A method for measuring the worth of a control rod in a nuclear reactor based on parameter inversion

Abstract

The application provides a control rod worth measurement method based on parameter inversion in a nuclear reactor, which comprises determining a nuclear cross section parameter of a core region where a control rod to be measured is located and further calculating a worth parameter of the control rod to be measured, wherein the step of determining the nuclear cross section parameter comprises: inserting the control rod to be measured into the core and recording a measured probe signal in the process; simulating insertion of the control rod to be measured into the core by a three-dimensional time-space dynamics program and calculating a corresponding simulated probe signal, wherein the core is divided into a plurality of basic calculation units provided with initial nuclear cross section parameters; judging whether the simulated probe signal is consistent with the measured probe signal, and in the case of inconsistency, updating the nuclear cross section parameter of a basic calculation unit where the control rod to be measured is located and recalculating the simulated probe signal until the recalculated simulated probe signal is consistent with the measured probe signal, and taking the nuclear cross section parameter used for the final calculation as the determined nuclear cross section parameter.

Description

Technical Field

[0001] This invention relates to nuclear reactor physics testing techniques, and in particular to a method for measuring the value of control rods in a nuclear reactor. Background Technology

[0002] Control rods play a crucial role in reactor startup, shutdown, and power regulation. For example, after a nuclear power plant replaces its nuclear fuel, it conducts startup tests, which are a key part of the overhaul. Among these tests, the control rod value measurement test is the main component and the most time-consuming part of the startup test.

[0003] Early methods for measuring the value of control rods included boron dilution, rod exchange, and neutron doubling period methods. For example, in the boron dilution method, control rods need to be inserted at an extremely slow rate, followed by adjusting the boron concentration in the moderator to bring the reactor to criticality. Reactivity is calculated only after the detector readings stabilize, making it a very lengthy process. In the rod exchange method, the group of control rods with the highest value is first calibrated using boron dilution. Then, using this group as a reference, the group of rods to be tested is inserted, while the reference group is slightly raised to compensate for the negative reactivity introduced by the tested group, maintaining the core's criticality. The value of the tested group can be estimated based on the value of the reference rods after the detector readings stabilize. The rod exchange method is slightly faster than the boron dilution method; however, measuring the value of a single group of rods still takes about 2 hours, meaning measuring the entire group would take 1-2 days, which is still a significant time expense in this field.

[0004] In the 1990s, Westinghouse proposed a new rod-cutting method called Dynamic Rod Cutting Method (DRWM). This method is based on the results calculated by the inverse dynamic formula of the point reactor. The reactivity can be easily calculated from the total core power using the inverse dynamic formula. However, there are two error factors in the actual core arrangement that prevent the detector signal from correctly reflecting the change in the total core power: (1) the influence of the space effect. The insertion of control rods will directly cause the change in the spatial distribution of transient neutrons in the core, so the detector reading during the rod insertion process is not proportional to the total core power; (2) the influence of the delayed neutron effect. The spatial distribution of delayed neutrons changes more slowly than that of transient neutrons. Therefore, the inverse dynamic formula yields a kind of "dynamic reactivity" rather than the static reactivity we expect. To reduce the impact of the above effects, the aforementioned dynamic bar-cutting method performs a high-precision computer numerical simulation of the bar insertion process before the experiment to obtain the static spatial correction factor (SSF) and dynamic spatial correction factor (DSF). During the experiment, the bar group to be tested is inserted to the bottom at the maximum step rate, and the detector signal of the whole process is recorded. Then, by analyzing the detector signal, the integral value and differential value of the bar group to be tested are obtained.

[0005] The dynamic bar marking method significantly reduces the time required for bar marking experiments, requiring only about 15 minutes to measure the value of a set of bars. This method has been adopted by many countries, and while there may be slight differences in implementation details for different reactor types, the basic framework is based on the dynamic bar marking method proposed by Westinghouse.

