than 5/9.
cXMTRr =T2 0.051 aXMTRr := (0.1%.*
, 90)0I0. (100C0 27F aXMTRr T2= 0.1350 aTT2 '. 100 k 180F) cy2in := 4 cXMTRr 2in= 0.150 aXMTRr a2in := a_1l aXMTRr =2in0.3003 a2PS := 5 cXMTRr 2PS := 0 aXMTRr 2 PS := 0 c o2 := SRSS(cXMTRr) c_o2 = 0.4364 a-_72 := SRSS(aXMTRr) a-a2 = 0.9502 I 812006 3:50 PM LaSaleUHS-A tCaxc, pare 2 1
MD0336 / 7 LaSalle UHS non-random errors The calculation indicates that all non-random uncertainty components for the transmitter are zero. The alternative calculation treats the M&TE uncertainties as non-random and applies calculation assumption 3.1 without dismissing the numerical result as insignificant. The alternative calculation also eliminates arbitrary factors of 1/2 that appear at various points in the calculation, and applies the ambient temperature variation which is addressed in the text of the calculation but omitted from the calculation itself. As indicated elsewhere, the lower ambient temperature limit seems unexpectedly high, but is not altered in the alternative calculation because no credible alternative estimate is available.
The RTD data show 0.214 ohms per degree F.
MTE2:= 1 HP meter uncertainties
.01%. 115.013+ .001%* 1000 cRAMTE2hp:= 0.050 aRAMTE2hp:=
0.214 aRAMTE2hp = 0.1005
(.0006%* 115.013 + .0001%* 1000) a 10.9 cTEMTE2hp:: 0.00395 aTEMTE2hp: 0.214 aTEMTE2hp = 0.0861 2 2 cMTE2hp := ,IcRAMTE2hp2 + cTEMTE2hp aMTE2hp : aRAMTE2hp2 + aTEMTE2hp cMTE2hp = 0.0502 aMTE2hp = 0.1323 Fluke meter uncertainties:
0.05%
- 115 + 26 0.01 + 0.02 cMTE2f:= 0.228 aMTE2f :=
0.214 aMTE2f = 0.4556 conservative selection:
cXMTRn MTE2 max(cMTE2hp,cMTE2f) aXMTRnMTE 2 := max(aMTE2hp,aMTE2f) cXMTRnMTE2 0.2280 aXMTRn MTE2= 0.4556 1
aXMT~ - oaXMTRn STD2:= 2 cXMTRn STD2 := 0 aXMTRnTD 2 4 MTE2 aXMTRn sTD2 0.1139 e2in := 3 cXMTRne2in:= c~el cXMTRne2in = 0.0000 aXMTRne2in := ayel aXMTRn e2in = 0.0000 NOTE: The calculation treats these values as random, but the alternative calculation treats them as non-random. The calculation values are presented here for comparison with the corresponding values in the alternative calculation. These values are included in the calculation as components of CAL2, presented in the "random" section as cXMTRrcAL2 = 0.2900 Also note that IcXMTRn = 0.2280 The cXMTERn vector is not used in the computation of results in this derivation. Instead, the net non-random uncertainty used herein is forced to the calculation final value.
cYe2 := 0 cle2 = 0.0000 a~e2 := Y aXMTRn a~e2 = 0.5695 1811812006 3:50 PM LaSaCeUHS-AftCalcxmcd pap¢ 3 05 1
MD0336 / 7 LaSalle UHS I/0 Module Errors(Module 3) random errors:
Elements: Values: Alternative Values:
RA3 := 1 clOMrRA3 := 0.0113 aIOMrRA3 := 0.0113 CAL3 := 2 clOMrCAL3 := 0 atOMrCAD := 0 The calculation asserts that there is no calibration error or drift. That does not seem a reasonable D3:= 3 clOMrD3 := 0 aiOMrD3 := 0 assumption, but there are no data available upon which an alternative estimate could be based.
o3in := 4 clOMr 3in := c_(2 alOMr 3in := aa2 clOMr 3in = 0.4364 alOMr 3in = 0.9502 The dropping resistor at the input to the 1/0 module is treated as a non-random error in the calculation. In most installations of this type, such a component would exist independently in each channel and the associated errors would therefore be considered to be random. The alternative calculation does not alter this treatment because there is insufficient detailed design information available to support an alternative treatment.
