Simulator of Reactor Kinetics

Transcription

1 Internatonal Journal of Instrumentaton Scence 2014, 3(1): 1-7 DOI: /j.nstrument Smulator of eactor Knetcs S. P. Dashuk *, V. F. Borsov A.P. Alexandrov esearch Insttute of Technology (NITI), , Sosnovy Bor, Lenngrad regon, ussa Abstract Ths paper descrbes the desgn concepts of dgtal-to-analog smulators of nuclear reactor reactvty and gves nformaton pattern about power sgnal whch corresponds to fxed value of reactvty. The man desgn concept for dgtal-to-analog smulator s decadc partton of power sgnal level wth normalzaton of decades to the specfed number whch corresponds to number of bts of dgtal-to-analog converter (DAC) and storng of the duplcated nformaton concernng the power sgnal. Ths paper proposes the desgn of smulator based on 12-bt DAC. The smulator has 1% relatve error for reactvty value correspondng to output sgnal of DAC-smulator wthn three decades of power sgnal varaton. Keywords Nuclear eactor, Power Sgnal, eactvty, Dgtal-to-Analog Smulator 1. Introducton For reactor montorng, specal-purpose calculaton nstruments called reactvty meters are wdely used [1, 2]. Functonal prncple of reactvty meter s based on the soluton of reversed equaton of reactor knetcs wth nput sgnal proportonal to neutron flux [1]. Perodc calbratons and functon tests of the reactvty meters should be performed n order to support relable operaton of reactor control system. For ths purpose specalzed nstruments, smulators of reactor knetcs, are used. These smulators can also be used for adjustment of reactvty meters n factory and for testng of nstruments of the reactor control and safety system. The smulator output sgnal models varaton of neutron flux (reactor power) at constant value of reactvty, the varaton correspondng to soluton of the known set of neutron knetcs equaton [3]: dn ρ β = n+ C, dt * λ 1 = (1) dc βn = λ, * C dt where n s the neutron densty; β, λ, are the characterstcs of the -th delayed neutron group; β s the fracton of delayed neutrons; l* s the prompt neutron lfetme; C s the concentraton of the -th group delayed neutron precursors; ρs the value of reactvty. * Correspondng author: yadashuk@mal.ru (S. P. Dashuk) Publshed onlne at Copyrght 2014 Scentfc & Academc Publshng. All ghts eserved 6 Ideally the output sgnal of smulator should correspond strctly to soluton of dfferental equaton system (1) wth respect to n(t) at constant value of reactvty whch should be set n the smulator,.e. output voltage U(t) or current I(t) versus tme s gven by: Ut () U pt ( ) pt I t = = Ae I0 Ae =, (2) = 1 = 1 where I 0 s the ntal current at the smulator outlet; U 0 s the ntal voltage at the smulator outlet; s the resstance of current-formng resstor; p are the roots of characterstc equaton resulted from (1); A are the coeffcents whose values depend on the reactvty value set n the smulator. In other words, deally the output sgnal of the smulator should be formed such that the value calculated from ths sgnal s dentcal to the set value. In realty ths sgnal can have some devatons from the deal one for a number of reasons. Consequently, there wll be an error n the calculated reactvty value. For the sake of smplcty, ths error s herenafter referred to as the reactvty modelng error. Untl qute recently, a tradtonal approach to developng reactvty smulators has been to use analog smulaton of reactor knetcs equatons [4] where the connecton between model and reactor parameters s determned by the followng equatons: 1 * λ = ; ρ = ; = C0 ; C β fb β 1 1 = β 2 2 = = β 6 6, where ρ, β s the set value of reactvty;, Ω s the resstance equal to parallel connecton of ; fb,, Ω are the correspondng values of resstance; C, C 0, F are the correspondng values of capactors.

