Time dependence of linear stability parameters of a BWR

In this work we present several tools to study the time dependence of the linear stability parameters of a BWR using neutron noise analysis. Particularly, we have studied the variation in time of the fundamental frequency of a signal using the short-time Fourier transform and we have compared this method with the calculation of a time dependent Power Spectral Density (PSD) function. The temporal variation of the decay ratio is analysed using a method based on an autoregressive model to fit the different blocks of the signal. The performance of the tools presented is compared analysing analytic signals and a real signal of Forsmark 1&2 Stability Benchmark.     

Assessment of the Prony's method for BWR stability analysis

It is known that Boiling Water Reactors are susceptible to present power oscillations in regions of high power and low coolant flow, in the power-flow operational map. It is possible to fall in one of such instability regions during reactor startup, since both power and coolant flow are being increased but not proportionally. One other possibility for falling into those areas is the occurrence of a trip of recirculation pumps. Stability monitoring in such cases can be difficult, because the amount or quality of power signal data required for calculation of the stability key parameters may not be enough to provide reliable results in an adequate time range. In this work, the Prony's Method is presented as one complementary alternative to determine the degree of stability of a BWR, through time series data. This analysis method can provide information about decay ratio and oscillation frequency from power signals obtained during transient events. However, so far not many applications in Boiling Water Reactors operation have been reported and supported to establish the scope of using such analysis for actual transient events. This work presents first a comparison of decay ratio and frequency oscillation results obtained by Prony's method and those results obtained by the participants of the Forsmark 1 & 2 Boiling Water Reactor Stability Benchmark using diverse techniques. Then, a comparison of decay ratio and frequency oscillation results is performed for four real BWR transient event data, using Prony's method and two other techniques based on an autoregressive modeling. The four different transient signals correspond to BWR conditions from quasi-steady to power oscillations. Power signals from such transients present a challenge for stability analysis, either because of the low number of data points or need of much iteration, and thus reducing their capability for real time analysis. The results show that Prony's method can be a complementary reliable tool in determining BWR's stability degree.     

Comments on local power oscillation phenomenon at BWRs

Under the framework of BWR stability analysis, local neutron-flux oscillation events have attracted the attention of a number of researchers. In 1996, an unusual instability event occurred at Forsmark-1 in which an irregular oscillation pattern with highly localized, relatively large-amplitude oscillations were measured. Some authors assumed that this behaviour was caused by the superposition of stable spatial mode limit cycle oscillations, where the BWR core as a neutron kinetics/-thermal-hydraulic coupled system is unstable. Subsequent time-series analysis of the local power range monitor (LPRM) signals resulted in a space-dependent decay ratio, an inexplicable result. Furthermore, noise analysis-based localization techniques pointed towards the existence of two strong “perturbation sources” in one of the two halves of the core, one of them coinciding with the radial position of an unseated bundle. In the scope of theoretical work, the possibility of a space-dependent decay ratio was discussed but not comprehensively understood. Motivated by these findings, the effect of local neutron-flux oscillations on the stability behaviour of BWR is discussed, and one possible interpretation is proposed which is able to explain the space-dependent decay ratio as well as the long term oscillation pattern. The RAM–ROM method is applied to a Forsmark measurement case, where an irregular oscillation pattern was found and to an operational point (KKB-B8) of NPP Brunsbüttel, where a local neutron-flux oscillation is superimposed on an unstable global power oscillation. The effect of the local neutron flux oscillating sources on the space- and time-dependent neutron field is described by a rigorous application of the mode expansion approach. The consequences to signal analysis are then discussed. It will be pointed out in the paper that when a BWR system is stable with regards to power oscillations but is driven by local neutron-flux oscillating sources, the decay ratio does not indicate the real BWR stability behaviour.     

