ML20087M417
| ML20087M417 | |
| Person / Time | |
|---|---|
| Site: | McGuire  |
| Issue date: | 03/23/1984 |
| From: | WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP. |
| To: | |
| Shared Package | |
| ML19268E719 | List: |
| References | |
| NUDOCS 8403290282 | |
| Download: ML20087M417 (59) | |
Text
{{#Wiki_filter:_ _ _ _ _ _ _ . _ _ _ _ _ _ _ . _ _ . _ _ _ _ - 6 1 ENCLOSURE 3 (NON-PROPRIETARY) i l 8403290282 540323 PDR ADOCK 05000369 -PDR P
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The attached document has been modiffed to reflect the use of i - Rosemount RTDs and is identified by the use of section, table and page nunters folicwed by the letter "b". A separate document reflecting the use of RdF RTDs has been written and is identified by the letter "a". e l 9 9 4 em e e e
& 3 8
i EROFR!ETARY C:J5S Ill
~'
Questions:
- 1. Provide and justify the variances and distributions for input parameters.
- 2. Justify that the nominal conditions used in the analyses bound all pemitted modes of plant operation.
- 3. Provide a block diagram depic*.ing sensor, processing equipment, computer, and readout devices for each parameter channel used in the uncertainty analysis. Within each element of the block dia-gram identify the accuracy, drift, range, span, operating limits, and setpoints. Identify the overall accuracy of each channel transmitter to final output and specify the minimum acceptable accuracy for use with the new procedure. Also identify the over-all accuracy of the final output value and maximum accuracy requirements for each input channel for this final output device.
Resconse : Rosenount RTDs I. INTRODLCTION Four operating parameter uncertainties are used in the uncertainty ana-lysis of the Improved Themal D4 sign Procedure (ITDP). These operating parameters are pressurizer pressure ' primar/ coolant temperature (T,yg), reactor power, and reactor coolant systent flow. These para-asters are monitored on a regular basis and several are used for control punoses. The reactor power is monitored by the perfomance of a secon-dary side heat balance (power calorimetric me'asuinent) at least once every 24 hours. The RCS flow'is monitored by the perfomance of a pre-cision flow calorimetric measumment at the beginning of each cycle. The RCS loop elbow taps can then be nomalized against the precision calorimetric and used fora:nthTy surveg1,ance (wittr'a small increase in total uncertainty) or a precisterr flow calorimetric can be perfor.:ed on 1b l i t .
EROFR!ETARY C'. ASS Ill the same surveillance schedule. Pressurizer pressure is a controlled parameter and the uncertainty for the Improved Themal Design Procedure reflects the use of thicontrol system. T ayg is a centro 11ed para- l meter thmugh the use of-the temperature input to the Control Rod con- l 1 trol system; the uncertainty presented here reflects the use of this control system. Since 1978 Westinghouse has been deeply involved with the development of several techniques to treat instrumentation uncertainties, errors, and allowances. The earlier versions of these techniques have been docu-mented for several plants; one approach uses the methodology outlined in WCAP-8567 " Improved Themal Design Procedure.0,2,0 wnich,fs based on l the conservative assumption that the uncertainties can be described with unifom probability distributions. The other approach is based on the more realistic assumption that the uncertainties can be described with nomal probability distributions. This assaption is also conservative
- in that the " tails" of the nomal distribution are in reality " chopped" at the extremes of the range, f.e., the ranges for uncertainties are finite and thus, allowing for seme probability in excess of the range ,
limits is a conservative assumption. This approach has been used to substantiate the acceptability of the protection system setpoints for several plants with a Westinghouse NSSS, e.g., D. C. Cook III4I, No d Anna Unit 1 Salem Unit 2 Sequoyah Unit 1. V. C. Sumer, and McGuire Unit 1. Westinghouse now believes that the latter approach can be used for the detemination of the instrumentation errors and allowances for the ITDP parameters. The total instrumentation errors presented in this response are based on this approach. II. METH0001.CGY The methodology used to combine the error components for a channel is basically the appropriate statistical combination of those groups of components which are statistically independent. i.e., not interactive. Those errors which are not independent are combined arittractically to The fem independent groups, which can then be systematically combined. statistical combination technique u' ed by Westinghouse is the [ 2b
- . - _ _ _ _ - . _ , _ . _ __l
,s p,30pg 2 .;?J( C'_A03 Ill tainties. 3+i'C of the instrumentation uncer-tions. The instrumentation uncertaintias are two sided distri .
The sum of both sides is equal to the range efor e.g., Rack Drift is typically [ er,that param t paraceter is [ 3+a.c . the range for this 3+a.c. as noted above and has been endorsed by the staffThis technige industry standards II' N. 0'0'7) and various The relationship between the error components cal and the statisti instrumentation error allowance for a channel ws: is defined 1. For parameter indication in the racks using a DVM;
"'+a.c Eq. 1 2.~
- For parameter indication utilizing the plant process computer;
, , + a .c Eq. 2 3.
For parameters which have control systems;
+ a.c .
~
Eq. 3 where: CSA = PMA = Channel Statistical Allowance
=
Process Measurement keuracy PEA Primary Element. Accuracy SCA =
=
Sensor Calibration Accuracy SD Sensor Drift i 3b l I i . . . _ . .
l l l FJa?.U T*Fil C'AS3 ll1 4 STE = Sensor Temperature Effects SPE = Sensor Pressure Effects RCA = Rack. CaTibration Accuracy RD = Rack Drift RTE = Rack Temperature Effects DVM = Digital Voltmeter Accuracy ID = Computer Isolator Drift A/D = Analog to Digital Conversion Accurai:y CA = Controller Accuracy The parameters above are as defined in reference 4 and are based on SAMA standard PMC-20-1973(10). However, for ease in understanding they are paraphrased below: PMA - non-instrument related measurement errors, e.g., tempera-ture stratification of a fluid in a pipe. PEA - errors due to metedng devices, e.g., elbows, ventuds, . oHfices, SCA - reference (calibration) accuracy for a sensor / transmitter, , SD - change irt input-output relationship over a peHod of time at reference conditions for a sensor / transmitter, STE - change in input-output relationship due to a change in ambient temperature for a sensor / transmitter, SPE - change in input-output relationship due to a change in static pressum for a a.p ' call ACA - reference (calibration) accuracy for all rack modules in loop or channel assuming the loop or channel is tuned to. this accuracy. This assumption eliminates any bias that could be. set up through c'alibration of individual modules in the loop or channel. RD - change in input-output relationship over a peded of time at reference conditions for the rack modules, RTE - change in input-output relationship due to a change in ambient temperature for the rack modules, DVM - the measurement accuracy of a digital voltmeter or culti-meter on it's most accurate applicable range for the l ! parameter measured. l ! 4b l \ f 1
. 1
i l ID - change in input-output relationship over a period of time at reference conditions for a control / protection signal isolating device, A/D - allowance for conversion accuracy of an analog signal to a digital signal for process computer use, CA - allowance for the accuracy of a controller, not including deadband. A more detailed explanation of the Westinghouse methodology noting the , interaction of several parameters is provided in reference 4. III. Instrumentation Uncertainties lhe instrumentation uncertainties will be discussed first for the two
- parameters which are controlled by automatic systems, Pressurizer pres-The uncertainties for both of sure,. and T,,9 (through Rod Control).
these parameters are listed on Table 1b, Typical Instrumentation Uncer-tafattes. 1.. b . Pressurizer Pressure Pressurizer pressure is controlled by a system that compares the sea-sured pressure against a mference value. The pnssure is measund by a Alfow-pnssure cell connected to the vapor space of the pressurizer.
