Neutron signal characterization of the power instability event at Laguna Verde BWR

Nuclear Engineering and Design 196 (2000) 327–336

Neutron signal characterization of the power instabilityevent at Laguna Verde BWR

Juan Blazquez, Jorge Ruiz *Department of Nuclear Fission, CIEMAT, A6. Complutense 22, 28040 Madrid, Spain

Received 25 January 1999; accepted 7 November 1999

Abstract

On January 24, 1995, a power instability event occurred in Laguna Verde, a BWR/5 commercial plant. Recordedpower oscillations were studied from the point of view of noise analysis. The 723-s long recorded signal comes fromaverage power range monitors and was bad conditioned for noise analysis practice; it was neither stationary in mean,nor in variance. The signal first stage corresponds to the stable reactor; the third stage, to the unstable reactor. Therewas a second intermediate stage regarded as a transition one. The signal was preconditioned and divided in smallblocks. Noise was analysed within each block in the amplitude, frequency and time domains. The analysis was aimedat on early recognition of instability by using the noise to discriminate between stable, transition and unstable state,regardless of the domain chosen for analysis. The experience obtained from studying real events, not depending onany physical model, are the ground for making safer operation procedures. © 2000 Published by Elsevier Science S.A.All rights reserved.

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1. Introduction

In a commercial BWR, power instability duringthe start-up process is an unusual event, althoughit occurs often compared with other anticipatedtransients. Nevertheless, some cases have beenreported in the past (Murphy, 1988; Bergdahl etal., 1990; Castrillo et al., 1991) without apparentdamage to the Plant. The BWR owner group,Licence Authorities and Vendors have encouragedthe research community to understand better the

events and to design operational procedures inorder to prevent new cases.

Two specific meetings (International Work-shop, 1989; Stability Symposium, 1989) devotedto the topic were organized as a consequence ofLaSalle County Station Unit 2 event (Araya et al.,1989; Cheng, 1988). Stability monitors — workstations measuring power decay ratio from neu-tron noise — have been developed and installedin nuclear power plants (NPP) (Lorenzen et al.,1991; Anegawa et al., 1995). Noise analysis ofBWR/6 neutron signal during a real instabilityevent (Blazquez and Ballestrın, 1995) reportedthat fluctuations were the dominant behaviour ofthe signal prior to instability; but in a few min-

* Corresponding author. Present address: National Instituteof Nuclear Research, Mexico. Tel.: +34-91-346-6123; fax:+34-91-346-6233.

E-mail address: [email protected] (J. Ruiz)

0029-5493/00/$ - see front matter © 2000 Published by Elsevier Science S.A. All rights reserved.

PII: S0029 -5493 (99 )00299 -X

J. Blazquez, J. Ruiz / Nuclear Engineering and Design 196 (2000) 327–336328

utes, fluctuations vanished and signal was oscillat-ing clearly. It was suggested that this changingbehaviour could be used for early recognitionpurposes. Several theoretical models explain thephenomenology (March-Leuba, 1986; Karve etal., 1997), being a guide for simple understandingof noise spectra.

In spite of being a research active field, occa-sionally, instability events still happened in NPP;such is the case of Laguna Verde, Mexico onJanuary 24, 1995. Instability occurred during thestart-up process and the power was 34%. Nodamage to the NPP was reported (Gonzalez et al.,1995; Farawila, 1998); the power began oscillatingwith growing amplitudes, when amplitude of os-cillations reached the maximum swing of 10%, theoperator then inserted the control rods scrammingthe reactor.

The process computer from the average powerrange monitors (APRM) recorded a signal of 723s. The signal was long enough to identify threestages during the event: the first one correspondsto stable reactor; in the third one, the reactor isclearly unstable; hence, the second stage was atransition period. This work features the noisesignal from each stage in three domains: the am-plitude, the frequency and the time domain. Thepurpose has been to learn from real signal eventsin order to design operational procedures forpreventing instability in future.

2. Data preconditioning

Following the report by Gonzalez et al. (1995),during start-up process, the reactor was at �34%power and 32% core flow. In order to operatewith speed high recirculation pumps, power wasincreased up to 37% by withdrawing two controlrods. At 03:20 h, the operator began closing flowcontrol valves causing power to decrease, due tovoid fraction negative reactivity feedback. Thereactor was slightly subcritical and power wasdecreasing.

