Method for on-line reconstruction of pin-by-pin power in pressurized water reactor based on fission matrix

Abstract

A kind of pressurized water reactor PIN level power online reconstruction method based on fission matrix, according to pressurized water reactor core model, pressurized water reactor power database, in-core detector response matrix database and high-order harmonic database are sequentially constructed, then high-order harmonic database is reduced dimension and in-core detector count is obtained by critical-burnup coupling as actual measurement value, in online stage, according to high-order harmonic database and in-core detector response matrix database, combined with actual measurement value, least square method is used to reconstruct the pin-by-pin power distribution of core.The present application uses the detector response matrix and high-order eigenvector under typical conditions constructed in advance, and only needs to calculate expansion coefficient in online stage to realize real-time monitoring.The present application makes full use of the actual measurement information of in-core detector, reconstructs the pin level power distribution in reactor, uses the detector response matrix and high-order eigenvector under typical conditions constructed in advance, and can realize real-time monitoring of reactor power.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of reactor control, and particularly relates to a pressurized water reactor PIN-level power online reconstruction method based on a fission matrix. BACKGROUND

[0002] It is of great significance to predict and prevent various accidents to monitor the three-dimensional power distribution of a reactor core online to ensure that relevant safety parameters do not exceed the design limit. However, existing reactor online monitoring systems such as BEACON and CECRO generally adopt the idea of combining online theoretical simulation calculation with actual detector measurement correction. The detector measurement correction part generally considers that the deviation between the actual measured reaction rate of the detector and the theoretical reaction rate can be used to fit the deviation between the assembly reconstruction power distribution and the simulation power distribution. For the power distribution inside the assembly, the amplitude of the reconstruction power distribution of the fuel rod in the assembly is adjusted by the ratio of the assembly reconstruction power to the assembly theoretical power, and the PIN-level fine reconstruction power cannot be directly obtained from the detector reading deviation.

[0003] In addition, the mechanism of the existing online monitoring system in correcting the theoretical power distribution also has defects. When the monitoring area is far away from each neutron detector, the spatial response function of the detector tends to zero, resulting in correction failure. The currently adopted method is that the area far away from the detector is not corrected, and the theoretical calculation value is directly output as the monitoring value. As a result, the calculation error is directly brought into the monitoring value, making the monitoring result less reliable. SUMMARY

[0004] The application provides a pressurized water reactor PIN-level power online reconstruction method based on a fission matrix to solve the problems that the prior art depends on the measurement value and the calculation value of the detector position to fit the three-dimensional power distribution of the whole reactor, only the assembly-level power distribution can be obtained, the PIN-level power is difficult to accurately obtain, and the fitting effect is poor for the area without detector coverage. The detector response matrix constructed in advance and the high-order eigenvector under typical conditions are used to realize real-time monitoring by only calculating the expansion coefficient in the online stage. The actual measurement information of the detector in the reactor is fully utilized to reconstruct the PIN-level power distribution in the reactor, and the detector response matrix constructed in advance and the high-order eigenvector under typical conditions are used to realize real-time monitoring of the reactor power.

[0005] The application is implemented by the following technical scheme:

[0006] The present application relates to a kind of PIN level power online reconstruction method based on fission matrix of pressurized water reactor, according to the model of pressurized water reactor core, pressurized water reactor power database, in-core detector response matrix database and high-order harmonic database are sequentially constructed, and high-order harmonic database is reduced dimension processing and in-core detector count is obtained as actual measurement value by critical-burnup coupling, in online stage, according to high-order harmonic database and in-core detector response matrix database, actual measurement value is combined, and least square method is used to reconstruct the pin-by-pin power distribution of core.

[0007] The high-order harmonic database is obtained by representing the reactor power as a linear combination of high-order harmonics, where the high-order harmonics are obtained by solving the fission matrix. The fission matrix is constructed based on the cell fission rate obtained from Monte Carlo simulation with fixed neutron source, representing the probability of a neutron generated by fission in one cell inducing fission in another cell. The fission matrix contains the core characteristics of the fission system, i.e., the eigenvalues and eigenvectors of the fission matrix are a spatially complete set. When the core state is similar to the calculation condition of the high-order eigenvector set, the same high-order harmonic library can be used for power expansion.

[0008] The in-core detector response matrix is obtained by fixed source calculation, which gives the contribution rate of the fission neutron source generated by each PIN cell in the assembly to the in-core detector reading, so as to obtain the mapping relationship between the core power distribution and the in-core detector count, i.e., the detector response matrix.

