CN112509716A - Reactor three-dimensional power probability distribution monitoring method based on information fusion theory - Google Patents
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Abstract
The invention provides a reactor three-dimensional power probability distribution monitoring method based on an information fusion theory, which comprises the following steps: evaluating uncertainty of the measurement information; determining detector information to be employed based on the monitored dynamic or steady state requirements; estimating the power distribution state of the reactor based on a Bayesian method; performing probability estimation of reactor core burnup distribution; and updating the probability of the core burnup distribution and estimating the performance of the fuel rod in real time. The method explores a detection information fusion method with different angles and different accuracies, based on a Bayesian framework, reduces information loss as much as possible, and solves the problem of matching measurement of different angles and different accuracies, so that spatial distribution information with higher accuracy is obtained, probability distribution of power values of any spatial point of a reactor core is provided, and further probability distribution of burnup values of any spatial point of the reactor core is provided.
Description
Technical Field
The invention belongs to the field of nuclear reactor operation monitoring, and particularly relates to a reactor three-dimensional power probability distribution monitoring method based on an information fusion theory.
Background
The core of reactor core condition monitoring is reactivity and power distribution monitoring. The reactivity change is reflected as a change in the overall power level to reflect critical safety. And the spatial power distribution change is one of the main causes of the thermal safety problem. Various sensor systems are typically deployed to measure core power distribution, including: (1) the reactor core movable detector system (MID) mentioned in "power distribution measurement of reactor core in gulf of the great asia nuclear power plant and processing thereof [ D ] (nuclear science and engineering, 1997(17)) is a measurement technology with highest precision in the prior art, in which a detector normally arranged outside a reactor is moved to the inside of the reactor for measurement and then moved out of the reactor core through a transmission device. The defect is that only periodic off-line measurement can be carried out, and real-time monitoring cannot be carried out; (2) in-reactor fixed self-powered neutron Detector Systems (FIDs) such as rhodium Rh, vanadium V, cobalt Co, and the like, which are arranged in a pressurized water reactor, mentioned in study of neutron detector response function characteristics in pressurized water reactor [ J ] (atomic scientific technology, 2019), by aqua regia et al, can continuously monitor changes in power distribution; (3) a reactor core inlet and outlet temperature measurement system (T/C) mentioned in study [ J ] of digitized modification schemes of reactor core cooling monitoring systems of pressurized water reactor nuclear power plants (nuclear science and engineering, 2012) by leigan et al measures changes in a fluid temperature field in a reactor core caused by power distribution; (4) the ex-core fixed neutron detector system (EXCORE) mentioned in AP1000 and VVER1000 ex-core nuclear measurement system design philosophy analysis [ J ] (Nuclear electronics and detection technology, 2014,34(5):671-4.) by Tangzhongming et al characterizes the response of neutron leakage from the edge component region out of the pressure vessel, and the axial information thereof characterizes the axial power information of the core edge component.
As shown in fig. 1, a reactor core containing fuel assemblies is deployed in a steel pressure vessel, and coolant flows in from the inlet of the loop, flows down the wall, enters the lower part of the core, takes away core heat in the axial height direction of the core, increases in temperature, and then enters the outlet of the loop to enter the heat exchanger for heat exchange. Therefore, from the viewpoint of temperature monitoring of the coolant, a large number of thermocouples are arranged at the loop inlet, the loop outlet and the core outlet. From the neutron detection perspective, a fixed off-core neutron detector system (EXCORE) is deployed at four quadrant angles outside the pressure vessel, a fixed in-core self-powered neutron detector system (FID) is deployed at a plurality of positions inside the reactor core, some reactors still deploy some movable detector systems (MID), the non-measurement time is deployed outside the reactor core, and the non-measurement time is along a pressure finger sleeve during measurement, enters the reactor core and is measured and then returns to the outside of the pressure vessel.
Due to the characteristics of the reaction mechanism of the detector, the discreteness of the sensitivity of the detector, the burnup of the detector material, the drift of the system and the like, the detector has different types of measurement errors. The existing reactor monitoring means all depend on the most accurate detector result as a reference, and periodically calibrate other measuring hardware according to the most accurate detector result. For example, although the MID cannot realize the on-line monitoring of the reactor, when the FID is deployed, the FID is calibrated according to the result of the MID, and then the continuous monitoring of the specific parameter is realized through the FID; and when no FID is deployed, monitoring of other specific parameters is realized by calibrating an EXCORE (for example, a method for calibrating a nuclear reactor out-of-core detector CN105006262B disclosed by the Chinese patent invention) and a T/C (for example, a method for calibrating a nuclear reactor core outlet thermocouple CN105895175B disclosed by the Chinese patent invention).
The detectors are reasonably arranged, but only can cover part of the reactor core, and the measurement information of the whole reactor position needs to be reconstructed. There have been a lot of works for performing three-dimensional or two-dimensional power distribution reconstruction for MID or FID, and the like, and the adopted methods are roughly divided into: (1) reconstruction is achieved under least square directly based on detector readings, coupled neutron diffusion and its higher order decomposition features. Such as harmonic expansion method, harmonic synthesis method, coupling coefficient method, intrinsic orthogonal decomposition method to combine the physical characteristics of the reactor; (2) optimal spatial interpolation based on reference power distribution. Such as polynomial expansion and thin-plate spline function fitting methods, geostatistical kriging interpolation methods, least squares support vector machine methods, radial basis function interpolation methods; (3) data assimilation methods, such as three-dimensional variational optimization method and its variation Kalman filtering, Bayesian inference method, etc.
