Pressurized water reactor PIN-level power online reconstruction method based on fission matrix

Abstract

The invention relates to a fission matrix-based pressurized water reactor PIN-level power online reconstruction method, which comprises the following steps of: sequentially constructing a pressurized water reactor power database, an in-reactor detector response matrix database and a high-order harmonic database according to a pressurized water reactor core model; the method comprises the following steps: performing dimension reduction processing on a high-order harmonic database, obtaining in-pile detector counting as an actual measurement value through critical-fuel coupling, and reconstructing the pin-by-pin power distribution of a reactor core by combining the actual measurement value according to the high-order harmonic database and an in-pile detector response matrix database in an online stage by utilizing a least square method. According to the method, the detector response matrix constructed in advance and the high-order feature vector under the typical condition are utilized, and real-time monitoring can be achieved only by calculating the expansion coefficient in the online stage. According to the method, the actual measurement information of the detector in the reactor is fully utilized, the PIN-level power distribution in the reactor is reconstructed, and the reactor power can be monitored in real time by utilizing the detector response matrix constructed in advance and the high-order feature vector under the typical condition.

Description

Technical Field

[0001] The invention relates to a technology in the field of reactor control, in particular to a pressurized water reactor PIN-level power online reconstruction method based on a fission matrix. Background Art

[0002] Online monitoring of the three-dimensional power distribution of the reactor core is important for predicting and preventing various accidents to ensure that the relevant safety parameters do not exceed the design limits. However, existing reactor online monitoring systems such as BEACON and CECRO mostly adopt the idea of ​​online theoretical simulation calculation combined with actual detector measurement correction. In the detector measurement correction part, it is generally believed that the deviation between the actual detector reaction rate and the theoretical reaction rate can be used to fit the deviation between the component reconstructed power distribution and the simulated power distribution. For the power distribution inside the component, it is assumed that the fine reconstructed power distribution function is consistent with the theoretical fine reconstructed power distribution function. The amplitude of the reconstructed power distribution of the fuel rods in the component is adjusted by the ratio of the component reconstruction power to the component theoretical power. The PIN-level fine reconstruction power cannot be directly obtained through the detector reading deviation.

[0003] In addition, the existing online monitoring system also has defects in the mechanism of correcting the theoretical power distribution. When the monitoring area is far away from each neutron detector, the detector spatial response function tends to zero, resulting in correction failure. The current method is: no correction is made for the area far away from the detector, and the theoretical calculated value is directly output as the monitoring value. The consequence of this is that the calculation error is directly introduced into the monitoring value, making the monitoring result even more unreliable. Summary of the invention

[0004] The present invention aims at the shortcomings that the prior art relies on the measured values ​​and calculated values ​​of the detector position to fit the three-dimensional power distribution of the whole reactor, and can only obtain the power distribution at the component level, and it is difficult to accurately obtain the PIN level power and the accuracy is low, and the prior art has the defect of poor fitting effect for areas not covered by the detector. A method for online reconstruction of the PIN level power of a pressurized water reactor based on a fission matrix is ​​proposed. By using the detector response matrix constructed in advance and the high-order eigenvectors under typical conditions, only the expansion coefficient needs to be calculated in the online stage to realize real-time monitoring. The present invention makes full use of the actual measurement information of the detectors in the reactor, reconstructs the PIN level power distribution in the reactor, and uses the detector response matrix constructed in advance and the high-order eigenvectors under typical conditions to realize real-time monitoring of the reactor power.

[0005] The present invention is achieved through the following technical solutions:

[0006] The present invention relates to a pressurized water reactor PIN-level power online reconstruction method based on a fission matrix. After a pressurized water reactor power database, an in-core detector response matrix database and a high-order harmonic database are sequentially constructed according to a pressurized water reactor core model, a dimension reduction process is performed on the high-order harmonic database and in-core detector counts are obtained as actual measurement values ​​through criticality-burnup coupling. In the online stage, the core pin-by-pin power distribution is reconstructed using a least squares method based on the high-order harmonic database and the in-core detector response matrix database in combination with actual measurement values.

[0007] The high-order harmonic database is obtained in the following way: the reactor power is expressed 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 Monte Carlo simulation of a fixed neutron source, and represents the probability that the neutrons produced by the fission of a certain cell induce 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 spatially complete sets. When the core state is similar to the calculation conditions of the high-order eigenvector set, this high-order harmonic library can also be used for power expansion.