Data were recorded from APRM. There are723 s available, sampled at 0.2-s intervals; there-fore, the whole sample has 3615 points which isplotted in Fig. 1. The signal was ill conditionedfor noise analysis because it is neither stationaryin mean, nor in variance. Although to eliminatethe trend, a common high-pass filter would sufficeto remove the dc component and the low fre-quency transient. A fourth order polynomials wasfitted to signal and subtracted, other superiororder polynomials were also tested, but they didnot improve substantially the stationary of thezero mean signal, obtained by trend removing.

The variance cannot be made stationary, so thenoise signal was divided into small blocks, 200points (each 40 s long), and regarded as stationarywithin the blocks. Having in mind that oscilla-tions have a period of 2 s, there are 20 oscilla-tions/block and therefore enough for tryingspectral analysis.

3. Analysis in the amplitude domain

Within each block, zero mean signal amplitudeshistogram is plotted in Fig. 2a, corresponding tostable reactor. It can be seen that amplitudes areGaussian form; the most likely amplitudes are thesmallest. That is expected for noise correspondingto normal operating conditions.

In Fig. 2c, the histogram block corresponds tounstable reactor. It can be noticed that the mostlikely amplitudes are not the highest but the low-est. It is a typical histogram for sinusoidal signals;in the case of vibrations, as a reference, particlestands longer with high amplitude because veloc-Fig. 1. Laguna Verde BWR signal (APRM).

J. Blazquez, J. Ruiz / Nuclear Engineering and Design 196 (2000) 327–336 329

Fig. 2. (a) Histogram for block 6 (stable). (b) Histogram for block 9 (transition). (c) Histogram for block 14 (unstable).


Fig. 2. (Continued)

ity is smaller there. It is remarkable that thehistogram is not symmetric but skewed to smalleramplitudes. This has been reported in the past(Blazquez et al., 1995) for a BWR/6, and it is dueto not linear behaviour of BWR oscillations. Inthis case, the kinetics equations applied to noise— not to signal —, are not linear because reactiv-ity depends on power through void fraction, so itcauses asymmetric power oscillation, a detailedexplanation is given by March-Leuba (1992).

A transition situation is plotted in Fig. 2b. Iflower amplitudes are dominant when reactor isstable, and higher amplitudes, when unstable, atransition period exists when low and high ampli-tudes are alike. A ratio of histogram relativefrequencies corresponding to low and high ampli-tudes will therefore be a simple basis for making adiscriminatory operational procedure, being moreuseful that using the skeweness for instabilityprevention.

4. Inverse kinetics

The operations causing instability were increas-ing the power by withdrawing two control rods,

and decreasing the coolant flow by closing recir-culation pumps control valves. In the operationmap, the core moved towards higher decay ratiolines and became unstable. It is interesting toanalyze how reactivity evolved, taking into ac-count the fact that the core was slightly subcriticalat the signal beginning. This is done using inversekinetics method.

As said above, the mean value power signal,P(t), comes from a fourth-order polynomial fittedto the recorded signal. If we define wR as:

wR(t)=1P

dPP

(1)

Where P is the mean power, the inverse kineticsmethod (Ackasu et al., 1971) stands for:

r(t)=wR(t)

l+wR(t)(2)

Here r is the reactivity in $. The prompt genera-tion time does not appear because the promptjump approximation is used.

Reactivity is plotted in Fig. 3. It is observedthat at signal beginning reactor was slightly sub-critical, and reactivity was decreasing as a conse-


Fig. 3. Reactivity of the Laguna Verde BWR signal (APRM).

quence of the decrease in flow and the associatedincrease in void fraction. At instant 201 s, reactiv-ity reached its minimum value; then, it increasescontinuously, being supercritical when reactorwas scrammed.

The first stage lasts �250 s; the transitionstage, up to instant 360 s, when reactivity startsgrowing; the third stage, unstable reactor, takesplace when reactivity increases as a ramp. There-fore, there is a correspondence between results ofnoise analysis, in amplitude domain, and inversekinetics.

5. Spectral analysis

The power spectral density (PSD) for theAPRM signal at normal operating conditions isplotted in Fig. 4. The interesting frequency regionlies on [0.1;1] Hz. A broad peak is observed over0.7 Hz; which means that reactor is very stable fornormal operating conditions. Several authorshave studied the spectra (Otaduy, 1977; March-Leuba, 1986); they concluded that transfer func-tion power/reactivity is explained basically withthree zeros and four poles. Two of the poles arereal, and the other one is complex conjugated.The high frequency real pole around 25 Hz lies

outside the region of interest. The low frequencyreal pole �0.3 Hz is due to heat transfer fromfuel to coolant. Complex poles are due to thechannel thermo-hydraulics: the bubbles transitiontime, which produce the broad spectral peak at0.7 Hz.