2 2 S. P. Dashuk et al.: Smulator of eactor Knetcs Fgure 1 shows an electrcal model of reactor knetcs, whch corresponds to (2). The parameters of ths model can be calculated usng physcal characterstcs λ, l* and α =β /β. A 1 s the measurng amplfe; A 2, A 3 are the scalng amplfers; C 0 s the capacty smulatng prompt-neutrons lfetme; C are the sx C crcuts, smulatng sx groups of delayed neutrons; VS s the voltage source for ntal condton adjustment; fb s the set of feedback resstors, whch determne the set reactvty; T s the voltage-current resstve transducer; S 1 s the swtch of voltage source; S 2 s the swtch of modelng start; S 3 s the postve\negatve reactvty swtch. C 0 VS C S 1 Fgure 1. reactvty) A 1 S 2 «-» Electrcal model of reactor knetcs (analog smulator of The man lmtaton of the analog crcut s slow changeover between smulaton modes because long-tme constants are needed for recovery of ntal condtons n C-crcuts. In practce ths leads to consderable tme losses durng preparaton of the smulator for operaton, because after each smulaton change 5-10 mnutes delay s requred before the ntal condtons can be set. Moreover, the parameters of C-crcuts of the analog smulator should be chosen takng nto account a specfc fuel composton or specfc type of reactor. Therefore, modfcaton of the electrc crcut and ts parameters s requred to perform calbraton of reactvty meters used for measurements n reactors wth dfferent fuel compostons or dfferent type reactors. Fnally, error of reactvty modelng sharply ncreases n analog smulators durng formaton of the output sgnal whch corresponds to negatve reactvty after a few decades of the output sgnal change («far-feld error»), because n ths case the desred sgnal value of the measurng amplfer decreases by a few decades and approaches becomes commensurable to the smulator nose. 2. Dgtal-to-Analog Smulator of eactvty «+» A good alternatve to analog smulator s a reactvty smulator based on dgtal-to-analog converter the functon whch s wdely used n dfferent techncal felds [5-7]. In D/A reactvty smulator output power sgnal s formed as output voltage of dgtal-to-analog converter (DAC), the law A 2 A 3 T Iout S 3 fb of ts tme varaton s set by a walkng dgtal code whch s formed ether n real tme from calculatons or from values stored n memory. The second alternatve s preferable for a hardware mplementaton of the smulator because a mnmum of hardware components are requred: no mcroprocessor and only memory element and very smple crcuts of data access control are needed. A lmtng factor for applcaton of DAC-smulators s addtonal error due to dscontnuty of DAC output voltage varaton, whle an error n the analog crcuts s caused by the amplfer nose only. Ths addtonal error s especally strong durng smulaton of sgnals for negatve reactvty wth small absolute value. Fgure 2 shows dagrams of relatve error δ for modelng of reactvty wth a set value of -0.1β usng a smulator based on 12-bt DAC. As the dagram shows, ths error sharply ncreases and becomes ntolerable, >1%, after half-decade of the power sgnal varaton. In the same stuaton, a smlar error for the analog smulator stays wthn 1% for power measurement wthn the whole decade. δ(%) I 1,E-04 1,E t(s) 10-5 Fgure 2. Processes n D\A reactvty smulator, whch operates n drect control mode drect control of DAC by contnuous power sgnal wth one current-formng resstor connected and one decade of the power sgnal varaton In order to reduce ths error the authors recommend the DAC-smulator [8] confguraton gven n fgure 3. We use ths dagram to llustrate the formaton of a negatve reactvty sgnal. In ths confguraton, the chosen nterval of the power sgnal varaton, whch corresponds to the chosen reactvty, s prelmnarly segmented and each of the segments corresponds to dentcal relatve varaton of ths sgnal. For convenence, decadc segmentaton s done. Data array s entered n the memory storage. Ths data conssts of N seral decades as a set of dgtal codes. Thus each of decades s prenormalzed on the gven number А=2k by multplcaton of the current values to value A/x, where k s a number of DAC bts, x s the value of power parameter at the begnnng of -th decade. Then a sequental sample of dgtal codes from the memory storage n program control unt s appled to the data-entry port P dac. In order to reduce ths error the authors recommend the DAC-smulator [8] confguraton gven n fgure 3. We use ths dagram to llustrate the formaton of a negatve reactvty sgnal. In ths confguraton, the chosen nterval of the power sgnal varaton, whch corresponds to the chosen δ 10-4 I(А)