The existing power distribution monitoring technology has the following problems:
(1) a large amount of probe information is not fused sufficiently efficiently. Different detectors information different sides of the reactor core state. From the point of view of information theory, the power distribution reconstruction only through MID or FID causes a lack of information utilization.
(2) The power uncertainty at any point in space cannot be determined. The current power distribution state can be effectively estimated through the MID/FID, but the current power distribution state is only a single 'best guess' which can occur, and cannot be expressed as probability space information in terms of probability. And the uncertainty evaluation of the peak value factor in the prior art is difficult to expand to any position of the whole pile. Further, the uncertainty of the burn-up distribution of the power distribution accumulation cannot be measured.
(3) The effect of detector failure on power uncertainty cannot be quantified. In the CPR unit operation technical specification, F is the reactor core flux map under the condition that the effective measuring channels are not less than 40dh、FqThe conservative uncertainty is 4% and 5%, respectively. However, in nuclear power plants such as gulf of great asia, south australia, yangjiang, urban defense and the like, the actual number of channels is lower than 40 due to blockage of the channels caused by probe jamming and the like, and at the moment, the influence of reduction of the number of channels is demonstrated due to the fact that a perfect theoretical framework is not provided, so that a more conservative operation strategy is caused, and the economy is sacrificed.
(4) The effect of detector uncertainty changes on power uncertainty cannot be quantified in real time. The FID accuracy decreases with longer service time, the T/C decreases with decreasing power level, etc. need to be considered.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a reactor three-dimensional power probability distribution monitoring method based on an information fusion theory.
The technical scheme adopted by the invention is as follows:
the reactor three-dimensional power probability distribution monitoring method based on the information fusion theory comprises the following steps:
s1, evaluating the uncertainty of the measurement information;
s2, determining the detector information to be adopted based on the monitored dynamic or steady-state requirements;
s3, estimating the reactor power distribution state based on a Bayes method, firstly estimating the power value and the uncertainty of the single type of detector, and then fusing the power values and the uncertainty of the different types of detectors based on a Bayes principle to obtain the final optimal power value and the uncertainty thereof.
Further, when the probe is a movable probe (MID), the uncertainty of the measurement information includes: repeatedly measuring uncertainty caused by a signal generating mechanism, uncertainty introduced by the change of the core state in the measuring process, uncertainty of mutual calibration of probes and uncertainty of alignment of the axial grillwork; when the detector is an in-pile self-powered neutron detector (FID), evaluating the precision of the detector by comparing the relative error of the FID current predicted by theory and the FID current measured; when the detector is a reactor core thermocouple, the stability of the ratio of the enthalpy rise of the coolant channel under different power steps to the integral power of the corresponding fuel assembly under the full-operation working condition is compared, and the accuracy of the thermocouple is evaluated; and when the detector is an extra-reactor fixed neutron detector (EXCORE), comparing the difference between the normalized current distribution represented by the extra-reactor detector and the theoretically normalized current distribution after the three-dimensional power distribution in the reactor core and the weight of the detector response matrix, and evaluating the precision of the extra-reactor detector.
Further, the determining the probe information to be adopted based on the monitored dynamic or steady-state demand in step S2 specifically includes:
during the steady state estimation of the reactor, the background power distribution under the current reactor state and the measurement values of various detectors need to be adopted;
and determining the detector information to be adopted according to different monitoring directions during the dynamic estimation of the reactor.
Further, the determining the detector information to be adopted according to the difference of the monitoring directions specifically includes:
when the working condition of the reactor only needs to carry out axial power distribution monitoring, an EXCORE measured value and background soft measurement are selected;
when the working condition of the reactor only needs to carry out radial power distribution monitoring, selecting a T/C measured value and a background soft measured value;
when monitoring the three-dimensional power distribution, the FID, T/C, EXCORE, and background soft measurements are selected.
Further, the weight influence factor w of the ith detector of the jth type on the (x, y, z) positioni,jIncluding a close range weight K1 and a precision weight K2, i.e., wiK1 × K2, wherein,
or
Is (x)i,yi,zi) A distance from (x, y, z), where p represents the order, α is a distance coefficient,
c is a normalization coefficient, N is the number of detectors, sigmaiDenoted as uncertainty of the ith detector.
Further, the estimating of the power value of the single-type detector and the uncertainty thereof in step S3 includes:
for a particular j-th detector type, there is NjA detector, j MID, FID, EXCORE, T/C, for any position (x, y, z) in three-dimensional space in the reactor, and its measured power value obtained by using the j-th type detector measurement information
Comprises the following steps:
wherein, wi,jExpressed as the weight influence factor of the (x, y, z) position of the ith detector pair of the jth type,
for the position (x) of the ith detector of the jth typei,yi,zi) Measured signal value of pref(x, y, z) is the theoretical predicted power value at the (x, y, z) position, Iref(xi,yi,zi) Is to xi,yi,ziTheoretical predicted current signal values for the j-th type of detector at the location;
uncertainty of power value at (x, y, z) according to error propagation theory
Comprises the following steps:
wherein the content of the first and second substances,
are all deterministic coefficients.