[0008] The in-core detector response matrix is ​​calculated by a fixed source to obtain the contribution rate of the fission neutron source generated by each PIN gate element in the component to the in-core detector reading, thereby obtaining the mapping relationship between the core power distribution and the in-core detector count, that is, the detector response matrix.

[0009] The reconstruction means that after the reactor power is expanded with high-order harmonics, the coefficients of the high-order harmonics are obtained by combining the detector response matrix and the simultaneous equations to reconstruct the reactor power. Technical Effects

[0010] The present invention calculates the fission matrix through the Arnoldi algorithm to obtain high-order eigenvectors and performs high-order harmonic expansion, combines the detector response matrix and the detector count in the reactor, and uses the least square method to achieve reactor power reconstruction. At the same time, only the expansion coefficient is calculated in the online stage, which reduces the complexity of online calculation. Through a sophisticated reconstruction method, the power distribution of each PIN level in the reactor is accurately reconstructed and the real-time monitoring of the reactor power is realized. Compared with the prior art, the present invention can accurately reflect the spatial distribution of power in the reactor, improve the monitoring capability of reactor power changes, and improve the spatial resolution of reactor monitoring. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 It is a flow chart of the present invention;

[0012] Figure 2 A schematic diagram of a core of an embodiment;

[0013] Figure 3is the distribution diagram of detector response coefficient within a single component;

[0014] Figure 4 A comparison diagram of the reconstruction of power distribution and criticality-burnup coupling calculation for the initial zero-burnup embodiment (fourth-order eigenvector);

[0015] In the figure: (a) the deviation between the intrinsic vector power and the reference solution, (b) the deviation between the 1st order vector reconstruction power and the reference solution, (c) the deviation between the 2nd order vector reconstruction power and the reference solution, (d) the deviation between the 3rd order vector reconstruction power and the reference solution, (e) the deviation between the 4th order vector reconstruction power and the reference solution;

[0016] Figure 5 A schematic diagram showing the comparison between the reconstructed power distribution and the criticality-fuel coupling calculation for the initial zero-fuel embodiment (9th-order eigenvector);

[0017] In the figure: (a) the deviation of the intrinsic vector power from the reference solution, (b) the deviation of the 1st-order vector reconstruction power from the reference solution, (c) the deviation of the 2nd-order vector reconstruction power from the reference solution, (d) the deviation of the 3rd-order vector reconstruction power from the reference solution, (e) the deviation of the 4th-order vector reconstruction power from the reference solution, (f) the deviation of the 5th-order vector reconstruction power from the reference solution, (g) the deviation of the 6th-order vector reconstruction power from the reference solution, (h) the deviation of the 7th-order vector reconstruction power from the reference solution, (i) the deviation of the 8th-order vector reconstruction power from the reference solution, (j) the deviation of the 9th-order vector reconstruction power from the reference solution;

[0018] Figure 6 It is a comparative schematic diagram of the reconstructed power distribution and criticality-burnup coupling calculation of the embodiment at a burnup depth of 400 days (fourth-order eigenvector);

[0019] In the figure: (a) the deviation between the intrinsic vector power and the reference solution, (b) the deviation between the 1st-order vector reconstruction power and the reference solution, (c) the deviation between the 2nd-order vector reconstruction power and the reference solution, (d) the deviation between the 3rd-order vector reconstruction power and the reference solution, and (e) the deviation between the 4th-order vector reconstruction power and the reference solution. DETAILED DESCRIPTION

[0020] like Figure 1 As shown, this embodiment relates to a method for online reconstruction of the PIN-level power of a pressurized water reactor based on a fission matrix, which uses a high-order harmonic expansion method to reconstruct the reactor power, that is, the power distribution is expanded using a high-order harmonic library, and the expansion coefficient of the high-order harmonic is obtained by combining the detector response with the least squares method, specifically: the detector count vector R = DP, where: D is the detector response matrix, the power distribution d n and f n The feature vectors p are n and higher order harmonics n The expansion coefficients of the high-order harmonic matrix M = [s0, s1, ..., sn ]; expansion coefficient vector X = (f0, f1, ..., f n ) T , that is, DMX=R.

[0021] The method specifically comprises:

[0022] Step 1: Figure 2 As shown, a pressurized water reactor core model is established, components with different enrichments are set, component types are divided according to their positions in the reactor, and neutron detectors are arranged in the central measurement channel of the characteristic components, which is the position of the yellow icon in the figure.