Decay ratio estimation based on time–frequency representations

A novel method based on bilinear time–frequency representations (TFRs) is proposed to determine the time evolution of the linear stability parameters of a boiling water reactor (BWR) using neutronic noise signals. TFRs allow us to track the instantaneous frequencies contained in a signal to estimate an instantaneous decay ratio (IDR) that closely follows the signal envelope changes in time, making the IDR a measure of local stability. In order to account for long term changes in BWR stability, the ACDR measure is introduced as the accumulated product of the local IDRs. As it is shown in this paper, the ACDR measure clearly reflects major long term changes in BWR stability. Last to validate our method, synthetic and real neutronic signals were used. The methodology was tested on the Laguna Verde Unit 1, two events were reported in the Forsmark stability benchmark.     

Development of Reactor Noise Monitor

A reactor noise monitor has been developed to provide a tool that serves the real time routine function of detecting anomalous states of operation in power reactors. In this monitor, RMS (root mean square) values and average frequencies of noise signals are calculated on a real time basis. The average frequency is defined as the frequency averaged by weighting with PSD (power spectral density) of the noise signal and proved to be equivalent to the ratio of an RMS value of the differentiated noise signal to an RMS value of the noise signal itself. Thus, the average frequency can be obtained on a real time basis by using a differentiator, an RMS calculator and a divider. The frequency components of 12 kinds of signals ranging of 0.01–36 Hz are divided into two or three frequency regions by band-pass filters and the RMS value and the average frequency of each frequency region are obtained by the digital calculation method. The performance of this monitor was tested by using a simulated anomalous signal with a peak on its PSD. From the test, it is proved that this monitor can detect more than changes of the RMS value and average frequency. The functions of this monitor were also confirmed at the actual BWR power plant.

In addition, a method to detect peak location of PSD is developed and the accuracy of the peak frequency measurement of the proposed method is investigated to be satisfactory.     

Detecting long-range correlation with detrended fluctuation analysis: Application to BWR stability

The aim of this paper is to explore the application of detrended fluctuation analysis (DFA) to study boiling water reactor stability. DFA is a scaling method commonly used for detecting long-range correlations in non-stationary time series. This method is based on the random walk theory and was applied to neutronic power signal of Forsmark stability benchmark. Our results shows that the scaling properties breakdown during unstable oscillations.     

BWR core-wide stability analysis with respect to dominant feedback mechanisms and characteristic poles

BWR core-wide stability is studied from the viewpoint of linear dynamic stability treated via poles of a closed-loop transfer function. The quantitative study is performed using a BWR noise model describing neutronic and thermal-hydraulic core dynamics. Transfer functions of neutron power to reactivity and core inlet flow are derived in explicit forms and their poles are evaluated both numerically and analytically. It is shown that the characteristic poles may be classed into three groups relating to neutronic process, fuel heat transfer and core void dynamics. In particular, the poles for the void dynamics take complex values and hence give rise to core-wide damped oscillation of neutron power. Furthermore, the study of characteristic poles serves for the stability analysis of the Ringhals-1 benchmark test data. It is shown and clarified that two stability indexes, decay ratio and resonance frequency, have clear dependence on reactor power and core inlet flow.     

Characterization of the new scintillator Cs_2LiYCl_6:Ce~(3+)

The first domestic inorganic scintillator, Cs_2LiYCl_6:Ce~(3+)(CLYC), was grown at Beijing Glass Research Institute using the vertical Bridgman method. In this work, we evaluated the performance of this new CLYC crystal in terms of its gamma-ray energy resolution and pulse shape discrimination(PSD) capability between neutrons and gamma rays. The decay times associated with different scintillation mechanisms were obtained by fitting decay functions to the neutron and gamma-ray waveform structures. We found an energy resolution of * 4.5% for 662-ke V gamma rays and efficient neutron/gamma PSD with a figure of merit of * 2.6. Under gamma-ray excitation, there is an ultrafast scintillation mechanism in CLYC with a decay time of approximately 2 ns, whereas there is no evidence of ultrafast decay under thermal neutron excitation. This work contributes to the promotion of domestic development of CLYC.     