, ances are made as indicated on Table 1b for the sensor / transmitter and the process racks / controller. As noted, the CSA for this function is
]+a,c,
[ ]+8'C irhich corresponds to a control accuracy of f The accuracy assumed in the ITDP analysis is [
]+"'C,thus, margin exists between analysis and the plant. Being a controlled para-meter, the nominal value of 2235 psig is reasonable and bounded by ITDP error analysis assumptions, i.e., assuming a noma 1, two sided distribu-tien for CSA and a 95+1 probability distribution (which will be docu- ' mented later in this response), e for the noted CSA equals
[ ,
']+"'C. Assuming a noma 1, two sided distribution for the ITDP assumption of [. .]+a,c and a 95+1 probability distribution results in a e = [ 7". Thus, Sb l
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margin exists between the expected and assumed standard deviations for Pressurizer pressure. 2.b. T AW T ayg is controlled by a system that compares the auctioneered high T ayg from the loops with a reference derived from the First Stage Turbine Impulse Pressure. T ayg is derivedfrom the average of the narrow range TH and TC from the bypass manifolds. The highest loop T ayg is then used in the controller. Allowances are made as noted on Table b for the sensor / transmitter and the process racks / controller. As noted, the CSA for this function is [ ]+a c which corre-sponds to an instrumentation accuracy of f ]+a,c. Assuming a nomal, two sided distribution for CSA and a 95+% prcbability distribu-tion results in a standard deviation, o = [- ]+a,c, However, this does not include the controller deaoband of + 1.5'F. To detennine the controller accuracy the instrumentation accuracy must.be combined with the deadband. Westinghouse has determined that the proba-l bility distribution for the deadband is [
].+a,c The variance for the deadband uncertainty is then:
[ ,j+a ic and the standard deviation, e :::[ ]+a,c, Combining statistically the standard deviations for instrumentation and deadband results in a controller standard deviation of: cy = fej2+#2
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1 EEC, Fl.IT.'?' CLASS 111 Therefore, the controller uncertainty for a 95+% nomal probability 1 distribution is s [ ].+ac This is the uncertainty assumed for the ITDP error analysis and reasonably bounds the nominal value corresponding to the full power T avg
- 3.b. Reactor Power Generally a plant performs a primary / secondary side heat balance once every 24 hours when power is above 15% Rated Themal Power. This heat balance is used to verify that the plant is operating within the limits of the Operating License and to adjust the Power Range Neutren Flux channels when the difference 'between the NIS and the heat balance is greater than that allowed by the plant Technical Specifications.
Assuming that the primary and secondary sides are in equilibr'um; the core power is detemined by suming the thermal output of the steam generators, correcting the total secondary power for steam generator bicwdown (if not secured), subtracting the RCP heat addition, adding the primary side system losses, and dividing by the core rated Stu/hr at full power. The equation for this calculation is: RP = fN \ 100 Eq. 4 3 L k{[Qg-Q,]+0 d / where; RP = Core power ( % RTP) N = Number of primary side loops 03g: = Steam Generator thermal output (Btu /hr)
=
Op RCP heat adder (Stu/hr) Q L
= Primary system net heat losses (Btu /hr)
H = Core rated Btu /hr at full power. For the purposes of this uncer',ainty analysis (and based on H noted above) it is assumed that the plant is at 100% RTP when the measurement is taken. Measurements performed at lower power levels will result in 8b 6
-m--s--e -. , , , - ._m ,
l EP.0FFJHARY CLAS3 ill different uncertainty values. However, operation at lower power levels results in increased margin to DNS far in excess of any margin losses due to increased measurement uncertainty. The themal output of the steam generator is detemined by a calorime-tric measurement defined as: - Eq. 5 Q; 3
=
(h , - h f) Wf where; - h = Steam enthalpy (Btu /lb) s hy = Feedwater enthalpy (B*w/lb) , W = Feedwater flow (1b/hr). f The steam enthalpy is based on the measurement of steam generator outlet steam pressure, assuming saturated conditions. The feedwater entpalpy is based on the measurement of feedwater temperature and an assumed ' feedwater pressure based on steamline pressure, plus 100 psi. The feed- ~ water flow is detamined by multiple measurements and a calculation based on the following: Eq. 6 Wf = (K)(F,) (VEf .te) where: K = Feedwater venturi flow' coefficient F, = Feedwater venturi correction for themal expansion
= Feedwater density (1b/ft3 )
l Pf ap = Feedwater venturi pressun drop (inches H2O). The feedwater venturi flow coefficient is the product of a numoer of constants including as-built dimensions of the venturi and calibration tests perfomed by the vendor. The themal expansion correction is based on the coefficient of expansion of the venturi material and, the Ob
* .ses 4
- -- -e --
l F.RO?R!ITA?.Y CLASS 111 difference between feedwater temperature and calibration temperature. Feedwater density is based on the. measurement of feedwater temperature and feedwater pressure.. The venturi pressure drop is obtained from the output of the differential pressure cell connected to the venturi. The RCP heat adder is detemined by calculation, based on the best esti-mates of coolant flow, pump head, and pump hydraulic efficiency. The primary system net heat losses are detemined by calculation, con-sideHng the following system heat inputs and heat losses: Charging flow Letdown flow Seal injection flow RCP themal barHer cooler heat removal Pressurizer spray flow PMssuMzer surge line flow Component insulation heat losses Component support heat losses " CRDM heat losses A single calcuated sum for full power operation is used for these los-ses/ heat inputs. The core power measurement is based on tbt following plant measurements: Steamline pressu m (P,) Feedwater temperature (Tf ) Feedwater pressure (Pf) Feedwater venturi differential pressure (ap) Steam generator blowdown (if not secured) and on the following calculated values: Feedwater ventuH flow coefficient (X) Feedwater venturi themal expansion correction (F,) Feedwater density (of)
, 10b 6+
5
- , , , . - - - - - ,- , , , ,, ,r----
F.RCFE! DRY CLASS 111 Feedwater enthalpy (hf ) Steam enthalpy (h3 ) Moisture carryover (impacts hs ) - Primary system net heat losses (Qg) RCP heat adder (Qp )
- s These measurements and calculations are presented schematically on Figure 1.
Starting off with the Equation 6 parameters, the detailed deMyation of the measurement errors is noted below. Feedwater Flow
.Each of the feedwater ventuds is calibrated by the vendor in a hydrau-Itc laboratory under controlled conditions to an accuracy of
[ J+a,b,c 5 of span. The calibration data which substantiates this accuracy is provided for all of the plant ventuds by the respective vendors. An additional uncertainty factor of [ 3*"'" % is included for installation effects, resulting in an overall flow coef- ' - ficient (K) uncertainty of [- 3*"'"5. Since steam generator themal output is proportional to feedwater flow, the flow coefficier.t uncertainty is expressed as [ ] t"'" 5. power.' The uncertainty applied to the feedwater venturi themal expansion correc-tion (F,) is based on the uncertainties of the measured feedwater tem-perature and the coefficient of thermal expansion for the venturi material, usually 304 stainless steel. For this material, a change of f 2*F l in the feedwater temperature range changes F, by [ 3a,b c 5 and the steam generator themal output by the same amount. For this deMya-tion, an uncertainty of [ '3*86C in feedwater temperature was assumed (detailed breakdown for this assumption is provided in the feed-water enthalpy section). This results in a total uncertainty in F aand f steam generator output of [ }+a.c5, 11b 4
~ i p.RC?R;UARY CLASS in s
Based on data introduced into the ASE code, the uncertainty in F, for 304 stainless steel is _+5 percent. This results in an additional uncer-tainty of [ 3+a,c % in feedwater flow. A conservative value of [ 3a c 1 is used in this analysis. , l Using the- ASE Steam Tables (1967) for compressed water, the effect of a [ .3+8'C error in feedwater temperature on the Gis [' 3+8'C 5 in steam generator themal output. An error of C 3+a c in feedwater pressure is assumed in the analysis
- (detailed breakdown of this value is provided in the steam enthalphy ~
section) . This results in an uncertainty in / of of [ 3+a,c g in steam generator themal output. The combined effect of the two results in a total ( of uncertainty of [ f* ' C 5 in steam generator themal output. Table Ib provides a listing of the instrumentation errors for feedwate,r l Ap (including an allowance for the venturi as defined above) assuming display on the prtcass computer. With the exception of the computer readout error, the electronics errors arc in percent sap span and must be translated into percent feedwater flow at' full power conditions. This is accomplished by multiplying the error in pe'rcent ap span by the conversion factor noted below: ((1 ] ( [soan of feedwater flew transmitter in % of nom I j 100 For a feedwater flow transmitter span of [ 3+8'" 5 nominal flow, the conversion factor is [ [*'C (which is the value used for this analysis) . As noted in Table 2b, the statistical sum of the errors for feedwater flow is [' 78 'C 5 of steam generator themal output. 12b O
EROF_R.ITARY CLASS ill Feecwater Enthaley The next major error component is the feedwater enthalpy used in Ecua-tion 5. For this parameter the major contributor to the error is the uncertainty in the feedwater temperature. Table Ib provides the' detailed error breakdcwn for this tagerature measurement assuming indication on the process cog uter. Statistically summing these errors (utilizing Eq. 2) results in a total tegerature error of [- pa.c% span. Assuming a span of [ pa,c results in a temerature error of [ ].+ac A conservative, bounding value of [ ]+a,c was assumed for this analysis. Assuming smaller spans results in smaller tem erature errors. - Using the ASME steam tables (1967) for cogressed water, the effect of a [ .]+a,c error in feedwater temperature on the feedwater enthalpy (h f
) is [ ]+a,c % in steam generator thermal output.