[0006] However, known dynamic bar-cutting methods of this type perform poorly when introducing large amounts of reactivity in a short period of time, and the measurement accuracy of differential values ​​is somewhat lacking. Furthermore, since it takes approximately 200 seconds for the control rod to be inserted from the top to the bottom of the core at the maximum step rate, this is still time-consuming, and the detector count rate drops by two orders of magnitude during the insertion process, reaching a minimum of 10. -11 A. Noise can have a significant impact on measurement results.

[0007] Furthermore, existing technologies also include the drop rod method for measuring reactivity or control rod value. These methods typically involve dropping the control rod to be tested directly into the reactor core in a free-fall manner. Reactivity is generally calculated using the ratio of the neutron count rate before and after the drop rod's fall, or by employing an inverse dynamic formula for the reactor core. For example, Chinese patent document CN100492547C uses an inverse dynamic formula for reactivity calculation, while CN109215822B uses a method of superimposing static reactivity with a correction factor generated by a spatiotemporal dynamics program. These known drop rod methods can only obtain the integral value of the test rod group, but not its differential value. Summary of the Invention

[0008] The present invention aims to propose a new method for measuring the value of control rods, which should be able to measure the value of control rods at a faster speed and with higher accuracy.

[0009] To address this, the present invention proposes a method for measuring the value of control rods in a nuclear reactor. This method includes determining the nuclear cross-sectional parameters of the core region where the control rod under test is located, related to the insertion depth of the control rod, and calculating the value parameters of the control rod based on the determined nuclear cross-sectional parameters. The step of determining the nuclear cross-sectional parameters includes: inserting the control rod under test into the core and recording time-correlated measured detector signals from pre-arranged neutron detectors used in the core during the insertion process; simulating the insertion of the control rod under test into the core using a three-dimensional spatiotemporal dynamics program and calculating the corresponding time-correlated simulated detector signals, wherein the core is divided into several basic computational units, each with preset initial nuclear cross-sectional parameters; determining whether the simulated detector signals match the measured detector signals, and if they do not match, updating the nuclear cross-sectional parameters of the basic computational unit where the control rod under test is located and recalculating the simulated detector signals until the recalculated simulated detector signals match the measured detector signals, and using the final nuclear cross-sectional parameters used to calculate the simulated detector signals as the determined nuclear cross-sectional parameters.

[0010] It is understood that the control rod value is a measure of the change in core reactivity caused by the insertion of a control rod into the core. The control rod affects reactivity by influencing the nuclear cross-section, particularly the absorbing cross-section, of its core region. This invention proposes that, to obtain the control rod value, the influence of the control rod on the regional nuclear cross-section can be determined first. This invention proposes that, using known computational tools, including three-dimensional spatiotemporal dynamics programs, the changes related to core physics caused by the free fall of the control rod within the core can be simulated. Furthermore, combined with knowledge of neutron detectors, the signals generated by the neutron detectors can also be simulated. This invention proposes that the objective can be set to match the simulated detector signal with the measured detector signal. The nuclear cross-section parameters of the core region where the control rod is located, related to the real-time position of the control rod under test, can be solved iteratively, thereby calculating the control rod value parameters.

[0011] Therefore, this invention provides a novel method for measuring the value of control rods.

[0012] Specifically, the aforementioned simulation of the insertion of the control rod under test into the reactor core using a three-dimensional spatiotemporal dynamics program and the calculation of the corresponding time-related simulated detector signal may include: performing a simulation using a three-dimensional spatiotemporal dynamics program to obtain the time-related simulated core power distribution corresponding to the simulated insertion process of the control rod under test into the reactor core; obtaining the detector response function corresponding to the actual neutron detector; and calculating the simulated detector signal based on the simulated core power distribution and the detector response function.

[0013] Specifically, the aforementioned determination of whether the simulated detector signal matches the measured detector signal may include: discretizing the simulated detector signal and the measured detector signal in time according to the same rules, and determining whether the norm of the difference between the simulated detector signal and the measured detector signal is less than a preset threshold. If it is less than the threshold, the simulated detector signal matches the measured detector signal; otherwise, the simulated detector signal does not match the measured detector signal.

