ML20035F373

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Transient Power Distribution Methodology
ML20035F373
Person / Time
Site: Prairie Island  Xcel Energy icon.png
Issue date: 03/31/1993
From: Zyduck J
NORTHERN STATES POWER CO.
To:
Shared Package
ML20035E769 List:
References
NSPNAD-93003, NSPNAD-93003-R, NSPNAD-93003-R00, NUDOCS 9304210209
Download: ML20035F373 (52)
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1 \\ 1 ) i l ABSTRACT I l This document is a Topical Report describing the Northern States Power Company ] (NSP) methodology for determination of V(z) factors. ] The methodology employed is explained and data obtained from Prairie Island Unit 1 Cycle 15 and Unit 2 Cycle 14 and Cycle 15 are presented to validate the I methodology. This methodology is applicable for both Prairie Island Units 1 and 2. A d t l i i i l a 4 I 2 3 of-52 ~..

o 1 l Prairie Island Units 1 and 2 Transient Power Distribution Methodology NSPNAD-93003 Rev. O l April 1993 l l i l 0 Prepared By Date 8 / k8 ['Y Reviewed By Date m Approved By Date ) 9T I 'l 9304210209 930412 PDR ADOCK 05000282 1 of 52 P PDR

( ( LEGAL NOTICE This report was prepared by or on behalf of Northern States Power Company (NSP). Neither NSP, nor any person acting on behalf of NSP: a. Makes any warranty or representation, express or implied, with respect to the accuracy, completeness, usefulness, or use of any information, apparatus, method or process disclosed or contained in this report, or that the use of any such information, apparatus, method, or process may not infringe privately owned rights; or b. Assumes any liabilities with respect to the use of, or for damages resulting from the use of, any information, apparatus, method, or process disclosed in the report. l 1 1 l 2 of 52

( ( I ABSTRACT This document is a Topical Report describing the Northern States Power company 1 (NSP) methodology for determination of V(z) factors. i The methodology employed ik explained and data obtained from Prairie Island Unit 1 Cycle 15 and Unit 2 Cycle 14 and Cycle 15 are presented to validate the methodology. This methodology is applicable for both Prairie Island Units 1 and 2. \\ i l I i l \\ l l i l l l 3 of 52

4 l s . [ I Table of Contents i I section Title Pace I Introduction 8 l i I II

Background

9 III computer Model 10 l IV Definitions 15 l ? V Elements Effecting 16 Power Distributions l VI Reference Conditions 21 3 VII Load Follow Power Ramps 27 [ VIII Load Follow operating Modes 29 i i IX TPD Case List Generation 34 [ i X Generic V(z) Analysis 42_ f and Case List ( XI TPD Analysis Summary 52 i i e i 1 I i 4 of 52 I

List of Tables Table Title Page IX.A Cycle specific Case List 36 X.A Generic Case List 44 ) 1 5 of 52 i

i List of Figures Pimire Title Pace III.A Computer Model Simulation 11 III.B Integrated Detector Response 12 III.C Measured & Predicted Detector 13 Reeponse, Unrodded III.D Measure & Predicted Detector 14 Response, Rodded V.A Core Power Distributions 18 V.B AI Bandwidth versus V(z) 19 V.C "3-6-3-12" Load Follow 20 VI.A Power Shapes (TAO's) vs V(z) 23 VI.B V(z) vs TAO Magnitude 24 VI.C PI Measured Equil. AO's 25 VI.D V(z) Dependence on Exposure 26 VII.A V(z) vs Power Ramps 28 VIII.A Operating Modes / AI Control 31 VIII.B V(z) vs Operating Modes 32 VIII.C V(z) Curves, Minus AO Mode 33 IX.A TPD Cyc?e specific case List 37 IX.B V(z) Generation Flow Chart 38 IX.C V(z) for 1 Cycle of Data 39 IX.D Summation of 14 V(z) Curves 40 IX.E Typical Output 41 6 of 52

i l List of Figures i i l Fleure Title Paes r [ X.A V(z) Curves, MOC & EOC 45 j i r X.B V(z) Generic Curves 46 X.C MOC & EOC, All V(z) Data 47 f I X.D P214 Generic Case List vs V(z) 48 j t X.E P115 Generic Case List vs V(z) 49 X.F P215 Generic Case List vs V(z) 50 X.G Generic Case List 51 l i i l r i l 1 l l 7 of 52 l-

( ( i l I. INTRODUCTION f y 1 i i This report describes NSP's Transient Power Distribution Methodology (TPD) { I used to generated V(z) curves applied on a cycle specific or generic basis. j t l Transient Power Distribution control strategies are based primarily on limiting the axial flux difference to a specified bandwidth about a Target [ Axial Offset (TAO). The target or reference condition is considered to be an ARD, Equilibrium Xenon condition, or Steady State condition, that determines l 4 ] the TAO. Throughout a transient, initiated from Steady State, the AI is j maintained within a target flux band via control rod motion that results in an i axial variation of the heat flux hot channel factor, F/. This axial a variation in F[ with respect to the equilibrium axial F[ defines an axial j V(z) factor which is applied to equilibrium F[ values to bound F[ values that [ could be measured at non-equilibrium conditions. l l I j l i d a I i i i 4 1 l 4 i 8 of 52

i 1-l l l i II. BACKGROUND j r f The NSP Prairie Island plant is a two loop 1650 MW. Westinghouse PWR. The 1 I l reactor power distribution monitoring system is a moveable incore fission I chamber system combined with four dual section excore ion chambers. The incere system is used to periodically perform a detailed three dimensional pawer. distribution analysis. The excore response is periodically calibrated to match the axial power distribution determined by the incere system. The ) excore system is continuously on-line and capable of indicating a core average f axial power shape. The purpose of the TPD analysis is to assure the reactor l operates within acceptable power distribution limits between periodic incore j maps by utilizing the on-line excore system. l l J \\ t i b 1 5 l l l 1 i 1 1 l l i l 9 of 52