3 Internatonal Journal of Instrumentaton Scence 2014, 3(1): reactvty, s prelmnarly segmented and each of the segments corresponds to dentcal relatve varaton of ths sgnal. For convenence, decadc segmentaton s done. DAC A S 1 1 P 11 S 2 S P 2 2 P 3 3 Program control unt S P S n n P P n n Data P da dac Output current Fgure 3. D\A smulator wth decadc swtchng of power parameter. A s the measurng amplfer; S are electronc swtches of current-formng resstors; are the current-formng resstors; P are the ports for entry of keyng sgnals; P dac s the port of entry for control data of DAC Such types of control data arrays can be formed for any specfed value of reactvty; therefore the changeover between two dfferent smulator modes,.e. changeover between dfferent ntal current and dfferent reactvty values durng sgnal formaton, takes almost no tme. Ths changeover reduces tself to a selecton of a control data array from the memory and connecton of one of the electronc swtches of current-formng set of resstors (selecton of ntal output current). Fgure 4 presents dagrams llustratng the smulator operaton. It s shown that power parameter decades are normalzed to the gven value A (see vertcal arrows n fg.4b) as the value of ths parameter decreases (fg.4а) leadng to a consequent change n the drvng voltage level (fg.4c) and current formng resstance at t 1, t 2, t 3,, t N n the end of decades (fg.4d). As a result, the smulator output current forms (fg. 4e), whch corresponds to the change n the power parameter of the reactor whch controls the reactvty value. Dagram 4c shows that n ths smulator the sgnal-to nose rato at the output port of the measurng amplfer has the same value n all decades of ts output sgnal varaton because the measurng amplfer output sgnal vares wthn only one decade n all decades of output sgnal varaton of the smulator. Another mprovement of dgtal-to-analog applcatons for reactvty smulaton problem s optmzaton of presentaton of data stored n memory [9]. Accordng to soluton of the reactor knetcs equatons, the reactor power for a fxed reactvty value begns to vary at an almost constant rate (one of the terms n the sum n the rght-hand sde of (2) becomes much greater than the others) at some moment after the reactvty jump. Fgure 4. Processes n D\A reactvty smulator desgned accordng to the dagram on the fg.3 Therefore, a sgnal varaton wthn ntervals (decades) can be duplcated begnnng from a certan nterval (decades) when segmentng the smulator output sgnal varaton nto ntervals (decades). The nterval sutable for begnnng of duplcaton and possble number of duplcated ntervals (decades) s determned by admssble error of reactvty value whch the reactvty meter calculates from the modfed sgnal. The error can be estmated from soluton of

4 4 S. P. Dashuk et al.: Smulator of eactor Knetcs the reversed knetcs equaton where reactor power s smulated by the modfed sgnal. The performed calculatons show that for practcal reactvty values the error does not exceed 1% of the reactvty value, f the relatve devaton of the smulated sgnal from the true one does not exceed 1% n each nterval (decade) after the duplcaton. Therefore, programmng of the memory devce n DAC-smulator does not requre recordng all the nformaton for the selected tme nterval of the power sgnal varaton. Only part of ths nformaton s qute suffcent and, thus, less memory volume s requred. To llustrate, we now compare smlar dagrams gven n fgure 4 and fgure 5. Let us consder n detal the dagrams for standard-memory DAC-smulator and DAC-smulator wth "reduced" memory volume. For both cases, n practce the normalzng number A was correspondng to the maxmal capacty of the 12-bt DAC based smulator. Obvously, for the standard-memory verson, nformaton about all decades of the power parameter varaton should be stored n the smulator memory (see D 1, D 2 D N n fg. 4b). A dfferent behavor s observed for "reduced"-memory DAC-smulator. Dagrams n fgure 5 show smulaton of the power sgnal correspondng to reactvty value of -0.1β. The nput code generaton (fg. 5b) uses the frst decade of the power parameter varaton, normalzed to A (fg. 5a) for nterval between 0 and t 1 and the second decade of the power parameter varaton, normalzed to A for t 1 t 2, t 2 t 3,, t N T ntervals, takng nto account the second decade dentty to all subsequent decades usng constant ten-fold multpler. In ths case t s suffcent to store nformaton only about two decades of the power sgnal varaton n the smulator memory as t s shown by D 1, D 2,, D 2 (fg. 5b). The correspondng level varaton of drvng voltage (fg.5c) and resstance of current-formng resstor at the end of decades (fg.5d) s performed K-1 tmes durng samplng of data correspondng to the end of the 1 st decade (t 1 moment) and N-K+1 tmes durng samplng of data correspondng to the end of the second decade ( t 2, t 3 t N. moments), where N s the quantty of decades, K s the number of the decade where replacement of the actual sgnal by the duplcated one does not lead to a reactvty modelng error above 1%. For K=2 sx-decade power sgnal varaton case, the mentoned level changes are performed one tme (K-1=2-1=1) and durng selecton of data correspondng to the end of the frst decade and fve tmes (N-K+1=6-4+1=5) durng the selecton of data correspondng to the end of the second decade. As a result, the smulator output current s formed (fg. 5e), whch adequately represents the ntal power parameter change for reactvty control usng as lttle data as possble needed for the reactor power sgnal smulaton. Snce the reactvty smulator should provde a set of reactvty values characterzng for a task to perform (calbraton or functonal check of the reactvty meter), then each reactvty value corresponds to a specfc K value, as t was mentoned before. Therefore, the reducton of the storage memory volume of the smulator as a whole s slghtly lower than a smlar reducton of data array calculated for one value of reactvty wth a small absolute magntude (±0.1β). As an example, for a practcal set of reactvty values the above mentoned optmzaton of data provdes 26 % and more than two-fold reducton of the memory volume for contnuous smulaton of reactvty n three and sx decades of the power sgnal varaton, respectvely (see Table 1 and 2). Fgure 5. Processes n D\A reactvty smulator wth «reduced» memory storage