Further, the final optimal power value and the uncertainty thereof in step S3 specifically include:
the fusion is carried out according to the naive Bayes principle, and comprises the following steps:
wherein p ismes(x, y, z) and σmesAnd (x, y, z) is the power value and the uncertainty thereof which are obtained by fusing the power values and the uncertainties estimated by the various detectors and are the best estimated power values and the uncertainty thereof.
Further, after step S3, the method further includes the following steps:
step S4: performing probability estimation on the burnup distribution of the reactor core;
step S5: and updating the probability of the core burnup distribution and estimating the performance of the fuel rod in real time.
Further, the performing probability estimation on the burnup distribution of the reactor core in step S4 includes estimating a burnup value and an uncertainty thereof at any position of the three-dimensional reactor space distribution, specifically:
for a certain point (x, y, z) in the reactor space, its burnup value But(x, y, z) is the integral of the power values at all operating moments, i.e.:
wherein the content of the first and second substances,
an estimate of the power value at the reactor core (x, y, z) position at time t;
assuming that the power values at the (x, y, z) positions at the two previous and next time instants are independent of each other, there are:
wherein
I.e., the uncertainty of the burnup estimate of the reactor core (x, y, z) position at time t, and
the uncertainty of the estimated value of the power at the position of the reactor core (x, y, z) at time t.
Further, the updating the probability of the core burnup distribution in step S5 to estimate the fuel rod performance in real time specifically includes:
real-time acquisition
And
to update the fuel consumption value and its uncertainty;
and (4) taking the updated burnup value and the uncertainty thereof as the real-time input of the fuel rod performance analysis software, so that the fuel rod performance of any one point in the reactor space can be obtained in real time.
Compared with the prior art, the invention can realize the following beneficial effects:
(1) the invention can obtain information with higher reliability by fusing the measurement information of the detectors with different types and different precisions arranged at different positions, and establishes a power distribution measurement method system with rich information and high precision under local scale;
(2) the original technology mainly adopts a measuring means with higher precision, for example, the measuring precision of the MID is higher than that of the FID, the EXCORE or the T/C, and the estimated value of the MID is mainly collected and informed no matter whether the subsequent consistency check is passed or not. And the consistency test is to judge whether the estimated value of the FID/EXTORE/TC is consistent with the MID or not, and when the estimated value of the FID/EXTORE/TC is within a 95-95% confidence interval of the measurement of the MID, the measurement of the EXTORE/TC and the MID is considered to be consistent. When the inconsistency occurs, the operation prompt or warning function is mainly used, and the power plant operator or the existing operation support system enters the corresponding processing program. However, the main control or information system still mainly uses the measurement result of the MID as the basis for measurement and control, so that other types of detector information such as FID \ exocore \ TC and the like are indirectly abandoned. In the application, various detectors are comprehensively considered, the utilization of the information is reduced, and the measurement information of the various detectors is fully fused based on the Bayesian framework, so that the error is reduced, and the subsequent estimation is more accurate.
(3) Compared with other methods, the method can obtain the power value and the uncertainty of the power value at any point in the reactor core space. When the power value and the uncertainty of each position are obtained, the uncertainty additionally introduced by the existing conservative safety analysis method can be reduced, so that the operation space and the operation flexibility are released, and the potential economy is further improved. For example, when the power peak value and the uncertainty of each position are obtained, various potential safety accidents can be analyzed in real time from a certain probability state of each potential power distribution of the reactor, and the safety margin of the current operation state under the accident occurrence condition is demonstrated, so that a safety analysis methodology based on actual measurement power distribution-power peak value-assumed conservative distribution is replaced, and the improvement of the power margin is realized.
(4) The present invention also makes it possible to obtain the fuel consumption value of each fuel assembly and its uncertainty. When the power value and its uncertainty at each position are obtained, the burnup value (including the change in nuclear density) and its uncertainty of each fuel assembly can be obtained by the power accumulation effect. When the behavior of the fuel rod under the current cycle is analyzed, the operation condition of the fuel rod is input, the best fuel consumption estimated value and the uncertainty thereof which are as accurate as possible can be used, and the traditional conservative fuel consumption peak value based on the power peak value is not used as the input, so that the performance evaluation of the worst fuel rod in the reactor core is more accurate, and the introduction of an overlarge penalty factor is avoided, thereby releasing the safety margin; when the burnup value and the uncertainty of the burnup value of each position are obtained, more economical and efficient reactor components can be rearranged in the refueling process of the reactor. In the general refueling process, part of fuel assemblies need to be unloaded, part of fuel assemblies remain, and part of fuel assemblies need to be newly added. In the prior art, the fuel consumption value of each fuel assembly is usually determined based on offline theoretical calculation, and has a large difference with the actual reactor operation state. The invention can accurately measure the burnup value and the uncertainty of each fuel assembly of the reactor, and can effectively evaluate the service performance of the fuel assembly, including value-added characteristics and the like. Compared with an off-line theoretical fuel consumption value, the fuel changing process based on the optimal estimated fuel consumption value is more reasonable and efficient, the number of newly added fuel assemblies (about 1000 ten thousand for a group of fuel assemblies) is effectively reduced, the fuel assemblies are arranged to meet the requirement of flattening power, so that the safety is improved, the residual reactivity of the fuel assemblies is fully utilized, the operation fuel changing period is prolonged, and the economy is improved.