l III. COMPUTER NODEL, N3P l l l l The computer methodology used to analyze the core power distribution uses an NSP code called N3P. NRC approval of this methodology for use on the Prairie Island Units is addressed in NSP topical NSPNAD-BIOl-A. The methodology has been approved for both core design and transient xenon power analysis. The model is a three dimensional nodal code based on FLARE. It uses 24 axial nodes and 26 radial nodes. The radial component of the code is normalized to i the diffusion theory code PDQ. The isotopic number densities and resultant l reaction rates are determined from the transport theory code CASMO. The j result is a very accurate and efficient three dimensional core analysis model. l The speed and ef ficiency of this model makes a detailed three dimensional ( transient xenon distribution analysis possible. i A typical computer simulation starts with a specified reference condition and transient modeling strategy. At the reference condition an axially dependent Equilibrium F/' value is obtained. At each time step during a load follow an axial dependent transient F " value is obtained. The ratio of these axially l g (Trans F ")+(Equil Fn"), at each time step define a i dependent F/' values, g particular axial dependent V(z) curve. The conglomeration of all V(z) curves i at each time step in a load follow result in a peak axial V(z) curve for a ) given reference condition and transient modeling strategy. See figure III.A l l for a flow chart of this process. l j Analysis of transients such as load follow operations are slow enough that N3P l modeling is adequate for both gross (core wide) and localized transient xenon behavier. To demonstrate this, N3P predictions were compared to four flux j l maps taken during a load follow sequence. The first flux map was taken at l equilibrium conditions prior to a load follow maneuver. The second flux map j l was taken after power reduction to 40% power, the third was taken just prior i to a ramp up to 100% power, and the fourth was taken shortly after reaching full power. The results of these four flux maps can be found in figures III.B through III.D. The first figure shows the integrated detector response, the l second displays measured and predicted detector responses for a typical l unrodded location, and the third figure shows the measured and predicted 1 response of a typical rodded location. The excellent comparisons of predicted to measured data display N3P's ability to model transient xenon behavior. l l l i 10 of 52 1

L ' C C l t t l 1 i l Figure Ill.A Computer Model Simulation INPUTS Reference Load Condition Follow -(Equilibrium) Strategy l Generate Equilibrium FO Nuclear's N3P Code I i Generate Transient FO Nuclear's i l Ratio FO Nuclear's Sum of Time per Time Step - Dependent V(z)'s -Limiting V(z) V(z) g ransient FOuiiiMiam'5d-per Load Follow -T ~ I-Strategy Data Editing 11 of 52

I a ( i Figuro III.3 \\ l i INTEGRATED DETECTOR RESPONSE 1 Xenon Modelling I Flux Map Comparisons l Equilibrium Prior to Ramp Down After Ramp Down j a 1 2 3 45 6 7 8 8 10 11 12 13 1 2 3 4 5 6-7 e s 10 11 12 13 - { hu] (=] ans. ner - muas. cues. 6 A-m om - ca.s. c.w too A-r) 3 3 Q c-C 'l

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C C IV. DEFINITIONS / PARAMETERS l A list of various acronyms and/or definitions used in the Transient Power Distribution Methodology are given below. More in depth definitions shall be presented throughout this topical as needed. TPD Transient Power Distribution Methodology represents the process utilized in the generation of a V(z) curve. AO Axial offset represents the ratio of the difference in reactor power, top to bottom, to the total reactor power. i AI Flux Difference, product of Axial Offset and fraction of operating power. tao Target Axial offset is an equilibrium (steady state core condition) all rods out Axial Offset used as a reference (target) value for flux difference monitoring. Bandwidth A window (range) of operationally allowed AI values about a TAO. l Load Follow Plant operating maneuver consisting in a decrease and increase in reactor power over a period of time. Power Ramp Magnitude of power change during load follow operations. Mode Core operating strategy utilized during load follow operations to control AI. F" Nuclear Hot Channel Factor, maximum local heat flux on surface of n a fuel rod divided by the average heat flux in the core. V(z) Ratio of transient to equilibrium predicted Fn" values applied to equilibrium measured Fn" values (for middle 80% of core) to bound F " values that could be measured at non-equilibrium conditions. n Transient F[ v(r) = Equilibrium Fl i 15 of 52

e 4 ( (. l V. Elements Effacting Power Distribution l I d i Axial power distributions are mainly effected by exposure, control rod position, power level swing, and xenon distributions (Figure V.A). Typical l axial power distributions at BOC are generally a symmetric dome shape and with [ r exposure tend to flatten out and even become more of a wash tub shape. l t a Axial offset (AO) and AI values provide a good measure of the power j distribution. The Ao is a ratio of the difference in power Detween the top and bottom halves of the reactor core to the total power in the core, l r a A. O. = Pr+ P, N where Pr= Power in Top Half of Core Pa= Power in Bottom half of Core AI represents the flux difference which is the product of Axial Offset and the l ratio of operating power to rated full power operation, i g3, ' Pr-P,' fg Pr+Ps 6 L Po, g i i where P= Operating Power Level Po= Rated Full Power By maintaining the flux difference within set lLmits (bandwidth) about an Axial offset, a controllable power distribution is maintained. Operation outside the AI bandwidth is restricted in accordance with NSP's Technical Specifications, section 3.10 The AI bandwidth about an axial offset has a pronounced effect upon reactor control and power peaking. The wider bandwidth allows AI to drif t f arther l which lands itself to more severe core oscillatory conditions which in turn drives power peaking resulting in a larger V(z). Figure V.B displays the effect of widening the AI bandwidth from a straight 5% band to a two tier bandwidth, 5% above 90% power and 10% at or below 90% power. The figure shows that V(z) is dependent upon the AI bandwidth. Below is a discussion of power distribution maintenance throughout a load follow maneuver. The modeling of the load follow scenario is such that boron is used to maintain criticality while control rods are used to maintain AI 16 of 52