[0023] Step 2: Before power reconstruction, construct a pressurized water reactor power distribution database, a harmonic database under typical conditions, and an in-core detector response matrix database, specifically including:

[0024] 2.1 Monte Carlo program is used to perform criticality-burnup coupling calculation to obtain the core power distribution under normal operating conditions. This distribution is used as the reference solution, that is, the true value of the core power distribution. The fission cross section is adjusted according to the 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 and the final power distribution is calculated, which is: Where: ψ(r,Ω,E,t) represents the energy spectrum of the neutron at position r, direction Ω and energy E. υ is the speed 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 approximately obtain the spatial and energy distribution of neutrons by simulating enough neutron trajectories and counting their propagation processes in the reactor;

[0025] 2.2 Using the fission matrix method to solve high-order harmonics: Since the fission matrix is ​​usually a large sparse matrix with a relatively high degree of diagonalization, when solving its high-order eigenvectors, it is first converted into a general matrix, and then the Arnoldi algorithm is used to construct a Krylov subspace in the iterative process to approximate the eigenvalues ​​of the matrix for solution. Finally, the high-order harmonic matrix M is obtained, which includes:

[0026] a) First, convert the sparse fission 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 by the following steps. First, select the initial vector b and normalize it to get The iterative process first calculates ω k =Aν k , and orthogonalize to get, Normalized to get Construct the Hessenberg matrix

[0027] b) By solving the small matrix H m The eigenvalue λ i and the eigenvector y i , and get the approximate eigenvalues ​​of the matrix A. Using the orthogonal matrix V constructed in the iterative process m To obtain the high-order eigenvectors of A: ν i =V m y i Finally, by processing the eigenvalues ​​and eigenvectors, a high-order harmonic matrix M is obtained. This matrix contains the high-order eigenvalues ​​and eigenvectors of the fission matrix A, which satisfies Aν=λν, where: ν is the eigenvector, λ is the eigenvalue;

[0028] 2.3 The influence of fission neutron sources in other components other than the component where the detector is located on the detector count is not considered, and considering the symmetry of the components, only the fixed source calculation needs to be performed at the 1 / 8 position in the single component: given a 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, and no longer counts the fission process of the next generation of neutrons. The calculated results are arranged according to the fixed source position to obtain the corresponding matrix D of the detector.

[0029] Step 3: Screen the high-order harmonic library and select the appropriate core harmonic group, that is, reduce the dimension of the core power distribution: the counts of the detectors in the characteristic components are combined into the detector count vector R, and the equation DMX=R is solved to obtain the expansion coefficient vector X. The elements in X are arranged from large to small in numerical value, and the high-order harmonics corresponding to the elements with large numerical values ​​are selected as the core harmonic group.

[0030] Step 4: In the core criticality-burnup coupling calculation, a Monte Carlo program is used to simulate a sufficient number of neutrons, and a detector is defined at the center of the characteristic component to perform fission rate statistics. The obtained value is used as the actual measurement value of the detector count.

[0031] The simulation means that in the Monte Carlo program, the detector obtains the numerical value by counting the number or energy of neutrons when passing through a specific area, and records the relevant data when the particles pass through the predetermined detector position by tracking the path of the particles in the core, and finally outputs these statistical data for analyzing the power distribution of the reactor.

[0032] The number stated Where: Φ DET (r) is the count obtained at the detector position r, N total is the total number of particles tracked during the simulation, is the indicator function. If the particle passes through the detector position, then Otherwise 0.

[0033] Step 5: Select the core harmonic combination selected in step 3 and combine it with the core detector response matrix, and use the least squares method to re-solve the equation DMX=R to obtain the core harmonic combination M=[s 0, s 1, …,s n ] 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 PIN-level power reconstruction value P with the result P0 obtained by criticality-burnup coupling calculation, and calculate the relative error of each PIN gate element The root mean square error of all PIN elements.

[0034] The root mean square error Where: P i is the power reconstruction value of the i-th PIN gate cell, P i0 is the true value of the power of the i-th PIN gate element, and m is the number of PIN gate elements in the reactor. The reconstruction accuracy is verified based on the relative error and the root mean square error.

[0035] After specific experiments, Figure 2 In the core model shown in the figure, the power reconstruction is performed using the above method. The detector is arranged at the center of each component. The reconstructed power data is compared with the critical result. The results are shown in Figure 4-Figure 6 shown.

[0036] From the component response coefficients shown in Table 1, it can be seen that the fixed source in the component where the detector is located contributes 96.9% to the detector count, and the 24 components in the two outer layers contribute only 3.1% to the detector count. Therefore, the response coefficient matrix can be solved for fixed source calculations in a single component.