(4) According to the invention, the uncertainty of the power value at the position (x, y, z) is established according to an error propagation theory, so that the uncertainty related to the power value of each position can be obtained, the influence of detector failure on the probability distribution of power distribution can be quantified in real time, and the influence of the uncertainty change of the detector on the uncertainty of the power value can be quantified in real time when the uncertainty of the detector changes due to the introduction of the uncertainty of the detector in the uncertainty expression.
Drawings
Fig. 1 is a schematic diagram of a reactor according to the prior art.
Fig. 2 is a flowchart of a monitoring method in the present embodiment.
FIG. 3 is a flow chart of the reactor static and dynamic monitoring in this embodiment.
Fig. 4 is a schematic diagram of bayesian information fusion in the present embodiment.
In fig. 1, a pressure vessel 01, a reactor core 02, a fuel assembly 03, a movable detector system 04, a pressure thimble 05, an in-core self-powered neutron detector system 06, a core exit location 07, an out-of-core neutron detector system 06, a loop inlet 09, and a loop outlet 10.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
Step 1: and evaluating uncertainty of the measurement information.
Weight w of influence of detector on power valueiThe power value is determined. And wiIs related in part to the uncertainty evaluation of the measurement information of all detectors. For this reason, the uncertainty of each position detector of each type needs to be quantitatively evaluated. The resulting uncertainty in the power value is also related to the uncertainty in the information for each detector, for which reason the uncertainty for each detector also needs to be evaluated.
One of the main challenges of reactor state estimation is noise interference, a signal that is random (unpredictable) and does not carry useful information. Due to noise, any measurement of a physical quantity is uncertain, the degree of uncertainty of which is usually expressed in 95% -95% confidence intervals of the probability distribution.
Taking MID of the CPR unit as an example, the uncertainty of the measurement information mainly includes: repeated measurement uncertainty caused by a signal generation mechanism, uncertainty introduced by the change of the core state in the measurement process, uncertainty of mutual calibration of the probes, uncertainty of alignment of the axial grids and the like are obtained by analyzing a large amount of repeated detection channel or probe redundant data. By analyzing the operating data of the nuclear power plant and finally determining the measurement uncertainty of a movable detector (MID) as sigmaMIDAnd is the same at all reactor measurement locations.
The calibration of the detector and the mutual calibration of the reactor measurement signals generally realize that the average errors a1 and a3 are small and can be approximately ignored, and particularly, the power value in the invention refers to the normalized power distribution (the average value is equal to 1.0), so the measurement involved in the process of the invention is generally unbiased. Under unbiased conditions, the upper limit of the 95% -95% confidence interval [ -U, U ] is: u-k σ, where σ is the standard deviation of the error, and k is determined by the size of the sample size, typically 1.96. Therefore, in the present invention, the uncertainty U is proportional to the standard deviation σ of the error under unbiased conditions, and therefore U and σ can be replaced almost equally in the expression or calculation formula, and for this reason, the uncertainty in the present invention is substantially identical in meaning to the standard deviation of the error.
It should be added that, in order to ensure the conservation of nuclear power operation, for the case where there is a deviation μ, the uncertainty may be U ═ μ | + k σ, and the application scenarios in the present invention are few, and the present invention is not described in detail.
Because it is difficult to directly assess the uncertainty if the FID is fixed in the reactor, the detector accuracy can be evaluated against the relative error of the theoretically predicted FID current and the measured FID current. Based on two considerations: (1) determining that the core design software can effectively predict the FID current, i.e., the prediction model is consistent with the measurement process (2) the FID measurement accuracy can be conservatively estimated. Generally speaking, FIDs of different geometries have different measurement accuracies, with longer FIDs having less uncertainty than shorter FIDs; its measurement uncertainty increases significantly as the FID burn-up increases. In general, the standard deviation a5 of the conservative measurement error for different FIDs ranges from about 1.5% to about 4.5%.
The higher the accuracy of the detector, the less its uncertainty.