i C C within a specified bandwidth about an Axial Offset. The driving force behind the load follow scenario is a time dependent power level swing. Utilizing this fact, a typical load follow scenario of a 3 hour power reduction, 6 hours at reduced power, a 3 hour ramp up, and 12 hours at full power has been chosen, referred to as a "3-6-3-12" load follow scenario (figure V.C). i 1. 3 Hour Ramo Down - Due to power redistribution, Axial Of f set shifts in the positive direction, xenon concentration builds in and the iodine concentration depletes. The boron concentration is increased over this time period (less with increasing xenon buildup) to drive the power level down while maintaining criticality. During this power reduction control rods may enter the core to maintain the AI within specified bandwidth, thus, lowering the necessary critical boron concentration and driving the Axial Offset toward the bottom of the core. l 2. 6 Hours at Reduced Power - Here the power level remains constant, 1 control rods are moved to control AI, and boron is removed to ) compensate for xenon buildup. 3. 3 Heur Pame Up - The power level is ramped back up to full powar while adjusting boron to maintain criticality. The power distribution shifts toward the bottom of the core and control rods are moved to control AI. This also depletes the xenon concentration increasing the need for additional boron and increases iodine production. 4. 12 Hours at Full Power - At full power the control rods are 1 basically stationary at some position (generally ARO) as dictated by control of AI within the specified bandwidth. The boron concentration initially increases to compensate for the depleted xenon concentration mentioned in the prior step and then decreases with xenon buildup. Over this period of full power operation the oscillation of the xenon distribution will be dampened which will aid in maintaining a stable core. l l 17 of 52

c c i l Figure V.A j ~ Reactor Core Relative Power Distributions i Due to Rods, Exposure, Power Reduction, and Xenon 1 Rod Bank Inserted EOC Exposure R R eP eP 3 O i 4 0 ew ew t e t a i r i i, v y e Bottom Top Bottom Top Axial Core Height Axial Core Height BOC,ARO Equilibrium l A i eP I o E ew t, i-i r y e Bottom Top i Axial Core Height Power Reduction Xenon Build at Bottom of Core A R eP ep 8o eo aw ew l t e

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b ( i l Figure V.C i a I "3-6-3-12" Load Follow Scenario R eP 10 3 3 aW te 6 lr v e 0 3 9 12 24 i Time (hr.s) 9 l l 20 of 52

C C l VI. Reference Conditions, TAO's At a particular exposure, reference conditions are set up to define starting i points for initiation of various load follow maneuvers. The reference conditions chosen for this type of analysis are Target Axial Offset values (TAO's). A specified TAO may be represented by an unlimited number of power j distributions each of which can be generated in a variety of ways. Through analysis NSP has found that for a given TAO the resulting V(z) is independent of the method of generating the reference power distribution. Figure VI.A displays the effects of generating a particular TAO value in two distinctly different methods. The figure contains two power distributions, one for each method of TAO generation, and the resultant V(z) curves. The first method of obtaining the TAO value was through the use of a continuous load follow depletion to the desired exposure, MOC. The second method of obtaining the same TAO condition was through a base load depletion to MOC adjusting the axial leakage. The plot demonstrates that two feasible yet distinctly different methods of generating a TAO result in virtuelly the same power shape and V(z) f actor. Hence, V(z) is independent of the method of generating the reference condition. For simplicity, method two is the preferable choice of TAO generation since it allows a feasible means of j generating the extreme negative TAO values and method one does not. j Furthermore, as will be discussed later, this analysis will use a bounding TAO approach. The bounding TAO approach dictates that the measured equilibrium axial offsets must be within the analyzed TAO values or additional analysis to bound the measured values will be necessary. Hence, the method of TAO generation is relatively insignificant. i Figure VI.B displays three MOC V(z) curves as a result of generating the reference conditions using Method 2 (leakage depletion). This figure displays three V(z) curves generated from three TAO's and shows that as the absolute magnitude of the TAO value increases so does V(z). The figure displays a behavior that suggests the + TAO case is most limiting at the bottom and middle of the core and the -TAO case is most limiting at the top of the core. Additional analysis has shown this behavior to be consistent. The dependence of V(z) on a target axial offset may also be deduced from the definition of axial offset, where A.O. = ( P -Ps) + (P +Ps). If the TAO is nearly 7 7 equal to zero than P =Pa and we have fairly uniform axially xenon ano. power 7 distributions, thus, local power peaking and V(z), by definition, are well behaved. If the TAO is much greater or less than zero (+5% or -10%), large xenon and power gradients exist axially across the core. This results in higher local power peaking which has a large effect on the V(z) factor. The 21 of 52

