ML20043C071

Westinghouse Revised Thermal Design Procedure Instrument Uncertainty Methodolgy for American Electric Power DC Cook Unit 2 Nuclear Power Station.

ML20043C071
Person / Time
Site:	Cook
Issue date:	05/31/1990
From:	Ciocca C WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP.
To:
Shared Package
ML17328A734	List: ML17328A733 ML20043C065 ML20043C071 ML20043C077
References
WCAP-12577, NUDOCS 9006010271
Download: ML20043C071 (33)

Text

1' WESTINGHOUSE PROPRIETARY CLASS 3 WCAP-12577 i

WESTINGHOUSE REVISED THERMAL DESIGN PROCEDURE

-INSTRUMENT UNCERTAINTY METHODOLOGY FOR AMERICAN ELECTRIC POWER D.C.000K UNIT 2.

NUCLEAR POWER STATION a

MAY, 1990 C.F.CIOCCA:

i I

I:

l

i This document contains information proprietary t'o Westinghouse Electric Corporation; it is submitted in confidence and is to be used solely.for the i purpose for which it is. furnished and returned upon request. This document and such.information'is not-to be reproduced, transmitted, disclosed or'used- i otherwise in whole or in part without the written  ;;

authorization of Westinghouse Electric Corporation. ' j i

Westinghouse Electric Corporation Energy-Systems

.P.O. Box 355-Pittsburgh, Pennsylvania 15230 .l, 1

Copyright by Westinghouse Electric 1990, (C) All Rights Reserved i

hO kbbCk 15 p PDC ]

l v ,

FOREWORD This document contains material that is proprietary to the Westinghouse Electric Corporation. The proprietary information has been marked by brackets. The basis for marking the information proprietary and the basis on which the information may be withheld from public disclosure is set forth in the affidavit of R.A.Wiesemann. Pursuant to the provisions of Section 2.790 of the Commission's regulations, this affidavit is attached' to the application for withholding proprietary information from public disclosure which accompanies this document.

This information is for your internal use only and should not be released to any persons or organizations outside the Office of Nuclear Reactor Regulation and the ACRS without the prior approval of Westinghouse Electric Corporation. Should it become necessary to obtain- such a) proval,  !

please contact R.A.Wiesemann, Manager, Licensing Programs, Westinglouse  !

Electric Corporation, P.O. Box 355, Pittsburgh, Pennsylvania 15230.

l 1

1 i

i i

l 1

a TABLE OF CONTENTS SECTION TITLE PAGE

)

-1. Introduction 1- l II. Methodology 2 l

Ill.

Instrumentation Uncertainties 4 IV. Conclusions 22 References 26-l l

i I

l 1

ii

.....----:--=------

LIST OF TABLES l-TABLE NUMBER TITLE- PAGE 1

Pressurizer Pressure Control- 5 System Accuracy 2 Rod Control- System Accuracy 7 j 3

Flow Calorimetric Instrumentation 15 _;

Uncertainties

-j 4

Flow Calorimetric Sensitivities 16 5 l Calorimetric RCS Flow Measurement 17  !

Uncertainties '

l 6

Cold Leg Elbow Tap Flow Uncertainty 20: >

7 Power Calorimetric Instrumentation 24 Uncertainties i i

8 Secondary Side Power Calorimetric 25 .!'

Measurement Uncertainties I

i i

I j

i i

iii

LIST OF ILLUSTRATIONS'-

FIGURE NUMBER TITLE PAGE 1

RCS Flow Calorimetric Schematic' 28 2

Power Calorimetric Schematic -29 i

I i

4

~i 1

i

.:l I

.j I

i s

iv- i

r WESTINGHOUSE REVISED THERMAL DESIGN PROCEDVRE INSTRUMENT VNCERTAINTY METHODOLOGY FOR AMERICAN ELECTRIC POWER D.C.000K UNIT 2 NUCLEAR POWER STATION l q

I. INTRODVCTION-i i

Four operating parameter uncertainties are used in the uncertainty I analysis of the Revised Thermal Design Procedure (RTDP). . These parameters. d are Pressurizer Pressure, Primary Coolant Temperature (Tavg), Reactor- l Power, and Reactor Coolant System Flow. They are frequently monitored.and several are used for control purposes. Reactor power is monitored.by the performance of a secondary side heat balance -(power calorimetric) once'- l every '24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br />. RCS flow-is monitored by the performance of a precision flow calorimetric at the beginning of each cycle. Pressurizer pressure is a controlled parameter and the uncertainty reflects the control system. 1 T

avg is a controlled parameter via the temperature input to the rod j control system and .the uncertainty reflects this control system.