[0014] In particular, the three-dimensional spatiotemporal dynamics program involved in this invention is preferably configured to handle numerical calculations related to the three-dimensional transient neutron diffusion equation.

[0015] Specifically, the control rods to be tested are inserted into the reactor core either by free fall or by controlled propulsion.

[0016] Specifically, the aforementioned calculation of the value parameters of the control rod under test based on the determined core cross-section parameters may include: obtaining the corresponding core cross-section parameters for each depth of the control rod under test in the core, thereby performing static calculations of the core to obtain the static reactivity of the core, and calculating the value parameters of the control rod under test based on the static reactivity of the core.

[0017] Specifically, the value parameters referred to in this invention include differential value and / or integral value. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the process for conducting a rod measurement test according to an embodiment of the present invention.

[0019] Figure 2 This is a schematic diagram of the calculation process for determining the nuclear cross-sectional parameters of the core region where the control rods are located, according to an embodiment of the present invention. Detailed Implementation

[0020] The specific embodiments and advantages of the present invention will be described below with reference to the accompanying drawings.

[0021] According to the present invention, a method for measuring the value of a control rod in a nuclear reactor includes: step S1, determining the nuclear cross-sectional parameters of the core region where the control rod to be tested is located, which are related to the insertion depth of the control rod to be tested; and step S2, calculating the value parameters of the control rod to be tested based on the determined nuclear cross-sectional parameters.

[0022] According to the present invention, step S1 may include two aspects: (1) conducting an actual rod insertion measurement test (actual test), in which a neutron detector for the reactor core is pre-arranged, and the control rod to be tested is inserted into the reactor core, and the detector signal (actual detector signal) corresponding to the entire process of the control rod to be tested being inserted into the reactor core is recorded. (2) performing simulation calculation and iterative update, wherein the reactor core is divided into several basic calculation units, each basic calculation unit is preset with initial nuclear cross-section parameters, starting from the preset parameters, a three-dimensional spatiotemporal dynamics program is called to simulate the rod insertion scenario, and the corresponding timing detector signal (simulated detector signal) under the simulated scenario is calculated, and then it is determined whether the simulated detector signal matches the actual detector signal, and if it is determined that they do not match, the nuclear cross-section parameters of the basic calculation unit where the control rod to be tested is located are updated and the simulated detector signal is recalculated, and so on, until the recalculated simulated detector signal matches the actual detector signal, and the nuclear cross-section parameters finally used to calculate the simulated detector signal are taken as the determined nuclear cross-section parameters.

[0023] It is understandable that the first simulation calculation based on preset parameters can be completed before the actual test. It is also understandable that, apart from the unknown nuclear cross-section parameters, other necessary scenario parameters used for simulation are readily available (e.g., core dimensions), or some scenario parameters can be specified, such as the action mode of the control rod under test (e.g., free fall, stepping, etc.).

[0024] Please refer to Figure 1 ,exist Figure 1The table shows, from left to right, an example flow of a test of an actual control rod measurement according to an embodiment of the present invention. The flow may be as follows: (1) lifting all control rods out of the core 1; (2) selecting the control rod 10 to be tested, inserting the selected control rod 10 into the core 1, and recording the detector signal (measured detector signal) from the pre-arranged neutron detector 2 for the core 1 as the control rod 10 moves from the top of the core to the bottom of the core over time; (3) lifting the control rod 10 out of the core, in preparation for the measurement test of other control rods 20.

[0025] In the context of the terminology used in this invention, the term "control rod" is not distinguished by singularity or plurality. For example, control rod 10 can be a single control rod or a group of control rods (also referred to as a "rod group"). Preferably, for safety reasons, a group of symmetrically arranged control rods is inserted to ensure the symmetry of the core power distribution; however, the method proposed in this invention can handle cases of skewed power distribution, therefore, theoretically, this invention can measure a single control rod.