[0037] Table 1 Component response coefficient distribution

[0038] The result of power reconstruction using 4th-order high-order eigenvectors is as follows Figure 4As shown in the figure, under zero burnup conditions, since the initial error itself is small, a 2.4% enrichment component in the pile is replaced with a 1.6% enrichment component. At this time, the maximum deviation between the eigenvector and the critical result is 62%. After dimensionality reduction, the 1st, 2nd, 3rd, and 5th order eigenvectors are selected, and the maximum deviation is reduced to about 38% after reconstruction using high-order eigenvectors. The RMSE of power deviation is also reduced from 13.98 to 7.48.

[0039] The results of power reconstruction using 9 high-order eigenvectors are shown in Figure 5 As shown, after dimensionality reduction, eigenvectors of order 1, 4, 3, 7, 2, 5, 8, 9, and 13 are selected for reconstruction, and the maximum deviation is reduced from 62% to about 35%. When the first 8 orders of fitting are used, the RMSE of the power deviation is reduced from 13.98 to 9.04.

[0040] like Figure 6 As shown, for the operating condition with a burnup depth of 400 days, in order to increase the initial error, the burnup depth of one of the components with an enrichment degree of 1.6% 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.

[0041] Compared with the prior art, the innovation of the present invention lies in the application of PIN-level high-order harmonics for power expansion, combined with the detector response matrix and the detector reading, which can achieve accurate reconstruction of the reactor power distribution and directly obtain the PIN-level power distribution. This technical means is different from the previous component-level high-order harmonic expansion technology, which significantly improves the spatial resolution of reactor power monitoring and can accurately reflect the changes in power in the reactor.

[0042] In addition, the present invention also proposes a new technical means, that is, to build a high-order harmonic database and a detector response matrix database in advance, through which only the harmonic expansion coefficient needs to be calculated during the online monitoring stage, which greatly simplifies the calculation process and improves the real-time and high efficiency of the system. This simplified online calculation process avoids the problem of requiring real-time calculation of complex models in traditional methods, and significantly improves the real-time monitoring capability of reactor power.

[0043] Through these innovative technical means, this method makes full use of the actual measurement information of the in-core detectors, can accurately reconstruct the power distribution of each PIN level in the reactor, can reduce the relative error and root mean square error between the power distribution and the Monte Carlo simulation results, and improve the accuracy and efficiency of reactor monitoring.

[0044] The above-mentioned specific implementation can be partially adjusted in different ways by those skilled in the art without departing from the principle and purpose of the present invention. The protection scope of the present invention shall be based on the claims and shall not be limited by the above-mentioned specific implementation. Each implementation scheme within its scope shall be subject to the constraints of the present invention.

Claims

1. A method for online reconstruction of pressurized water reactor PIN level power based on fission matrix, characterized in that: According to the PWR core model, the PWR power database, in-core detector response matrix database and high-order harmonic database are successively constructed. The high-order harmonic database is subjected to dimensionality reduction and the in-core detector counts are obtained as actual measurement values ​​through criticality-burnup coupling. In the online stage, the core pin-by-pin power distribution is reconstructed using the least squares method based on the high-order harmonic database and the in-core detector response matrix database combined with the actual measurement values.

2. The method for online reconstruction of pressurized water reactor PIN level power based on fission matrix according to claim 1 is characterized in that: The high-order harmonic database is obtained in the following way: the reactor power is expressed as a linear combination of high-order harmonics, wherein the high-order harmonics are obtained by solving the fission matrix, which is constructed on the basis of the cell fission rate obtained by Monte Carlo simulation of a fixed neutron source, and represents the probability that the neutrons produced by the fission of a certain cell induce 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 spatially complete sets. When the core state is similar to the calculation condition of the high-order eigenvector set, this high-order harmonic library is also used for power expansion.

3. The method for online reconstruction of pressurized water reactor PIN level power based on fission matrix according to claim 1 is characterized in that: The in-core detector response matrix is ​​calculated by a fixed source to obtain the contribution rate of the fission neutron source generated by each PIN gate element in the component to the in-core detector reading, thereby obtaining the mapping relationship between the core power distribution and the in-core detector count, that is, the detector response matrix.

4. The method for online reconstruction of pressurized water reactor PIN level power based on fission matrix according to claim 1 is characterized in that: The reconstruction means that after the reactor power is expanded with high-order harmonics, the coefficients of the high-order harmonics are obtained by combining the detector response matrix and the simultaneous equations to reconstruct the reactor power.