[0009] The reconstruction refers to: after expanding the reactor power with high-order harmonics, combining the detector response matrix, and solving the equation set to obtain the coefficients of high-order harmonics, the reactor power is reconstructed.

[0010] Technical effects

[0011] The present application calculates the high-order eigenvectors by Arnoldi algorithm and performs high-order harmonic expansion, combines the detector response matrix and in-core detector count, and realizes the reconstruction of reactor power by least square method, while only calculating the expansion coefficients in online stage, reduces the complexity of online calculation, realizes the accurate reconstruction of power distribution of each PIN level in reactor by fine reconstruction method, and realizes the real-time monitoring of reactor power. Compared with the prior art, the present application can accurately reflect the spatial distribution of reactor power, improve the monitoring ability of reactor power change and improve the spatial resolution of reactor monitoring. BRIEF DESCRIPTION OF DRAWINGS

[0012] Figure 1 The flowchart of the present application is shown in Figure 1;

[0013] Figure 2 The schematic diagram of the embodiment core is shown in Figure 2;

[0014] Figure 3 For single assembly in-vessel detector response coefficient distribution map;

[0015] Figure 4 For initial zero burnup embodiment reconstructed power distribution versus critical-burnup coupling calculation (4th order eigenvector);

[0016] In the figure: (a) eigenvector power versus reference solution deviation, (b) 1st order vector reconstructed power versus reference solution deviation, (c) 2nd order vector reconstructed power versus reference solution deviation, (d) 3rd order vector reconstructed power versus reference solution deviation, (e) 4th order vector reconstructed power versus reference solution deviation;

[0017] Figure 5 For initial zero burnup embodiment reconstructed power distribution versus critical-burnup coupling calculation (9th order eigenvector);

[0018] In the figure: (a) eigenvector power versus reference solution deviation, (b) 1st order vector reconstructed power versus reference solution deviation, (c) 2nd order vector reconstructed power versus reference solution deviation, (d) 3rd order vector reconstructed power versus reference solution deviation, (e) 4th order vector reconstructed power versus reference solution deviation, (f) 5th order vector reconstructed power versus reference solution deviation, (g) 6th order vector reconstructed power versus reference solution deviation, (h) 7th order vector reconstructed power versus reference solution deviation, (i) 8th order vector reconstructed power versus reference solution deviation, (j) 9th order vector reconstructed power versus reference solution deviation;

[0019] Figure 6 For initial zero burnup embodiment reconstructed power distribution versus critical-burnup coupling calculation (4th order eigenvector);

[0020] In the figure: (a) eigenvector power versus reference solution deviation, (b) 1st order vector reconstructed power versus reference solution deviation, (c) 2nd order vector reconstructed power versus reference solution deviation, (d) 3rd order vector reconstructed power versus reference solution deviation, (e) 4th order vector reconstructed power versus reference solution deviation. DETAILED DESCRIPTION

[0021] As Figure 1 shown, the present embodiment relates to a PIN-level power online reconstruction method for a pressurized water reactor based on a fission matrix, which reconstructs the reactor power by using a high-order harmonic expansion method, i.e., expanding the power distribution by using a high-order harmonic library, and combining the detector response to obtain the expansion coefficients of the high-order harmonics by using a least square method, specifically: detector count vector R = DP, wherein: D is a detector response matrix, power distribution d n and f n are eigenvectors p n and high-order harmonics s nThe expansion coefficients; the higher-order harmonic matrix M = [s0, s1, ..., s n Expand the coefficient vector X = (f0, f1, ..., f n ) T That is, DMX = R.

[0022] The method specifically includes:

[0023] Step 1, as follows Figure 2 As shown, a pressurized water reactor core model is established, and components with different enrichment levels are set. Based on the location of components with different enrichment levels within the reactor, the component types are classified, and neutron detectors are arranged in the central measurement channels of the characteristic components, i.e., the positions indicated by the yellow icons in the figure.