5 Internatonal Journal of Instrumentaton Scence 2014, 3(1): Experments Fgure 6 shows the tme varaton of the power sgnal and correspondng error of reactvty ρ=-0.1β modeled by the smulator shown n fg. 3. The smulaton was performed n three decades of the power sgnal varaton usng the reduced memory 12-bt DAC based smulator. Let us note that the purpose of the current study was to obtan the value of error for reduce-memory DAC smulator as good as the value of error for analog smulator ( 1%). Ths problem has successfully been solved. It may be assumed that standard-memory DAC smulator would have much less error, but ths fact wasn t proved expermentally. Fgure 7 shows smlar dagrams for the case wth drect control of DAC by contnuous power sgnal wth one current-formng resstor connected. The comparson between fg.7 and fg.6 llustrates advantages of the proposed methods as appled to D\A reactvty smulators. In partcular, the dagram n fgure 6 shows that the error of reactvty smulaton exceeds 300% at the end of the thrd decade of the power sgnal varaton. We also can see that ths error exceeds ±1% even at the frst half-decade as mentoned above. Based on ths, t can be concluded that stayng n the error range of ±1% usng 12-bt DAC requres formaton of the power sgnal by sewng of power sgnal varaton half-decades wth approprate swtchng between current-formng resstors. Data gven n fg.6 s obtaned from «sewng» of sx half-decades. Fgure 7. Tme hstory of current and relatve error for smulaton of ρ=-0.1β reactvty of drect control of DAC by contnuous power sgnal wth one current-formng resstor connected Fgure 6. Tme hstory of current I and relatve error δ of reactvty smulaton ρ=-0.1β for D\A reactvty smulator wth «reduced» memory storage Table 3 shows the current values of control codes for 12-bt DAC at selected ponts of half-decade «sewng» and correspondng values of current-formng resstor resstances and output currents. Table 1. Comparson of standard and reduced memory volumes for three decades of power varaton ρ, β Number of decades, where the dscrepancy of the reactvty calculated for normalzed decades does not exceed 1% Volume of data array for three decades words n Volume of data array for normalzed decades words n -0, , , , > > , , , , Total volume of data array for three decades words n elatve unt Total volume of data array for normalzed decades words n elatve unt ,74

6 6 S. P. Dashuk et al.: Smulator of eactor Knetcs ρ, β Table 2. Comparson of standard and reduced memory volumes for sx decades of power varaton Number of decades, where the dscrepancy of the reactvty calculated for normalzed decades does not exceed 1% Volume of data array for sx decades words n Volume of data array for normalzed decades (number of words n -0, , , , > > , , , , Total volume of data array for sx decades words n elatve unt Total volume of data array for normalzed decades words n elatve unt ,45 Table 3. Decadc sewng of 12-bt DAC Task code esstance of the current-formng resstor*[mω] Output current [А] DAC reference voltage of the measurng amplfer [V] 0, ,0 0, , ,4 0, ,0 0, , ,77 0, ,0 0, , ,4 0, ,0 1, , ,78 0, , , ,4 0, ,0 17, , ,78 Decade number Conclusons Testng of the descrbed methods for desgnng D\A smulators of reactor knetcs and also methods for groupng and presentaton of control data showed ther advantages over tradtonal analog smulators. The D\A smulators are ready to use mmedately after a change between operaton modes and have almost nvarable level of the relatve devaton from ts specfed value n reactvty correspondng to DAC-smulator output sgnal. The devaton s wthn at least three decades of the power sgnal varaton. Use of the obtaned data n desgnng D\A smulators can sgnfcantly mprove ther performance characterstcs. The authors would lke to thank N.A. Vnogorov for hs help wth calculatons and for precous comments. EFEENCES [1] Yu. A. Kazansky, E.S. Matusevch. Expermental methods of reactor physcs. М.: Energoatomzdat, p. 39. [2].. Bagdasarov, V.A. Lttsky //Atomc Energy Vol. 76. el. 3. p [3] G.. Kpeen. Physcs of Nuclear Knetcs. М.: Atomzdat, p. 202.

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