ML091250571

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WCAP-14788, Rev. 3, Westinghouse Revised Thermal Design Procedure Instrument Uncertainty Methodology for Point Beach 1 & 2, Power Uprate (1775 Mwt - Core Power with Feedwater Venturis, or 1800 Mwt - Core Power with LEFM on Feedwater Header)
ML091250571
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Site: Point Beach  NextEra Energy icon.png
Issue date: 02/28/2009
From: Moomau W
Westinghouse
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Office of Nuclear Reactor Regulation
References
WCAP-14788, Rev 3
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Westinghouse Non-Proprietary Class 3 WCAP-14788 Febriuary 2009 Revision 3 Westinghouse Revised Thermal Design Procedure Instrument Uncertainty Methodology for Point Beach 1 & 2 Power Uprate (1775 MWt

- Core Power with Feedwater Venturis, or 1800 MWt - Core Power with LEFM on Feedwater Header)

Westinghouse

WESTINGHOUSE NON-PROPRIETARY CLASS 3 WCAP-14788 Revision 3 Westinghouse Revised Thermal Design Procedure Instrument Uncertainty Methodology For Point Beach 1 & 2 Power Uprate (1775 MWt - Core Power with Feedwater Venturis, or 1800 MWt - Core Power with LEFM on Feedwater Header)

W. H. Moomau*

Controls, Procedures & Setpoints February 2009 Reviewer: T. P. Williams*

Controls, Procedures & Setpoints Approved: M. B. Cerrone*

Manager, Controls, Procedures & Setpoints ElectronicallyApproved Records Are Authenticated in the Electronic Document Management System Westinghouse Electric Company LLC 4350 Northern Pike Monroeville, PA 15146-2886

© 2009 Westinghouse Electric Company LLC All Rights Reserved

TABLE OF CONTENTS LIST OF TABLES ..................................................................................................................... ii

1.0 INTRODUCTION

..................................................................................................................... 1 2.0 M ETHODOLOGY .................................................................................................................... 3 3.0 INSTRUM ENTATION UNCERTAINTIES ........................................................................... 6 3.1 Pressurizer Pressure ..................................................................................................... 6 3 .2 Tav g ...................................................................................................................................... 9 3.3 Calorimetric RCS Flow Measurement (Using LEFM on Feedwater Header) ......... 15 3.4 Reactor Power Measurement ....................................................................................... 24 3.4.1 Power M easurement (Using Feedwater Venturis) ..................................................... 24 3.4.2 Power Measurement (Using LEFM on Feedwater Header) ...................................... 31 4.0 RESULTS / CONCLUSIONS .............................................................................................. 38

5.0 REFERENCES

....................................................................................................................... 39 WCAP-14788 February 2009 i Revision 3

LIST OF TABLES Table 3-1 Pressurizer Pressure Control and Indication Uncertainty 7 Table 3-2 Tavg Rod Control and Indication Uncertainty 10 Table 3-3 Calorimetric RCS Flow Measurement Uncertainties 20 Table 3-4 Calorimetric RCS Flow Measurement Sensitivities 21 Table 3-5 Calorimetric RCS Flow Measurement Uncertainty 22 Table 3-6 Calorimetric Power Measurement Uncertainties (venturi) 28 Table 3-7 Calorimetric Power Measurement Sensitivities (venturi) 29 Table 3-8 Calorimetric Power Measurement Uncertainty (venturi) 30 Table 3-9 Calorimetric Power Measurement Uncertainties (LEFM) 35 Table 3-10 Calorimetric Power Measurement Sensitivities (LEFM) 36 Table 3-11 Calorimetric Power Measurement Uncertainty (LEFM) 37 WCAP- 14788 February 2009 ii Revision 3

1.0 INTRODUCTION

Revision 0 of this report was completed to support an upgrade to the fuel product at uprated conditions of 1650 MWt - core power for both Units 1&2 at the Point Beach Nuclear Plant (PBNP). The fuel product to satisfy the intended requirements was the Westinghouse 14 X 14 PERFORMANCE + 422 fuel assembly. To utilize this new fuel assembly at the uprated conditions, a new accident analysis was required in addition to recalculating and revising the Instrument Uncertainty Methodology. Revision 0 of this report superseded "ITDP Instrument Uncertainty Report" dated June 7, 1984 (84WE*-G-044).

Revision I of this report was completed to support a 1.4% uprate from the uprated condition of 1650 MWt -core power. This 1.4% uprate was possible due to the installation of an ultrasonic Leading Edge Flow Meter (LEFM) on the feedwater header. This LEFM is used to perform the required daily calorimetric power measurement and continuous Reactor Thermal Output (RTO) calculation on the Plant Process Computer System (PPCS). The previous fuel analysis was performed at 2% above the rated full power value of 1650 MWt - core power. This 2% accounted for the power measurement uncertainty. Therefore, the improved LEFM feedwater flow measurement allowed an additional power increase equivalent to the difference between the 2% and the reduced power measurement uncertainty obtained using the LEFM. The new power measurement uncertainty was included in this revision.

Revision 2 of this report was completed to reflect additional changes to the calorimetric measurements. The power measurement uncertainty that uses the Caldon LEFM to measure feedwater flow and feedwater temperature was recalculated to include feedwater pressure transmitter P-2245 and its associated computer input to replace channels P-2289 'and P-2290. The calorimetric RCS flow measurement uncertainty was recalculated to include the Caldon feedwater temperature measurement to replace the TE-3111 resistance thermometer bridge measurement and to include a feedwater pressure reading from the LEFM display panel, rather than using a digital voltmeter.

Revision 3 of this report is completed to reflect design parameter changes for an Extended Power Uprate to 1800 MWt - core power. Power operation at 1800 MWt - core power is possible only when the Caldon LEFM is operable. If the LEFM is inoperable, the maximum power operation is 1775 MWt - core power based on the use of the feedwater venturis.

Four operating parameter uncertainties are used in the uncertainty analysis of the Revised Thermal Design Procedure (RTDP). These parameters are Pressurizer Pressure, Primary Coolant Temperature (Tavg), Reactor 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) at least 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 calorimetric flow measurement at the beginning of each cycle. Pressurizer pressure is a controlled parameter and the uncertainty reflects the utomatic control system. Tavg is a controlled parameter via the temperature input to the automatic rod control system, WCAP- 14788 February 2009 1 Revision 3

and the uncertainty reflects this automatic control system. The RTDP is used to predict the plant's DNBR design limit. The RTDP methodology considers the uncertainties in the system operating plant parameters, fuel fabrication and nuclear and thermal parameters and includes the use of various DNB correlations. Use of the RTDP methodology requires that variances in the plant operating parameters are justified. The purpose of the following evaluation is to define the specific PBNP instrument uncertainties for the four primary system operating parameters that are used to predict the plant safety analysis DNBR design limit via the RTDP, and to determine the starting points of certain plant parameters in some of the accident analyses.