Assuming a [ .]+a.c error in feedwater pressure (detailed break-down provided in the steam enthalpy section) results in a [ .pa.c%effectinhf and steam generator thermal output.
~
The combined effect of the two results in a total hf uncertainty of [ pa,c%. A conservative value (based on round-off effects of individual instrumentation errors) of [ pa,c%forh f uncer-tainty is used in this analysis (as noted on Table 2b). Steam Enthaley
- The steam enthalpy has two contributors to the calorimetric error, steamline pressure and the moisture content. For steamline pressure the errors are as noted on Table Ib, assuming display on the process compu-ter. This results in a total instrumentation error. (utilizing Eq. 2) of
[ pa.c 5 span. Based on a 1200 psig span this equals [ ].+ac A conservative value of [ pa,cisassumed
. in this analysis. The feedwater pressure is assumed to be 100 psi higher than the steamline pressure with a conservatively high measure-ment error of [ ].+a,c Table Ib provides a breakdewn of expected errors if feedwater pressure is measured directly and displayed 13b S
t ERO.:RiETA.T( CL'S3111 , I on the process computer. The results indicate an expected error of C ']+a,c, well within the assumed value. Using the ASME Steam Tables (1967) for saturated water and steam, the effect of a [ ]+a,e(g ,3+a.c) error in steamline pressure on the steam enthalpy (h ) is [ ]+8'C.% in steam generator 3 themal output. Thus a total instrumentation error of [. .]***C in steamline pressun results in an uncertainty of [ ]**'C 5 in steam generator themal output. The major contributor to hs uncertainty is moisture content. The nominal or best estimate perfomance level is assumed to be [ ]+8'C t, which is the design limit to protect the high pressure turbine. The most conservative assumption that can be made in regards to maximizing steam generator themal output is a steam moisture content of zero. This conser-vatism is introduced by assigning an uncertainty of [ ']**'# 1 to the moisture content, which is equivalent through enthalpy change to [ 3+C % of themal output. The combined effect of the steamline pmssure and moisture content on the total sh uncertainty is [ ']+a.c % in steam generator themal output. 1.0o0 Power The loop power uncertainty is obtained by statistically combining all of the error components noted for the steam generator themal output (Q3g) in tems of'1oop power. Within each loop these components are independent
. effects (or fomed into independent quantities) since they are independent measurements. Technically, the feedwater temperature and pressure uncer-tainties are comon to several of the ermr components. However, they are treated as independent quantities because of tne conservatism assumed and the arithmetic sumaticn of their uncertainties before squaring them has no significant effect on the final result.
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'i ERCPRLUA?Y C' ASS !!! -
The only effect which tends to be dependent, affecting all loops, is the accumulation of crud on the feedwater ventuMs, which can effect the ap for a specified flow. Although it is conceivable that the crud accumulation could affect the static pressure distribution at the ven-tud throat pressure tap in a manner that would result in a higher flow for a specified ap, the reduction in throat ama resulting in a lower flow at the specified ap is the stronger e'ffect. All reported cases of venturi fouling have been associated with a significant loss in elec-trical output, indicating that the actual themal power has been below the measured power rather than above it. Losses in net power generation which have been correlated with ventud fouling have occurred in about half of the more than 20 Westinghouse pressurized water reactors oper-ating in the United States. These power losses have been generally in the range of two to three percent. Power losses have also occurred in at least three, and possibly five plants out of the more than ten West-inghouse plants operating abroad. In no case has venturi fouling been reported which resulted in a non-conservative feedwater flow measure-ment. Because the venturi crud fomations ha've resulted in a conserva-tive, reduced power condition, no uncertainty has been included in the analysis of power measurement error for this phenomenon. The net pump heat uncertainty is deHved in the following manner. The primary system net heat losses and pump heat adder for a four loop plant am sumaHzed as follows: Systems heat losses - 2.0 s t Component conduction and convection losses - 1.4 Pump heat adder +18.0 l Net Heat input to RCS +14.6 Wt 15b l i
l g gpgiETARY CLAS3 lil , t The uncertainties for these quantities are as follows: The uncertainty on system heat losses, which are essentially all due to charging and letdown flows, has been. estimated to be [ ]+a,c : of the calculated value. Since direct measurements are not possible, the uncertainty on component conduction and convection losses has been assumed to be f 78'C 5 of the calculated value. Reactor coolant pump hydraulics are known to a relatively high confidence level, supported by the system hydraulics tests perfonned at Prairie Island II and by input power mea-surements from several plants, so the uncertainty for the pump heat adder is estic:ated to be [ . pa,c of the best estimata value. Considering these parameters as one quantity which is designated the net pump heat uncertainty,-the combined uncertainties are less than [ 3+a.c of the total, which is equivalent to p pa,c;of core power. The Total Loop Power uncertainty (noted in Table 2 as [ 7"' C %) is the statistical sum of the Loop Power uncertainty (Q I"' C %, 3 ;), [ and the Net Pump Heat Addition, i' ]+"'"%. The Total Secondary Power uncertainty is the statistical coc5fnation of the Loop Power uncertainty and the number of primary side loops in the plant. As noted in Table 2b, the Secondary Power uncertainty for N loops is as follows: N = 4 uncertainty = 11.2 % power 3 + 1.4 5 power 2 + 1.7 % power In all cases the total Secondarf Power uncertainty is less than or equal to the historically used value of + 2 % power. For ITDP, credit is-taken for the increased knowledge of reactor power and the values noted above are used in the ITDP error analysis, f.e., the standard deviation for reactor power, at the 95+% probability level is: IGb e
, - . , - - r,, - ,,e, , , - , - - - ,m- ,m,- , w -
-w --n-,
l l py;oFRiiETARY Cf AS3 til . 1 FIGURE 1 PC'4ER CALORIMETRIC SCHEMATIC i l P P T AP j s f f 1' , h h F, K 3 f of V W : f
/
O - mensund q,g_ C - calculated V C Other Loops Y t Og O { A {0; con Power
, 17b a
ERC?R:ITARY CLASS 111 . TABLE 2 b SECONDARY P0hTR CALORIETRIC EASUREENT UNCERTAINTIES Power Cemoonent Instrument Error Uncertainty Feedwater Flow.
._, _ +a,c Yenturi, K Thermal Expansion Coefficient Temperature Material Density Temperature Pressure Electronics .
AP Cell P,alibration Sensor Pressure Effects Sensor Temperature Effects Sensor Drift Rack Calibration Rack Temperature Effects Rack Drift Computer Isolator Drift Computer Readout Total Electronics Error e l Total Feedwater Flow Error I(e)2 l 4 l 13b S
ERCFR!!iARY CLASS Ill s TABLE 2b (Cont)
- SECONDARY POWER CALORIMETRIC MEASUREMENT UNCERTAINTIES Power Cemonent Instrument Error Uncertainty Feedwater Enthalpy __
Tecoerature (Electronics)
- +a c RTD Calibration R/I Converter Rack Accuracy Rack Tegerature Effects Rack Drift Ccquter Isolator Drif t Com uter Reacout Total Electronics Error fr(e)2 Feedwater Teg erature Error Assumed Pressure Total Feecwater Enthalpy Error ljI(e)2 Steam Enthalpy Steamline Pressure (Electronics)
Pressure Cell Calibration Sensor Tegerature Eff ects Sensor Drif t Rack Calibration Rack Tegerature Effects 1 l 10b
I cROPRlETARY C' A33 til , TABLE 2 b(Cont) i SECCNDARY P0kT.R CALORIETRIC EASUREENT UNCERTAINTIES Power Cemeonent Instrument Error Uncertainty Steam Enthalpy (Conti)
+a,c _ _-+a,c Rack Drift Cocputer Isolator Orift -
Computer Readout Total Electronics Error f:(e)2 Steamline Pressure Error Assumed Moisture Carryover Total Steam Enthalpy Error fI(e)2 Loop Power Uncertainty f t(e)2 Net Pump Heat Addition Uncertainty
~ ~ '
Total Loop Power Uncertainty (8) Total Secondary Power Uncertainty f[I(e)23fg where N = 4 loops + 1.2% 3 loops + 1.4t 2 loops + 1.7% o 20b 4 E^
V
. . ??.:ETGY C:. ASS ill NOTES FOR TABLE 2 b
- 1. Temperature effect on Themal Expansion Coefficient is assumed to be linear with an uncertainty of [ ']+a,b,c per 2*F change.