At start-up conditions, bubble transition time islonger, so the peak shifts to the left about 0.5 Hz.It is higher and sharper; meaning that reactor isless stable during start-up. A signal with only acomplex pole will exhibit oscillations; but with

Fig. 4. PSD for APRM stationary signal.


Fig. 5. (a) PSD for block 6 (stable). (b) PSD for 9 (transition).(c) PSD for 14 (unstable).

The transfer function depends on bubble transi-tion time. When this time, �2 s, is made greaterthan 10 s, the low frequency real pole cancels withone zero (Blazquez et al., 1995); hence, the trans-fer function rests only with a complex conjugatedpole pair, meaning that noise would have onlyoscillations but no fluctuations. Large bubblestransition time corresponds with small coolantflow, a condition for instability. Therefore, theorysuggests that in case of instability the real polewill be negligible against the complex pole. In-deed, it happened in the reported BWR/6 event(Blazquez and Ballestrın, 1995), and recentlyagain in Laguna Verde.

In the stable stage, the noise signal PSD isplotted in Fig. 5a; the real pole is embedded in anew complex pair peaked on 0.3 Hz. Notice thatthe operator was handling the drive flow controlvalve. In the transition stage, Fig. 5b, the real polestarts decreasing; and during the unstable stage,the real pole vanishes, Fig. 5c.

The reported BWR/6 showed one more peak inPSD: the harmonic at 1 Hz. It was an out ofphase instability case; the signal was measuredwith APRM, which averages several local rangemonitors. A detailed explanation can be found inFarawila (1998), in Fig. 6 the Cofrentes case isshown. Nevertheless, in Laguna Verde, the har-monic has small amplitude, in spite of noise signalcoming from APRM. It was concluded that thiswas a global instability case.

The stability monitoring is normally performedthrough decay ratio (DR). Acute DR calculationrequires a long stable signal, in order to calculatethe signal Fourier transform. In terms of monitor-ing, it is enough with estimating DR, becauseprecision is not required for alarming. As seenbefore, the transition stage does not last morethan 2 min; hence, any monitoring system mustquickly alarm.

In a 40-s block, the signal can be regarded asstationary, but there are only 200 points, so DR isonly estimated. It is preferable to consider these200 points as a time series and estimate the au-toregressive (AR) coefficients; impulse responseand DR are then calculated. That is the way it isdone in commercial on line DR monitoring.

only a real pole, fluctuations; and with both,fluctuations are embedded in oscillations. That isthe case when noise is analyzed during start-up;but when reactor becomes unstable, the noisepattern changes.


As an alternative, the ratio of real pole tocomplex pole PSD amplitude can be used toactivate the alarm. It is not necessary calculatingPSD for each frequency but only for two, corre-sponding to poles; therefore, computation time issaved. In Fig. 7, it is plotted this ratio for theblocks. It is observed that transition stage beginsafter block no. 7, �280 s from the signal origin.Inverse kinetics shows that on this time, the reac-tivity ramp just began. The plot discriminatesclearly stable from unstable stages.

Having in mind that the real pole vanishedduring instability, a quicker monitoring procedurecan be designed, making not necessary to calcu-late PSD. If there are not fluctuations but oscilla-tions, and the frequency is well defined, 0.5 Hz.,this means in intervals of 10 s, and the signal mustcontained five peaks. Considering a ‘coincidence’as the appearance of a maximum after 2 s, andtesting for 10 s, an alarm can be established

(Kreuter et al., 1995). The coincidence rate will below when fluctuations destroy the well defined 0.5Hz pattern; then, the reactor is stable. When thecoincidences rate is high, the reactor is unstable.

There are two problems with this approach:there is no control over fluctuations appearance,so, false alarms are expected; and the 0.5 Hzspectral pattern does not hold for out of phaseinstability event because of the 1-Hz harmonic. Asan alternative, it is easier to measure the meanfrequency on the 10-s signal. It must be around0.5 Hz still, but fluctuations — the real pole —will change this pattern; hence, when pattern isirregular, the reactor is stable; but when meanfrequency is fixed, the reactor is unstable. Theyare the same ideas, but the performance isquicker.

In Fig. 8 monitor performance is plotted. Thestable stage shows large fluctuations around themean frequency. Transition stage is not clear;frequency fluctuations are smaller. Unstable stageis recognized easily because the frequency is con-stant. This monitor would to activate alarm withthe time about 300 s. Watching the original signal,Fig. 1, one appreciate that is the time when theoperator should act for controlling instability.