Westinghouse has been involved with the development of several techniques to treat instrumentation uncertainties. An early version (for D. C. Cook 2 and Trojan) used the methodology outlined in WCAP-8567 "Improved Thermal Design Procedure," (2,3,4) that is based on the conservative assumption that the uncertainties can be described with uniform probability distributions. Another approach is based on the more realistic assumption that the uncertainties can be described with random, normal, two sided probability distributions.(5)

This approach is used to substantiate the acceptability of the protection system setpoints for many Westinghouse (6) plants, e.g., D. C. Cook 2 , V. C. Summer, Wolf Creek, Millstone Unit 3 and others. The second approach is now utilized for the determination of all instrumentation uncertainties for the RTDP parameters and protection functions.

The determination of pressure, temperature, power and RCS flow uncertainties are applicable for PBNP Units I

& 2 for power levels up to 1800 MWt - core power when the daily calorimetric power measurement is based on the LEFM on the feedwater header, for 18 month fuel cycles + 25% per the plant Technical Specifications, and for a full power Tavg window of 558.0 to 577.07F.

February 2009 WCAP- 14788 WCAP-14788 February 2009 2 Revisionn

2.0 METHODOLOGY The methodology used to combine the error components for a channel is the Square Root of the Sum of the Squares (SRSS) of those groups of components that are statistically independent. Those errors that are dependent are combined arithmetically into independent groups, which are then combined by SRSS. The uncertainties are considered to be random, two sided distributions. The sum of both sides is equal to the range for that parameter, e.g., Rack Drift is typically [ ]a,% the range for this parameter is [ ]a.

This technique has been utilized before as noted above, and has been endorsed by the NRC staftf7,8'10) and various industry standards (112). This report meets the requirements of ISA-67.04.01-200612) and Regulatory Guide 1.105, Revision 3(9).

The relationships between the error components and the channel instrument error allowance are variations of the (13) basic Westinghouse Setpoint Methodology and are defined as follows:

1. For precision parameter indication using Special Test Equipment or a digital voltmeter (DVM) at the input to the racks; 2

CSA = {(SMTE + SCA) 2 + (SPE) 2 + (STE) 2 + (SMTE + SD)2 + (SRA)

+ (RDOUT) 2 }11/2 + BIAS Eq. 1

2. For parameter indication utilizing the plant computer; 2 2 2 CSA = {(SMTE + SCA) 2 + (SPE) 2 + (STE) + (SMTE + SD) + (SRA) 2

+ (RMTE + RCA) 2 + (RTE) 2 + (RMTE + RD)

+/- (RMTEp; 5 + RCApc) 2 + (RTEpc) 2 + (RMTEpc + RDpc) 2 } 1/2

+ BIAS Eq. 2

3. For parameters with closed-loop automatic control systems, the calculation takes credit for

]pc; WCAP-14788 February 2009 3 Revision 3

CSA = {[(PMA 2 + (PEA) 2

+ (SMTE + SCA) 2 + (SPE) 2 + (STE) 2 + (SMTE + SD) 2 + (SRA) 2

+ (RMTE + RCA) 2 + (RTE) 2 + (RMTE + RD)2 + (RMTE + RCA)2 1ND + (RTE) 21ND 2 2

+ (RMTE + RD) 2IND + (RDOUT) IND ]/N + (REF) + (CMTE + CA)2}1/2

+ BIAS Eq. 3 where:

CSA Channel Statistical Allowance PMA Process Measurement Accuracy PEA Primary Element Accuracy SRA Sensor Reference Accuracy 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 RTE = Rack Temperature Effects RD Rack Drift RDOUT Readout Device Accuracy CA Controller Allowance CMTE Controller Measurement and Test Equipment Accuracy REF Reference signal for automatic control system IND Indicator.

PC = Plant Computer.

N = Number of credited redundant indicators PMA and PEA terms are not included in Equations 1 and 2 since the equations are to determine instrumentation uncertainties only. PMA and PEA terms are included in the determination of control system uncertainties.

(14)

The parameters above are defined in References 5 and 12 and are based on ANSI/ISA-51.1-1979 (R1993)

However, for ease in understanding they are paraphrased below:

PMA - non-instrument related measurement errors, e.g., temperature stratification of a fluid in a pipe.

PEA - errors due to a metering device, e.g., elbow, venturi, orifice.

WCAP- 14788 February 2009 4 Revision 3

SRA - reference accuracy for a sensor/transmitter.

SCA - calibration tolerance for a sensor/transmitter.

SMTE - measurement and test equipment used to calibrate a sensor/transmitter.

SPE - change in input-output relationship due to a change in static pressure for a differential pressure (d/p) transmitter.

STE - change in input-output relationship due to a change in ambient temperature for a sensor or transmitter.

SD - change in input-output relationship over a period of time at reference conditions for a sensor or transmitter.

RCA - calibration accuracy for all rack modules in loop or channel.

RMTE - measurement and test equipment used to calibrate rack modules.

RTE - change in input-output relationship due to a change in 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 its most accurate applicable range for the parameter measured, or 1/2 the smallest increment on an indicator (readability).

CA - allowance of the controller rack module(s) that performs the comparison and calculates the difference between the controlled parameter and the reference signal.

CMTE - measurement and test equipment used to calibrate the controller rack module(s) that perform(s) the comparison between the controlled parameter and the reference signal.

REF - the reference signal uncertainty for a closed-loop automatic control system.

IND - indicator accuracies are used for these uncertainty calculations. Control board indicators are typically used.

PC - plant computer accuracies are used for these uncertainty calculations.

BIAS - a one directional uncertainty for a sensor/transmitter or a process parameter with a known magnitude.

A more detailed explanation of the Westinghouse methodology noting the interaction of several parameters is provided in Reference 13.

WCAP-14788 February 2009 5 Revision 3

3.0 INSTRUMENTATION UNCERTAINTIES The instrumentation uncertainties will be discussed first for the two parameters which are controlled by automatic systems, Pressurizer Pressure and Tavg (Through automatic rod control).

3.1 Pressurizer Pressure Pressurizer pressure is controlled by a closed-loop automatic control system that compares the measured vapor space pressure to a reference value. This uncertainty calculation takes credit for the closed-loop control system design where [ ]a,,. The control channel uncertainties for the automatic control system include allowances for the pressure transmitters, the process racks, and the control system reference setpoint. The pressurizer pressure control system reference setpoint is generated by the setting of a variable potentiometer on the Main Control Board manual/automatic station. The reference setpoint (Pref) is adjusted and verified by the plant operators with the control board indicators. This uncertainty calculation also includes the control board indicators for verification of the automatic control system performance.

On Table 3-1, the calculated control system uncertainty for this function using Equation 3 is [ ]a*c with a [ ]a C bias corresponding to [ ]a,, with a [ ]aC bias. Included in the control system uncertainty is an allowance for pressure overshoot or undershoot due to the interaction and thermal inertia of the heaters and spray. An allowance of [ ]a"c is made for this effect. The standard deviation for the control system is [ ]aC for a normal, two sided probability distribution.