- 2. Conservative assumption for value, particularly if steamline pressure
+ 100 psi is assumed value. Uncertainty for steamline pressure noted in Steam Enthalpy.
- 3. To transfom error in percent 4p span to percent of feecwater flow at 100 of nominal feedwater flow; multiply the instrument error by:
2 [1/2 Sean of feedwater flow transmitter in cereent of neminal flow ( ) 100 In *.his analysis the feedwater flow transmitter span is assumed to be L ]+a.c : of nominal flow.
- 4. In this analy' sis assumed an error of [' ]+a,c and a maximum swing in feedwater pressure frem no load to full power of [200 psi].**'C
- 5. [
3+a,c
- 6. ' [ 3+"'C span of [ 3+8'C equals [ ]+a,c which equals
[ 3+a,c power. -
- 7. Conservative assumpticn for instrumentation error for this analysis.
'8. Statistical sum of Loop Power Uncertainty and Net Pump Heat Addition Uncertainty.
l 21b
l E02RiETARY OLUS !!! N =4 e = +a.c power l 1 3 power l 2 power I 4.b. RCS FL,0W The Improved Themal Design Procedure (ITDP) and some plant Tech-nical Specifications require an RCS flow measurement with a high degree of accuracy. It is assumed for this error analysis, that this flow measurement is perfomed within seven days of calibrating the measurement instrumentation therefore, drift effects are not included (except where necessary due to sensor location). It is also assumed that the calorimetric flow measurement is perfomed at the beginning of a cycle, so'no allowances have been made for feed-water venturi crud buildup. The flow measurement is perfomed by detemining the steam generator themal output, corrected for the RCP heat input and the loop's share of p'rimary system heat losses, and the enthalpy rise (ah) of the primary coolant. Assuming that the primary and secondary sides are in equilibrium; the RCS total vessel flow is the sum of the individual primary loop flows, i.e., V RCS
- EWL . (Eq. 7)
The individual primary loop flows are detamined by correcting the themal output of the steam generator for steam generator blowdctm (if not secured), subtracting.the Ri:P heat addition, adding the loop's share of the primary side system losses, dividing by the primary side enthalpy rise, and multiplying by the specific volume of the RCS cold leg. The equatien for this calculation is: Q ? L L " ITI QSG ~ 0 0 + T $ IY e1 (Eq. 8) ong-na c 22b i e
PICEKiETARY CLASS !!! . where; V = Loop flow (gpm) t 3 y = 0.1247 gpm/(ft /hr) . 0 = Steam Generator themal output (Stu/hr) 33 Op
= RCP heat adder (Btu /hr)
Q = Primary system net heat losses (Stu/hr) t V = Specific volume of the cold leg at TC (ft /lb) e N = Number of primary side loops h = Not leg enthalpy (Stu/lb) 3 h = Cold 1eg enthalpy (Stu/lb). e The themal output of the steam generator is detemined by the same calorimetric measurement as for reactor power, which is defined as:
. (Eq. 5)
Q33 = s(h -h)Vf f where; h 3 = Steam enthalpy (Stu/lb) h = Feedwater enthalpy (Stu/lb) f W = Feedwater flow (1b/hr). f The steam enthalpy is based on measurement of steam generator outlet The feedwater enthalpy steam pressure, assuming saturated conditions. is based on the measurement of feedwater temperature and an as;umed The feed-feedwater pressure based on steamline pmssure plus 100 psi. water flow is datamined by multiple measurements and the same calcula-tion as used for reactor power measurements, which is based on the foi-lowing: (Eq. 6) V f = (K) (F,){V of de} where; X = Feedwater venturi flow factor
= Feedwater venturi cor'rection for themal expansion F, 3 O - Feedwater density (1b/ft )
f ap = Feedwater venturi pressure drcp (inches H2O). 23b r - v -- v -%- ,-x-+
I EiC?RiETARY CLASS ll1 ., The feedwater venturi flow coefficient is the product of a number of constants including as-built dimensions of the venturi and calibration tests perfomed by the.vtador. The thermal expansion correction is-based on the coefficient of expansion of the venturi material and the
- difference between feedwater temperature and calibration temperature.
Feedwater density is based on the measurement, of feedwater temperature and feedwater pressure. The venturi pressure drop is obtained from the output of the differential pressure cell connected to the venturi. The RCP heat adder is deter.nined by calculation, based on the best esti-mates of coolant flow, pump head, and pump hydraulic efficiency.
. The primary system net heat losses are detamined by calculation, con-sidering the following system heat inputs and heat losses:
Charging flow Letdewn flow Seal injection flow RCP themal barrier cooler heat removal Pressurizer spray flow Pressurizer surge line now Component insulation heat losses Component support heat losses CRDM heat losses. A single calculated sum for full power operation is used for these los-ses/ heat inputs. The hot leg and cold leg enthalpfes are based on the measurement of the hot leg temperature, cold leg temperature and the pressurizer pressure. The cold leg specific volume is based on measurement of the cold leg temperature and pressurizer pressure. The RCS flow measurement is thus based on the following plant measure-ments: I I 24b i i e
ERCERiETARY CUsSS 111 Steamline pressure (P,) Feedwater temperature (Tf ) - Feedwater pressure'(Pf ) Feedwater venturi differential pressure (ap) Hot leg temperature (TH I Cold leg temperature (T I C Pressurizer pressure (Pp ) Steam generator blowdown (if not secured) and on the following calculated values: Feedwater venturi flow coefficients (K) Feedwater venturi thermal expansion correction (F,) Feedwater density (cf) Feedwater enthalpy (hf) Steam enthalpy (h3) Moisture carryover (impacts ,h3 ) Primary system net heat losses (Qg) RCP heat adder (Qp ) Hot leg enthalpy (hM I Cold leg enthalpy (he ). These measurements and calculations are presented schematically on Figure 2. Starting off with the Equation 6 parameters, the detailedd'erivation of the measumment errors is noted below. Feedwater Flow Each of the feedwater venturf s is calibrated by the vendor in a hydrau-ifes laboratory under controlled conditions to an accuracy of [ 3+a,b,c t of span. The calibration data which substantiates this accuracy is provided for all of the plant venturis b1 the respec-tive vendors. An additional uncertainty factor of [ J+a,c t is 25b l O
, - = =
EROPRIETARY C ASS 111 , included for installation effects, resulting in an overall flow coef- ' ficient(X)uncertaintyof[ 1+a c 5. Since RCS loop flow is proportional to steam generator themal output which is proportional to i feedwater flow, the flow coefficient uncertainty is expressed as [ pa.c g fja,, The uncertainty applied to the feedwater venturi themal expansion cor-rection (F,) is based on the uncertainties of the measured feedwater temperature and the coefficient of themal expansion for the venturi material, usually 304 stainless steel. For this material, a change of
+ 2*F in the feedwater temperature range changes F, by
( pa,b c : and the s' team generator themal output by the same amount. For this derivation, an uncertainty of p pa,c in feedwater temperature was assumed (detailed breakdown for this assump-tion is provided in the feedwater enthalpy section). This results in a negligible impact in F, and steam generator output. i Based on data introduced into the ASif Code, the uncertainty in F, for 304 stainless steel is + 5 5. This results .n an additional uncert:.inty of [* 78'C 5 in feedwater flow. A co<servative value of [ [*
- C 5 is used in this analysis.
Using the ASME Steam Tables (1967) for compressed water, the effect of a [ pa.c error in feedwater temperature on the / o f is [ pa.c 5 in steam generator themal output. An error of [ pa.c in feedwater pressure is assumed in this analysis
.( detailed breakdcwn of this value is provided in the steam enthalpy section) . This results in an uncertainty in of [ pa,c 5 in steam generator themat output. The combined effect of the two results in a total < o f unceM:afnty of [ pa.c%insteam generator themal output.