Theoretical prediction of FID current and measurement of FID current
In the case of a large number of statistical differences, the average of the deviations is
The standard deviation of the deviation is:
when the detector is a reactor core thermocouple, the stability of the ratio of the enthalpy rise of the coolant channel under different power steps to the integral power of the corresponding fuel assembly under the full-operation working condition is compared, and the accuracy of the thermocouple is evaluated. The outlet thermocouple is arranged at the center of the top of the fuel assembly, the inlet thermocouple is arranged at the inlet of the loop, and the measured fluid temperature is converted into enthalpy rise of the fluid channel, so that the axial integral power of the assembly is represented. T/C measurement uncertainty refers to the degree of change in the ratio of component power characterized by its enthalpy rise to the real component power (measured by the MID). The more stable (evaluable) the ratio, the less uncertainty in the T/C measurement. It is mainly affected by the core power level: (1) the increase of the self measurement accuracy error caused by the power reduction (2) the uncertainty caused by the flow field change of the transverse water flow mixing under low power. The uncertainty of the method is approximately as follows along with the change of the reactor core power P:
where a is the standard deviation of error at full power and b is the coefficient. And analyzing and obtaining the values of a and b according to the measured data of a large number of operation of the power plant in Australia Ridges. T/C uncertainty σT/CFor the assessment, reference is made to patent CN 105895175A, "a method for calibrating a thermocouple at the outlet of a nuclear reactor core", generally associated with operating power conditions of T/C, generally a < 1%, b < 4.5%.
And when the detector is an extra-reactor fixed neutron detector (EXCORE), comparing the difference between the normalized current distribution represented by the extra-reactor detector and the theoretically normalized current distribution after the three-dimensional power distribution in the reactor core and the weight of the detector response matrix, and evaluating the precision of the extra-reactor detector. The CPR unit is provided with six sections of sensitive sections in the axial direction of the out-of-pile detector, while the three-generation pressurized water reactor is generally provided with only an upper sensitive section and a lower sensitive section, and can only represent the axial power deviation AO of the reactor core as (UP-DW)/(UP + DW) 100%, wherein UP and DW respectively represent the measured values of the upper section and the lower section. The weighting of the axial power of the reactor core edge assembly and the current weighting of the reactor outside detector have a linear relation, and the linear coefficient is not changed along with the change of the reactor core fuel consumption or the refueling circulation. The linear coefficients need to be updated if and only if an out-of-stack detector replacement occurs.
Uncertainty of the EXCORE σEXCOREFor the evaluation, reference is made to patent CN105006262A "a method for calibrating a nuclear reactor detector outside the reactor. Error standard deviation sigma for characterizing core edge assembly power weighted distribution by using core axial distribution of out-of-core detectorEXCORE＜1％。
Step 2: the detector information to be employed is determined based on the monitored dynamic or steady state requirements.
When the reactor is operated, a steady-state physical experiment of the reactor is still needed besides the need of dynamically tracking the state change of the reactor system. The physical experiment is a periodic steady-state flux diagram experiment, so that the power and xenon poison of the reactor are stable and unchanged within a certain time, and the measurement result of the experiment is used for verifying the consistency of the designed reactor and the operated reactor. This consistency is reflected in: on one hand, the safety of the actually operated reactor is also ensured because the reactor is designed and subjected to detailed safety analysis and demonstration (safety inspection); and on the other hand, the design value is consistent with the actual value, so that the reliability of the design software prediction is further verified. The periodic steady-state experiment requires the core to remain steady for a period of time and to provide a reference theoretical power distribution (here as a soft measurement datum).
As shown in fig. 3, in order to make the best use of the detector information of the nuclear reactor, during steady state (periodic) estimation of the reactor, it is necessary to simulate the background power distribution in the current reactor state by using theoretical calculation and use the background power distribution as soft measurement data, and at the same time, include the measured value of MID, the measured value of FID, the measured value of T/C, and the measured value of exocore as measurement information.
As shown in fig. 3, in the dynamic simulation process of the reactor, since the control or monitoring emphasis is slightly different in the transient process, for example, when only the axial power distribution monitoring needs to be performed in the current reactor operating condition, the exact measurement value and the background soft measurement may be selected. When the reactor operating conditions only require radial power distribution monitoring, then the T/C measurement and the background soft measurement can be selected. When monitoring of three-dimensional power distribution is required, the FID, T/C, EXCORE, and background soft measurements may be selected to make the best use of the nuclear reactor's detector information.
And step 3: probability estimation of reactor power distribution based on a bayesian approach.
Less accurate detectors may contain some information that a more accurate detector cannot cover and therefore should not always be discarded for their coarse accuracy, it is reasonable to fuse estimates of various accuracies together and reconcile the respective limitations. The invention is intended to perform three-dimensional power distribution reconstruction and error estimation thereof based on independent types of measurement information respectively. And then based on a naive Bayes principle, probability fusion among different power distributions is carried out.
The probabilistic estimation of the reactor power distribution of the present invention, as shown in fig. 4, includes two steps: (1) estimating a power value and probability based on the background measurement information and the measurement information of the specific type of detector; (2) and synthesizing different types of detector information, carrying out information fusion, and determining the final power value estimation and the probability estimation thereof. The method comprises the following specific steps:
step 3.1: the single type detector is based on state estimation of error propagation theory.
In the present invention, there is N for a particular jth detector typejAnd a detector, j ═ MID, FID, exact, T/C.