WCAP-14788 February 2009 Revision 3 6

Table 3-1 Pressurizer Pressure Control and Indication Uncertainty***

Parameter Allowance*

a,c Process Measurement Accuracy (PMA)

Primary Element Accuracy (PEA)

Sensor Reference Accuracy (SRA)

Sensor Calibration Accuracy (SCA)

Sensor Measurement & Test Equipment Accuracy (SMTE)

Sensor Temperature Effects (STE)

Sensor Drift (SD)

Rack Calibration Accuracy (RCA)

Rack Measurement & Test Equipment (RMTE)

Rack/Indicator Temperature Effect (RTE)

Rack Drift (RD)

Indicator Calibration Accuracy (RCAIND)

Indicator Measurement & Test Equipment (RMTEIND)

Indicator Drift (RDIND)

Indicator Readability (RDOUTIND)

Reference Accuracy (REF)

Thermal Inertia (TI)

Bias (Sensor Ambient Pressure (SAP))

Bias (Seismic (SSE))

In percent span (800 psig) Range = 1700 - 2500 psig 15 psi setting tolerance around 2235 psig Channels P-429, -430, -431 & -449 (channel indications are not averaged)

      • Results have been rounded to reflect the appropriate number of significant digits based on the accuracy of the input information.

WCAP- 14788 February 2009 7 Revision 3

Table 3-1 (continued)

Pressurizer Pressure Control and Indication Uncertainty Control Uncertainty =

I(PMA)2 + (PEA) 2 + (SRA) 2 + (SCA + SMTE) 2 + STE 2 + (SD + SMTE) 2 +

+/- j(RCA+RMTE)2 + RTE 2 + (RD + RMTE) 2 + (random)

(RCA IND + RMTE IND ) 2 + (RD IND + RMTE IND )2 + RDOUTIND 2 + REF 2

+ TI

+/- SAP (bias) a,c (random)

(bias) a,c Control System Uncertainty (random)

(bias)

WCAP- 14788 February 2009 8 Revision 3

3.2 Tavg Tavg is controlled by a system that compares the high Tavg from the loops with a reference derived from the First Stage Turbine Impulse Chamber Pressure. Tavg is the average of the narrow range TH and TC values. The high loop Tavg is then used for rod control. Allowances are made (as noted on Table 3-2) for the RTDs, transmitter and the process racks/indicators and controller. The CSA for this function is dependent on the type of RTD, pressure transmitter, and the locations of the RTDs, i.e., in the Hot and Cold Leg bypass manifolds.

Based on one TH and one TC RTD per channel to calculate Tavg and with the RTDs located in the hot and cold leg bypass manifolds, the calculated CSA for the channel using Equation 3 is [ ]pc. Assuming a normal, ac two sided probability distribution results in a channel standard deviation (s I) of However, this does not include the deadband of 1.5°F for automatic control. The Tavg control sytem accuracy is the combination of the instrumentation accuracy and the deadband. The probability distribution for the deadband has been determined to be ac

]. 'eThe variance for the deadband uncertainty is then:

(S2)2 [ ] a,c a,c where [ ]c. Combining the variance for instrumentation and deadband results in a control system variance of:

(ST) 2

= (s 1 )2 + (s2 )2 = [ ac The control system ST = I ]a,c for a total random uncertainty of [ ].

An additional bias of [ ]c for Tcold streaming (in terms of Tavg) based on a conservative I ]a Tcold streaming uncertainty is included in Table 3-2. An additional bias of [ pa,c for R/E (Resistance to voltage) linearization (in terms of Tavg) based on a [ ]p R/E uncertainty is included in Table 3-2. An additional bias of [ ]p for the RTD self-heating effect (in terms of Tavg) based on a ac

'c RTD self-heating uncertainty is included in Table 3-2. The total uncertainty of the control system with the additional biases is [ ]' random and [ ] 'c bias.

WCAP- 14788 February 2009 9 Revision 3

Table 3-2 Tavg Control and Indication Uncertainty*

Parameter Allowance (% of Tavg 530-630 'F range)

Tavg alc Process Measurement Accuracy (PMA) [ ] 2C

]a,c PMA 2 [

Sensor reference accuracy (SRA)

Sensor calibration accuracy (SCA)

Sensor drift (SD)

Bias1 (cold leg temperature streaming)

Bias 2 (R/E linearization)

Bias 3 (Self-heating effect)

Dual current source - Dana amplifier calibration accuracy (RCATr-401AITM-401A)

Dual current source - Dana amplifier measurement & test equipment (RMTEm- 4ol1ATM-401 A)

Dual current source - Dana amplifier temperature effect (RTETT-401AJTM-401A)

Dual current source - Dana amplifier drift (RDTrr4OiArrM_401A)

E/I converter calibration accuracy (RCATM-4OBB)

E/I converter measurement & test equipment (RMTETM.4OIB)

E/I converter temperature effect (RTETM-4OBB)

E/I converter drift (RDTm-401BB)

  • Results have been rounded to reflect the appropriate number of significant digits based on the accuracy of the input information.

WCAP-14788 February 2009 10

  • v Revision 3

Table 3-2 (continued)

Tavg Control and Indication Uncertainty*

Tavg a,c Isolator calibration accuracy (RCArM-401c)

Isolator measurement and test equipment (RMTETM-401c)

Isolator temperature effect (RTETM401c)

Isolator drift (RDTM-401c)

Indicator calibration accuracy (RCATI-401)

Indicator measurement and test equipment (RMTE TI-401)

Indicator temperature effect (RTETI-401)

Indicator drift (RD TI-401)

Indicator readability (RDOUT)

Turbine Pressure Allowance (% of pressure 0-650 psig range) a,c Sensor reference accuracy (SRA)

Sensor calibration accuracy (SCA)

Sensor measurement & test equipment accuracy (SMTE)

Sensor temperature effect (STE)

Sensor drift (SD)

Sensor seismic effect (SSE) - treated as a bias Isolator calibration accuracy (RCA PM-485A)

Isolator measurement & test equipment (RIVTE PM-485A)

Isolator temperature effect (RTE PM-485A)

Isolator drift (RD PM-485A)

  • Results have been rounded to reflect the appropriate number of significant digits based on the accuracy of the input information.