[0026] Figure 1 Two or more control rods are shown as an example only, but more control rods may be used in practice. Measurements for each or each set of control rods are performed sequentially according to the procedure described above.

[0027] In some embodiments, the control rod 10 is inserted into the core 1 in a free-fall manner, which significantly saves testing time and improves efficiency. In other embodiments, the control rod 10 is inserted into the core 1 in a controlled-push manner, for example, by inserting it at a maximum step rate. In principle, the present invention allows for various rod insertion methods.

[0028] Neutron detector 2 may be any neutron detector, such as a proportional counter. In some embodiments, neutron detector 2 can be used to measure, for example, the neutron flux density at a location in space. Neutron detector 2 is arranged inside and / or outside the reactor core. There may be one or more neutron detectors 2.

[0029] The signal generated by neutron detector 2 reflects the real-time status of neutrons in the reactor core, and therefore also reflects the operating status of the reactor core, particularly the real-time power distribution of the reactor core.

[0030] In some embodiments, the neutron detector 2 is informationally connected to a computational analysis unit (not shown), which is configured to perform computational analysis on signals from the neutron detector 2. Specifically, the computational analysis unit is configured to invoke a three-dimensional spatiotemporal dynamics program. Specifically, the computational analysis unit outputs value parameters, including differential and / or integral values, for one or a set of control rods used in the experiment.

[0031] In some embodiments, the signal from the neutron detector 2 is time-discrete, or is processed (e.g., by a computational analysis unit) to be time-discrete.

[0032] In some embodiments, the following processing is performed to remove noise from the measured detector signal: a moving average is applied, followed by de-meaning. The detector noise in the experiment mainly consists of two parts: background noise, which can be considered a constant value; and Gaussian noise caused by counting fluctuations, etc. Using a moving average to filter the Gaussian noise, followed by de-meaning to obtain a signal with a mean of 0, effectively filters out the background noise. It is worth noting that if a free-fall method is used for rod insertion, each insertion only takes 2-3 seconds, resulting in a high count rate after insertion and making it less susceptible to noise.

[0033] Please refer to Figure 2 , Figure 2 This is a schematic diagram of the calculation process for determining the nuclear cross-sectional parameters of the core region where the control rods are located, according to an embodiment of the present invention.

[0034] Essentially, the calculation used as an example utilizes simulations of reactor operating conditions and detector responses, attempting to iteratively solve for core region nuclear cross-sectional parameters related to the depth (or “rod position”) of the control rods inserted into the core, with the iterative goal of making the simulated detector signal substantially consistent with the measured detector signal.

[0035] This calculation involves the use of a three-dimensional spatiotemporal dynamics program. Three-dimensional spatiotemporal dynamics programs are known in the art for simulating and analyzing complex physical processes within nuclear reactors. Theoretically, this invention can employ any three-dimensional spatiotemporal dynamics program, such as the program mentioned in the paper "Transient Block Green's Function Method and Its Coupling with Thermo-Hydraulic Dynamics".

[0036] For example, the three-dimensional spatiotemporal dynamics program 3 divides the test reactor core 1 into several basic computational units (e.g., homogenized nodes). Here, it is understood that a basic computational unit is a spatial region whose nuclear physical properties (e.g., the equivalent nuclear cross-sectional parameters of that region) are determined by its contents (e.g., the fuel assemblies and control rods of the core). It is understood that as the control rods are inserted into the core, the space occupied by the control rods in the core will change, and thus the nuclear cross-sectional parameters of the basic computational unit in which the control rods reside will change.

[0037] In this embodiment of the invention, the core cross-sectional parameters of the regions corresponding to each control rod position are the quantities to be determined. For example, core cross-sectional parameters are preset for each basic calculation unit, and other necessary parameters or settings are provided (such as spatial size parameters, control rod action modes, etc., which are easy to keep consistent with actual rod insertion tests), so that the three-dimensional spatiotemporal dynamics program 3 can perform reactor physics simulation calculations, especially simulating rod insertion scenarios, and calculating the required reactor physics information.