Wavelet approach for analysis of neutronic power using data of Ringhals stability benchmark

We have studied neutronic power oscillation in a boiling water nuclear reactor for three different scenarios of the Ringhals stability benchmark with a proposed wavelets-based method: the first scenario is a stable operating state which was considered as a base case in this study, and the last two correspond to unstable operating conditions of in-phase and out-of-phase events. The results obtained with the methodology presented here suggest that a wavelet-based method can help the understanding and monitoring of the power dynamics in boiling water nuclear reactors. The stability parameters frequency and decay ratio were calculated as a function of time, based on the theory of wavelet ridges. This method allows us to analyze both stationary and highly non-stationary signals. The resonant frequencies of the oscillation are consistent with previous measurements or calculated values.     

Remark on the role of the driving force in BWR instability: In memory of George Kosály 1933–2009

Simple models of BWR instability, used e.g. in understanding the role of the various oscillation modes in the overall stability of the plant, assume that each oscillation mode can be described by a second order system (a damped harmonic oscillator) driven by a white noise driving force. Change of the decay ratio (DR) of the observed signal is, as a rule, associated with the changing of the parameters of the damped oscillator, mainly its damping coefficient, and is interpreted in terms of the change of the stability of the system. However, conceptually, one cannot exclude cases when the change of the response of a driven damped oscillator is due to the change of the properties of the driving force. In this work we investigate the effect of a non-white driving force on the behaviour of the system. A question of interest is how changes of the spectrum of the driving force influence the observed autocorrelation function (ACF) of the resulting signal. Hence we calculate the response of a damped harmonic oscillator driven by a non-white driving force, corresponding to the reactivity effect of propagating density fluctuations in two-phase flow. It is shown how in some special cases such a driving force, when interpreting the neutron noise as if induced by a white noise driving source, can lead to an erroneous conclusion regarding the stability of the system. It is also concluded that in the practically interesting cases the effect of the coloured driving force, arising from propagating density fluctuations, is negligible.     

Multivariate Empirical Mode Decomposition applied to the estimation of the decay ratio and out-of-phase oscillations in BWRs

This work presents a novel method based on the Multivariate Empirical Mode Decomposition (MEMD) to estimate the Decay Ratio (DR) and the apparition of a possible out-of-phase oscillation in Boiling Water Reactors (BWRs). The MEMD algorithm, have the potential to find common oscillatory modes within multivariate data called Intrisic Mode Functions (IMF). Based on this fact, we implement the MEMD technique to find the common oscillatory mode (density wave) in BWRs considering the measurements obtained in each Local Power Range Monitor (LPRM) through the entire core. These IMFs, analyzed simultaneously in time, permit to obtain an estimation of the DR and; also give some considerations about an incipient out-of-phase oscillation through the phase measured between two specific LPRMs. Effectiveness of the proposed method is demonstrated on a specific challenging case from the Forsmark stability benchmark.     

Analysis of a BWR Stability Behavior using Generalized Discrete Shannon Functions. Application to Ringhals and Forsmark Benchmarks Data

In this paper we have introduced a new methodology to on-line signal conditioning and monitoring to determine the stability parameters of the BWR NPP, that is, the determination of the effective Decay Ratio DR and the frequency of the main oscillation causing instability events. This method is based on the generalized discrete Shannon function convolution, which removes the noise and filters the signal in a specified frequency band. We have focused our attention in noise signals, first on analytic ones to check how the algorithm works, and then we have tested it with some real neutron signals. The algorithm works very well with dirty real signals providing good results, even in the case of short time series. Main attemption has been focused on decomposing signals to detect when a global and/or a regional oscillations are taking place in a BWR. This methodology can be implemented in on-line monitors to determine the stability parameters of the BWR reactors, that is, the determination of the effective decay ratio (DR) and the frequency of the main oscillation causing instability events.     

Measurement of large negative reactivity of an accelerator-driven system in the Kyoto University Critical Assembly