WCAP- 14788 February 2009 1l Revision 3

Table 3-2 (continued)

Tavg Control and Indication Uncertainty*

Parameter Allowance (% of Tavg 530-630 *F range)

Tavg Control Racks

_ a,c Module TM40IEE calibration accuracy (RCATM4OIEE)

Module TM401 D calibration accuracy (RCATM401D)

Module TM401H calibration accuracy (RCATM40oH)

Module TM401M calibration accuracy (RCATM4O1M)

Module TM401P calibration accuracy (RCArM4o0IP)

Module TM401N calibration accuracy (RCATM4oIN)

Module TM4011 calibration accuracy (RCATM4011)

Module TM401 EE drift accuracy (RDTM40o1EE)

Module TM401D drift accuracy (RDM4O1 D)

Module TM401H drift accuracy (RDTM40IH)

Module TM401M drift accuracy (RDTM40IM)

Module TM401P drift accuracy (RDTM4OIP)

Module TM40IN drift accuracy (RDTM401N)

Module TM4011 drift accuracy (RDTM4OII)

Module TM401EE M&TE accuracy (RMTETM4O1EE)

Module TM401D M&TE accuracy (RMTETM4OID)

Module TM401H M&TE accuracy (RMTETM4OIH)

Module TM401M M&TE accuracy (RMTETM4OlM)

Module TM401P M&TE accuracy (RMTETM4OlP)

  • Results have been rounded to reflect the appropriate number of significant digits based on the accuracy of the input information.

WCAP-14788 February 2009 12 Revision 3

Table 3-2 (continued)

Tavg Control and Indication Uncertainty*

Parameter Allowance Tavg Control Racks Module TM401N M&TE accuracy (RMTETM401N)

Module TM4011 M&TE accuracy (RMTETM40I)

Number of Hot Leg RTDs per channel Nh=l Number of Cold Leg RTDs per channel Nc=1 Number of Tavg channels N=4 (3 of 4 channel indications are averaged)

Tavg at no load = 547 'F Tavg at full power = 577 'F Tavg range = 530-630 'F Range of pressure = 0-650 psig Turbine pressure at full power = 544 psig Deadband = +/- 1.5 'F 2

Sad = SRA2 + SCA2 + SD re= (RMTETT-401A/TM-401A +RDTT-401A/TM-401A )2 +(RMTETT-401A/TM-401A + RCArTT401A/-TM_4OA )2 +

RTE 2TF-401A/TM-401A 2 2 rack temp = (RMTETM-401BB +RDTM-401BB )2 (RMTETM-401BB +RCATM-40BB ) +RTE TM-401BB isotemp (RMTETM-401C +RDTM-40]C )2 + (RMTETM_401c + RCATM-401C )2 + RTE 2TM-401C 2

ind= (RMTETI_401 + RDTI-401)2 + (RMTETI. 401 +RCATI_401) 2

+RTE 2 TI-401 +RDOUT TPP= (upper range of pressure - lower range of pressure)/ (turbine pressure at full power - lower range of pressure) = (650-0)/ (544-0) =119.49%

Turbsens= (TPP/Tavg span)*(Tavg at full power - Tavg at no load) =0.36

  • Results have been rounded to reflect the appropriate number of significant digits based on the accuracy of the input information.

WCAP-14788 February 2009 13 Revision 3

Table 3-2 (continued)

Tavg Control and Indication Uncertainty 2

sensorurb =

2

[(SMTE + SD) trb + STE 2 turb + (SMTE + SCA) 2tub + SRA 2turb jx Turb _ sens rack turb = [(RMTE PM-485A + RD PM-485A )2 + RTE 2PM-485A + (RMTE PM-485A + RCA PM-485A )2 ix Turb - sens 2 rackconrol = (RMTETM401EE + RCATM 40EE )2 + (R 2

MTE7M401D + RCA.1M40D ) + (pRMTETM 4OlH + RCATM401H )2 2

2

+ (RMTETM4 0M + RCATM4 0IM ) + (RMTEY401P + RCA7A440op ) + (RMTETM40IN + RCATM 4OIN )2

" +/-(RATETM4011 + RCA7M4 0,I )2 + (RMTETM401EE + RDTM4 01 E ) 2 + (RMTETM401D + RDy440o1D )2 2

M 4 01H + RD7M401H ) + (RMTETM4 01M + RDTM4 OJM )2 + (RWEYM 401P + RDAM40 11) 2

+ (RMTEM 2

+ (RA1TE7 + RAM401 N ) + (RMJTE 7 M 4 011 + RDTM 4 Ol1 )2 4 0o1N Channel Uncertainty =

2 rid rid + re re i)

PMJN + - + + rackiemp + iSOtemp + ind Nh Nc FN~h  ;

N-1 PAL42/2 + sensor,.rb + rackurb + rackco,ýtol

]a,c I

Negative Bias = negative value of Bias, + negative value of Bias2 - SSE = [ ]a Positive Bias = positive value of Bias, + positive value of Bias 2 + Bias 3 + SSE = p ca.c Summary of results:

a,c Channel Sigma (random)

Control System Sigma (random)

Control System Uncertainty (random)

Control System Bias (bias)

WCAP-14788 February 2009 14 Revision 3

3.3 Calorimetric RCS Flow Measurement (Using LEFM on Feedwater Header)

RTDP and Point Beach's Technical Specifications require an RCS flow measurement with a high degree of accuracy. A total RCS flow measurement every fuel cycle, typically 18 months, is performed to verify RCS flow and to normalize the RCS flow instrument channels. Interim surveillances performed with the plant computer ensure that the RCS flow is maintained within the assumed safety analysis values, i.e., Minimum Measured Flow (MMF). The 18 month RCS flow surveillance is satisfied by a secondary side power-based calorimetric RCS flow measurement. The calorimetric flow measurement is performed at the beginning of a fuel cycle near full power operation.

Eighteen month instrument drift is used in this uncertainty analysis for hot and cold leg RTDs, and for feedwater pressure, steam pressure and pressurizer pressure transmitters.

A LEFM installed on the feedwater header is used to determine total feedwater flow and feedwater temperature.

Feedwater temperature indication by the LEFM is compared to individual loop feedwater temperatures that are then adjusted, if necessary.

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 = ZiIN(WL)i Eq. 4 The individual primary loop volumetric flows are determined by correcting the thermal output of the Steam Generator for Steam Generator blowdown (if not secured), subtracting the RCP heat addition, adding the loop's share of the primary side system losses, dividing by the primary side enthalpy rise and multiplying by the Cold Leg specific volume. The equation for this calculation is:

WL = WIQG -. O.P + (01 /NW)(Vc)

(hH - hc) Eq. 5 where; WLL Loop Flow (gpm)

A = Constant conversion factor 0.1247 gpm/(ft 3/hr)

Q = Steam Generator thermal output (BTU/hr)

Q = RCP heat addition (BTU/hr)

QL Primary system net heat losses (BTU/hr)

WCAP-14788 February 2009 15 Revision 3

3 V = Specific volume of the Cold Leg at TC (ft /lb)

N = Number of primary side loops hH = Hot Leg enthalpy (BTU/lb) hC = Cold Leg enthalpy (BTU/lb).

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

QsG = (hý- hf)Wf Eq. 6 where; hs = Steam enthalpy (BTU/Ib) hf = Feedwater enthalpy (BTU/Ib)

Wf Feedwater flow (LEFM feedwater header flow divided by

  1. loops)(lb/hr).