6. Monitoring in the time domain

Noise analysis in the time domain is normallyperformed by fitting an AR model to recordedtime series. The Laguna Verde signal was notstationary, so it was divided into blocks of shortsintervals of 40 s. Being 0.2 s the sampling time,autocorrelation function was calculated up to 200s. AR coefficients were calculated using only pre-liminary values of autocorrelation.

The following steps are to determine how manyAR coefficients are required for a proper repre-sentation of the signal. With the monitoring pur-pose, and interested in alarming, the number ofAR coefficients would fixed to be 2. More explic-itly, blocks time series were fitted to:

xj=a1xj−1+a2xj−2+o−b1oj−1−b2oj−2 (3)

where x is the signal value at instant tj ; ai is thetwo AR coefficients; bi is the moving average

Fig. 6. PSD for Cofrentes and Laguna Verde APRM noisesignal.


Fig. 7. Amplitude ratio real/complex.

Fig. 8. Reactivity and mean frequency.


(MA) coefficients; and o is the driven Gaussianwhite noise. Coefficients were fitted followingstandard time series treatment (Box and Jenkins,1970). The reason that only two AR coefficientswere used is found in (Haykin, 1979); a puresinusoid signal plus white noise is modelled byexactly two AR coefficients and two MA coeffi-cients, being equal to the AR and MAcoefficients.

In this case, the signal is not exactly a sinusoid,but it is a good approximation when reactor isunstable. Because of signal growing amplitudes, itis contemplated that MA coefficients would bedifferent. Therefore, the stable stage would fitbadly to Eq. (3); this fit result would be accept-able for the unstable stage. The goodness of the fitcan be regarded as a test for monitoring stability.

A more elaborated monitor is based on thefollowing ideas: let x(t) be a standard oscillatoryprocess:

d2xdt2 +2zw

dxdt

+w2x=o(t) (4)

where z is the damping and v=2pf. Seen as anAR expression, Eq. (4) is transformed into:

xj+1=2+2zvDt+ (vDt)2

1+2zvDtxj+

−11+2zvDt

xj−1

+oj(Dt)2 (5)

Identifying a1 and a2, the AR coefficients, itresults:

−1a2

=1+2zwDt (6)

−a1

a2

=2+2zwDt+ (wDt)2 (7)

For oscillations a2 is always negative. Eliminat-ing the damping term from Eqs. (6) and (7):�

−1a2

�=�

−a1

a2

�− [1+ (wDt)2] (8)

Eq. (8) represents a straight line of slope unityand negative vertical axis intercept. When blocksare plotted in this particular map, Fig. 9, thestable stage is discriminated clearly from unstable.From Eq. (6) it is seen that −1/a2 grows withdamping z ; hence, stable stage corresponds tohighest points on map. A linear regression fitshows that slope is close to unity: 1.09, andintercept is negative: −0.71. This happened indefiance of the signals that were not pure oscilla-tions. Ballestrın (1996) reported a similar result inBWR/6 real instability out of phase event.

The monitor computations will be performedvery fast, because in order to obtain two ARcoefficients only the three initial values of the ARfunction are required, in contrast to spectral anal-ysis, which needs the whole function and perform-ing integrals for Fourier transform besides. Themoving average terms of the fit, Eq. (3), coulddelay the alarm, but for the sake of stable–un-stable discrimination are not essential.

7. Conclusion

A real signal of power instability event fromLaguna Verde BWR/5 starting up has been ana-lyzed. Signal was ill conditioned for noise analy-sis, this notwithstanding, three stages arediscerned: stable, transition and unstable.

In the amplitude domain, the transition stage isdetected when lower and higher noise amplitudeshave similar probability. In the frequency domain,the real pole vanishes and fluctuations becomealmost pure oscillations; the 1-Hz harmonic didnot appear. In time domain, oscillations arereflected in only two AR coefficients, enough fordiscriminating.Fig. 9. AR-map of Laguna Verde BWR signal (APRM).


All those just described alternatives do notclaim to replace traditional DR stability surveil-lance, but complement it. Thresholds require de-tailed research, mainly for those NPP withoutunstable signals recorded, but being quicker, thesealternatives stand for a safer operation one stepfurther.

Appendix A. Nomenclature

a Autoregressive coefficientb moving average coefficientf frequency (Hz)

reactor power (%Mw)P(t)xj neutron noise signal (%Mw)

signal sampling time (s)Dtone group delayed neutron precursorsl

constant (s−1)o driven Gaussian white noise (%Mw)

reactivity ($)r

2pf (s−1)v

wR inverse reactor period

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Neutron signal characterization of the power instability event at Laguna Verde BWR