Westinghouse has been involved with the development of several : techniques to treat instrumentation uncertainties. An early version (for ;D. C. Cook: l 2 and Trojan) used the methodology outlined in WCAP-8567 " Revised Thermal.

Design Procedure",(l'2'3) which is based on the conservative assumption that the uncertainties.can be described with uniform probability 1 distributions. Another approach (for McGuire and Catawba);is based on the more realistic assumption that the-uncertainties can be described with' I random, normal, two sided probability distributions.(4) This approach: j is used to substantiate the acceptability of the protection system setpoints for many Westinghouse plants, e.g.,- D. C. Cook.2(5), V. C. j Summer, Wolf Creek, Millstone Unit 3-and others. The second approach is. j now utilized for the determination of-all instrumentation errors for both-  !

RTDP parameters and protection functions. '

I l

6

t L II. METHODOLOGY t

The methodology used to combine the error components for a channel.is the l square root of the sum of 'the squares of those groups of' components which are statistically independent. Those errors that are dependent are combined arithmetically into independent groups, which are then systematically combined. The uncertainties used are considered to be l random, two sided distributions. The sum of both sides is equal to the  ;

range for that parameter, e.g., Rack Drift is typically I

( ) a,c, the range for this parameter is [ ]+a,c, This technique has been utilized before as noted above, and has been endorsed by the NRC staff (6,7,8,9) and various industry standards (10,11),

The relationships between the error components and the channel instrument  ;

error allowance are variations of the basic Westinghouse Setpoint Methodology (12) and are defined as follows:

1. For precision parameter indication using Special Test Equipment or a DVH at the input to the racks; CSA = ((SCA + SMTE + SD)2 + (SPE)2 + (STE)2+ (RD00T)2)1/2

+ BIAS Eq. 1 l

2. For parameter indication utilizing the plant process computer; CSA = ((SCA + SMTE + SD)2 + (SPE)2 + (STE)2 + (RCA + RMTE + RD)2

+ (RTE)2 + (10)2 + (A/D)2)1/2 + BIAS -Eq. 2

3. For parameters which have control systems; CSA = ((PMA)2 + (PEA)2 +(SCA + SMTE + SD)2 + (SPE)2 + (STE)2 l + (RCA + RMTE + RD + CA)2 + (RTE)2)1/2 + BIAS Eq. 3 PMA and PEA terms are not included in equations 1 and 2 since they are intended to determine instrumentation uncertainties only. PMA and PEA terms are accounted for separately in this methodology except for the determination of control system uncertainties.

i

.where:

CSA = Channel Allowance-PMA = Process Measurement Accuracy PEA = Primary Element Accuracy I SCA = Sensor Calibration Accuracy SMTE = Sensor Measurement and Test Equipment Accuracy SPE = Sensor Pressure Effects STE = Sensor Temperature Effects SD- = Sensor Drift '

RCA = Rack Calibration Accuracy RMTE = Rack Measurement and-Test Equipment Accuracy -j RTE = Rack Temperature Effects RD = Rack Drift RDOUT = Readout Device Accuracy '(DVM or gauge)

ID = Computer Isolator Drift 1 A/D =

Analog to Digital Conversion Accuracy i CA = Controller Accuracy l The parameters above are as defined:in' references'5 and 12'and are' based 4 on SAMA Standard PMC 20.1,1973(13). However, for ease.in i

understanding they are paraphrased below:

PMA - non-instrument related measurement errors, e.g., 4 temperature stratification of a fluid in a pipe, ,a PEA - errors due to a metering device, e.g., elbow, venturi,. l orifice, 'I SCA - reference (calibration) accuracy for a ' sensor or l transmitter, SPE - change in input-output relationship due to a change in static pressure for a differential pressure (d/p) cell, STE - change in input-output relationship =due to a change in ,

ambient temperature for a sensor or transmitter, l SD -

change in input-output relationship over a period of time at reference conditions for a sensor or transmitter, RCA - reference (calibration) accuracy for all rack modules in loop or channel assuming the loop or channel is string calibrated, or tuned, to this accuracy.