In the invention, for any position (x, y, z) in three-dimensional space in the reactor, the measured power value of the position is obtained by using the measurement information of the jth type detector
Comprises the following steps:
wherein the content of the first and second substances,
for the position (x) of the ith detector of the jth typei,yi,zi) A measured signal value (e.g. current signal) of (a), pref(x, y, z) is the theoretical predicted power value at the (x, y, z) position, Iref(xi,yi,zi) Is to xi,yi,ziThe theoretical prediction current signal value of the jth type detector at the position can be obtained by calculating a neutron transport theory and a detector theoretical response model according to nuclear design software under the condition of determining the operating condition of the reactor, and is a determined distribution value. w is ai,jWeight influence factor, w, for the (x, y, z) position of the ith detector pair, denoted as the jth typei,jThe determination of (a) requires special consideration, including two layers: on the one hand (x)i,yi,zi) The higher the accuracy of the position detector i, the lower the uncertainty, the higher its power weight value for the (x, y, z) position, on the other hand, (x)i,yi,zi) The closer the detector position is to the (x, y, z) position, the neutron diffusion at that position, and so onThe closer the physical process is, the higher its weight value is.
In the invention, the influence weight w of the detector i on the power valueiK1 × K2 includes two components, a proximity weight and an accuracy weight, wherein the distance weight component is determined after determination according to the geometry of the reactor and the arrangement scheme of the detectors unless replacement, update, etc. of the detectors occur requiring recalculation of different detector influences. The accuracy part characterizes the accuracy of the different detectors:
In the present invention, the j-th type is considered in (x)i,yi,zi) Position detector measurement signal
Uncertainty of
Differences in the location of the detectors and the operating conditions of the reactor, such as changes in power levels or control rods, etc., should be taken into account. In addition, because of the potential for replacement of the detectors, a new freshly stacked detector is typically less uncertain than a detector that has been irradiated within the stack for one or more cycles of operation.
According to the theory of error propagation, there is an uncertainty in the value of the power at (x, y, z)
Comprises the following steps:
wherein the content of the first and second substances,
are all deterministic coefficients, calculated by theory.
In the present invention, when
When the change occurs in real-time,
and the real-time change is realized, so that the real-time estimation of the uncertainty is realized.
It should be noted in particular that the uncertainty evaluation of step 1 is directed to
The evaluation is carried out.
Refers to the j-th type of detector (j: MID, FID, EXCORE, T/C) in (x)i,yi,zi) Uncertainty of detector signal of position. The uncertainty evaluation in this step is given to all
In the case of (a), an uncertainty is achieved for the power value at an arbitrary position (x, y, z)
Is estimated.
When (x)i,yi,zi) When the detector of the position fails, the invention can approximately consider that the detector information at the position has great uncertainty (untrustworthy), namely sigmaI(xi,yi,zi) → infinity, when the weighting factor of the detector K2, wi→ 0, i.e. eliminating this detector effect from the guest.
The failure of the detector has important influence significance on the operation of the reactor. When there are more detectors, i.e. N increases, resulting in σPThe (x, y, z) reduction, i.e. the more detector information, helps to reduce the estimation uncertainty of the power distribution. When the detector is reduced to a certain extent, then σP(x, y, z) is increased, especially in the weight of (x, y, z)
Larger detectors fail, which may lead to sigmaP(x, y, z) increases. When sigma isPWhen (x, y, z) increases to a certain extent, the penalty factor f (x, y, z) for the power value here is large, and f × max (P (x, y, z)) < limit is likely to be reachedFqTherefore, the safety criterion of nuclear power operation is met, namely, risks of power reduction operation or shutdown and the like can be met. (max (P (x, y, z)) is the peak power value, and generally during the operation of the reactor, it is desirable that the power distribution is more uniform (i.e. the normalized power distribution is close to 1.0, so that the coolant can sufficiently take away the core heat, and the heat is prevented from being accumulated in a certain peak area of the core, so that the temperature of the area is insufficiently cooled, the damage to the fuel elements and the outer cladding material is caused, and the radioactive substances in the fuel are releasedFqIt is very muchThe key is that. The limit may be determined by analyzing various types of presumed operational incidents that may occur with a nuclear reactorFqIs measured. If the minimum value is exceeded, enough safety margin can not be ensured under various accidents of safety analysis, and a certain potential operation safety risk exists. Such as limitFqNot exceeding this value, 1.5, helps to limit the non-uniformity of the power distribution and reduce the safety risk, and exceeding this value, according to the requirements of the operating specifications, may face risks of reduced power operation or shutdown. However, since the measured power distribution P (x, y, z) is obtained by comprehensive calculation from different information sources, it has uncertainty of multiple angles. For this purpose, a penalty factor, also called engineering factor f, is defined, for example equal to 1.03 or 1.05, according to its uncertainty, so as to guarantee: f × max (P (x, y, z)) < limitFq)
Step 3.2: integration of different types of detectors to obtain final power value by real-time estimation
And uncertainty of power value
With information from different detectors Ijj-MID, FID, exact, T/C as independent information sources for the power values at the (x, y, z) positions respectively
And its uncertainty
After estimation, under the condition that the error distribution is supposed to accord with the Gaussian hypothesis, the invention carries out fusion according to the naive Bayes principle, and comprises the following steps:
wherein p ismes(x, y, z) and σmesAnd (x, y, z) is the power value and the uncertainty thereof which are obtained by fusing the power values and the uncertainties estimated by the various detectors and are the best estimated power values and the uncertainty thereof.