c_o3 := SRSS(clOMr) c_(73 = 0.4365 a_o3 := SRSS(alOMr) a_G3 = 0.9502 non-random errors The calculation shows most non-random uncertainties as zero. It shows the resistor error as non-random, although it would seem reasonable to expect such a term to be random. The alternative calculation does not alter this approach.
e3SR := 1 cIOMne3sR := 0.018 alOMneOs := 0.02%
- 90 alOMne3sR = 0.0180 e3in := 2 clOMne3in := cle2 alOMne3in:= aYe2 cYe3 := Z clOMn cOe3 = 0.0180 aFe3 := I alOMn aYe3 = 0.5875 Total UncertaintyEstimate Since each module uncertainty estimate incorporates the uncertainty from the preceding module, the uncertainty estimate for the last module in the sequence includes all uncertainties in the channel. The total error is the sum of the random and non-random errors.
Thus, for a single channel:
cTE := cu3 + cle3 IcTE = 0.4545 1 aTE := aol3 + a5e3 aTE = 1.5377 1 If two, three, or four readings are averaged, then the uncertainty of the average is reduced:
c c*3_____ __ a (33 c_uAvg2 c- + cYe3 [c-oAvg2 = 0.3267 1 aaAvg2 := a + a~e3 [a_cAvg2 = 1.2594 a o3 c_aAvg3 c- + cYe3 ccAvg3 = 0.2700. a_*Avg3 := - + aY-e3 a-(Avg3= 1.1361 c Y3 a (3 c cFAvg4 - + c~e3 cGyAvg4 0.2363 asiAvg4 := - + aYe3 a_*Avg4 = 1.0626 NF4 %F4 1$11812006 3:50PM aSalleUS-AltCal-xmcd PL¢4 of 5 1
MD0336 / 7 LaSalle UHS Appendix: Verification of RTD Temperature/ResistanceFactor 100.5 114.799ý d(F):= for n e 0.. rows(F) - 2 100.6 114.820 F n+11 Fn,1 100.7 114.842 fl F Fn+1,0 _-
0 1 Fn,0 100.8 114.863 100.500 114.799 100.600 114.820 0.210000 d 100.9 114.884 100.700 114.842 0.220000 101.0 114.906 114.863 .2 0.210000 100.800 101.1 114.927 0.210000 100.900 114.884 3 0.220000 101.2 114.949 101.000 114.906 4. 0.210000 101.100 114.927 5 0.220000 101.3 114.970 114.949 101.200 0.210000 101.4 114.992 101.300 114.970 0.220000 101.400 114.992 '8 0.210000 T:= 101.5 115.013 d(T) =
101.500 115.013 A 0.210000 rows(T) = 21.0000 101.6 115.034 ii 0.220000 101.600 115.034 0.210000 T 10 = 101.5000 T10,1 = 115.0130 101.7 115.056 101.700 115.056 12- 0.220000 101.8 115.077 101.800 115.077 13' T20,0 = 102.5000 T20,1 = 115.2270 0.210000 101.900 115.099 14 0.220000 101.9 115.099 15 102.000 115.120 0.210000 102.0 115.120 102.100 115.142 0.210000 T20,1 T10,1 102.200 115.163 17 0.220000 = 0.214000 102.1 115.142 17ý T20,0 102.300 115.184 0.210000 T10,0 102.2 115.163 102.400 115.206 102.500 mean(d(T)) = 0.214000 102.3 115.184 115.227 102.4 115.206 0.3-102.5 115.227) 101.5 0.2- an(d(T))
F:= 1 d(T) 0.1-100 C18 180 100.5 i10 101.5 102 102.5 (o)
T Calculation ref 5.4.1 lists the resistance temperature coeficient as 0.00385 fA/fl/C: Rt := 0.00385 a T10,1
- C Rt = 0.2460 he discrepancy between the quoted value and the data is: Rt - mean(d(T)) 149533 mean(d(T))
Calculation ref 5.4.1 lists repeatability as 0.2F, but ref 5.4.3 lists accuracy as 0.06% *Tugo 0.06% at OC. The ref 5.4.3 specification results in a net accuracy estimate of:. 0.3225 mean(d(T))
This discrepancy may be due to differing definitions of "accuracy" and 0.06%
- T "repeatability" and so is not addressed in the alternative calculation. 0.2805 using specification R/T data Rt 1811812006 3:50PM LaSalleUHV-AltCac.xmcd Dage5o51