It is assumed that the ap cell (usually.a Barton or Rosemount) is read Toca11y and socn after the ap cell and local meter are calibrated (within 7 days of calibration). This allows the elimination of process-9 2Gb e
- , ,- . - - , , . , - - , , . . . . , . . - . , , - . - - , ,, ,- e
f EROPRIETARY CLASS Ill rack and sensor drif t errors from consideration. Therefore, the ap cell errors noted in this analysis are [ 3+a,c 5 for calibration and[ ]+a,c % for reading error of the special high accuracy, local gauge. These two errors are in % ap span. In order to be useable in this analysis they must be translated into % feedwater ficw at full power conditions. This is accomplished by multiplying the error in % Ap span by the conversion f actor noted below: I\I l sean of feedwater flow transmitter in cercent of nominal flowI 7 j( U 100 For a feedwater flow transmitter span of [ ]+a,c % nominal flow, the conversion f actor is [ ]+a,c (which is +he value used in this analysis). As noted in Table 3b,the statistical sum of the errors for feedwater flow is [ ]+a.C % of steam generator thermal output. 1 Feedwater Enthaley l l The next major error component is the feedwater enthalpy esed in Equa-tion 5. For this parameter the major contributor to the error is the uncertainty in the feedwater temperature. It is assumed that the feed-water temperature is determined through the use of an RTD or thermo-couple whose output is read by a digital voltmeter (DVM) or digital multimeter (DMM) (at the output of the RTD or by a Wheatstone Bridge for RTD's, or at the reference junction for thermoccuples). It is also assumed that the process components of the above are calibrated within 7 days prior to the measurement allowing the elimination of drift effects. Therefore, the error breakdown for feedwater temperature is as noted on Table 2. The statistical combination of these errors results in a total feedwater temperature error of [ ]+a,c, 27b b
EROPRIETARY Ct.A33 til Using the ASME Steam Table (1967) for comtessed water, the effect of a [ pa,c error in f eedwater tenerature en the feedrater enthalpy (h f ) is [ pa,c 1 in steam generator thermal output. Assuming a [ pa,c error in feedwater pressure (detailed break-down provided in the Steam enthalpy sectten) results in a [ pa.c%effectinhf and steam generator thermal output. The ccmbined effect of the two results in a total hf uncertainty of [- pa c % steam generator thermal output, as noted on Table 1. Steam Enthaley The steam enthalpy has two contributors to the calorimetric error, steamline pressure and the moisture content. For steamline pressure the error breakdown is as noted on Table Ib. This results in a total instru-mentation error of [ pa,c%,whichequals( pacfora 1200 psi span. For this analysis a conservative value of [ J+a,c is assumed for the steamline pressure. The feedwater pressure is assumed to be 100 psi higher than the steamline pressure with a conser-vatively high- measurement error of [ pa c. If feedwater pres-sure is measureden the same basis as the steamline pressure (with a DVM) theerroris[ .pa c % span, which equals [ pa,cfora 1500 psi span. Thus, an assumption of an error of [ pa,cis very conservative. Using the ASME Steam Tables (1967) for saturated water and steam, the effect of a ( pa,c([ pa,c) error in steamline pressure on the steam enthalpy is [ ya c % in steam generator thermal output. Thus, a total instrumentation error of [ ya.c resul ts in an uncertainty of [ pa.c % in steam generator thermal output, as noted on Table 3b. The major contributor to hs uncertainty is moisture content. The nominal or best estimate performance level is assumed to be [ pa c g which is the design limit to protect the high pressure turbine. The most conservative assustion that can be made in regards to maximizing steam 20b e p 4
- - - , , ~ , , ,- , - ,
l l l 1 FRC?RETARY C. ASS Ill .. generator themal output is a steam moisture content of zero. This conser-vatism is introduced by assigning an uncertainty of [ ]+a c 5 to the moisture content, which is equivalent through enthalpy change to f ]+a,c % of themal output. The czbined effect of the steamline pnssun and moisture content on the total hg uncertainty is [ ]+a,c 5 in steam generator themal output. Secondary Side Loco Power The loop power uncertainty is obtained by statistically combining all of the error components noted for the steam generator themal output (Q3 ;) in tems of Stu/hr. Within each loop these components are independent effects since they an. independent measurements. Technically, the feed-water temperature and pressure uncertainties are comon to several of the error components. However, they are treated as independent quantities because of the conservatism assumed and the arithmetic suncation of their uncertainties before squaring them has nn significant effect on the final resul t. The only effect which tends to be dependent, affecting all loops, would be the accumulation of crud on the feedwater venturf s, which can affect the ap for a specified flow. Although it is conceivable that the crud accu-mulation could affect the static pressure distribution at the venturi throat pressure tap in a manner that would result in a higher flow for a specified ap, the reduction in throat area resulting in a lower flow 'at the specified ap is the stronger effect No uncertainty has been included in the analysis for this effect. If venturi fouling is detected 1 by the plant, the venturi should be cleaned, prior to perfomance of the measurement. If the' venturi is not cleaned, the effect of the fouling on the detemination of the feedwater flow, and thus, the steam generator power and RCS flow, should be measured and treated as a bias, i.e., the error due to venturf fouling should be added to the statistical sumation of the rest of the measurement errors. 2Cb i t I e *e
. . FROFRIETARY CLASS !!!
The net pug heat uncertainty is derived in the following manner. The i I
- primary system net heat losses and pump heat adder for a four locp plant are summarized as follows:
System heat lossis -2.0 Mt Component conduction and convection losses -1. 4 Pump heat adder +18. 0 Net Heat input to RCS +14.6 W t The uncertainties for these quantities are as follows: The uncertainty on systems heat losses, which is essentially all due to charging and letdown f10ws, has been estimated to be [ ]+a.c % of the calculated value. Since direct measurements are not possible, the uncertainty on cormonent conduction and convection losses has been assumed to be [ ]+a c 1 of the calculated value. Reactor coolant pump hydraulics are known to a relatively high confidence level, supported by the system ' hydraulics tests perforced at Prairie Island II and by irput power mea-
' surements.f rom several plants, so the uncertainty f or the purg heat adder is estimated to be [ pa,c % of the best estimate value.
Considering these parameters as one quantity which is designated the net pug heat uncertainty, the ecmbined uncertainties are less than [ ]+a.c % of the total, which is [
- ]+a,c1ofcorepower.
The Total Secondary Side Loop Power Uncertainty (noted in Table 3b as [ pa.c %) is the statistical sum of the secondary side loop power uncertainty (0 $ g), [
]+a,c %, and the net pump heat addi-tion,[. 3+a,c5, Primary Side Enthaley
. The primary side enthalpy error contributors are TH and TC measure-ment errors and the uncertainty in pressurizer pressure. The instrumen-tation errors for TH are as noted on Table Ib. These irrors are based 3Cb
, RRCFRIETARY CLAS3111 on the assumption that the Om has been recently calibrated (within 7 days prior to the measurement) and the DVM is used to read the output of the RTD, or a bridge, thus allowing the elimination of drift effects in '
the racks. The statistical combination of the above errors results in a total TH uncertainty of [ j+a.c, Table Ib also provides the instrumentation error breakdown for T C
. The errors are based on the same assumptions as forHT , resulting in.a l total TCuncertaintyof[ ]+a.c, Pressurizer pressure instrumentation errors are noted on Table Ib. A sensor drif t allowance of [- pa,c 1 is included due to the dif-ficulty in calibrating while at pcwer. It is assumed calibration is I