gradients will tend to induce oscillatory core conditions when load following, further aggravating local power peaking and increasing the V(z) factor. Utilizing the above information a bouading set of TAO values can be generated based upon past core operations. Figure VI.C contains measured Axial Offset data from cycle 10 through 15 fer Prairie Island units 1 and 2. This data suggests that the TAO is exposure dependent and trends from about +3% to -St, BOC to EOC, respectively. The V(z) factors dependence on exposure has also been shown through analysis, figure VI.D. This exposure dependence is due in part to the ability of maintaining the balance of core reactivity. As exposure is accumulated the reactor core boron concentration decreases. This decrease in boron concentration makes reactivity maintenance more difficult due to slower dilution capabilities. Hence, control rods are utilized significantly more for reactivity management which induce larger AI changes, thus, increasing power peaking and V(z). Furthermore, near EOC the xenon distribution has a greater tendency to oscillate, aggravating AI and V(z) even more. To avoid unrealistic V(z) factors due to uncontrollable oscillations near EOC a definition of what EOC represents is needed. EOC, for purposes of a V(z) analysis, is defined as the point in core life when approximately 150 ppm boron remains in the core. This value was chosen as a reasonable value beyond which the plant will not " typically" load follow for two reasons. The first is that load follow maneuvers beyond this boron concentration are avoided if possible due to the reduced dilution rate available and the second being the cost of processing the large amount of waste water generated. The end result of all the above information is that exposure dependent V(z) curves or an EOC V(z) curve could be generated that would bound possible core operations from EOC to BOC through the use of extreme TAO reference conditions. These curveu would apply for exposures at or below which they were analyzed provided the measured equilibrium axial offset values are within the TAO values used in the TPD analysis. m 22 of 52

i { ngure VI.A { Power Shapes for a +5% TA0 vs Relationship to V(z) i MOC l l Power Shapes 1.32 p q + _..-p_. 4 ---. { _.l.- i_. I I i I ~A-l 1.24 4. -,.- -j-..t 4 j 1.28 l > { -4 e i .. -.4.. i l i 120 j a_-,- -f- .,i ; -.j i i A-# NN -I - * ' l l -~ i i--- _MY bY' ' f i i m! 4-4-pM ! cox- < .g T- - -g.P' .-4 4-- -. - l-g,.f{ I .-,"- -) -,9 -,-- J -Qp Vf y % m m -- W l t -. ;- jh_4- _ H. _ _ --4 -. 4. H _.. p-p,-- -j...-.-, 0 E !i/3 q p _4._-. _4 . j -. j.j., a i ^ p O D ES... 4'[/ 4 l --._4... i C. I 7 - .j 0.83

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{ Figure VI.B { V(z) Dependence on TAO Magnitude MOC Sensitivity on TAO's +5%, -5%, & -10% TAO's l _ _ __.a. 4_ l l.__]!__e [. L tio4 _. + d --... - j..) t oss j, _, - r- .7 j ~ 'j Pq22) l A%. ._-{ _.. j-j p' i.oes 9 TAh d drTkCT-( i l L -t V T ~ ~"}~ i .j 4 1.074 - l - \\, d l -~~ --' '- l ' _4_4.a L ll i 1 k 4 I--{ - - - - --{--[ f f-h 4 ,p,. _._. ) E . [. j l f ,l9 -~h ?-h i TW ~ h- -f N75T I A ~1 ~~" ~- I j O Nk: \\i -'l* i --t -' ~ " _Q_.N_, '] _q__L_-.g_j--p.."j i __._j_. ._._j _; L 4.__ I j I a i c32 --.-l A_i;j %l .j-r.---{-;-.] } { -FH-- l +\\+A A/+- -i+ T i- - Th _._j _ _ __ ._ L_._._._ Q_ 9 f g_p.. ._ _uj _ 7 _l f. _. -{. g

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Figure VI.C O o, 1 i i t i 4 i i i i + p. Q i n'< - c"s< \\ i 6l) i PO o b I l O O - e,?, o d .O _. -._.-. _. - g< OO :O O O

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Figure Yi.D V(z) Dependence on Exposure Sensitivity on 800. MOC. & EOC 1.1s il t l I I i l i i 4 i r i i 3 y p q-- -,p-7 y i 1.15 4 .)- ) 7 _4_. 1.14 _i._j _.-~ ..) w h, ii ,,,3 i i N i + t n ... 3 ~.._$-.. W ,.Lk -& .,. ~ 1.12 m l 1 ..I, -- - i-I I MM f% i 4 3 ( 'l l " - ~ ~ i i [ l l - _) _LJ. ,A .L._.1. i...J.. ) i T*=;meAr bs'1 "+ e'H I F i %rb'

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VII. Icad. Follow Power Ramps Given a reference condition (TAO), a transient is induced by performing a load follow maneuver. The industry standard "3-6-3-12" load follow scenario is used with two power ramps, 1. 100% Power to 30% Power, 100-30% l 2. 100% Power to 50% Power,100-50% A third power ramp, 100-70%, was found (through a sensitivity study and reasoning) to be bounded by the 100-50% ramp. An explanation for 'cnte is

  • hat while the control rod insertion is similar in both ramps it is skigr.ily deeper in the 100-50% ramp.

The deeper rod insertion leads to larger Al s.Jangs and larger V(z) values. The sensitivity study went on to show that the 100-30% j ramp did not always bound the 100-50% ramp due to rod insertion beyond core mid-plane. Rod insertion beyond core mid-plane allows the power distribution j to shift in the positive direction (opposite of the control rod insertion), thus, depending on the reference condition being used, may increases or decrease the subsequent AI swing and V(z) vals e upon return to full power. Hence, the 100-30% ramp will not always bound he 100-50% ramp and both power ramps are utilized in the TPD analysis. f l 1 J l \\ I l 4 I. l i 27 of 52

