NUCLEAR INSTRUMENTS AND METHODS 118 (1974) 273-278; (0 NORTH-HOLLAND PUBLISHING C
A DIGITAL METHOD FOR REACTOR-PERIOD MEASUREMENT SERGIO G. MUNDIM Instituto de Engenharia Nuclear, Rio de Janeiro, Brazil Received 23 November 1973 A digital method to measure the period of a nuclear reactor is described which is derived from the definition formula of the period . The instrument, whose basic circuit is explained, is able to process the period every8s, with a self-adapting accuracy circuit which keepstheerrors at their minimumvalues.Integrated
circuits are used, allowing for simple and cheap assembling. (The method wasdeveloped. asarequisite for a Master of Science. degree at COPPE, Federal University of Rio de Janeiro, Brazii, in February 1971 .)
1. Introdiletion
forthe conventional analog instrument . Some present good accuracy, but a too long response time, i .e., of the order of magnitude of the period . Others present good response, but introduce errors of more than 10% or even 20% in the period processed. Others present too
Fission reactions in areactor can be controlled by a parameter whichexpressesthevariation of the neutron population . Considering these reactions processed as an exponentialphenomenon, its e-folding time is called
short ranges of calculated periods.
periodofthereactor.Theneutron counting is performed by a system which produces a voltage pulse each time a neutron crosses a detector placed at its input. The conventional system of measuring the period
2. Principle of operationof the digital method The proposed method permits the processing of any positive value of period with an error of less than 10°íp for low count rates and less than 5% for higher count rates and a response time always below the value of the
does notmake useof pulses, but a current is generated in the detector, which is proportional to the neutron flux crossing it. The detector current Iis then related to the period Tthrough of period:
eq . (1), which is the definition
1 _ _t _dl T
1 dt
A logarithmic amplifier, followed by adifferentiating circuit, makes the output voltage proportional to the derivative of the input current, i.e ., to the inverse of
the period . Before describing thedigital method,we list some of its advantages:
a) elimination of the differentiating circuit, which is a source of possible instability problems ; b) direct treatment of the reactor output information (pulses) ; c) use of logic circuits, taking advantage of their
modular characteristics, which results in better assembling and maintenability ; d) better reliability due to the logic principles of operation and to the use of integrated circuits ; e) numerical output and display of the period. Some digital period meters were developed in the past, e.g., Vincent), Martin), Lehr and Mathis 5), but so farnone have been commercially used as asubstitute
period. The formula for the period calculation by the proposed method is derived from the definition of period, eq. (1), considering neutron populations N, and N2 measured within a time interval 0. Eq . (2) shows the approximation formula used, the value of N beingconsidered as the average value between the two populations measured anddN as thedifference N2- N,
The period to be processed is expressed in eq . (3), which is the basic formula for the method : T=
0
N2+N, N2 -N,
.
3. Errors affecting the method a) Theuse of eq . (3), thebasic formula, as an approximation of the period definition eq. (2), introduces an error in the calculation of the period which decreases as the counting interval decreases. Tiùs error is proportional to the neutron counting rat^, as table 1 shows, N2 beingexpressed as a function of N, .
273
274
S. G. MUNDIM TABLE 1
TABLE 2
Error in the calculation of theperiod by eq. (3).
Estimated period, counting interval, and total error values for three ranges of neutron levels. Periods longer than 512 s were considered as infinite.
N:
Error (%)
10 NI 6 Ni 2 Ni 1 .5 Ni 1 .3 Ni 1 .2 Nt Ll- Ni LOSNi NI
Range (C .P.S.)
Estimated Period T (s)
Interval 0 (s)
T/0
Error (%1
0- 2000 2000- 50 000 50 000-100 000
10- 16 16-64 64-512
8 16 32
1 .25- 2 1 - 2 2 -16
10-8 12-4 <4
41 25
3.8 1.25
0.48 0.375 0.275 0.040 0
b) As the neutron counting hasto be integrated over a certain time between two points of the exponential function which expresses the neutron variation, in order to obtain reasonable statistics, the method employs the average value of the function and considers it an instant measurement. The error produced by this procedure draws the period calculation to the safety side when the period is not stable and vanishes for stable periods. For this reason, the error produced by theaveragevalue procedure, is not to be considered in the calculation. c) The Poissonstatistic treatment givento the method considers the square root of the measurement as the
absolute error in the measurement . The relative error varies inversely with the square root of the number of neutrons counted. d) Finally, the error due to the dead time of the coanting system may be considered as à limiting factor, but it can be neglected either by the use of a counting system with good characteristics or by connecting a dead-time correction structure to the counting system output, as suggested by Seda3). The total error affectingthe method is then found by adding the errors presented in (a) and (c), i .e ., the one introduced by thebasicformulaofthemethod to theone due to the counting statistics. Both vary, in opposite sense, when related to the ratio Tl8 and their sum presents a minimum region, as shown in the curves of fig I . The choice of the operating parameters for the
EltaOa %,
Yo
Iv
10
s. -b
1
4
s
s
r
9 10
FqS. P. Totalerror caused by the use of the basic formula forthe method [eq. (3)] and thecounting statistics . Each crve is related to acounts-per-second range of thesystem.