The steam enthalpy is based on the measurement of steam generator outlet steam pressure assuming saturated conditions. The feedwater enthalpy is based on the measurement of feedwater temperature and nominal feedwater pressure. The feedwater flow is determined by LEFM measurements.

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

The primary system net heat losses are determined by calculation, considering the following:

Charging flow Letdown flow Seal injection flow RCP thermal barrier cooler heat removal Pressurizer spray flow Pressurizer surge line flow Component insulation heat losses Component support heat losses CRDM heat losses A single calculated sum for 100% Rated Thermal Power (RTP) operation is used for these losses or heat inputs.

WCAP-14788 February 2009 16 Revision 3

The Hot Leg and Cold Leg enthalpies are based on the measurement of the Hot Leg temperature, Cold Leg temperature and the nominal Pressurizer pressure. The Cold Leg specific volume is based on measurement of the Cold Leg temperature and nominal Pressurizer pressure.

The RCS flow measurement is thus based on the following plant measurements:

Steamline pressure (Ps)

Feedwater temperature from LEFM (Tf)

Feedwater pressure (Pf)

Feedwater flow from LEFM Hot Leg temperature (TH)

Cold Leg temperature ( T C)

Pressurizer pressure (Pp)

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

Feedwater density (pf)

Feedwater enthalpy (hf)

Steam enthalpy (hs)

Moisture carryover (impacts hs)

Primary system net heat losses (QL)

RCP heat addition (Qp)

Hot Leg enthalpy (hH)

Cold Leg enthalpy (hC).

The derivation of the measurement and flow uncertainties on Table 3-5 are noted below.

Secondary Side The secondary side uncertainties are in four principal areas, Feedwater flow, Feedwater enthalpy, Steam enthalpy and net pump heat addition. These areas are specifically identified on Table 3-5.

For the measurement of Feedwater flow, the LEFM is located on the feedwater header and provides a total flow.

The accuracy to which the total flow is determined is based on calculations performed by the manufacturer of the LEFM.

Using the NBS/NRC Steam Tables it is possible to determine the sensitivities of various parameters to changes in Feedwater temperature and pressure. Table 3-3 notes the instrument uncertainties for the hardware used to perform the measurements. Table 3-4 lists the various sensitivities. As can be seen on Table 3-5, Feedwater WCAP-14788 February 2009 17 Revision 3

temperature uncertainties have an impact on Feedwater density and Feedwater enthalpy. Feedwater pressure uncertainties impact Feedwater density and Feedwater enthalpy.

Using the NBS/NRC Steam Tables, it is possible to determine the sensitivity of Steam enthalpy to changes in Steam pressure and Steam quality. Table 3-3 notes the uncertainty in Steam pressure and Table 3-4 provides the sensitivity. For Steam quality, the Steam Tables were used to determine the sensitivity at a moisture content of

]a,c. This value is noted on Table 3-4.

The net pump heat addition uncertainty is derived from the combination of the primary system net heat losses and pump heat addition and for PBNP is:

Net Heat input to RCS +6.0 MWt The uncertainty on system heat losses, which is essentially all due to charging and letdown flows, has been estimated to be ],c of the calculated value. Since direct measurements are nota,c possible, the uncertainty on component conduction and convection losses has been assumed to be [ ] 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 Unit 2 and by input power measurements from several other plants.

a~c Therefore, the uncertainty for the pump heat addition is estimated to be [ ]' of the best estimate value.

Considering these parameters as one quantity, which is designated the net pump heat addition uncertainty, the combined uncertainties are less than [ p of the total, which is[ ]c 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 3-5. Three primary side parameters are actually measured, TH, 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 3-3 and the sensitivities are provided on Table 3-4. The hot leg streaming is split into random and systematic components. For PBNP where the RTDs are located in bypass manifolds, the hot leg temperature streaming uncertainty components are pa(ý random and [ pc systematic.

The cold leg enthalpy and specific volume uncertainties are impacted by TC and Pressurizer pressure. Table 3-3 notes the TC instrument uncertainty and Table 3-4 provides the sensitivities.

Parameter dependent effects are identified on Table 3-5. 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 WCAP-14788 February 2009 18 Revision 3

instrument bias values. As a result, the calculation explicitly accounts for dependent effects and biases with credit taken for sign (or direction of impact).

Using Table 3-5, the 2 loop uncertainty equation (with biases) is as follows:

a,c (random)

(bias) a,c (random)

(bias)

Based on the number of loops; number, type and measurement method of RTDs, and the vessel Delta-T, the flow uncertainty is:

  1. ofloops flow uncertainty (% flow) ac LI 2 (random)

(bias)

WCAP-14788 February 2009-19 Revision 3

Table 3-3 Calorimetric RCS Flow Measurement Uncertainties*

(% Span)

FW TEMP FW PRES FW FLOW STM PRESS TH TC PRZ ac LEFM SRA SCA SMTE SPE STE SD BIAS R/E RMTE RTE RD RDOUT RCApC RMTEPC RDpc CSA

  1. OF INSTRUMENTS USED l/Header 1 ]/Header 3/Loop 2/Loop 2/Loop 4 OF psi  % Flow psi OF OF psi INST SPAN= (1) 1500(2) 10 0 0) 1400(4) 150(') 150(5) 800(6) a,c INST UNC.

(RANDOM)-

(BIAS) =

NOMINAL 458.0 0 F 701 psia 100% Flow 601 psia 611.1 OF 542.9 OF 2250 psia (1) Feedwater temperature measurement is from an LEFM on the feedwater header.

(2) Pressure (P-2245) is read from the LEFM display panel.

(3) Flow (F-3 110) is measured with an LEFM on the feedwater header.

(4) Pressure (P-468, -469, -478, -479, -482, -483) is measured with a digital voltmeter at the input of the process instrumentation.

(5) Temperature is measured with a digital voltmeter at the output of the R/E process instrumentation modules.

(6) Pressure (P-429, -430, -431, -449) is measured with a digital voltmeter at the input of the process instrumentation.

(7) Provided by PBNP.

  • Results have been rounded to reflect the appropriate number of significant digits based on the accuracy of the input information.

WCAP-14788 February 2009 20 Revision 3

Table 3-4 Calorimetric RCS Flow Measurement Sensitivities**

a,c FEEDWATER FLOW

-n LEFM DENSITY TEMPERATURE PRESSURE FEEDWATER ENTHALPY TEMPERATURE PRESSURE hs hf Dh (SG)

STEAM ENTHALPY PRESSURE MOISTURE HOT LEG ENTHALPY TEMPERATURE PRESSURE hH hC Dh (VESS)

COLD LEG ENTHALPY TEMPERATURE PRESSURE COLD LEG SPECIFIC VOLUME TEMPERATURE PRESSURE

  • Provided by PBNP.
    • Results have been rounded to reflect the appropriate number of significant digits based on the accuracy of the input information.