RTE - change in input-output relationship due to a change in i ambient temperature for the rack modules,

RD -

change in input-output relationship over. a period of time at reference conditions for the rack modules, RDOUT - the measurement accuracy of a special test local. gauge, digital voltmeter or multimeter on it's most accurate applicable range.for the parameter measured,  ;

ID -

change in input-output relationship.over a period of time j at reference conditions for a control or protection signal- j isolating device, f

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 j deadband. j BIAS - a non-random uncertainty.for a sensor or. transmitter.or a l process parameter.' '

A more-detailed explanation of the Westinghouse methodology noting the i interaction of several parameters is provided in references 5 and 12.

III. Instrumentation Uncertainties I I

The instrumentation uncertainties will be-discussed first for the two  !

parameters which are controlled by automatic systems, Pressurizer- 1 Pressure, and Tavg (through Rod Control). I

1. PRESSURIZER PRESSURE  !

Pressurizer Pressure is controlled by comparison of the measured vapor space pressure and a reference value. Allowances are made for the transmitter and the process racks or controller. As.noted on Table 1,-

the electronics uncertainty for this function is [ ]+a,c which corresponds to an accuracy of [ ]+a,c. In addition.to the controller accuracy, an allowance is made for pressure overshoot or undershoot due to the interaction and thermal inertia of the heaters and spray. Based on an evaluation of plant operation, an allowance of

[ ]+a,c was made for this effect. An additional bias of

( ]+a,c was include for a zero span shift during' calibration of the transmitter. Therefore, a total control system uncertainty of i l

1 4

i.

I l [ ]+a,c is calculated, which results in a standard deviation of [ ]+a,c (assuming a normal, two sided probability  ;

distribution). The pressurizer pressure controller does not have a i

deadband.

TABLE 1 I

PRESSURIZER PRESSURE CONTROL SYSTEM ACCURACY

+a,c t SCA =

SMTE=

STE =

SD =

BIAS-RCA = 1 RMTE=

RTE -

RD -  !

CA - 'l

+a,c l ELECTRONICS UNCERTAINTY'-  !

PLUS ELECTRONICS UNCERTAINTY =

PLUS  !

l .

CONTROLLER UNCERTAINTY = j I

i i

i i

i

-1 e

1

2. TAVG~ ,

I T

ayg is controlled by a system that compares the auctioneered high T ayg from the loops with a reference, usually derived from the First Stage Turbine Impulse Chamber Pressure. T avg is the average of the narrow range TH and TC values. The highest loop Tavg is then used  !

in the controller. The T avg channel accuracy is treated as two instruments, Thot and Tcold. Allowances are made (as noted on Table

2) for the RTDs, transmitter and the process racks and controller. The assumption is made that " string" calibration is used for process racks, -

I so that the rack accuracy is constant from the input to' controller. The CSA for this function _is dependent on the type'of RTD, pressure transmitter, and the' location of the RTDs, i.e., in.the RTD bypass manifold or in the Hot and Cold Legs. Based on the assumption that one TH and one TC cross-calibrated Rdf RTDs. are used to calculate Tavg and the RTDs are located in-the RTD bypass manifold, the CSA for the electronics is [ ]+a,c. Assuming a normal,= two' sided probability distribution results in an electronics standard deviation l (s})of[_ ]+a,c, l

However, this does not include the controller deadband of.i 1.5 0F..

For T avg the controller accuracy is the combination of the instrumentation accuracy and the deadband. The probability distribution for the deadband has been determined to be [

).+a,c The variance for the deadband uncertainty is then:

(s2) "l 3+"' -

i Combining the variance for instrumentation and deadband results in a controller variance of: I (sT) = (si)2 + (s2) "I l**'"

The controller sT " l 3+"' for a total uncertainty of

[ ]+a,c, j l

I -

- ~. .

TABLE 2 R0D CONTROL SYSTEM ACCURACY

.Tavg TURB PRES'

+a,c PMA =

SCA =

SMTE=

STE =

SD =

BIAS =

RCA = 1 RMTE-RMTE= i RTE =

RD =

CA =

BIAS =

1. RTDs USED - TH = 1 TC = 1 j

+ a , c; '

ELECTRONICS CSA -

ELECTRONICS SIGMA =  !