5. The method for online reconstruction of PIN-level power of a pressurized water reactor based on a fission matrix according to any one of claims 1 to 4, characterized in that: include: Step 1: Establish a pressurized water reactor core model, set components with different enrichments, classify component types according to their positions in the reactor, and arrange neutron detectors in the central measurement channel of the characteristic components, i.e., the position of the yellow icon in the figure; Step 2: Before power reconstruction, construct a pressurized water reactor power distribution database, a harmonic database under typical conditions, and an in-core detector response matrix database, specifically including: 2.1 Monte Carlo program is used to perform criticality-burnup coupling calculation to obtain the core power distribution under normal operating conditions. This distribution is used as the reference solution, that is, the true value of the core power distribution. The fission cross section is adjusted according to the 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 and the final power distribution is calculated, which is: 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, S(r,Ω,E,t) is the external source term, and the Monte Carlo program approximately obtains the spatial and energy distribution of neutrons by simulating enough neutron trajectories and counting their propagation processes in the reactor; 2.2 Using the fission matrix method to solve high-order harmonics: Since the fission matrix is ​​usually a large sparse matrix with a relatively high degree of diagonalization, when solving its high-order eigenvectors, it is first converted into a general matrix, and then the Arnoldi algorithm is used to construct a Krylov subspace in the iterative process to approximate the eigenvalues ​​of the matrix for solution, and finally a high-order harmonic matrix is ​​obtained; 2.3 The influence of fission neutron sources in other components other than the component where the detector is located on the detector count is not considered, and considering the symmetry of the components, it is only necessary to perform fixed source calculations at 1 / 8 of the position in a single component: given a 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, and no longer counts the fission process of the next generation of neutrons. The calculated results are arranged according to the fixed source position to obtain the corresponding matrix D of the detector; Step 3: Screen the high-order harmonic library and select the appropriate core harmonic group, that is, reduce the dimension of the core power distribution: the counts of the detectors in the characteristic components are combined into the detector count vector R, and the equation DMX=R is solved to obtain the expansion coefficient vector X. The elements in X are arranged from large to small in value, and the high-order harmonics corresponding to the elements with large values ​​are selected as the core harmonic group; Step 4: In the core criticality-burnup coupling calculation, a Monte Carlo program is used to simulate a sufficient number of neutrons, and a detector is defined at the center of the characteristic component to perform fission rate statistics, and the obtained value is used as the actual measurement value of the detector count; Step 5: Select the core harmonic combination selected in step 3 and combine it with the core detector response matrix, and use the least squares method to re-solve the equation DMX=R to obtain the core harmonic combination M=[s 0, s 1, …,s n ] 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 PIN-level power reconstruction value P with the result P0 obtained by criticality-burnup coupling calculation, and calculate the relative error of each PIN gate element The root mean square error of all PIN gate elements.

6. The method for online reconstruction of pressurized water reactor PIN level power based on fission matrix according to claim 5 is characterized in that: The high-order harmonic matrix is ​​obtained in the following way: a) First, convert the sparse fission matrix into a general matrix to make it suitable for the Arnoldi algorithm. The Arnoldi algorithm iteratively constructs a Krylov subspace to approximate the eigenvalues ​​and eigenvectors of the matrix. Given an initial vector, the Krylov subspace is constructed through the following steps. First, the initial vector b is selected for normalization to obtain The iterative process first calculates ω k =Aν k , and orthogonalize to get, Normalized to get Construct the Hessenberg matrix b) By solving the small matrix H m The eigenvalue λ i and the eigenvector y i , get the approximate eigenvalues ​​of matrix A, and use the orthogonal matrix V constructed in the iterative process m To obtain the high-order eigenvectors of A: ν i =V m y i Finally, by processing the eigenvalues ​​and eigenvectors, a high-order harmonic matrix M is obtained. This matrix contains the high-order eigenvalues ​​and eigenvectors of the fission matrix A, which satisfies Aν=λν, where: ν is the eigenvector and λ is the eigenvalue.

7. The method for online reconstruction of pressurized water reactor PIN level power based on fission matrix according to claim 5 is characterized in that: The simulation means that in the Monte Carlo program, the detector obtains the numerical value by counting the number or energy of neutrons when passing through a specific area, and records the relevant data when the particles pass through the predetermined detector position by tracking the path of the particles in the core, and finally outputs these statistical data for analyzing the power distribution of the reactor.

8. The method for online reconstruction of pressurized water reactor PIN level power based on fission matrix according to claim 7 is characterized in that: The number stated Where: Φ DET (r) is the count obtained at the detector position r, N total is the total number of particles tracked during the simulation, is the indicator function. If the particle passes through the detector position, then Otherwise 0.

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