And 4, step 4: probabilistic estimation of reactor core burnup distribution.
The invention patent ZL201410253319.5 reactor core monitoring power uncertainty analysis method at flux map time and continuous time discloses a method for quantitatively solving uncertainty of a reactor power distribution peak value, the method only gives conservative uncertainty of the power peak value, the power peak value generally occurs in the center position of a reactor core, a non-control rod assembly or a region with high enrichment degree or low fuel consumption, and a hot spot region can be shifted along with the change of the operation process of the reactor. For example, in regions with high power peaks at the beginning of the operating cycle, the power may decrease at the end of the operating cycle as the fissile nuclide is consumed. From a safety standpoint, power in non-power peak regions (e.g., regions of the reactor near the outer edge) may not be of concern, but from an economic standpoint, with the next cycle on, the components at the bottom of the edge power crossover may be refurbished into the middle core region, which may be the hot spot region for the new cycle. For this reason, it is necessary to determine the power value and its uncertainty for each location inside the core.
For a certain point (x, y, z) in the reactor space, its burnup value But(x, y, z) is the integral of the power values at all operating moments, i.e.:
wherein the content of the first and second substances,
an estimate of the power value at time t for the reactor core (x, y, z) position.
The invention assumes that the power values at the (x, y, z) positions of the two moments before and after are independent of each other, and in this case:
wherein
Uncertainty of burnup estimate for reactor core (x, y, z) position at time t, and
the uncertainty of the estimated value of the power at the position of the core (x, y, z) of the reactor at time T, denoted as the reactor's runtime, generally in days, the longer the runtime the longer its burnup value.
And 5: and updating the probability of the core burnup distribution and estimating the performance of the fuel rod in real time.
In the invention, the real-time estimation of the probability distribution of the three-dimensional power distribution of the reactor refers to the real-time estimation of the power value of any position (x, y, z) of the three-dimensional power distribution of the space
And its uncertainty
In the invention, the real-time estimation of the probability distribution of the burnup distribution of the reactor core means that the burnup value Bu of any position (x, y, z) of the spatial three-dimensional distribution can be estimatedt(x, y, z) and its uncertainty
In the present invention, the performance of the fuel rod at the (x, y, z) position, burnup value But(x, y, z) and power values
The influence of (c). Before the invention is put forward, Bu cannot be obtained in real timet(x, y, z) and
when the performance of the fuel rod is evaluated, a very conservative burn-up value and power value are given in the whole operation period, so that the performance of the fuel rod cannot be optimally estimated, and the evaluated performance is biased to deteriorate and be conservative, so that the possibility of the operation flexibility of the reactor, such as rapid power lifting and the like, is limited.
In the invention, Bu is obtained in real timet(x, y, z) and
and its uncertainty, so Bu can be used by fuel rod performance analysis softwaret(x, y, z) and
the method is used as real-time input, the performance of the fuel rod at any point in the reactor space is calculated on line in real time, and from the aspect of reactor monitoring, the direct monitoring of the fuel rod parameters related to safety is realized, the operation boundary is released, and the method is favorable for improving the economy of a power plant.
Obtaining a probabilistic estimate of the core burnup distribution plays a crucial role in the first safety barrier (i.e., fuel clad) of the reactor. Because as the burn-up progresses, the performance of the fuel rods, such as the PCI effect, the maximum tolerable fuel core or cladding temperature, etc., tends to deteriorate, thereby affecting the flexibility and safety of the reactor operation.
Wherein R istAnd the fuel rod performance evaluation index is characterized by the performance evaluation index of the fuel rod at the x, y and z positions at the time t. fun is fuel rod performance analysis software, and represents evaluation index calculated by fuel rod performance analysis software such as Transurans and COPERNICThe specific calculation process is the prior art and is not described herein.
It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.
Claims (10)
1. The method for monitoring the probability distribution of the three-dimensional power of the reactor based on the information fusion theory is characterized by comprising the following steps of:
s1, evaluating the uncertainty of the measurement information;
s2, determining the detector information to be adopted based on the monitored dynamic or steady-state requirements;
s3, estimating the reactor power distribution state based on a Bayes method, firstly estimating the power value and the uncertainty of the single type of detector, and then fusing the power values and the uncertainty of the different types of detectors based on a Bayes principle to obtain the final optimal power value and the uncertainty thereof.
2. The method for monitoring the probability distribution of the three-dimensional power of the reactor based on the information fusion theory as claimed in claim 1, wherein when the detector is a movable detector (MID), the uncertainty of the measurement information comprises the uncertainty of repeated measurement caused by a signal generation mechanism, the uncertainty introduced by the change of the core state in the measurement process, the uncertainty of mutual calibration of the probes and the uncertainty of the alignment of the axial grids; when the detector is an in-pile self-powered neutron detector (FID), evaluating the precision of the detector by comparing the relative error of the FID current predicted by theory and the FID current measured; when the detector is a reactor core thermocouple, the stability of the ratio of the enthalpy rise of the coolant channel under different power steps to the integral power of the corresponding fuel assembly under the full-operation working condition is compared, and the accuracy of the thermocouple is evaluated; and when the detector is an extra-reactor fixed neutron detector (EXCORE), comparing the difference between the normalized current distribution represented by the extra-reactor detector and the theoretically normalized current distribution after the three-dimensional power distribution in the reactor core and the weight of the detector response matrix, and evaluating the precision of the extra-reactor detector.