CONTROLLER SIGMA =

CONTROLLER BIAS =

CONTROLLER CSA- =

1

]

4 i

. ),

i i

3.

RCS FLOW i

RTDP and some plant Technical Specifications require an RCS flow ]

measurement with a high degree of accuracy. It is assumed for this j error analysis that th9 flow measurement is performed within thirty l days el calibrating tne measurement instrumentation. Therefore, i except where necessary due to sensor location, drift effects are not l l included, It is also assumed that the calorimetric flow measurement i is performed at the beginning of a cycle, i.e., no allowances have

, been made for Feedwater venturf fouling, and above 70% RTP.

The flow measurement is performed by determining the Steam Generator thermal output (corrected for the RCP heat input and the loop's share of primary system heat losses) and the enthalpy rise (Delta-h) 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.,

WRCS = N(W L ). Eq. 4 The :adtvidual primary loop volumetric flows are determined by correcting the thermal output of the Steam Generator for Steam l Generator blowdown (if not secured), subtracting the RCP heat addition, adding the loop's share of the primary side system losses.

l dividing by the primary side enthalpy rise and multiplying by the.  ;

Cold Leg specific volume. The equation for this calculation is:

WL = 1A)l0 SC - PQ d /N))fV L C1 (hH-h) C Eq. 5 where; WL = Loop flow (gpm)

A = 0.1247gpm/(ft/hr)3 Qg3

- Steam Generator thermal output (Btu /hr)

=

Qp RCP heat addition (8tu/hr)

Qt

- Primary system net heat losses (Btu /hr)

VC

- Specific volume of the Cold Leg atc T !,ft3 /lb) $

8-d

l N = Number of primary side loops h

H

= Hot Leg enthalpy (Blu/lb) hC

= Cold Leg enthalpy (Btu /lb).

The thermal output of the Steam Generator is determined by a precision secondary side calorimetric measurement, which is defined as:

Osg = (hs hr)W7 Eq. 6 where h 3

- Steam enthalpy (Btu /lb) hr - Feedwater enthalpy (Btu /lb)

=

Wr Feedwater flow (1b/hr).

The Steam enthalpy is based on measurement of Steam Generator outlet Steam pressure, assuming saturated conditions. The feedwater enthalpy is based on the measurement of Feedwater temperature and Feedwater pressure. The Feedwater flow is determined by multiple measurements and the following calculation:

Wr-(K)(F,)((pt)(d/p))l/2 Eq. 7 where; K =

Feedwater venturi flow coefficient 4 F

a Feedwater venturi correction for thermal expansion pr = Feedwaterdensity(1b/ft) 3 d/p =

Feedwater venturi pressure drop (inches H2O).

The Feedwater venturi flow coefficient is the product of a number of constants including as-butit dimensions of the venturi and calibration tests performed by the vendor. 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, j

RCP heat addition is determined by_ calculation, based on the best estimate of coolant flow, pump head, and pump hydraulic efficiency.

-9

l  !

p . .

l The primary system net heat losses are determined by calculation, considering the following system heat inputs and heat losses:  !

Charging flow ,

Letdown flow f

Seal injection flow  !

RCP thermal barrier cooler heat removal ,

Pressurizer spray flow  !

Pressurizer surge line flow I l Component insulation heat losses l

Component support heat losses l CRDM heat losses.

A single calculated sum for 100% RTP operation is used for these losses  :

or heat irguts.-

The Hot Leg and Cold Leg enthalpies 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

( measurements: -

t Steamline pressure (P3 )

Feedwater temperature (Tr)

Feedwaterpressure(P) f ,

feedwater venturi differential pressure (d/p) l Hot leg temperature (Tg)

Coldlegtemperature(T) C Pressurizer pressure (Pp )  :

Steam Generator blowdown (if not secured) and on the following calculated values:

P Feedwater venturi flow coefficients (K)

• Feedwater venturi thermal expansion correction (Fa )

feedwater density (pt) r

. - , - ~ -

7-- .

Feedwater enthalpy (br)

Steam enthalpy (hs )

Moisture carryover (impacts hg )

Primary systeni net heat losses (Qt )

RCPheataddition(Q) p Hot Leg enthalpy (hH)

Cold leg enthalpy (hC )*

These measurements and calculations are presented schematically on Figure 1.