Large negative reactivity of a subcritical system driven by a pulsed 14 MeV neutron source has been measured in the Kyoto University Critical Assembly. The subcriticality of the accelerator-driven system (ADS) ranged in effective multiplication factor roughly from 0.98 to 0.92, which corresponded to an operational range of an actual ADS proposed by Japan Atomic Energy Agency. As the measurement technique, pulsed neutron method, power spectral analysis for pulsed neutron source, accelerator-beam trip method were employed. From neutron count decay data obtained by the pulsed neutron experiment, not only the prompt-neutron decay constant of fundamental mode but also a higher spatial mode could be derived. The subcriticality was also determined from the fundamental decay constant. The measured cross-power spectral density consisted of a familiar correlated reactor-noise component and many uncorrelated delta-function-like peaks at the integral multiple of pulse repetition frequency. The fundamental prompt-neutron decay constant, i.e., the subcriticality determined from the latter uncorrelated peaks was consistent with that obtained by the above pulsed neutron experiment. However, the magnitude of the former correlated component was reduced with an increase in the subcriticality and eventually this component became almost white at deeply subcritical state ranging in the multiplication factor under 0.95. Consequently, the determination of the decay constant from the correlated component was impossible under such a subcritical state. As data analysis method for the beam trip experiment, both the conventional integral count method and the least-squares inverse kinetics method (LSIKM) were employed. The LSIKM analysis led to the consistent subcriticality with that obtained by the pulsed neutron experiment, while the integral count method significantly underestimated the subcriticality. This underestimation originated from a residual background count, which was maintained after the beam trip. The LSIKM was mostly not influenced by such a slight count rate.     

252Cf随机脉冲源方法测量球形钚系统瞬发中子衰减常数

²⁵²Cf随机脉冲源方法由早期的重复脉冲源方法演变而来,是测量核系统瞬发中子衰减常数α的有效方法。采用该方法测量了钚球装配31 mm、29 mm厚钢反射层核系统的α,在有效信号和噪声的比例为1∶1的情况下,得到的瞬发中子衰减谱信噪比为7∶1,最小二乘拟合结果依次为2.25 μs^-1和3.00 μs^-1,拟合误差为±0.02 μs^-1。与Rossiα方法的测量结果进行了比较,两种测量方法的结果差异小于1.3%。     

On the possibility of the space-dependence of the stability indicator (decay ratio) of a BWR

A model is proposed for the explanation of the space-dependence of the so-called decay ratio (DR) which is used to quantify the stability properties of boiling water reactors (BWRs). The study was prompted by the observation of a strongly space-dependent decay ratio in an instability event at the Swedish Forsmark-1 BWR. Prior to that event, the space-dependence of the DR was neither observed, nor assumed possible in the theoretical models of instability.The model proposed here is based on a previous suggestion by one of the authors on how to model the estimation of the DR in case of two different types of oscillations (instabilities) being present in the core simultaneously. The model was earlier only used in a space-independent form, but here its applicability is extended such that space-dependence of the oscillations is also accounted for, by using a noise simulator. The investigations show that the DR, as determined by the individual LPRMs (neutron detectors) at different positions, can be strongly space-dependent if at least two different oscillations with differing DR and space-dependence exist in the core simultaneously. The observed space-dependence of the DR in the Forsmark case can be reconstructed by the model.     

Application of Polarity Correlation Method to Graphite Moderated Reactor

The polarity correlation method has been applied to an experiment for measuring the prompt mode neutron decay constant of a reactor with a long neutron lifetime. Measurements have been performed in the SHE VIII-l at critical and several subcritical steady states (0~ — 1$).

The analog signal of detector output is converted to a polarity signal having only one-bit of information on the amplitude of the detected signal. The polarity correlation function is obtained as the correlation function between two polarity signals. Attention has been paid in the design of the correlator to obtain ample stability in operation. Using a digital computer, the prompt mode neutron decay constant is determined with 2% experimental accuracy from the decay curve of the polarity correlation function. A series of the prompt mode neutron decay constants is fitted to an approximated expression of inhour equation to obtain βl. The value of each prompt mode neutron decay constant was found to be in good agreement with that measured by the pulsed neutron technique. The polarity correlation method is particularly applicable to critical or near critical state where a pulsed neutron source cannot be effectively introduced.

In Appendix, an estimation is made for the error in the measured polarity correlation function due to unbalanced mean setting level in the experiment.     