[0038] For example, the time-dependent core power distribution (corresponding to the simulated control rod insertion process) is calculated using the three-dimensional spatiotemporal dynamics program 3.

[0039] For example, a response function of neutron detector 2 is obtained, which reflects the relationship between the detector signal and the core power distribution, particularly the response of the detector signal to the core power distribution. It is understood that the response function is determined by the properties of neutron detector 2 itself and can be obtained through methods known in the art.

[0040] Therefore, by combining the input response function, it is possible to predict the response of neutron detector 2 to the simulated core power distribution, and thus obtain the simulated detector signal corresponding to the simulated rod insertion process.

[0041] This invention also allows for the calculation of analog detector signals through other methods not illustrated.

[0042] The simulated detector signal is compared with the previously measured detector signal to determine whether the current simulated detector signal matches the measured detector signal. If they do not match, the core cross-sectional parameters of the basic calculation unit where the control rod under test is located are updated and the simulated detector signal is recalculated. This process is repeated until the simulated detector signal matches the measured detector signal. The final core cross-sectional parameters used for calculation (generally, the preset parameters need to be iterated and the last updated parameter is taken) are used as the final determined core cross-sectional parameters and output or stored as the calculation result.

[0043] For example, the analog detector signal and the measured detector signal are discretized in time according to the same rules. Therefore, the time-related signal can be converted into a finite-dimensional vector. Based on this, the difference between the analog detector signal and the measured detector signal is calculated, and then the norm of the difference vector, such as the second-order norm (i.e., root mean square error), is determined to be less than a preset threshold. If it is less than the threshold, it is considered that the current analog detector signal and the measured detector signal have matched.

[0044] Understandably, it is possible to conduct Figure 1 Before the measurement experiment, the simulated detector signal calculation based on preset parameters is performed, that is, the initial values ​​of the iteration are calculated and stored in advance to save computing power and improve efficiency.

[0045] For example, the update logic (search logic) for the kernel cross-section parameters to be determined can employ common optimization algorithms, such as Newton-type algorithms, or some heuristic algorithms, such as particle swarm optimization, genetic algorithms, etc.

[0046] In particular, in some embodiments, the calculation process for determining the nuclear cross-section parameters of the present invention is mathematically equivalent to solving the following system of nonlinear equations:

[0047]

[0048] in, This represents the analog detector signal. The values ​​represent the measured detector signal, where Σ represents the nuclear cross-section parameter to be determined (especially the region equivalent nuclear cross-section parameter), t represents time, r represents the neutron position vector, E represents the neutron energy, R(r,E,t) represents the detector response function, p(r,E,t) represents the core power distribution, Φ(r,E,t) represents the core neutron flux distribution, F represents the neutron production operator, L represents the neutron leakage operator, and S(r,E,t) represents the neutron source term. Other unmentioned symbols should be understood according to their usual meanings in reactor physics.

[0049] It can be understood that Equation 1a corresponds to the aforementioned method of making the simulated detector signal match the measured detector signal, Equation 1b corresponds to the aforementioned method of obtaining the simulated detector signal from the response function and the core power distribution, and Equation 1c corresponds to the aforementioned method of using a three-dimensional spatiotemporal dynamics program for simulation.

[0050] It is understandable that the regional equivalent core cross-section parameter Σ is related to the position (insertion depth) of the control rod in the core.

[0051] Furthermore, to solve the above nonlinear equation system, a fully implicit difference scheme can be used for time discretization. The time-discrete equation system takes the form:

[0052]

[0053] In some embodiments, the step of determining the kernel cross-section parameters to be determined in this invention is equivalent to iteratively solving the aforementioned nonlinear equation system. Exemplarily, classical Newton's method, Chord's method, Shamanskii method, and other nonlinear iterative methods can be employed.