The derivation of the measurement errors and flow uncertainties on Table 5 are noted below, i

Secondary Side The secondary side uncertainties are in four principal areas, Feedwater flow, Feedwater enthalpy, Steam enthalpy and RCP heat addition. These four areas are specifically identified on Table 5.

For the measurement of feedwater flow, each Feedwater venturi is calibrated by the vendor in a hydraulics laboratory under controlled conditionstoanaccuracyof[ ]+a,bc. The calibration data which substantiates this accuracy is provided to the plant by the vendor. An additional uncertainty factor of [ ]+a,cis included for installation effects, resulting in a conservative overall flow coefficient (K) uncertainty of [ .1 + a , c . Since RCS loop flow is prop 3rtional to Steam Generator thermal output which is proportional to Feedwater flow. the flow coefficient uncertainty is expressedas[ )+a,c. It should be noted that no allowance '

is made for venturi fouling. The venturis should be inspected, and cleaned if necessary, prior to performance of the precision measurement. .

If fouling is present but not removed, its effects must be treated as a b flow bias. 1 The uncertainty applied to the Feedwt.ter venturi thermal expansion correction (F a) is based on the uncertainties of the measured Feedwater temperature and the coefficient of thermal expansion for the venturi

. I

~

- _ _ - - - -_ i

material, usually 304 stainless steel. For this material, a change of 11Of in the nominal Feedwater temperature range changes F, by 1 0.002 % and the Steam Generator thermal output by the same amount.

An uncertainty in F, of i 5 % for 304 stainless steel is used in this analysis. This results in an additional uncertainty of [ )+a,c in feedwater flow. Westinghouse uses the conservative value of

( )+ac, Using the 1967 ASME Steam Tables it is possible to determine the sensitivities of various parameters to changes in Feedwater temperatute and pressure. Table 3 notes the instrument uncertainties for the hardware used to perform the measurements. Table 4 lists the various sensitivities. As can be seen on Table 4, feedwater temperature uncertainties have an impact on venturi F , Feedwater density and Feedwater enthalpy. Feedwater-pressure uncertainties impact feedwater density and feedwater enthalpy.

Feedwater venturi d/p uncertainties are converted to % Feedwater flow using the following conversion factor:

% flow - (d/p uncertainty)(1/2)(transmitter span /100)2 Typically, the feedwater flow transmitter span is [ ]+a,c of nominal flow.

Using the 1967 ASME Steam Tables again, it is possible to determine the sensitivity of Steam enthalpy to changes in Steam pressure and Steam quality. Table 3 notes the uncertainty in Steam pressure and Table 4 provides the sensitivity. For Steam quality, the Steam Tables were used todeterminethesensitivityatamoisturecontentof( )+8'C. This value is noted on Table 4.

1 The net pump heat uncertainty is derived from the combination of the primary system net heat losses and pump heat addition and are summarized

)

for a four loop plant as follows: j System heat losses 2.0 MWt Component conduction and convection losses 1.4 Pump heat adder tild Net Heat input to RCS + 8.6 MWt The uncertainty on system heat losses, which is essentially all due to charging and letdown flows, has been estimated to be [ )+ac of the calculated value. Since direct measurements are not possible, the uncertainty on component conduction and convection losses has been assumed to be [ )+a,c of the calculated value. Reactor coolant pump hydraulics are known to a relatively high confidence level, supported by system hydraulics tests performed at Prairie Island 11 and by input power measurements from several plants, therefore, the uncertainty for the pump heatadditionisestimatedtobe[ )+a,c of the best estimate value.

Considering these parameters as one quantity, which is designated the net ,

pump heat uncertainty, the combined uncertainties are less than

[ )+a,c ofthetotal,whichis[ )+ac of core power.

Primary Side The primary side uncertainties are in three principal areas, Hot leg enthalpy, Cold leg enthalpy and Cold Leg specific. volume. These are specifically noted on Table 5. Three primary side parameters are actually measured, Tg, TC and Pressurizer pressure. Hot Leg enthalpy-is  :

influenced by TH, Pressurizer pressure and Hot Leg temperature streaming.

The uncertainties for the instrumentation are noted on Table 3 and the sensitivities are provided on Table 4. The Hot leg streaming is split into random and bias (systematic) components. For D.C. Cook Unit 2 with direct immersion RTDs located in RTD bypass manifolds fed by scoops in the legs, the streaming uncertainty is ( )+a,c for both random and systematic components.