Figura VII.A V(z) Dependence on Power Ramp 100-30%. 100-50% & 100-70% 1.16 A I i l..l-,i., l t i i 1.15 i I I I I l l 1_.1 1 I ! _4-_d4 I i l l I l l I i i i d i i e 1.14 - 5 l I,i.. i l i l,i_.w_ I i - 1_. }' 1 + 4 _.4 i i i i I j i i ,,,3 a j i i i TlN i i i I l I i 2 =m ri ~-- j 3 1 i i i i i i i i 1 7 l f ,,,, ' _DJ j / i 'l i i i i l 6 1 I + i Y, A 1 i } i j j T'"_'/ i ,~

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C C VIII. Load Follow Operating Modes After establishing the reference conditions and the load follow structure the various core operating strategies utilized during load follow maneuvers must be defined. The intent of the operating strategies / modes is to provide a set of conditions that bound the allowable operating regime. Since there are an unlimited number of operationally allowed strategies / modes, a list of bounding modes has been developed. The list consists of four modes, Rebound, Float, Plus AO, and Minus AO, described below (graphically in figure VIII.A). This operating strategy dictates that during a load follow Rebound - RBD AI will be maintained as positive as possible (within target bandwidth) above 90% power. At or below 90% power the AI shall be maintained as negative as possible (within target bandwidth). The purpose of this mode is to maximize control rod duty and impose control rod forced xenon oscillations. This mode effects the V(z) significantly near the top and bottom of the core which would be expected due to the control rod motion dictated. Float - FLT - This operating strategy dictates that during a load follow AI will be maintained within the target bandwidth. The purpose of this mode is to minbmize operator intervention by allowing AI to float within the target bandwidth. This mode of operation effects the V(z) significantly just below the middle of the core since this mode c f operation allows AI to drift preferentially in the negative direction. Plus AO - PLO - This operating strategy dictates that during a load follow AI will be maintained as positive as possible (within target bandwidth) and minimize control rod insertions at all times. The purpose of this mode is to maximize the boration/ dilution system duty. This mode of operation effects V(z) significantly just above the middle of the core since this mode of operation pulls AI in the positive direction. Minus AO-MAO This operating strategy dictates that during a load follow AI will be maintained as negative as possible (within target bandwidth) at all times. The purpose of this mode is to maximize control rod insertions at all times during core operations. This mode of operation effects V(z) near the bottom of the core due to deep insertion of control rods. 29 of 52

  • -Of these four modes, the MAO mode has the least effect cn V(z)'due to constant control rod insertions which dampen AI swings, therefore, minimizing xenon and i

f power oscillations. Figure VIII.C displays the MAO mode V(z) factors which show very little difference between the ramps and tao's. This data suggests that only the -TA0 cases be run using the MAO mode. This can be explained since the MAO mode will maintain AI as negative as possible at all times using control rod insertions. These rod insertions will have a dampening effect upon a + TAO but not on a -TAO condition. The other three modes are fairly-unique and provide various areas of limiting V(z) factors so no elimination of i cases can be performed. t Figure VIII.B displays the general shape of the four modes. l i i i l l r 1 l 30 of 52 .--.-~

i o Figure Vill.A Operating Modes / Delta I Control REBOUND FLOAT PWR*90% j FWRs=90% PWR*90% j PWRc=90% Power Power O

S
  • al

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= J

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  • ' i Figure VIII.B 1

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{ rigure VIII.c { l l l l f 1 i l l l i i l r l V(z) Curves, MAO Mode i 2 ".1 1 l-- +-,! !.+,- 4 -+- 4 4. - 1 E 94 s I 1 4.. 4._.- j 4-. !H } :-4 4-.+ 4 -~4-4 ---f - - 4 i 3,,g p ._-4. 4_ -- --4---+--- l 1 OS - _ i . wi:'::1M:~h r i 1.- 108"] (j3QM ' OMe-+-. - L_-,-.-._,_ .., I i 1.07 y ,_.q_,_,.,..,.4 1 1.oe -g- _;_..p.. ; t_ 1.05 3 _. _4 _,.. i a: 1 i _ _j. j i y a_.-.4._ q q _._. _.-_4.-+. q.. 4 - 1 04 i.cs y _4 q__. 4_ g 1 c2 p..g.4

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C C ^ i I 1 II. TPD Case List Generation l The result of using reference conditions (TAO's), power ramps, and operating ) modes to bound the allowable operating space is a cycle specific V(z) case l list (Table IX.A), or what NSP refers to as the " Cube" of cases (Figure IX.A). l l l The " Cube" of cases is a finite set of transient modeling strategies which, j through analysis and arguments presented earlier, bound the Tech Spec allowable operating regime. A summarization of the results used to generate the " Cube" are provided below as well as a discussion of how to generate a V(z) curve for a given cycle. Summary of Criteria for Generation of the " Cube" of Cases 1. V(z) increases with an increase in absolute m,agnitude of TAO's. 2. V(z) increases with Exposure. 3. V(z) increases with an increase in AI bandwidth. 4. V(z) increases with larger power reductions (i.e. 100-50% vs 100-70%). 5. V(z) increases at mid-core with power reductions >50% (i.e. 100-30%). 6. V(z) varies with mode of load follow (RBD, FLT, PAO, or MAO). 7. The MAO mode using both ramps off the + TAO may be eliminated. Utilizing the above criteria a V(z) case list, the " Cube" of cases, was generated. Using the case list and a flow chart (figure IX.B) a cycle specific V(z) curve can be produced as discussed in the steps below. E,E, ... Egx generate reference 1. At a particular Exposure N=E, 2 3 i conditions, + TAO and -TAO, that bound feasible operating TAO's. 2. Using both iTAO's generate equilibrium axial Fn" values. 3. From each TAO a "3-6-3-12" load follow scenario is performed for various power ramps and modes while observing a specified AI bandwidth. 4. 100-50% and 100-30% power ramps are used during the load follow from each TAO. 5. For each power ramp at each TAO, four modes of operation are modeled, Rebound, Float, Plus AO, and Minus AO (MAO from -TAO only). "6. Each of 14 load follow scenarios result in a set of time dependent transient axial F " curves which are reduced to a maximum transient n axial Fg" c.urve for a total of 14 unique Fn" curves per exposure point. 7. The 14 maximum transient axial F " values are then divided by the n equilibrium axial Fn" values to obtain 14 maximum axial V(z) curves for the particular exposure point chosen, figure IX.C. These 14 V(z) curves are then summarized into one bounding exposure dependent V(z) curve, l figure IX.D. 8. Repetition steps 1 through 7, for each exposure point chosen constitutes 34 of 52