performed only as required by plant Technical Specifications. Statistically combining these errors results in the total pressurizer pressure uncertainty equaling [ pa.c1ofspan,whichequals i f ya.cforan[ pa.c span. In this analysis a conservative value of [ pa,c is used for the instrumentation error for pressurizer pressure. The effect of an uncertainty of [ pa.cinTg on hg is [ pa.c % of Icep flow. Thus, an error of [ pa c in TH introduces an uncertainty of [ ]+a.c percent in hg . An error of [ ya.cinT ]+a,c% inh. C isworth[ e Therefore, an error of [ pa.cinTC results in an uncer-tainty of [ .ya c % in heand locp flow. An uncertainty of [- ]+a c in pressurizer pressure introduces an error of [ pa c % in hgand[ ]+a.c % in ch . Statistically combining the hot leg and cold leg temperature and pressure uncertain-ties results in an h3uncertaintyof( ]+a,c 5, an he uncer-tainty of [ ya.c , and a total uncertainty in ah of s [ ]+a,c%inloopflow. Statistically combining the Total Secondary Side Loop Pcwer Uncertainty (in Stu/hr) with the primary side enthalpy E?rtainty (in Stu/lb), 31b
.e N e e S
. FROFR!ITAR'I C:.A33 ill FIGURE 2 RCS FLCW CALORIMETRIC SCHE".ATIC TH P p Tg p;. P T ap f f b -
Y l , hg h h, h e F C of , 3 K I
\/ u sh y
_.1 r b- Ogg IP+ Measured O
+'
( + +
= -
Calculated a p.. -{ O p S I g',: If h RCS FTcw 32b G 8
, ,. . , - . . . . - - - -n-- - ,, ,-
FRCFRiE~ARY CLASS .*ll TABLE 3b CALCRIMETRIC RCS FLOW MEASUREMENT UNCERTAINTIES FICw Ceneenent Instrument Errer(1) Uncertainty Feecwater .lew ~
+a.c Venturi, K Thermal Expansion Ccefficient Tegerature Material ,
Density Tegerature Pressure
~
Instrumentation ap Cell Calibration - Ap Cell Gauge Readcut Tota'lInstrumentationErrorfr(e)2 Total Feecwater Flow Errer fE(e)2 Feedwater Enthalpy Temperature (Electronics) RTD Calibration DVM Accuracy Total Tegerature Errorfr(e)2 Pressure Total Feecwater Enthalpy ErrorfE(e)2 M M-33b 4
FJ.0?RiETARY O'J S3 !!! TABLE 3b (Cont) CALCRIMETRIC RCS FLCW MEASUREMENT UNCERTAINTIES Flow Cemoonent .. Instrument Error (1) Uncertainty
+a,c Steam Enthalpy ,,;,,,,, - - -
Steamline Pressure (Electronics) Pressure Cell Calibration Sensor Teg erature Effects Rack Calibration Rack Temperature Effects DVM Accuracy Total Electrcnics Error fI(e)2 Steamline Pressure Error Assumed Moisture Carryover Total Steam Enthalpy Error fE(e)2 Secondary Side Locp Power Uncertainty fI(e)2 Net Pu@ Heat Addition Uncertainty + 20% Total Secondary Side Loco Pcwer UncertaintyfI(e)2 Primary Side Enthalpy TH (Electronics) , RTD Calibration DYM Accuracy T H Instrumentation Error fI(e)2 Tg Tegerature Streamino Error Tg Tegerature Error fI(e)2 d 34b
I FROFRETARY CLASS lil TABLE 3b (Cont) CALCRIMETRIC RCS FLCW MEASUREMENT UNCERTAINTIES Ficw Cc=c enent Instrument Errer(1) Uncertainty
+a c TC (Electronics)
RTD Calibration DVtt Accuracy T C InstrumentationErrorfI(e)2 Pressurizer Pressure (Electronics) Pressure Cell Calibration Senser Temperature Effects Sensor Drif t Rack Calibratien Rack Teg erature Effects din Accuracy Total Pressurizer Pressure Errorfr(e)2 Pressurizer Pressure Error Assumed TH Pressure Effect T H Total Error [I(e)2 TC Pressure Effect T C Total Error fI(e)2 Total ah Uncertainty [I(e)2 Primary Side Locp Flew Uncertaintyft(e)2
~ ~
Total RCS Flow Uncertainty f[I(e)2]jy ' where N = 4 lecps + 1,5% 3 locps + 1.75% 2 1ceps + 2.1% 35b
, F3CFRIETARY CLASS lil .
NOTES FOR TABLE 3b l l
- 1. Measurements performed within 7 days af ter calibration thus Rack Drif t, and where possible Sensor Drif t, effects are not included in this analy-sis. .,
- 2. Conservative assugtion for value, particularly if steamline pressure l
+ 100 psi is assumed value. Uncertainty for steamline pressure noted in steam enthalpy.
- 3. To transform error in percent Ap span to percent of feedwater flow at 100% of nominal feedwater flow; multiply the instrument error by:
2 1/2 Soan of f eedwater flow transmitter in cercent of nominal flow ( )\ 100 ) In this analysis the feedwater ficw transmitter span is assumed to be [ ]+a,c 5 of nominal flow.
- 4. Reading error for multiple readings of a Barton gauge. .
S. Conservative assuntion for instrumentation error for this analysis.
- 6. Maximum allowed moisture carryover to protect HP turbine.
- 7. Calibration accuracy of [ j+a,c span of [' ]+a.c which equals
[ J+a, c ,
- 8. Credit taken for the 3 tap scocp RTD bypass loop in reducing uncertain-ties due to temperature streaming.
- 9. Convoluted sum of T H Teg erature Error and TH Pressure Effect.
- 10. Convoluted sum of TC Instrumentation Error and TC Pressure Eff ect.
- 11. Convoluted sum of Tg Total Error and TC Total Error.
3Gb o
l I: P.RCPRIETARY CU.SS 111 l 1
~
l results in a Primary Side Loop Flow Uncertainty of [ J+a,c % loop flow. The RCS flow uncertainty is the statistical combination of the primary side loop flow error and the number of primary side loops in the plant. As noted in Taide 3b, the RCS Flcw uncertainty for N loops is: N=4 uncertainty = + 1.5 % flow _ 3 = + 1.75 % flow , 2 = + 2.1 % flow. For ITDP, credit is taken for the increased knowledge of RCS flow and the values noted above are used in the ITCP error. analysis, i.e., the standard deviation for RCS flow, at the 95+5 probability level is:
+a,c N=4 e = 5 flow 3 = % flow 2 =
1 flow
- 5. USE OF AN LIFM If a plant uses a Leading Edge Flow Meter (LIFM), from the Oceanics Division of Westinghouse, for the measurement of feedwater flow, several changes are made in the calorimetric power and flow uncertainty analy-ses. The following are typical LEFM uncertainties in mass flow (1bs/hr):
- a. A nominal accuracy of C 3+a c flow. This is based on a feedwater temperature uncertainty of [ [* ' C and a feedwater pressure uncertainty of [ pa,c,
- b. For each [ 3+a.c increase in Feedwater temperature uncer-tainty, the mass flow uncertainty increases by [ 3+a,c, l
- c. For a feedwater pressure uneartainty greater than
[ 3+8'C but less than [ 3'C, the mass flow uncertainty increases by [ 3+C. l 1 l 37b 4
E.9CPRIETARY CLASS 111 Thus, for a typical LEFM installation with a feedwater temperature uncertainty of [ .3+a.c and a pressure uncertainty less than [ 3+a.c, the mass flow uncertainty is [ ]+8'C fl ow. 1 The effect of the use of an LIFM is seen' primarily in the measurement of Reactor Power. The following table provides a comparison of the uncer-tainties for a power calorimetric using a feedwater venturi and an LEFM. It is assumed for these calculations that a measurement device (either a venturi or an LEFM) is in the feedwater line to each steam generatcr. l 1
. 1 3Cb h
l
. . EECFRIETARY CLASS til TABLE 4b CCMPARISCN OF VENTURI VS. LE M PC'4R CALORIETRIC UNCERTAINTIES Yenturi* LEFM Reactor Power ,
+a,e Feedwater Temperature Feedwater Flow Feedwater Enthalpy Steam Enthalpy Loop Power Uncertainty {
Total Loop Power Uncertainty
- Tctal Secondary Power Uncertainty - -
l 4 loops 1 1.25 RTP 1 0.4% RTP 3 loeps 1 1.4% RTP + 0.4% RTP 2 loops t 1.7% RTP 1 0.55 RTP
- from Table 2 due to [ pa.c assumption The impact of the LEFM on RCS Flow measuremnt is considerably less (primarily due to the [ ]**'C feedwater temperature error already being assumed and the prime error contributors beingyT and gT for primary side ah). However, the following table notes the differences between the two measurteents for an RCS Flow calorimetric measurement. For these calculations it is assumed that a measurement device (either a venturi or an LEFM) is in the feedwater line to each steam generator.
39b
- e
1 I l EKOFRIETARY CLASS !!! - 1
. s l
TA3LE Sb CCMPARISON OF VENTURI VS. LEFM FLCW CALCRIMETRIC UNCERTAINTIES Venturi
- LEFM RCS Flow - - +a,c Feedwater Ficw Feedwater Enthalpy Steam Enthalpy Secondary Loop Pcwer Uncertainty Total Secondary Power Uncertainty Primary Enthalpy Primary Locp Flow Uncertainty Total RCS Flow Uncertainty - -
4 locos + 1.5% ficw + 1.45% ficw 3 loops + 1.75% flow + 1.7% ficw 2 locps + 2.1% flow + 2.05% ficw
-
- frem Table 3b j due to [ ]+a.c assumption l Therefore, if a plant has installed an LEFM to measure feecwater ficw
. credit would be taken in the ITDP error analysis for the lower uncer-tainty in Reactor Power, but no credit would be taken in RCS flow.