REACTOR-PERIOD MEASUREMENT proposed instrumentwas made based on the minimum regions of the curves of fig . 1 and by estimating some characteristic values for the period over three ranges of neutron levels: start-up, increasing and power. Table 2 gives the estimated period, the proposed counting interval and the total error values in these three ranges. 4 . Circuit description The instrument has been designed as a specificpurpose computer which processes eq. (3). The sum and the difference between two neutron measurements are executed simultaneously and the quotient between them is found by the successive-subtraction method, counting a clock pulse into both the sum and subtraction` registers. This quotient is registered in the period register having been automatically multiplied by the constant }B from eq . (3). The value of this constant is programmed to be always a -power of 2 (as shown in tablet), which makes its multiplication by the other term on the right hand side of eq . (3) just a shift operation . Fig. 2 shows a compact block-diagram of the apparatus, where ACI, AC2, AC3 and AC4 constitute four accumulator registers which process the period calculation . BCD is the period register,
27 5
C the control unit and L a structure to produce the voltage levels to inhibitor allow the counting of pulses into the registers. The instrument works as followe . Initially ACIcontains N,, to which NZ is added in the :next operation* forming the sum NZ +N, in ACI . Simultaneously N2 is being counted into AC3 and added to the complement of N, in AC2 and AC4, forming the difference
P' Fig. 2. Block diagram of the digital period meter. BCD is the display register and ACI, 2, 3 and 4 are the accumulator registers.
276
5. G. MUNDIM
N2 -N, in both registers. The control unit C sends a ed . by the BCD register ; conditioned by the order of pulse which opens a gate to allow the content of AC2 to be subtracted successively from thecontent of ACI, counting I into BCD each time a subtraction is completed. AC4 contains the difference N2-N in order to save thecontent of AC2 forthe next subtraction . At the end of the process, BCD displays the value of the period and AC3 contains the value of N2 which is transferred to ACI in order to prepare it for the next cycle. At this stage, N2becomes N, in ACIandanew N 2 will be counted, as in the first cycle. Actually, register ACI is composed of four registers which contain values of N, in four successive instants . Oneof these values is considered as theactual N, each time a new cycle begins . N2 is counted into AC2 . The order of registering N, in ACI makes the right setting of the time interval between the two countings N, and N2 possible. For instance, thetime interval between the presentcounting N2 and theformer counting N, is 32 s, which is the maximum time interval. The time between N2 and the second N, counting is 24 s (this interval is not used) ;the third NI counting is done 16 s before N 2 and the last one: i.e ., the most recent N, counting, is done 8 s before N2. One must observe that the present counting N 2 is taken just after the most recent N, counting and that any counting is performed in 8 s. The selection of the right register to be used in ACI is done by the control unit C, automatically commandE."
magnitude of the last period displayed in it. Finally; N2 is transferred to one of the ACI registers chosen by C; being nowlabelled as the most recent N, counting . The complete circuit of the instrument is shown in fig. 3. 5. Simulation under real data conditions Theverification of theproposed method wasperformed at the Triga reactor of the "Instituto de Pesquisas Radioativas", University of Minas Gerais, and at the Argonnaut reactor of the Instituto de Engenharia Nuclear, Brazilian Nuclear Energy Commission . Real data were collectedin the reactors andthe functions of the instrument were programmed in a general-purpose digital computer. Figs 4-6 show the different cases considered in theexperiment . Thefull curves represent the total maximum error calculated foreach case and the spots indicate the maximum real errors found in each period processed . Almost all the spots fall below the theoretical curve in cases 1 and 3. For higher count rates, in the saturation region of the system, the majority of thespotsstill remainsbelow thecontinuous curvein case 2although notas far as in theothercases. This was due to saturation of the counting system for higher count rates. Table 3 shows the conditions esta )lished in the3 cases of the experiment.