(

j u

The Cold leg enthalpy and specific volume uncertainties are impacted by T C and Pressurizer pressure. Table 3 notes the T C instrument uncertainty and Table 4 provides the sensitivities.

Noted on Table 5 is the plant specific RTD cross calibration systematic allowance. When necessary, an allowance is made for a systematic temperature error due to the RTD cross-calibration procedure. No allowance was necessary for this plant.

Parameter dependent effects are identified on Table 5. Westinghouse has determined the dependent sets in the calculation and the direction of interaction, i.e., whether components in a dependent set are additive or subtractive with respect to a conservative calculation of RCS flow. The same work was performed for the instrument bias values. As a result, the calculation explicitly accounts for dependent effects and biases with credit taken for sign (or direction of impact), i Using Table 5, the 4 loop uncertainty equation (with biases) is as follows:

- +a',c Based on the number of loops, number, type and measurement method of RTDs, and the vessel Delta-T, the flow uncertainty is:

1. of loops flow uncertainty (% flow)

+a,c 4

14-

\

+

n -=

TABLE 3 FLOW CALORIMETRIC INSTRUMENTATION UNCERTAINTIES

(% SPAN) FW TEMP FW PRES FW d/p STM PRESS TH TC PRZ PRESS

-- -- +a,c SCA =

SMTE-SPE =

STE =

SD =

R/E =

RDOUT=

BIAS =

CSA =

1. OF INST USED 1 1 4 0F psia  % d/p psia CF Of psia INST SPAN = 600, 1500. 120. 1200. 120. 120, 800.

INST UNC. -

+ac (RANDOM) -

INST UNC.

=

(BIAS)

NOMINAL = 449. 707, 820, 607.5 511.7 2100, i

l

• Based on instrumentation used in the RCS Flow Calorimetric procedure.

See AEP letter AEP(R)-W 88 010, dated April 27, 1988 1

i l

l TABLE 4 FLOW CALORIMETRIC SENSITIVITIES i

FEEDWATER FLOW

• =

TEMPERATURE

= '

MATERIAL DENSITY TEMPERATURE =

PRESSURE =

DELTA P = '

FEEDWATER ENTHALPY TEMPERATURE = .

PRESSURE =

h. =

1203.6 BTV/LBM l h*r =

429.3 BTU /LBM

=

774.3 BTU /LBM Dh(SG)

STEAM ENTHALPY  ;

+a,c

! PRESSURE = '

MOISTURE =

' HOT LEG ENTHALPY TEMPERATURE =

PRESSURE =

h =

589.3 BTU /LBM-H h =

501.1 BTV/LBM D(VESS) =

l 88.1 BTU /LBM

=

Cp(Tg) 1.353 BTU /LBM OF COLD LEG ENTHALPY

+a,c TEMPERATURE =

PRESSURE =

Cp(T)C

=

1.172 BTU /LBM OF COLD LEG SPECIFIC VOLUME ~

+a,c TEMPERATURE -

PRESSURE =

TABLE 5 CALORIMETRIC RCS FLOW MEASUREMENT UNCERTAINTIES COMPONENT INSTRUMENT ERROR FLOW UNCERTAINTY FEEDWATER FLOW +a,c

~

VENTURI

. THERMAL EXPANSION COEFFICIENT TEMPERATURE MATERIAL DENSITY TEMPERATURE PRESSURE DELTA P FEEDWATER ENTHALPY TEMPERATURE PRESSURE STEAM ENTHALPY PRESSURE MOISTURE NET PUMP HEAT ADDITION HOT LEG ENTHALPY TEMPERATURE STREAMING, RANDOM STREAMING, SYSTEMATIC PRESSURE COLD LEG ENTHALPY TEMPERATURE PRESSURE COLD LEG SPECIFIC VOLUME TEMPERATURE PRESSURE RTD CROSS CAL SYSTEMATIC ALLOWANCE

• , ** , +, ++ INDICATE SETS OF DEPENDENT PARAMETERS l  :

TABLE 5 (CONTINUED)