the generation of an exposure dependent set of V(z) curves. There are approximately 170 individual transient Fn" curves per unique load follow scenario that make up a maximum transient axial Fn" curve. Thus, there are a total of 2380 transient axial Fo" curves that rake up one maximum curve at a particular exposure point. Figures IX.E and IX.F contain typical data output during the first 12 hours of a load follow scenario at one particular exposure for one particular case in the " Cube" of V(z) cases. A "3-6-3-12" load follow scenario was used starting from a tao of +5%. The operating strategy consisted of a 100-50% power ramp in Rebound Mode. Figure IX.E shows power, boron, core average temperature, control rod position, AI behavior, and the resultant V(z) curve during the load follow. j A set of exposure dependent V(z) curves can be reduced by the choice of bounding tao values and exposure points analyzed. This type of reduction is possible since the V(z) factor becomes more conservative with exposure and increasing the magnitude of the TA0 values chosen as reference conditions. For ex ample, TA0's of +5 and -10% could be chosen at EOC then the 14 cases would I represent a V(z) curve that is bounding from BOC to EOC, though it would be l very conservative at BOC. A less conservative yet legitimate analysis may include 3 or 4 exposure points and exposure dependent TAO's. The choice of TA0 values would be made to bound possible measured equilibrium axial off sets over a specified exposure range. For example, if an exposure of 2 GWD/MTU was chosen with +4% and -l% TA0 values then the resultant V(z) factor from a TPD analysis would be applicable from BOC to 2 GWD/MTU provided the measured equilibrium axial offset values remain within the TAO values analyzed. If the next exposure chosen for analysis was 5 GWD/MTU and tao values of +2% and -4% were analyzed. The resulting V(z) factor would be applicable from 2 GWD/MTU l to 5 GWD/MTU provided the measured equilibrium axial of f sets are within the +2% to -4% TAO range analyzed. Furthermore, the TPD analysis at 5 GWD/MTU could be applied from BOC to 5 GWD/MTU provided the measured equilibrium axial offsets remain within +2% to -4%. This process may be continued to EOC at i 1 j various exposures and TAO values. The underlying principle in the whole process is that the measured equilibrium axial offsets must be within the l cnalyzed TA0 values across the applicable exposure range. If the measured equilibrium axial offset were to exceed this window of analysis, additional analysis would be necessary. I l 35 of 52

t { { I Table II.A J J cycle specific cast. List 1 Exposures Targets Power Ramps Modes i N + TAO 100-30% Rebound Float Plus AO a 100-50% Rebound Float Plus AO -TAO 100-30% Rebound Float Plus AO Minus AO i 100-50% Rebound Float Plus AO Minus AO " N represents one particular exposure step. i l 36 of 52

b FIGURE IX.A TPD CASE LIST CYCLE SPECIFIC ANALYSIS CONDITIONS A. Exposures - Various (EOC at a minimum)

8. Target A.O.

- Various (Two at a minimum) C. 3-6-3-12 Load Follow Power Swings 100-50%,100-30% D. Delta-l Bandwidth - Various j MODES A. Rebound - PWR>90% Maintain delta 1 at top of band i i PWR(=90% Maintain delta I at bottom of band B. Float - Let system define delta i path, operator intervention only to keep delta-l within band C. + A.O. - Keep delta l at top of band always D. - A. O. - Keep delta I at bottom of band always ] Ovcle Soecific Case List (Der Excosure. Point) { -TAO TARGETS i + TAO. ' ,.:.................,s'................, ' -AO i i i Modes M O +AO Ramps E Float S TAO's 7 7 Rebound 100-30% 100-50% ..'".'.J:. RAMPS a'-"'/,*12- / i 37 of 52

C C Figure II.B V(z) Generation Flow Chart input Criteria: h........ I 1. j Exposure j .p.............. + TAO -TAO 2+ 3. j Generate 3-6-3-12* Load Follow } Equilibrium & Delta i Bandwidth i FQ Curves 4. 100-50% 100-30% l !~ 5. j RBD l FLT l PAO l l M AOl { 6. 14 Transient { [' Axial FQ Curves l 7. l l i Ratio Transient FO i over i Equilibrium FO Repeat Steps 1. t hr u 7. l........! 8. Summarize V(z) Curves into one set of Exposure Dependent V(z) Curves 38 of 52

l f ngure IX.c { i V(z) Curves for One Cycle of Doto l Rebound Floot Dli ll: _r l a !!l i{t i i si .l, i t -l-t e si i 'I l I i{TW 7D. Thr k iW il 6 I i 4 4 i i 1.14 n.14 ili ~ T'T i i i ili i i i i i e i i i ill i i

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( ( nrure Di.D Surnmation of 14 V(z) Curves on Prior Figure into 1 Curve 1.16 l l l L_1J_. 1 1. 1 i l i i i I t I l i i l i i i t I I i.is I i i I I I I I l f l I I l !_M) 1.14 i l i i i l i i i i f! i l l i iP i ~ a1. 1 i m 1, I i I I. / _i 1% i i cR /!W I i i i I ,,3 ! "s' I i l I / I "I thI i- / I i M i i i i !PI i i i i \\i i t i l i ,~,, i"\\'7:~ !. /: I i i i