WCAP- 14788 February 2009 21 Revision 3

Table 3-5 Calorimetric RCS Flow Measurement Uncertainty****

COMPONENT INSTRUMENT UNCERTAINTY FLOW UNCERTAINTY

(% flow) a,c FEEDWATER FLOW LEFM DENSITY TEMPERATURE PRESSURE 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

++ Indicates Sets of Dependent Parameters Provided by PBNP Results have been rounded to reflect the appropriate number of significant digits based on the accuracy of the input information.

WCAP- 14788 February 2009 22 Revision 3

Table 3-5 (continued)

Calorimetric RCS Flow Measurement Uncertainty****

COMPONENT FLOW UNCERTAINTY

(% flow)

BIAS VALUES a,c COLD LEG ENTHALPY TEMPERATURE COLD LEG SPECIFIC VOLUME TEM PERATURE FLOW BIAS TOTAL VALUE

  • a,,

SYSTEM UNCERTAINTY (random)

(bias)

        • Results have been rounded to reflect the appropriate number of significant digits based on the accuracy of the input information.

(1) The bias and random portions of the calculated uncertainties have been separated for proper use by Westinghouse thermal hydraulic analysis.

WCAP-14788 February 2009 23 Revision 3

3.4 Reactor Power Measurement 3.4.1 Power Measurement (Using Feedwater Venturis)

The plant is required to perform a primary/secondary side heat balance at least 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 of 1800 MWt - core power when using the LEFM (or 1775 MWt - core power when using the feedwater venturis), and to adjust the Power Range Neutron Flux channels when the difference between the Power Range Neutron Flux channels and the heat balance is greater than allowed by the plant Technical Specifications. PBNP also. continuously calculates the reactor thermal output (RTO) to ensure that the power limit is not exceeded.

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 Btu/hr at rated full power. The equation for this calculation is:

RP = _{a=LQSG-ZQp + (O /N)KI}(100) Eq. 7 H

where; RP = Core power ( % RTP)

N = Number of primary side loops QSG = Steam generator thermal output (BTU / hr) as defined in Eq. 6 Qp = RCP heat addition (BTU / hr) as defined in Eq. 5 QL = Primary system net heat losses (BTU / hr) as defined in Eq. 5 H = Rated core power (BTU / hr).

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 feedwater flow in Equation 6 is determined by multiple measurements and the following calculation:

Wf = (K)(Fa){(p f)(d/p)} Eq. 8 where:

Wf = Feedwater loop flow (lb/hr)

K = Feedwater venturi flow coefficient WCAP- 14788 February 2009 24 Revision 3

Fa = Feedwater venturi'correction for thermal expansion Pf = Feedwater density (lb/fl 3 )

d/p = Feedwater venturi pressure drop (inches H 2 0).

The feedwater venturi flow coefficient is the product of a number of constants including as-built 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 transmitter connected to the venturi.

The power measurement is thus based on the following plant measurements:

Steamline pressure (P,)

Feedwater temperature (Tf)

Feedwater pressure (Pf)

Feedwater venturi differential pressure (dip)

Steam generator. blowdown (if not secured);

and on the following calculated values:

Feedwater venturi flow coefficients (K)

Feedwater venturi thermal expansion correction (Fa)

Feedwater density (pf)

Feedwater enthalpy (hf)

Steam enthalpy (hj)

Moisture carryover (impacts hs)

Primary system net heat losses (QL)

RCP heat addition (Q,)

Secondary Side The secondary side power calorimetric equations and effects are the same as those noted for the calorimetric RCS flow measurement (secondary side portion), Equation 6.

For the measurement of feedwater flow, each feedwater venturi is calibrated by the vendor in a hydraulics laboratory under controlled conditions to an accuracy of [ ]a,,. The calibration data that substantiates this accuracy is provided to the plant by the vendor. An additional uncertainty factor of

] is included for installation effects, resulting in a conservative overall flow coefficient (K) uncertainty of

]a,,. Since the calculated steam generator thermal output is proportional to feedwater flow, the flow coefficient uncertainty is expressed as [ ]*. It should be noted that no allowance is made for

  • WCAP-14788 February 2009 25 Revision 3

feedwater venturi fouling. The effect of fouling results in an indicated power higher than actual, which is conservative.

The uncertainty applied to the feedwater venturi thermal expansion correction (Fa) is based on the uncertainties of the measured feedwater temperature and the coefficient of thermal expansion for the venturi material, 304 stainless steel. For this material, a change of+ 1.0 OF in the nominal feedwater temperature range changes Fa by

[ ]p, and the steam generator thermal output by the same amount.

Based on data introduced into the ASME Code, the uncertainty in Fa for 304 stainless steel is + 5 %. This results in an additional uncertainty of p, in power.

Using the NBS/NRC Steam Tables it is possible to determine the sensitivities of various parameters to changes in feedwater temperature and pressure. Table 3-6 notes the instrument uncertainties for the hardware used to perform the measurements. Table 3-7 lists the various sensitivities. As can be seen on Table 3-7, feedwater temperature uncertainties have an impact on venturi Fa, 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)(FLOWmax/FLOWnominal) 2.

The feedwater flow transmitter span (FLOWmax) is 123.6% of nominal flow.

Since it is necessary to make this determination daily, the plant computer is used for the calorimetric power measurement. As noted in Table 3-8, Westinghouse has determined the dependent sets in the calculation and the direction of interaction. This is the same as that performed for the calorimetric RCS flow measurement, but applicable only to power. The same was performed for the bias values.

Using the power uncertainty values noted on Table 3-8, the 2 loop uncertainty (with bias values) equation is as follows:

a,c (random)

(bias)

February 2009 WCAP- 14788 WCAP-14788 February 2009 26 Revision 3

a,c (random)

(bias)

Based on the number of loops and the instrument uncertainties for the four parameters, the uncertainty for the secondary side power calorimetric measurement using the feedwater flow venturis is:

  1. of loops power uncertainty (% power) a,c 2

I I (random)

(bias)

WCAP-14788 February 2009 27 Revision 3

Table 3-6 Calorimetric Power Measurement Uncertainties (venturi)*

(% Span)

FW TEMP FW PRES FW D/P STM PRESS a,c SRA =

SCA =

SMTE =

SPE =

STE -

SD =

BIAS =

RCA =

RMTE RTE RD -

A/D =

RCA1 so =

RMTE1 so=

RTE1 so =

RD1 so =

CSA =

  1. OF INSTRUMENTS USED I/Loop 1/Loop 2/Loop 3/Loop psi  % d/p psi INST SPAN = 500(') 1600(2) 123.6% Flow(3) 1400(4) a,c INST UNC.