[0024] Step 2: Before power reconfiguration, construct a pressurized water reactor power distribution database, a harmonic database under typical conditions, and an in-reactor detector response matrix database, specifically including:

[0025] 2.1 The core power distribution under normal operating conditions is obtained by performing criticality-burnup coupled calculations using the Monte Carlo program. This distribution is used as the reference solution, i.e., the true value of the core power distribution. The fission cross section is then adjusted according to fuel consumption and fission product changes to ensure that the reactor always maintains a critical state. The evolution of the reactor over time is dynamically simulated to calculate the final power distribution, specifically: Where ψ(r,Ω,E,t) represents the energy spectrum of the neutron at position r, direction Ω, and energy E. υ is the velocity of the neutron, ∑ s (E) is the scattering cross section, and S(r,Ω,E,t) is the external source term. The Monte Carlo program can approximate the spatial and energy distribution of neutrons by simulating a sufficient number of neutron trajectories and statistically analyzing their propagation process in the reactor.

[0026] 2.2 Solving for higher-order harmonics using the fission matrix method: Since fission matrices are typically large, sparse matrices with relatively high diagonalization, when solving for their higher-order eigenvectors, they are first converted into general matrices. Then, the Arnoldi algorithm is used, constructing a Krylov subspace during the iteration process to approximate the eigenvalues ​​of the matrix for solution. The final higher-order harmonic matrix M is obtained, specifically including:

[0027] a) First, transform the sparse split matrix into a general matrix to make it suitable for the Arnoldi algorithm. The Arnoldi algorithm approximates the eigenvalues ​​and eigenvectors of the matrix by iteratively constructing a Krylov subspace. Given an initial vector, the Krylov subspace can be constructed through the following steps. First, select the initial vector b and normalize it to obtain... The iterative process first calculates ω k =Aν k After orthogonalization, we obtain... Normalization Constructing Hessenberg matrix

[0028] b) By solving the eigenvalue λ m and eigenvector y i of the small matrix H i , the approximate eigenvalue of the matrix A is obtained. The high-order eigenvector of A is obtained by using the orthogonal matrix V m constructed in the iteration process: v i = V m y i . Finally, through the processing of the eigenvalue and eigenvector, the high-order harmonic matrix M is obtained, which contains the high-order eigenvalue and eigenvector of the fission matrix A, which satisfies A v = λ v, where v is the eigenvector and λ is the eigenvalue;

[0029] 2.3 Without considering the influence of the fission neutron source in other assemblies except the assembly where the detector is located, and considering the symmetry of the assembly, only 1 / 8 of the positions in a single assembly are calculated for the fixed source: in the case of a given known neutron source, the distribution of neutron flux is obtained by simulating the propagation, scattering, absorption and other processes of neutrons, and each fixed source calculation only considers the fission caused by the neutron source, without further statistics of the fission process of the subsequent generation of neutrons. The calculated results are arranged according to the fixed source position to obtain the corresponding matrix D of the detector.

[0030] Step 3, screening the high-order harmonic library and selecting the appropriate core harmonic group, i.e. reducing the dimensionality of the core power distribution: the detector counts in the characteristic assembly form a detector count vector R, the equation DMX = R is solved to obtain the expansion coefficient vector X, and the elements in X are arranged in descending order of value, and the high-order harmonics corresponding to the elements with large values are selected as the core harmonic group.

[0031] Step 4, in the core criticality-burnup coupling calculation, a sufficient number of neutrons are simulated using the Monte Carlo program, and a detector is defined at the center position of the characteristic assembly to perform fission rate statistics, and the obtained value is taken as the actual measured value of the detector count.

[0032] The simulation refers to: in the Monte Carlo program, the detector obtains the value by counting the number or energy of neutrons passing through a specific region, by tracking the path of particles in the core, recording the relevant data when the particles pass through the predetermined detector position, and finally outputting these statistical data for analysis of the power distribution of the reactor.

[0033] The number Where: Φ DET (r) is the count obtained by statistics at the detector position r, N totalis the total number of particles tracked in the simulation, is the indicator function, if the particle crosses the detector position, otherwise 0.

[0034] Step 5, select the core harmonic combination from step 3, combine the core detector response matrix, and solve the equation DMX = R using least square method to get the core harmonic combination M = [s 0, s 1, …,s n ] and the expansion coefficient vector X = (f 0, f 1, …,f n ) T , reconstruct the PIN level core power distribution P = MX = f0s0+f1s1+...+f n s n . Compare the reconstructed PIN level power P with the result from criticality-burnup coupling calculation P0, calculate the relative error for each PIN cell and the root mean square error for all PIN cells.