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( ( Figure II.E l Typical output l I toad rouow scouao (IMD FDuDW s0Dum0 I Powm REaSnuaJn:w urECs power RED 5NJMN URCs t [ t j I .\\ f' I j k / ,l i. 1 1 1 j f 1 "" ..'L I~ \\ J ._\\ l /_ J l Wl \\ /j l ? l i , 4,= 7 = [ i i f too rouowicoamo LDAD scuow scDamo Powm RCDSnanum unOs POWER REDSNJDON DTIDs i j f [m l i ..~ ? w., 7_ x i r 1-l .i i / \\ / i i i 7-n i n \\ ] 1 \\. l\\ f- \\ j g_. l b l 's All, a %= l I i i ,4 1 i i ? A t l l too rou.ow scouac LcAo soupw scouao power REDSNJDON EFTEUs PUwDt RE XSMdJDON ETTICs ~ l b"'T. l 1 F i A_ i m [ ~ [

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( ( i I. Generic V(s) Analysis and Case List l NSP has utilized the " Cube" of cases to analyze three cycles of. data, P214, j Pil5, and P215. The analysis was performed at MOC and EOC using TAO's of +5% and -10% and the " Cube" of cases. The resulting V(z) curves are displayed in figure X.A and display very similar behavior and magnitudes which lead to the l generation of bounding (Generic) V(z) curves at MOC and EOC (figure X.B). l The three cycles chosen represent a varied selection of core design strategies utilized by NSP. These strategies include such design criteria as 48 and 52 l bundle reloads, mixed enrichment reloads, Nat-U blanketed and non-blanketed l 1 cores, and various amounts and concentrations of Gadolinia loadings. The end i result shows very consistent V(z) results from cycle to cycle. f I The choice of +5% and -10% TAO values came from the measured Axial Offset data j accumulated over 10 cycles provided earlier in figure VI.C. The TAO's were l chosen since they bound all plant measured Axial Offsets at any exposure. f Only two exposures were chosen, MOC and EOC, to reduce the volume of data l output. EOC, for purposes of this analysis, is defined as the point in core a life when about 150 ppm boron exists at 100% full power steady state operation. ( One reason for a boron concentration definition of EOC is that the boron concentration will dictate the manner of AI control due to boration/ dilution [ system constraints, thus, driving the V(z) factor. Other reasons for a boron j concentration definition of EOC were provided earlier. MOC is based on a Core t Average Exposure (CAE) of approximately 23 GWD/MTU. The choice to use core l average erposure for a generic analysis versus other variables such as boron [ concentration or cycle exposure was that these variables vary more from cycle { to cycle than core average exposure. I The three cycles of data resulted in over 7000 individual V(z) curves, 170 per case in the " Cube", that make up the resultant Generic V(z) curve. The resultant V(z) data from three cycles (14 cases per cycle) are plotted in ] figure X.C along with the Generic V(z) curve. The generic curve was drawn to bound the maximum axial V(z) values generated during the three cycles of analysis. i Figures X.D, X.E, and X.F display three cycles of maximum MOC and EOC V(z) l t curves, the Generic Curve, and seven cycle specific curves that represent the bounding V(z) curves from the set of 14 cases. This set of seven curves represent the Generic case list necessary to run each cycle to qualify the use of the generic V(z) curves. The choice of these cases was made because they provide the limiting V(z) values upon which the Generic curve is based. The Generic case list is provided in Table X.A and Figure X.G. 42 of 52 [ - ~. -

l.... ( ( Qualification for use of generic curves require that the generic case list be run and show that the resultant V(z) curves do not exceed the generic curve. Otherwise, a cycle specific analysis will need to be run. l l An expansion of the generic set of curves for more exposure points, different t i TAO's, other AI bandwidths, and the such would be possible provided at least 3 cycles of data were analyzed using the full

  • cube" of cases.

l l l 1 ) l l 43 of 52 i

- -- -..,~. l a . 1 Table I.A 1 I i l i Generic Case List i Exposures Targets Power Ramps Modes i "E, l + TAO 100-30% Float i l Plus AO 100-50%- Plus A0 j a i i I 1 .l -TAO 100-30% Rebound l Minus AO ) j i a i a j 100-50% Rebound. Float 4 MOC E, = a CAE of 23.GWD/MTU-EOC E, = 150 ppm boron remains at equilibrium 100% power ARO conditions. [ v ) t i y l j I a 3 4 t i l I i 44 of 52 r .m. - -, - - -, -, -...... -... -.. + - - ..--=e--,.. -.m... rm,.-..