(RANDOM) =

(BIAS) =

NOMINAL = 458.0 'F 701 psia 100 % Flow 601 psia (a) Included in RCA (1) Feedwater temperature measurement is from channels T-2104 and -2105 (2) Feedwater pressure measurement is from channels P-2289 and -2290 (3) Feedwater flow measurement is from channels F-466, -467, -476 and -477 (4) Steam pressure measurement is from channels P-468, -469, -478, -479, -482 and -483.

  • Results have been rounded to reflect the appropriate number of significant digits based on the accuracy of the input information.

WCAP-14788 February 2009 28 Revision 3

Table 3-7 Calorimetric Power Measurement Sensitivities (venturi)*

FEEDWATER FLOW ax Fa TEMPERATURE MATERIAL DENSITY TEM PERATURE PRESSURE DELTA P FEEDWATER ENTHALPY TEMPERATURE PRESSURE hs hf Dh (SG)

STEAM ENTHALPY PRESSURE MOISTURE

  • Results have been rounded to reflect the appropriate number of significant digits based on the accuracy of the input information.

WCAP-14788 February 2009 Revision -3 29

Table 3-8 Calorimetric Power Measurement Uncertainty (venturi)***

COMPONENT INSTRUMENT UNCERTAINTY POWER UNCERTAINTY

(% power) a,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 POWER BIAS TOTAL VALUE 2 LOOP UNCERTAINTY

  • *, INDICATES SETS OF DEPENDENT PARAMETERS
  • Results have been rounded to reflect the appropriate number of significant digits based on the accuracy of the input information.

(1) The bias and random portions of the calculated uncertainties have been separated for proper use by Westinghouse thermal hydraulic analysis.

February 2009 WCAP- 14788 WCAP-14788 February 2009 Revision 3 30

3.4.2 Power Measurement (Using LEFM on Feedwater Header)

The plant performs a primary/secondary side heat balance at least 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 of 1800 MWt - core power when using the LEFM on the feedwater header, and to adjust the Power Range Neutron Flux channels when the difference between the Power Range Neutron Flux channels and the heat balance is greater than allowed by the plant Technical Specifications. PBNP also continuously calculates the reactor thermal output (RTO) to ensure that the power limit is not exceeded.

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 Btu/hr at rated full power. Equation 7 is used for this calculation.

For the purposes of this uncertainty analysis 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 thermal output of the Steam Generator is determined by a secondary side calorimetric measurement that is defined by Equation 9 as:

QSG = (hs - hf)Wf _ (hs hsgbd)Wsgbd Eq. 9 where; h Steam enthalpy (BTU/lb) s h ff Feedwater enthalpy (BTU/lb) h sgbd = Steam generator blowdown enthalpy (BTU/lb)

W = Feedwater flow (LEFM feedwater header flow divided by f

  1. loops)(lb/hr)

W sgbd Steam generator blowdown flow (lb/hr).

The steam enthalpy is based on the 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 and feedwater temperature are determined by a LEFM measurement on the main feedwater header, and it is assumed that the loop feedwater flows are equal.

WCAP-14788 February 2009 31 Revision 3

The steam generator blowdown flow is the outlet flow from the steam generators used to control water chemistry, and is determined by measurement from the steam generator loop blowdown flow orifice and the following calculation:

W3gbd = (K)(Fa)(a) {(2)(g&)(pf)(d/p)}12 Eq. 10 where; K = Steam generator loop blowdown flow orifice coefficient Fa = Steam generator loop blowdown flow orifice correction for thermal expansion a = Steam generator loop blowdown flow orifice area

= Gravitational constant (32.174 ft/sec 2)

Pf = Steam generator loop blowdown flow density (lb/ft3) d/p Steam generator loop blowdown flow orifice pressure drop (inches H 20).

The steam generator blowdown orifice flow coefficient is the product of a number of constants including as-built dimensions of the orifice and pipe internal diameter. The thermal expansion correction is based on the coefficient of expansion of the orifice material and the difference between steam generator blowdown temperature and calibration temperature. Steam generator blowdown density and enthalpy are based on the measurement of steam generator steam pressure. The blowdown liquid enthalpy is assumed to be equal to that of a saturated liquid at the measured steam pressure. The orifice pressure drop is obtained from the output of the differential pressure indicator.

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

The primary system net heat losses are determined by calculation, considering the previously defined system heat inputs and heat losses.

A single calculated sum for 100% RTP operation is used for these losses or heat inputs.

The power measurement is thus based on the following plant measurements:

Steamline pressure (P,)

Feedwater temperature (Tf - from LEFM)

Feedwater pressure (Pf)

Feedwater header flow (from LEFM)

Steam generator loop blowdown flow orifice differential pressure (d/p)(if not secured);

and on the following calculated values:

Steam generator loop blowdown flow orifice coefficient (K)

Steam generator loop blowdown flow orifice thermal expansion correction (Fa)

Steam generator loop blowdown flow orifice area (a)

Feedwater density (pf)

WCAP- 14788 February 2009 32 Revision 3

Feedwater enthalpy (hr)

Steam enthalpy (h,)

Steam generator blowdown enthalpy (hsgbd)

Steam generator blowdown density (pf)

Moisture carryover (impacts h,)

Primary system net heat losses (QL)

RCP heat addition (Qp)

The derivation of the measurement uncertainties and the calorimetric power measurement uncertainties on Table 3-11 are noted below.

Secondary Side The secondary side power calorimetric equations and effects are the same as those noted for the calorimetric RCS flow measurement (secondary side portion), Equation 6.

For the measurement of feedwater flow and feedwater temperature, an LEFM is installed on the feedwater header, and the accuracies have been provided by PBNP.

Using the NBS/NRC Steam Tables it is possible to determine the sensitivities of various parameters to changes in feedwater temperature and pressure. Table 3-9 notes the instrument uncertainties for the hardware used to perform the measurements. Table 3-10 lists the various sensitivities. As can be seen on Table 3-11, feedwater temperature uncertainties have an effect on feedwater density and feedwater enthalpy. Feedwater pressure uncertainties affect feedwater density and feedwater enthalpy.

Using the NBS/NRC Steam Tables again, it is possible to determine the sensitivity of steam enthalpy to changes in steam pressure and steam quality. Table 3-9 notes the uncertainty in steam pressure and Table 3-10 provides the sensitivity. For steam quality, the NBS/NRC Steam Tables were used to determine the sensitivity for a moisture content of [ ]a,,C,and the value associated with the limiting power measurement uncertainty is noted on Table 3-10.

The net pump heat addition uncertainty is derived from the combination of the primary system net.heat losses and pump heat addition and was previously summarized as noted for the calorimetric RCS flow measurement (secondary side portion):

Since it is necessary to make this determination daily, the plant computer is used for the calorimetric power measurement. As noted in Table 3-11, Westinghouse has determined the dependent sets in the calculation and the direction of interaction. This is the same as that performed for the calorimetric RCS flow measurement, but applicable only to power. The same was performed for the bias values.