6.b NORMALIZED ELSCW TAPS FOR RCS FLCW MEASUREMENT Based on the results of Table 3b', in order for a plant to assure opera-tion within the ITDP assumptions an RCS ficw calorimetric would have to be performed once every 31 EFPD. However, this is an involved procecure which requires considerable staff and setup time. Therefore, many plants perform one flow calorimetric at the beginning of the cycle and normalize the 1cep elbew taps. This allows the operater to quickly determine if there has been a significant reduction in locp flow on a shif t basis and to avoid a long monthly procedure. The elbcw taps are 40b 4
l i E10FR!ETARY CLASS 111 ' forced to read 1.0 in the precess racks af ter performance of the full power flow calori, metric, thus, the elbow tap and it's ap cell are seeing normal cperating conditions at the time of calibration / normal-12ation and 1.0 corresponds to the measured icep ficw at the time of the measurement. For monthly surveillance to assure plant operation consistent with the ITDP assu::ptions, two means of detemining the RCS flow are available. One, to read the loep flows f rcm the process ccmputer, and two, to mea-sure the output cf the elbcw tap ap cells in the process .tcks with a DVM. The uncertainties for both methods and their convolution with the calorimetric uncertainty are presented below. Assuming that only one elbcw tap per icop is available to the process computer results in the following elbcw tap measurement uncertainty: Iap span % flow %sp span % flow pg +a c gg +a,c PG RTE 5CA RD SPE ID STE A/D SD Readout op span is converted to ficw on the same basis as provided in Note 3 of Table 3b for an instrument span of [ ]+a c Using Eq. 2 results inaloopuncertaintyof[ ]+" flow per loop. The total uncer-tainty for N loops is:
~
N = 4 +a c ficw 3 2 The instrument /=easurement uncertainties for nomalized elbow taps and the flow calorimet ~; O ' statistically independent and are 95+t preb-ability values,. W>.4rore, the statistical ccmbination of the standard deviations results in the following total ficw uncertainty at a 95+% probability: 41b m .ee% a b
EROFR!ETARY Cu23111 4 loeps 1 1 7% flow 3 locps 1 2.0 2 locps 1 2.3 Another method of using ermalized elbow taps is to take DVM readings in the process racks of all three elbcw taps for each locp. This results in average f' lows for each loop with a icwcr instrumentation uncertainty f or the total RCS flow. The instrumentation uncertainties f or this measurement are:
%Ap span % flow %t.p span % flow
+a,c +a,c pg 59 PG RG SCA RTE SPE RD STE DVM
- Readout ap span is. converted to flew on the same basis as provided in Note 3 of Table 3b for an ir.strument span of ( ]+a.c Using Eq.1 results in a channel uncertainty of [~ 3***C flow. Utilizing three elbew j+a,c taps (which are independent) results in a loop uncertainty of [
ficw per loop. The total uncertainty for N loops is:
+a c f) g, N = 4 3
2 The calorimetric and the above noted elbow tap uncertainties can be statistically combined as noted earlier. The 954 probability total flow uncertainties, using three elbow taps per loop are: 4 loops 11.6% flow . 3 loops 11.8 l 2 locos 1 2.2 l l The following table summarizes RCS Gow neasurement uncertainties. 42b _a__ , ,
i l EROPR!ETARY CLASS 111 TABLE 6b TOTAL FLOW MEASURE.YENT UNCERTAINTIES
.. Locps 4 3 2 Calorimetric uncertainty * ;t 1.5 j; 1.75 f; 2.1 Total uncertainty 3 elbow taps / loop ". ;t1.6 f;1.8 j; 2.2 Total uncertainty 1 elbow tap / loop j; 1.7 j; 2.0 f; 2.3 Calorimetric uncertainty noted assumes feedwater measurement with a venturi, however, use.cf an LEFM for feedwater measurement results in essentially the same value.
IV. M10BASILITY JUSTIFICATION As noted in Section III, it is Westihghouse's belief that the total uncertainty for Pressurizer Pressure, Tavg, Reactor Power, and RCS Flow are normal, two sided, 95+% probability distributions. This sec-tion will substantiate that position with a ecmparison between three approaches, the first being that noted in Section II, the second involves determination of the variance assuming a uniform probability distribution for each uncertainty and then determination of the 95% probability value assuming a one sided normal distribution, and the third involves determination of the variance assuming a normal, two sided probability distribution for each uncertainty and then determina-tion of the 95% probability value assuming a two sided normal distribu-tion. Table 7b lists the results of the three approaches. Column 1 lists the values noted for CSA on Table Ib which are determined through the use of l equations 1, 2, or 3, whichever is applicable to that particular func- _ tion. Column 2 lists the variance for each function assuming the uncer-tainty for each of the parameters listed in Section 2 is a uniform prob- .
- ability distribution. For this assumption, i
43b p 4
EROFRIETARY CLA33 til
)
2 2 n e = 7 ,, Eq. 9 whert R equals the range of the parameter. The variance for the func-tion equals the arithmetic sum of the parameter variances. From a safety point of view deviation in the direction of non-conservatism is important. Therefort, Column 3 Ifsts the one sided 95% probability values based on the variances provided in Column 2, i.e., the one sided 95% probability value for' near nomal distribution can be reasonably approximated by: 1.645 e, 2 l Column 4 lists the variance for each function assuming the uncertainty for each of the parameters listed in Section 2 is a near noma 1, two sided probability distribution. Efforts have been made to conserva-tively determine the probability value,for each of the parameters, see Table 8. For example, [
~
1+a.c The corre-spending Z'value listed on Table 8 is from the standard normal curve where: I = (x - u)/o Eq.10 . The variance for a parameter is then the square of the uncertainty divided by its Z value:
,2 , unce ainW Eq.11 44b l
l l l ,
EROPRIETARY CLASS Ill The variance for the function equals the arith: etic sum of the parameter variances. From the variance the two sided 95% orobability value for a nomal distribution can,be calculated: 1.96h To sumari:e; iolumn 1 is.the results of Equations 1, 2, and 3. Column l 2 is the total variance assu=ing uniform probabilty distributions, i.e., o;= R)2 .g2 + ... = (2 uncj [ (2 unc2 + Eq. j2 Column 3 is 1.645 Column 4 is the total variance assuming near nomal probability distri-butions, i .e.,
/ unc2 e 2 = lf une jl +1 Y + ... Eq.13 (Al) ( h )l Column 5 is 1.56 .
! A comparisori of Columns 1, 3, and 5 will show that the approach used in Section 2 results in values more consenative than those of Columns 3 and 5. Thus, it can be concluded that the results presented in Section 3 are total uncertainties with probabilities in excess of 951. Confidence Ifmits are applicable only to a particular data set, which in this case not available. Therefore, based on the relatively small num-ber of reports indicating large values of deviation, i.e., the number of instances where a channel fails a functional test is very small as com-pared to the many thousands of functional tests perfomed Westinghouse believes that the total uncertainties presented on Table Ib are 95% prob-ability values at a high confidence level. 45b
., , _-4 -,- __ y. .- . .,-_
n . _ -. . -
EP.CERIETARY CLASS 111 ,, V. CONCLUSICHS The preceding sections. provide what is believed to be a reasonable means of accounting for instrument and measurement errors for four parameters used in the ITCP analysis. The assu=ptions used in this response are generic and conservative. It is the intent of this response to generi-cally resolve any concerns with the measurement and control of Reactor Power, RCS Flow. Pressurizer Pressure and T ayg as they are applied to ITDP. As such, plant specific responses will provide only that informa-tion which indicates that 1) the instrument and measurement uncertain-ties for that plant are consistent with or conservative with respect to those presented here, or 2) specific instrument and/or measumment uncertainties for that plant are not consistent with tnose presented. In the second case the impact of the inconsistency on the four parsa-eters will be provided with corresponding new total uncertainties if the impact is sufficiently large. 4 46b
t TABLE 7b , COMPARISON OF STATISTICAL E Til005 . 3 4 5 1 2 951 Probability Variance 951 Probabillty Variance Hethod 2 Method 2 Method 3 Method 3 Method 1 sa,c-Pressurizer Pressure - Control T,,g - Control Steamlina Pressure - Com'puter Feedwater Temperature - Computer feedwater Pressure - Computer t
" -o Feedwater an - Computer m
, Q Pressurizer Pressure - DVM l 3 Steamilne Pressure - DVM L1
, g .