[0035] The root mean square error where P i is the reconstructed power of the i-th PIN cell, P i0 is the true power of the i-th PIN cell, and m is the number of PIN cells in the reactor. The reconstruction accuracy is verified by the relative error and the root mean square error.

[0036] Through specific experiments, in the core model shown in Figure 2 , the above method is used for power reconstruction, the detectors are arranged at the center of each assembly, the reconstructed power data are compared with the criticality results, and the results are shown in Figures 4-6 .

[0037] As can be seen from the assembly response coefficients shown in Table 1, the contribution of the fixed source in the assembly where the detector is located to the detector count reaches 96.9%, and the contribution of the 24 assemblies outside to the detector count is only 3.1% in total. Therefore, the response coefficient matrix can be solved in the single assembly by fixed source calculation.

[0038] Table 1 Assembly response coefficient distribution

[0039]

[0040]

[0041] The results of power reconstruction using 4th order high-order eigen vectors are shown in Figure 4As shown, under zero-burnup conditions, since the initial error is relatively small, replacing a 2.4% enrichment component in the reactor core with a 1.6% enrichment component results in a maximum deviation of 62% from the critical result. After dimensionality reduction, selecting the 1st, 2nd, 3rd, and 5th order eigenvectors and reconstructing using higher-order eigenvectors, the maximum deviation is reduced to approximately 38%. The RMSE of the power deviation also decreases from 13.98 to 7.48.

[0042] The result of power reconstruction using 9 higher-order eigenvectors is as follows: Figure 5 As shown, after dimensionality reduction, the 1st, 4th, 3rd, 7th, 2nd, 5th, 8th, 9th and 13th order eigenvectors were selected for reconstruction. The maximum deviation was reduced from 62% to about 35%. When using the first 8 order fittings, the RMSE of the power deviation decreased from 13.98 to 9.04.

[0043] like Figure 6 As shown, for the case of a burn-out depth of 400 days, in order to increase the initial error, the burn-out depth of one of the components with a 1.6% enrichment was changed to 200 days. The 1st, 2nd, 3rd and 5th order eigenvectors were still used for reconstruction, and the RMSE of the power deviation was reduced from 5.16 to 3.59.

[0044] Compared with existing technologies, the innovation of this invention lies in the application of PIN-level high-order harmonics for power decomposition. By combining the detector response matrix and detector readings, it is possible to achieve accurate reconstruction of the reactor power distribution and directly obtain the PIN-level power distribution. This technique differs from previous component-level high-order harmonic decomposition techniques, significantly improving the spatial resolution of reactor power monitoring and accurately reflecting changes in power within the reactor.

[0045] Furthermore, this invention proposes a novel technical approach: pre-constructing a high-order harmonic database and a detector response matrix database. Using this database, only the harmonic expansion coefficients need to be calculated during the online monitoring phase, greatly simplifying the calculation process and improving the system's real-time performance and efficiency. This simplified online calculation process avoids the problem of requiring real-time calculation of complex models in traditional methods, significantly improving the real-time monitoring capability of reactor power.

[0046] Through these innovative technical means, this method makes full use of the actual measurement information of the in-core detectors, enabling precise reconstruction of the power distribution of each PIN level in the reactor. It can reduce the relative error and root mean square error between the power distribution and the Monte Carlo simulation results, thereby improving the accuracy and efficiency of reactor monitoring.

[0047] The above specific embodiments can be partially adjusted in different ways by those skilled in the art without departing from the principles and purposes of the present application, the protection scope of the present application is subject to the claims and is not limited by the above specific embodiments, each implementation within the scope is subject to the present application.