3. The method for monitoring the three-dimensional power probability distribution of the reactor based on the information fusion theory as claimed in claim 1, wherein the determining the detector information to be adopted based on the monitored dynamic or steady-state requirement in step S2 specifically comprises:
during the steady state estimation of the reactor, the background power distribution under the current reactor state and the measurement values of various detectors need to be adopted;
and determining the detector information to be adopted according to different monitoring directions during the dynamic estimation of the reactor.
4. The method for monitoring the three-dimensional power probability distribution of the reactor based on the information fusion theory according to claim 3, wherein the determining the detector information to be adopted according to the different monitoring directions specifically comprises:
when the working condition of the reactor only needs to carry out axial power distribution monitoring, an EXCORE measured value and background soft measurement are selected;
when the working condition of the reactor only needs to carry out radial power distribution monitoring, selecting a T/C measured value and a background soft measured value;
when monitoring the three-dimensional power distribution, the FID, T/C, EXCORE, and background soft measurements are selected.
5. The method for monitoring the probability distribution of the three-dimensional power of the reactor based on the information fusion theory as claimed in claim 1, wherein the estimating the power value of the single-type detector and the uncertainty thereof in step S3 includes:
for a particular j-th detector type, there is NjA detector, j MID, FID, EXCORE, T/C, for any position (x, y, z) in three-dimensional space in the reactor, and its measured power value obtained by using the j-th type detector measurement information
Comprises the following steps:
wherein, wi,jExpressed as the weight influence factor of the (x, y, z) position of the ith detector pair of the jth type,
for the position (x) of the ith detector of the jth typei,yi,zi) Measured signal value of pref(x, y, z) is the theoretical predicted power value at the (x, y, z) position, Iref(xi,yi,zi) Is to xi,yi,ziTheoretical predicted current signal values for the j-th type of detector at the location;
uncertainty of power value at (x, y, z) according to error propagation theory
Comprises the following steps:
wherein the content of the first and second substances,
are all deterministic coefficients.
6. The method for monitoring the probability distribution of the three-dimensional power of the reactor based on the information fusion theory as claimed in claim 5, wherein the j typeThe weight influence factor w of the ith detector on the (x, y, z) positioni,jIncluding a close range weight K1 and a precision weight K2, i.e., wiK1 × K2, wherein,
or
Is (x)i,yi,zi) A distance from (x, y, z), where p represents the order, α is a distance coefficient,
c is a normalization coefficient, N is the number of detectors, sigmaiDenoted as uncertainty of the ith detector.
7. The method for monitoring the probability distribution of the three-dimensional power of the reactor based on the information fusion theory as claimed in claim 1, wherein the step S3 of the final optimal power value and the uncertainty thereof specifically includes:
the fusion is carried out according to the naive Bayes principle, and comprises the following steps:
wherein p ismes(x, y, z) and σmesAnd (x, y, z) is the power value and the uncertainty thereof which are obtained by fusing the power values and the uncertainties estimated by the various detectors and are the best estimated power values and the uncertainty thereof.
8. The method for monitoring the probability distribution of the three-dimensional power of the reactor based on the information fusion theory according to any one of claims 1 to 7, wherein the method further comprises the following steps after the step S3:
step S4: performing probability estimation on the burnup distribution of the reactor core;
step S5: and updating the probability of the core burnup distribution and estimating the performance of the fuel rod in real time.
9. The method for monitoring the probability distribution of the three-dimensional power of the reactor based on the information fusion theory as claimed in claim 8, wherein the step S4 of performing the probability estimation on the burnup distribution of the reactor core includes estimating a burnup value and an uncertainty thereof at any position of the three-dimensional distribution of the reactor space, specifically:
for a certain point (x, y, z) in the reactor space, its burnup value But(x, y, z) is the integral of the power values at all operating moments, i.e.:
wherein the content of the first and second substances,
an estimate of the power value at the reactor core (x, y, z) position at time t;
assuming that the power values at the (x, y, z) positions at the two previous and next time instants are independent of each other, there are:
wherein
I.e., the uncertainty of the burnup estimate of the reactor core (x, y, z) position at time t, and
the uncertainty of the estimated value of the power at the position of the reactor core (x, y, z) at time t.
10. The method for monitoring the probability distribution of the three-dimensional power of the reactor based on the information fusion theory as claimed in claim 8, wherein the step S5 of updating the probability of the core burnup distribution and estimating the performance of the fuel rod in real time specifically comprises:
real-time acquisition
And
to update the fuel consumption value and its uncertainty;
and (4) taking the updated burnup value and the uncertainty thereof as the real-time input of the fuel rod performance analysis software, so that the fuel rod performance of any one point in the reactor space can be obtained in real time.
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