1 i e ** * { ngure X.A V(z) Curves, MOC 3 Cycles of Doto 6 i.is l l iiit ll l ~- i i l l 6 i ~~i i i i i i 1 i i i I 1~~'- f ~ i -*~ f ~ * ~ l 1.15 I b h 'T ~~'~~ ~ ~~ ~ ' ' ' ' ^ ~ ~ i i 1.14 l f -f'- " ~ ~ f l i i i 4 1.13 l ! !++ l l l

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{ Figure X.B V(z) Generic Curves Summary of three cycles & Generic MOC "" " i 1 I i 1 i I t ~~ 1.15 i i I t I t l li l I i I i i I e I I l I I I I l i I i i i i l i 1 j i i i i i i i I i i i i I i e i t a i i t i i i i I 4 i t i i i i i i i i I I i t I t 1.13 q I ) %K! l l l l l WW d fI Z IIi o '~ M_ ' I i f f i t t [lC 1/h'['I'! Pf i i f I ? l t T i I Q t I Al 3/ i I i i i i i l w .g ua w i << 3 e i i 4 i 4 _L i i i& N iele'r'i i i i i I i i i g O l l l l l l u 1.08 i l I i i j i j l i i i i i i i j 1 i I i i i t i a_Li l I i i I I i i I i l i I I i l i i i 1 1 I i l 1 i i I t 1 i i 4 i i i i 5 i t i { i i i e t i i i i i i t i i i t i i i t 4 1 6 1 i j i i d i t i - i t 1 t i i I i } I 5 { I I k i i ~ T MUL. 2 l 4 + 1.C3 f 4 l l 1 J t i t t Y , x, I, l l I, I l I l I l l I I 1 2 3 4 5 6 7 8 9 to 11 12 13 14 15 16 17 18 19 20 21 22

  • 3 24 Axiol Height (nodes)

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l Figure X.D ,e, MOC Generic V(z) vs Generic Case List V(2) P214 MOC LIO I - 1 f.'-* 1 1 F i I, i 1.1 S .w. _.c. - p-4. f - _ _4_.__- ...,_. 4 1 i'i. ._..._ y q._._j __ q -. 4_ r.4 - - l i I 1 13 k .4 b (d, p p - +.- p a 7 i%_ M,lhh' , M d, n}J' + "~ N E-.._- N, EC I b'" # N, M '-- W, a .c d 1 A! A ii w -x. LD8lM.ua...= ' m. w i I e -p. i

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e =*e Figure X.E l l MOC Generic V(z) vs Generie Case List V(z) l P115 MOC l I 10 i i i i i i i i i i i i i i I l r i t + 1 I i i i I I I g l l l 4.. p-p __4 .+- i i i 8 14 i i "i i i i P r i i fi l 4~*d ' - C h j a & M + C + pod l esk ' l ~i -w -+ am + ww ,,,hh E% 1 /4 I _. #"' + -d l 3dM+n [ 'i-s*PEdej&hN w#+-imd 'u i 1.( l . l ~ YT_~. $ l.g' - hY ~~*'O ^ ' ' , _gy , Mj.; ; E : FEM fl N-N _O -H---i j ' ~t h.-*-i-*- [ l 1 <8'

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t i.. C C 4 Figure X.G t 4 i Generic Case List Shaded boxes represent generic case list. 1 ( { i Power Ramps i 100-30% 100-50% l -TAO i.$m.O. x W~. J-dne w;

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a! v ww. w w Targets am'tter.~,wwnsfW w s. ms m.. u ,i g &. p. u ,n %$ t~1 M l gg' / + TAO,' / i i + AO - M wy / i p a.i / / p___.________q-o j p___.. _ _ _ _ _. _ + l l d i I i a -AO l l g i e a g i e i M A, F LT M sn #m#>6 i ew m s

  1. m

~r c~ WD MS smws?w$'"a3 e.W kf?*st Wit 6b~%ve.tlh%kW L. O @.V?$1J% %;nr 4"cNWijp4ww~ q >M 3@ w: t';a "1%4Q.s*we3Ayrk?W' d +AO r;._M, u e* ** um k *"a W 'e i mw + W#u%d2W a #4 x RBMENN F ^ <gm i _w;wa w.a a we ,v SM $$$5@i#M;mg ..g EMGM$$$n f#I.S RBD l e ~ S s n; dg[m 'epeu4 u [DE$!Pr.T,k~%QW*% IES!~I[ d ?k{ OkE r>Wmmwme#>J$ d t cc A Ly p;.x;;ispc~ w w w.e a var 22-- 1 gw pur .w ;w uv FLT w Q$Yl %3QDdM i*s - S$$ " 7?.W M&; M.i&_@MN._..F.F,. F -TAO m s Targets RBD + TAO 100-30% 100-50% Power Ramps 1 51 of 52 1 l 1 .,,.y

( ( II. TPD Analysis Summary The Transient Power Distribution Methodology presented within this report is intended to provide NSP with a method of generating a cycle specific or generic V(z) factor for application to equilibrium Fn" values to bound F " n values that could be measured at non-equilibrium conditions. This methodology . consists of using an industry standard "3-6-3-12" load follow scenario, two power ramps, 100-30% and 100-50%, and four operating strategies, Rebound, Float, Plus AO, and Minus AO at various TAO conditions and exposures to generate V(z) f actors that bound allowable Tech Spec operating regimes. r Utilization of this methodology on a cycle specific basis is quite simple and straight forward with only three requirements; 1. The cycle specific case list be used as presented within this methodology, the " Cube" of cases (see table IX.A and Figure IX.A). 2. The cases run represent allowable Tech Spec operating conditions. 3. The analyzed Target Axial Offset values bound the measured equilibrium axial offsets over the exposure range of interest. Utilization of this methodology on a generic basis requires the following; 1. The generic curve being used was generated from at least 3 cycles of data and that no Tech Spec changes to power distribution control strategies have occurred since the generation of the generic curve. 2. The generic case list represents the limiting cases necessary to run for qualification of the generic V(z) curve (see table X.A and Figure X.G). 3. The analyzed Target Axial Offset values bound the measured i equilibrium axial offsets over the exposure range of interest. Regardless of the case list utilized the Transient Power Distribution methodology allows the following. 1. Analysic caing various reference conditions (TAO's). j 2. Analysis using various exposures. I 3. Analysis using various AI bandwidths. Items not specifically addressed that may influence power distribution control will need to be evaluated on an item specific basis. 52 of 52}}

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