WCAP-14788 February 2009 33 Revision 3

Using the power uncertainty values noted on Table 3-11, the 2 loop uncertainty (with bias values) equation is as follows:

a,c (random) a,C (random)

Based on the number of loops and the instrument uncertainties for the four parameters, the uncertainty for the secondary side power calorimetric measurement is:

  1. ofloops power uncertainty (% power) 2 I (random)

(aaoc WCAP-14788 February 2009 34 Revision 3

Table 3-9 Calorimetric Power Measurement Uncertainties (LEFM)*

(% Span)

FW TEN IP FW PRES FW FLOW STM PRESS SG BI ~OWDOWN (HEADE:R) (HEADER) FLOV aýc LEFM -

SRA =

SCA =

SMTE =

SPE =

STE -

SD =

BIAS =

RCA =

RMTE RTE =

RD =

A/D cal=

A/D rmte=

A/D drft=

RDOUT=

RCA1 so =

RMTE1 so=

RTE1 so =

RD1 sO =

CSA =

  1. OF INSTRUMENTS USED 1/Header I 1/Header 3/Loop I/Loop UNITS OF psi  % flow psi  % flow INST SPAN = (1) 1500(2) (3) 1400(4) 1.36% rated'5 )

feedwater flow(rfwf)

INST UNC.

a8c (RANDOM)

(BIAS)

NOMINAL = 458.0 OF 701 psia 100% Flow 601 psia 15000 lb/hr/loop (a) Included in RCA (1) Feedwater temperature measurement is from the LEFM on the feedwater header.

(2) Feedwater pressure measurement is from transmitter P-2245 and read by the plant computer.

(3) Feedwater flow measurement is from the LEFM on the feedwater header.

(4) Steam pressure measurement is from channels P-468, -469, -478, -479, -482 and -483.

(5) Steam generator loop blowdown flow is from channels F-5940 and-5941 (range: 0-50000 lb/hr)

(6) Provided by PBNP

  • Results have been rounded to reflect the appropriate number of significant digits based on the accuracy of the input information.

WCAP-14788 February 2009 35 Revision 3

Table 3-10 Calorimetric Power Measurement Sensitivities (LEFM)**

a,c FEEDWATER DENSITY TEMPERATURE PRESSURE FEEDWATER ENTHALPY TEMPERATURE PRESSURE hs hf Dh (SG)

STEAM ENTHALPY PRESSURE MOISTURE S.G. BLOWDOWN FLOW Fa TEMPERATURE MATERIAL DENSITY PRESSURE DELTA P S .G. BLOWDOWN ENTHALPY PRESSURE

  • Provided by PBNP
    • Results have been rounded to reflect the appropriate number of significant digits based on the accuracy of the input information.

February 2009 WCAP-14788 Februaey 2009 Revision 3 36

Table 3-11 Calorimetric Power Measurement Uncertainty (LEFM) )

COMPONENT INSTRUMENT UNCERTAINTY POWER UNCERTAINTY a,c FEEDWATER FLOW (HEADER) (% POWER)

LEFM FEEDWATER DENSITY TEMPERATURE PRESSURE FEED WATER ENTHALPY TEMPERATURE PRESSURE STEAM ENTHALPY PRESSURE MOISTURE NET PUMP HEAT ADDITION STEAM GENERATOR LOOP BLOWDOWN FLOW ORIFICE (FLOW COEFF.)

THERMAL EXPANSION COEFF.

TEMPERATURE MATERIAL DENSITY PRESSURE DELTA P STEAM GENERATOR BLOWDOWN ENTHALPY PRESSURE BIAS VALUES POWER BIAS (TOTAL VALUE) 2 LOOP UNCERTAINTY

  • , **, *** Indicates sets of dependent parameters Provided by PBNP (1) Results have been rounded to reflect the appropriate number of significant digits based on the accuracy of the input information.

(2) The bias and random portions of the calculated uncertainties have been separated for proper use by Westinghouse thermal hydraulic analysis.

WCAP- 14788 February 2009 37 Revision 3

4.0 RESULTS / CONCLUSIONS The preceding sections provide the methodology to account for pressure, temperature, power and RCS flow uncertainties for the RTDP analysis. The uncertainty calculations have been performed for PBNP with the plant specific instrumentation and calibration procedures. The following table summarizes the results and the limiting uncertainties that are used in the PBNP safety analysis.

Parameter Calculated Uncertainty Uncertainty Used in Safety Analysis Pressurizer Pressure ac +/-50.0 psi (random)

  • 2.0 psi (bias)

Tavg +/- 5.0 °F (random)

  • 1.4 'F (bias)

Power (feedwater venturis) +2.0% power (random)

-0.1% power (bias)

(at 1775 MWt - core power)

Power (LEFM on header) +/-0.6% power (random)

(at 1800 MWt - core power)

RCS Flow (calorimetric measurement) +2.4% flow (random)

+0.2% flow (bias)

WCAP-14788 February 2009 38 Revision 3

5.0 REFERENCES

1. Westinghouse WCAP-11397-P-A, "Revised Thermal Design Procedure", dated 04/89.
2. Westinghouse letter NS-CE-1583, C. Eicheldinger to J. F. Stolz, NRC, dated 10/25/77.
3. Westinghouse letter NS-PLC-51 11, T. M. Anderson to E. Case, NRC, dated 5/30/78.
4. Westinghouse letter NS-TMA- 1837, T. M. Anderson to S. Varga, NRC, dated 6/23/78.
5. Westinghouse letter NS-EPR-2577, E. P. Rahe Jr. to C. H. Berlinger, NRC, dated 3/31/82.
6. Westinghouse Letter NS-TMA-1835, T. M. Anderson to E. Case, NRC, dated 6/22/78.
7. NRC letter, S. A. Varga to J. Dolan, Indiana and Michigan Electric Company, dated 2/12/81.
8. NUREG-0717 Supplement No. 4, Safety Evaluation Report related to the operation of Virgil C. Summer Nuclear Station Unit No. 1, Docket 50-395, 08/82.
9. Regulatory Guide 1.105 Rev. 3, "Setpoints for Safety-Related Instrumentation", dated 12/99.
10. NUREG/CR-3659 (PNL-4973), "A Mathematical Model for Assessing the Uncertainties of Instrumentation Measurements for Power and Flow of PWR Reactors", 02/85.
11. ANSI/ANS Standard 58.4-1979, "Criteria for Technical Specifications for Nuclear Power Stations".
12. ANSI/ISA-67.04.01-2006, "Setpoints for Nuclear Safety-Related Instrumentation".
13. Tuley, C. R., Williams T. P., "The Significance of Verifying the SAMA PMC 20.1-1973 Defined Reference Accuracy for the Westinghouse Setpoint Methodology", Instrumentation, Controls, and Automation in the Power Industry, June 1992, Vol.35, pp. 497-508.
14. ANSI/ISA-51.1-1979 (R1993), "Process Instrumentation Terminology".

WCAP- 14788 February 2009 39 Revision 3

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