CALORIMETRIC RCS FLOW MEASUREMENT UNCERTAINTIES COMPONENT FLOW UNCERTAINTY BIAS VALUES - --

+a,c FiEDWATER PRESSURE DENSITY ENTHALPY STEAM PRESSURE ENTHALPY PRESSURIZER PRESSURE ENTHALPY HOT LEG ENTHALPY COLD LEG SPECIFIC VOLUME - COLD LEG FLOW BIAS TOTAL VALUE 44,C SINGLE LOOP UNCERTAINTY WITHOUT BIAS VALUES)

N LOOP UNCERTAINTY WITHOUT BIAS VALUES)

N LOOP UNCERTAINTY WITH BIAS VALUES) l As noted earlier, the precision flow calorimetric is used as the reference for the normalization of the Cold leg elbow taps. Assuming that the elbow tap d/p transmitters are used to feed the plant process computer, it is a simple matter to perform a periodic flow surveillance. Table 6 notes the instrument uncertainties for normalization of the elbow taps, assuming one elbow tap per }_

loop. The d/p transmitter uncertainties are converted to % flow on the same basis as the feedwater venturi d/p, The elbow tap uncertainty is then combined with the precision flow calorimetric uncertainty. This combination of uncertainties results in the following total flow uncertainty: __

c-

1. of loops flow uncertainty (% flow) 4 i 1.9 The corresponding value used in RTDP is:

1. of loops standard deviation (% flow)

+a.c 4

\

TABLE 6 COLD LEG ELBOW TAP FLOW UNCERTAINTY INSTRUMENT UNCERTAINTIES

% d/p SPAN  % FLOW

+a,c PMA =

PEA =

SCA =

SPE =

STE =

SD =

RCA =

RMTE=

RTE =

RD =

ID =

A/D =

RDOUT=

BIAS.

FLOW CALORIM. BIAS =

FLOW CALORIMETRIC =

INSTRUMENT SPAN =

+a,c SINGLE LOOP ELBDW TAP FLOW UNC = ,

N LOOP ELBOW TAP FLOW UNC =

N LOOP RCS FLOW UNCERTAINTY (WITHOUT BIAS VALUES) -

N LOOP RCS FLOW UNCERTAINTY - --

(WITH BIAS VALUES) =- 1.9

l l

4. Reactor Power Generally a plant performs a primary or secondary side heat balance once every 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br /> when power is above 15% Rated Thermal Power. This heat balance is used to verify that the plant is operating within the limits of the Operating License and t3 sdjust the Power Range Neutron Flux channels when the difference between the NIS and the heat balance is greater than that required by the. plant Technical Specifications.

Assuming that the primary and secondary sides are in equilibrium; the core power is determined by summing the thermal output of the steam generators, correcting the total secondary power for Steam Generator blowdown (if not secured), subtracting the RCP heat addition, adding the primary side system losses, and dividing by the core rated Btu /hr at full power. The equation for this calculation is:

RP = HN)(O gg - Op i_(Q L/_fil))(100)

H Eq. 8 where; RP = Corepower(%RTP)

N = Number of primary side loops Osc Steam Generator thermal output (BTV/hr) as defined in Eq. 6 Qp =

RCP heat adder (Btu /hr) as defined in Eq. 5 Qt Primary system r.et heat losses (Btu /hr) as defined in Eq. 5 H =

Core rated Btu /hr at full power.

For the purposes of this uncertainty 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 different uncertainty values. However, operation at lower power levels results in increased margin to DNB far in excess of any margin losses due to increased measurement uncertainty.

The secondary side power calorimetric equations and effects are the same as those noted for the precision flow calorimetric (secondary side

e 8 portion), equations 6 and 7. The measurements and calculations are presented schematically on Figure 2. Table 7 provides the instrument uncertainties for those measurements performed. Since it is necessary to make this determination daily, it has been assumed that the plant process computer will be used for the measurements. The sensitivities calculated are the same as those noted for the secondary side on Table

4. As noted on Table 8, Westinghouse has determined the dependent sets in the calculation and the direction of interaction. This is the same as that performed for the RCS flow calorimetric, but applicable only to i power. The same was performed for the bias values noted. It should be noted that Westinghouse does not include any allowance for Feedwater venturi fouling. The effect of fouling is to result in an indicated power higher than actual, which is conservative. ,

Using the power uncertainty values noted on Table 8, the 4 loop uncertainty (with bias values) equation is as follows:

+a,c Based on the number of loops and the instrument uncertainties for the four parameters, the power measurement uncertainty for the secondary  ;

side power calorimetric is:

1. of loops power uncertainty (% RTP)

+a,c 4

IV. CONCLUSIONS The preceding sections provide the methodology for what Westinghouse believes is a reasonable means of accounting for instrument J

w __

uncertainties for pressure, temperature, power and RCS flow for use in the RTDP analysis. The plant specific instrumentation has been reviewed for D.C. Cook Unit 2 and the uncertainty calculations are ,

completed. These uncertainty values or more conservative values are used in the RTDP analysis.

d o j

l l TABLE 7 POWER CALORIMETRIC INSTRUMENTATION UNCERTAINTIES

(% SPAN) FW TEMP FW PRES FW d/p STM PRESS

+a. c SCA =

SMTE=

SPE =

STE =

SD =

BIAS =

RCA =

RMTE-RTE =

RD =

ID =

A/D =

CSA =

0F psia  % d/p psia INST SPAN = 600. 1200. 120. 1200.

INST UNC - --

+a,c (RANDOM) =

INST UNC

=

(BIAS)

NDMINAL = 449. 707. 607.

• Based on installed plant instrumentation. See AEP letter AEP(R)-W 88-010, dated April 27, 1988 l .' -

L l

TABLE 8 SECONDARY SIDE POWER CALORIMETRIC MEASUREMENT UNCERTAINTIES COMPONENT INSTRUMENT ERROR POWER UNCERTAINTY 4a,c FEEDWATER FLOW -- --

VENTURI THERMAL EXPANSION COEFFICIENT TEMPERATURE MATERIAL DENSITY TEMPERATURE PRESSURE DELTA P FEEDWATER ENTHALPY TEMPERATURE PRESSURE STEAM ENTHALPY PRESSURE MOISTURE NET PUMP HEAT ADDITION BIAS VALUES  !

FEEDWATER DELTA P FEEDWATER PRESSURE DENSITY ENTHALPY STEAM PRESSURE ENTHALPY POWER BIAS TOTAL VALUE INDICATE SETS OF DEPENDENT PARAMETERS

$1NGLE LOOP UNCERTAINTY (WITHOUT BIAS VALUES) l N LOOP UNCERTAINTY (WITHOUTBIASVALUES)

N LOOP UNCERTAINTY (HITHBIASVALUES)

,~

O REFERENCES

1. Westinghouse letter NS-CE-1583, C. Eicheldinger to J. F. Stolt, NRC, dated 10/25/77.

2. Westinghouse letter NS PLC Sill, T. M. Anderson to E. Case, NRC, dated 5/30/78.

3. Westinghouse letter NS TMA-1837 T. M. Anderson to S. Varga, NRC, dated 6/23/78.

4. Westinghouse letter NS-EPR 2577. E. P. Rahe Jr. to C. H. Berlinger, NRC, dated 3/31/82.

5. Westinghouse Letter NS TMA 1835 T. M. Anderson to E. Case, NRC, dated 6/22/78.

6. NRC letter, S. A. Varga to J. Dolan, Indiana and Michigan Electric Company, dated 2/12/81.

7. NUREG 0717 Supplement No. 4, Safety Evaluation Report related to the operation of Virgil C. Summer Nuclear Station Unit- No.1, Docket 50-395, August, 1982.

8. Regulatory Guide 1.105 Rev. 2, " Instrument Setpoints for Safety Related Systems", dated 2/86.

j

9. NUREG/CR-3659 (PNL-4973), "A Mathematical Model for Assessing the Uncertainties of Instrumentation Measurements for Power and Flow of PWR Reactors",2/85,

10. ANSI /ANS Standard 58.4-1979, " Criteria for Technical Specifications for Nuclear Power. Stations".

11. ISA Standard S67.04,1982, "Setpoints for Nuclear Safety Related Instrumentation Used in Nuclear Power Plants"

o i

l. 12. Tuley, C. R., Miller, R. B., " Westinghouse Setpoint Methodology for Control  !

and Protection Systems", IEEE Transactions on Nuclear Science, February, .

1986, Vol. NS 33 No. 1, pp. 684 687. I l '

13. Scientific Apparatus Manufacturers Association, Standard PMC 20.1, 1973,

" Process Measurement and Control Terminology". I l 1 I

l

(

[

l i

1.

l 1

i