%
NR
Fig. 4. 'Case 1 ; T10= 1 .8. Almost all theactual errors remain below the calculated total error represented by the solid line .
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REACTOR-PERIOD MEASUREMENT
120
200
300
Nx 1000
Fig . 5. Case 2 ; TIB =3. Saturation of the counting system shoves a less favorable condition for error consideration .
10 Fig. 6.
20
30
40
50
60
70
en
90
N .1000
100
Case 3 ; TIO=4. Similarly to fig. 4, the majority of the spots representing actual errors stay below the total-error solid line. TABLE 3
Experimental conditions for three cases.
Case 1 Case 2 Case 3
T10
Period
Fig.
1 .8 3 4
positive positive positive
4 5 6
The instrument was also simulated in blocks by a simulator program [see Pereira")] implemented in a computer at "COPPE, University of Rio de Janeiro" . A previous set of data was chosen as checking data and
applied to the simulator. All results were consistent. A prototype is under construction at the "Instituto de Engenharia Nuclear", Rio de Janeiro, based on the test made with real data and the simulated instrument. In this prototype, integrated circuits are being used and it is expected that its performance will be consistent with the theory and experiments developed, allowing for the construction of a digital period meter for two research reactors of the Brazilian Commission for Nuclear Technology. 6. Conclusion Reactor periods have so far been measured by analog systems which make use of a logarithmic
27 8
S . G. MUNDIM
amplifier coupled to a differential amplifier. Such indicates that the digital system is cheaper than the instruments, besidesworking with good accuracy, cause analog and if the performance of the proposed the output information from the reactor to be trans- instrument fits the established standards for period formed into electric current before being processed meters, we will use the digital - period meter as a into period. On the other hand, the period does not substitute for the analog one or even as a parallel appear in numerical form, but its reading depends on channel working as a 2-out-of-3 system or other the visual ability of the operator . criteria of instrumentation philosophy. The digital period meter processes the output information from the reactor (pulses) directly and displays Refereuces the period in numerical form which can easily be read, 1) C . H. Vincent et al ., Nucl . Instr. and Meth. 26 (1964) 221 . 1) printed or even processed by another computer. C. Vincent, Nucl. Insu, and Meth. 31 (1964) 345. The proposed instrument presents a response which s) J. Seda, Nucl. Insu. and Meth . 59 (1968) 179. is always less than the value of the period (8 s for a) J. Martin, Étude et réalisation d'un ensemble de calcul puissance période pour le contrôle d'un réacteur nucléaire, pet ;nds varyingfrom 10 s to infinite) and an error less Rapport CEA-R 3026 (Saclay, 1966) . than 5®fó in the range after the start-up of the reactor. s) S. Lehr and V. Mathis, Nucl. Engng Sci. ConC AIES, A circuit which takes care of the automatic changing Cleveland, Ohio (1959) paper 60-512 . of time interval between countings wasalso added and s) J. D. Schmidt, A digital start-up control unit for nuclear reactors,'IRE Intern . Convention (March 1961). this is conditioned by the last period processed. For Instruments Co., Applicatior of digital techniques to larger periods, the time interval may be fixed in 16 or 7) Ford reactor control systems, NYO-850(1, USAEC (Fob. 1957). 32 s, while for shorter periods, the time interval is s) Ford Instruments Co ., NYO-8501, USAEC (June 1957) . equal to 8 s. Anyway, theresponse time is always equal s) Ford Instruments Co ., NYO-8502, USAEC (Oct . 1957). lo) G . Gauthier, Essais d'un périodemttre digital et comparaison to 8 s, no matter what the time interval is. de ses performances avec celles d'un p6riodemètre analogique A prototype of the instrument is being constructed du type PLSM, Note CEA-N730 (Saclay 1965). at the "lnstituto de Engenharia Nuclear", Rio de 11) G . S . Brunson, Nucleonics 15 (1957) 132. Janeiro, using,modules of integrated circuits in order 32) L. Pereira and P. Bianchi Franga, Um simulador genérico to make a final test in the research reactor of the com conceitos de microprogramag6es, COPPE, UFRJ, ref. (1970). Institute. Afterthat, it is intended to adapt the instru- la) EE-385 S. G . Mundim, Um método digital para medidas de período ment to the standards established for period meters em um reactor nuclear (A digital method for measuring and to make a comparative cost analysis in both the period in a nuclear reactor), Thesis submitted at COPPE analog and the digital instruments . If this analysis (UFRJ), Rio de Janeiro, for Master degree (Fob. 1971).