Claims

1. A method for online reconstruction of pin-level power in a pressurized water reactor based on a fission matrix, characterized in that, Specifically comprising: Step 1, a pressurized water reactor core model is established, different enrichment components are set, different enrichment components are divided according to the positions of the components in the reactor, and a neutron detector is arranged in the center of the characteristic component; Step 2, before power reconstruction, a pressurized water reactor power distribution database is constructed, a harmonic database under typical conditions, and a reactor detector response matrix database, specifically comprising: 2.1 The core power distribution under normal operation condition is obtained by coupling the criticality and burnup calculation with Monte Carlo method, which is taken as the reference solution, i.e. the true value of the core power distribution. Then the fission cross section is adjusted according to the fuel burnup and the change of the fission product, ensuring the reactor always remains critical. The dynamic simulation of the reactor evolution over time is performed, and the final power distribution is calculated, which is specifically: where: represents the energy spectrum of the neutron at position , direction and energy , is the velocity of the neutron, is the scattering cross section, is the external source term. The Monte Carlo program approximates the spatial and energy distribution of the neutron by simulating a sufficient number of neutron trajectories and statistically obtaining their propagation process in the reactor; 2.2 The high-order harmonic matrix is obtained by solving the fission matrix method; 2.3 Without considering the influence of the fission neutron source in other components except the component where the detector is located, and considering the symmetry of the component, only 1 / 8 of the positions in the single component need to be calculated: in the case of a given known neutron source, the distribution of the neutron flux is obtained by simulating the propagation, scattering and absorption of the neutrons, and each fixed source calculation only considers the fission caused by the neutron source, without further statistics of the fission process of the subsequent generation of neutrons, the results obtained are arranged according to the fixed source position, and the detector response matrix D is obtained. Step 3, the high-order harmonic library is screened, and the appropriate core harmonic group is selected, that is, the dimensionality of the reactor core power distribution is reduced: the detector count vector R is composed of the detector count in the characteristic component, the equation DMX=R is solved, the expansion coefficient vector X is obtained, the elements in X are arranged in descending order of value, and the high-order harmonics corresponding to the elements with large values are selected as the core harmonic group, wherein M is the high-order harmonic matrix; Step 4, in the core criticality-burnup coupling calculation, a sufficient number of neutrons are simulated by using a Monte Carlo program, and a detector is defined at the center position of the characteristic component to perform fission rate statistics, and the obtained value is used as the actual measured value of the detector count; Step 5: Select the core harmonic combination chosen in Step 3 and combine it with the core detector response matrix. Then, use the least squares method to resolve the equation DMX=R to obtain the higher-order harmonic matrix. expansion coefficient vector Reconstructing PIN-level core power distribution The relative error of each PIN gate cell is calculated by comparing the PIN-level power reconstruction value P with the result P0 obtained from the critical-fuel coupling calculation. The root mean square error across all PIN gates; The high-order harmonic matrix is obtained by the following method: a) first convert the sparse fission matrix to a general matrix to make it suitable for Arnoldi algorithm, which constructs a Krylov subspace by iteration to approximate the eigenvalues and eigenvectors of matrix A, given an initial vector b, the Krylov subspace is constructed by the following steps, first normalize the initial vector b to get , the iteration process first calculates , orthogonalization to get , normalization to get , construct the upper Hessenberg matrix ; b) By solving the eigenvalues and eigenvectors of the small matrix , the approximate eigenvalues of matrix A are obtained, and the high-order eigenvectors of A are obtained by using the orthogonal matrix constructed in the iteration process: Finally, through the processing of the eigenvalues and eigenvectors, the high-order harmonic matrix M is obtained, which contains the high-order eigenvalues and eigenvectors of the fission matrix A, and satisfies , where: is the eigenvector, is the eigenvalue; The simulation refers to: in the Monte Carlo program, the detector obtains the value by counting the number or energy of neutrons passing through a specific area, and by tracking the path of particles in the core, when the particles pass through the predetermined detector position, the relevant data is recorded, and finally the statistical data is output for analyzing the power distribution of the reactor; The number where: is the number of counts statistically obtained at the detector position r, is the total number of particles tracked during the simulation, is an indicator function that is 1 if the particle crosses the detector position, and 0 otherwise.

2. The method of claim 1, wherein the method is characterized by, The high-order harmonic database is obtained by the following method: the reactor power is represented as a linear combination of high-order harmonics, wherein the high-order harmonics are obtained by solving the fission matrix, the fission matrix is constructed on the basis of the cell fission rate obtained by the Monte Carlo simulation of the fixed neutron source, and represents the probability of the fission of a certain cell generating neutrons inducing fission in another cell. The fission matrix contains the core characteristics of the fission system, that is, the eigenvalues and eigenvectors of the fission matrix are a complete set in space, when the core state is similar to the calculation condition of the high-order eigenvector set, the same high-order harmonic library is used for power expansion.

3. The method of claim 1, wherein the method is characterized by, The reactor detector response matrix is obtained by fixed source calculation, which obtains the contribution rate of the fission neutron source generated by each PIN cell in the component to the reactor detector reading, and obtains the mapping relationship between the reactor core power distribution and the reactor detector count, that is, the detector response matrix.

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