Feedwater Temperature - DVM -< g Tgg - DVH g o> TC - DVH
~ E Notes for Table 7 b
- 1. Uncertainties presented in columns 1, 3 and 5 are in 1 span.
j
- 2. While values noted are listed to the second decimal place, values are accurate only to the first decimal place. Second place is noted for round-of f purposes only.
O
ERCPRIETARY C'. Ass 11l . TABLE 8
. UNCERTAINTY PROSABILITIES.
Two Sided Two Sided Nomal Probability (5) . , Noma 1, 2 Value 4 i _ +a.c PMA PEA SCA SD SPE RCA RD RTE DVM ID A/D CA 9 4Cb 9 4e
- e a
.. y - y---,-. __ ,
. ERCFR;ETARY CLAS3111 .
REFERENCES
- 1. Westinghause letter NS-CE-IS83, C. Eicheldinger to J. F. Stolz, NRC, dated 10/25/77.
- 2. Westinghouse letter NS-PLC-5111, 7. M.. Anderson to E. Case, NRC, dated S/30/78.
- 3. Westinghouse letter NS-TMA-1837. T. M. Anderson to S. Yarga, NRC, dated 6/23/78.
- 4. Westinghouse letter NS-TMA-183S, T. M. Anderson to E. Case, NRC, dated 6/22/78.
S. NRC letter, S. A. Yarga to J. Dolar., Indiana and Michigan Electric Company, dated 2/12/81.
- 6. NUREG-0717 Supplement No. 4, Safety Evalestion Report related to the operation of Virgil C. Sumer Nuclear Station, Unit No.1 Docket 50-395, August, 1982.
- 7. NRC preposed Regulatorf Guide 1.10S Rev. 2, "InstFJment Setpoints",
dated 12/81 for implementation 6/82.
- 8. ANSI /ANS Standard 58.4-1979, " Criteria for Technical Specifications for Nuclear Power Stations".
- 9. ANSI /N719 ISA Standard 567.04, Oraft F, S/22/79, "Setpoints for Nuclear Safety-Related Instrumentation used in Nuclear Power Plants".
- 10. Scientific Apparatus Manufacturers Association, Standard PMC-20-1-1973, " Process Measurement and Control Tenninology".
9 1 49b ! l J . l
4 1 ENCLOSURE 4 (PROPRIETARY) ) e
-+
TABLE 1 , MCGUIRE ITDP Sensitivity (% DNBR/% Parameter) Uncertainty Equhalent Typical Thir. ele Parameter Hominal Value Range Standard Deviation Cell Cell Power
+(a.c) 100% Power 90-120% 60% Power -2.13 -1.98 Inlet Tenperature :s 559.6*F 529.6-610*F 1.95'F -8.10 -7.10 5
Pressure 2280 psia 1805-2430 psia 15.2 psfa 2.07 1.71 h Vessel Flow 393600 ' 275520 - 0.85% Flow
- 1.41 1.26 402000 GPM o"
fu e $ Effective Flow 0.94 .866% Flow Fraction (Bypass) l.41 1.26 5 2 3 . F ", 1.49 1.49 - 1.72 2.43% F " -2.42 -2.16 u F
,3 1.0 1.0 - 1.021 .0182 -0.96 -0.89 TillNC IV -
2% DNBR 1.0 1.0 Transient Code -
.5% DNBR 1.0 1.0 l
I
e WEs7INGHOUsE PROPRIETARY, class 2 _ TABLE. 2 - CALCULATI0tt OF DESIGN ONER LIii1T FOR hPICAL CEL!.
'(
.y
) = S j
1
) +S 2 (42)' ?***Sn (
. n.
where e = standard deviation v = mean ' S = . sensitivity Parameter Mean (p) e e/p 2 S S[e)2
. - ~~ - +(a c),
Pcwer 1.0 .0060 .006000 -2.13 .0001633. - Tin 559.6 1.95 .003485 -8.10
.0007968 Pressura 2280 15.2 .006667 2.07 .0001905 '
. Flew 1.0 .0085 .008500 1.41 .0001436
. ' Bypass .94 .00866 .009213 1.41 .0001687 N
Fy 1.49 .0362 .024300 -2.42 .0034581 F[q,) 1.0 .0182 .018200 -0.96 .0003053 THINC 4 1.0 .02 .020000 - 1.0 .0004000
~
Transient Code i.0. _
.005 .005000 1.0 .0000250 I = .0056513 .
e ( y) = I S = .075175 - n ( n) om aden Umh 1,17 Design DNBR- Limit = I-(Comoined e)(1.645)._ , 1-(.075175)(1.545) Design DNER Limit = 1.335 30 W ee =-e *
- em w me e . 4 , o e. . e es ee e
- emps 4 en 4
WEs7tNGHCUsE PRCPRIETARY,Ct. Ass 2 TABLE 3 CALC'JLATIcti 0F DESIGN DH3R LIiili FOR. THIMBLE CELL
'( ) +3 2 ( I+***I n
.. y ) = 5) 1 ,2 e n.
where e = stan:!ard deviation
. y = nean
- S = . sensitivity Parariter Mean (u) -
e e/u 5 2 S[e)2
~ - ,(a ,:)
. N .
Power , 1.0 .0060
.006000 -1.98 .0001411 Tin 559.6 1.95 .003485 -7.10
.0006122 Pressure 2280 15.2 .006667 1.71 .0001300
. Flew 1.0 .0085 .008500 1.26 .0001147
- Bypass .94 .00866 .009213 1.26 .0001347 N
rg 1.49 .0362 .024300 -2.16 .0027550 e Fg) 1.0 .0182 .018200 -0.89 .0002524 , THINC 4 1.0 .02 . .020000 - 1.0 .0004000 Transient Co'de 1.0 .005 .005000 1.0 .0000250 I = .0045751 ( y) = I Sn( n
= .067639
<U "'
- t " I'II Design ONER Lic.it = l-(Ccmoined e)(1.545)-- =
1-(.067639)(1.645) Design 'ONBR Limit = 1.316 - 31
. 6 m y ese e e em e . = e o se e og g 7 r
a .+ e .,- - ENCLOSURE 4 (NON-PROPRIETARY) a e I i I e
TADLE 1 MCGUIRE ITDP
.* Sensitivity
(% DNDR/% Parameter) Uncertainty Equ.tvalent Typical Thisable Paraneter Nominal Value Range Standard Deviation Cell Cell
~
4 (a .c ) Power 100% Power Inlet Tenr7rature 559.6*F Pressure 2200 psia S5 Vessel Flow M u, 393600 irj m Si m' Effective Flow . < 0.94 Fraction (Dypass) 9 N h v>. F ),49 g E F 1.0 g,3 TilINC IV - Transient Code - t h 9 e
E 3 0 ? R!I T A R Y O' 43 3 til TAELE. 2 CALC"LATION OF DESIGN ON3R LIMIT ?CR nPICAL CZ!.L
'(
) = S) ) +S 2 ( ) ?***S n 2 Ib whers e = standard deviation v = mean S = . sensitivity Paraceter Mean (v) e e/u s 2 s(g)2
- ~
~
+(a,c)
Pcuer 1.0 Tn i 559.6 Pressurt 2280
. Ficw 1.0 Sypass .94 N
r g 1.49 e Fg 3 1.0 THINC 4 1.0 TransientC$de i.0 . t = .0056513 (vy )
= dSn (g)2 2 v
=
.075175 n
00"I' tic' '- i*iI = 1.17 Design CNER Limit = 1-(Com:nnec )(1.c.45) j
..g,g75375jg,345)
Design DNER Limit = 1.325 30 s
O E.TC.O.El7Y CLis33 til TABLE 3 CALCULATICN OF DESIG:{ Oti3R LIIiIT FOR mIMsts c31,1, e (E)2,3 1g)2.3 2j 2z c i),2 , , , ,a 2 g;2 y 1 r2 -
- n.
where e = standard deviation
. y = mean S = . sensitivity Parariter Mean (v) e e/p 3 2 3 (e)2 "l +(a ,c)
Power l' . 0 Tn i 559.5 Pressure 2280 Rcw 1.0 Bypass .94 N r,Lq 1,49 e F,f4,3 1.0 TdI?ic 4 1.0 TransientCSde 1.0 t = .0045751 .
= 2 '
(u,) 5n (h) un
= .CS7639 0 " I*IiO"'i#i0 = l 17 Design C!i3R Lir.it = 1-(Cer.:inec J(1.':.45)-- 1-(.067639)ti.645)
~
Design 'CNBR Limit = 1.316 -
*. 31 b
+}}