Pulsed neutron source measurements in the subcritical ADS experiment YALINA-Booster

A subcritical zero-power source-driven coupled core, the YALINA-Booster, has been constructed for experimental investigations of neutron kinetics of source-driven systems. In this study, the reactivity of two subcritical configurations has been determined by the area ratio method. The prompt neutron decay constants have been evaluated through slope fitting of the prompt neutron decay as well as through the pulsed Rossi-α method. It is shown that the slope fitting method and the pulsed Rossi-α method give stable results whereas the area ratio method results show spatial dependence. The reasons for the spatial spread are addressed.     

Measurement of kinetic parameters in the fast subcritical core MASURCA

In the MUSE shared cost action of the European Fifth Framework Program measurements have been performed to investigate the neutronic behavior of the fast subcritical core MASURCA coupled with the GENEPI accelerator. The aim is to examine the applicability of different measurement techniques for the determination of the main kinetic parameters. The measurement of Rossi-alpha distributions, recorded with the accelerator turned off, showed that the analysis of the obtained distributions is feasible for deep subcritical levels, but with strongly deteriorated statistics. From Rossi-alpha distributions, recorded with the pulsed neutron source in operation, the alpha decay constant was easily derived due to good statistics on the correlated signal resulting from the strong intensity of the neutron pulse. When applying the pulsed neutron source analysis, the reactivity (in dollars) together with the ratio of the mean neutron lifetime l and the effective delayed neutron fraction β_eff is immediately derived. Although these first results are very promising, further measurements are needed to qualify the method at larger subcritical levels which are representative for future ADS.     

Power spectral analysis for a thermal subcritical reactor system driven by a pulsed 14 MeV neutron source

A series of power spectral analyses for a thermal subcritical reactor system driven by a pulsed 14 MeV neutron source was carried out at Kyoto University Critical Assembly (KUCA), to determine the prompt-neutron decay constant of the accelerator-driven system (ADS). The cross-power spectral density between time-sequence signal data of two neutron detectors was composed of a familiar continuous reactor noise component and many delta-function-like peaks at the integral multiple of pulse repetition frequency. The prompt-neutron decay constant inferred from the reactor noise component of the cross-power spectral density was consistent with that obtained by a pulsed neutron experiment. However, the reactor noise component of the auto-power spectral density of each detector was hidden by a white chamber noise in the higher-frequency range and this feature resulted in a considerable underestimation of the decay constant. For several runs with a low pulse-repetition frequency, furthermore, we attempted to infer the decay constant from point data of the delta-function-like peaks. The analysis for a run under a slightly subcritical state resulted in the consistent decay constant; however, those for other runs under significantly subcritical states underestimated the decay constant. Considering the contribution of a spatially higher mode to the point data, the above underestimation was solved to obtain the consistent decay constant. While the Feynman-α formula for a pulsed neutron source is too complicated to be fitted directly to variance-to-mean ratio data, the present analysis on frequency domain is much simpler and the conventional formula based on the first-order reactor transfer function is available for fitting to power spectral density data.     

Determination of prompt-neutron decay constant from phase shift between beam current and neutron detection signals for an accelerator-driven system in the Kyoto University Critical Assembly

A unique power spectral analysis for a subcritical reactor system driven by a pulsed 14 MeV neutron source was carried out at the Kyoto University Critical Assembly (KUCA). In this analysis, a complex cross-power spectral density between time-sequence signal data from an accelerator beam ammeter and a neutron detector was measured to determine the prompt-neutron decay constant of an accelerator-driven system (ADS) from the phase data of the spectral density. Assuming the one-point kinetics model, in theory, the decay constant can be arithmetically derived from the phase at the integral multiples of the pulse repetition frequency. However, the actual derivation from the phase at a pulse repetition frequency of 20 Hz considerably underestimated the prompt-neutron decay constant, compared with that obtained by a previous pulsed neutron experiment, and the derived decay constant apparently decreased with an increase in the multiple of the pulsed repetition frequency. Considering a lag time in detector response, the above underestimation and the above apparent decrease were solved to obtain the consistent decay constant. While both previous power spectral analysis and Feynman-α analysis for pulsed neutron source require non-linear least-squares fits of the respective complicated formulae, the present analysis makes the fitting unnecessary except at regular calibration of the lag time. This feature is advantageous for a robust online monitoring of subcritical reactivity of an actual ADS.