[0054] In some embodiments, the core cross-sectional parameters of the core region where the control rod under test is inserted into the core are calculated by correcting for control rod end effects. For example, assuming t i-1 Flux distribution at time Φ i-1 The value of t has been determined; now we need to solve for t. i Flux distribution at time Φ iand cross section Σ i We inserted the control rod section into the segment cross-section. The value was determined using a flux-weighted (reaction rate conservation) method, and based on this cross section. Solve for the next time step t i flux distribution At this time, according to Flux-weighted summation is performed on the cross section of the nodal segment to obtain... like Then it is considered that convergence has occurred; otherwise, according to Solve Then according to calculate Until

[0055] Step S1 can therefore be achieved.

[0056] According to the present invention, step S2 may specifically include: obtaining the corresponding nuclear cross-section parameters for each position of the control rod to be tested in the core, thereby performing static calculations of the core to obtain the static reactivity of the core, and then performing further calculations based on the static reactivity of the core to obtain the value parameters (integral value and / or differential value) of the control rod to be tested.

[0057] The present invention has the following advantages: (1) Since the calculation is performed by a three-dimensional spatiotemporal dynamics program, there is no need to make a point-to-pile approximation. Therefore, the spatial effect generated by the control rod motion can be fully considered, and a higher accuracy control rod value measurement result can be obtained; (2) In particular, compared with DRWM, the present invention allows the control rod to be tested to be directly and freely dropped into the core, thereby further shortening the measurement test time. This also avoids the situation of the detector count rate being too low and reduces the influence of noise; (3) Compared with the known drop rod method in the prior art, the present invention allows the integral value and differential value of the control rod to be tested to be obtained at one time.

[0058] Although some embodiments of the invention have been shown and described, those skilled in the art will understand that various combinations, variations, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A method for measuring the value of control rods in a nuclear reactor based on parameter inversion, the method comprising: Determine the nuclear cross-sectional parameters of the core region where the control rod to be tested is located, which are related to the insertion depth of the control rod to be tested; and The value parameters of the control rod under test are calculated based on the determined nuclear cross-section parameters. The determination of the nuclear cross-sectional parameters related to the insertion depth of the control rod in the core region where the control rod to be tested is located includes: Insert the control rod under test into the reactor core and record the time-dependent measured detector signals from the pre-arranged neutron detectors used in the reactor core during the insertion process. The insertion of the control rod under test into the reactor core was simulated using a three-dimensional spatiotemporal dynamics program, and the corresponding time-correlated simulated detector signal was calculated. The reactor core was divided into several basic computational units, each with preset initial nuclear cross-section parameters; and Determine whether the simulated detector signal matches the measured detector signal. If they do not match, update the core cross-sectional parameters of the basic calculation unit where the control rod under test is located and recalculate the simulated detector signal until the recalculated simulated detector signal matches the measured detector signal. The final core cross-sectional parameters used to calculate the simulated detector signal are then used as the determined core cross-sectional parameters.

2. The method for measuring the value of control rods in a nuclear reactor based on parameter inversion according to claim 1, characterized in that, The step of simulating the insertion of the control rod under test into the reactor core using a three-dimensional spatiotemporal dynamics program and calculating the corresponding time-related simulated detector signal includes: performing a simulation using the three-dimensional spatiotemporal dynamics program to obtain the time-related simulated core power distribution corresponding to the simulated insertion process of the control rod under test into the reactor core; obtaining the detector response function corresponding to the neutron detector; and calculating the simulated detector signal based on the simulated core power distribution and the detector response function.

3. The method for measuring the value of control rods in a nuclear reactor based on parameter inversion according to claim 1, characterized in that, The step of determining whether the simulated detector signal matches the measured detector signal includes: discretizing the simulated detector signal and the measured detector signal in time according to the same rules, and determining whether the norm of the difference between the simulated detector signal and the measured detector signal is less than a preset threshold. If it is less than the threshold, the simulated detector signal matches the measured detector signal; otherwise, the simulated detector signal does not match the measured detector signal.

4. The method for measuring the value of control rods in a nuclear reactor based on parameter inversion according to claim 1, characterized in that, The three-dimensional spatiotemporal dynamics program is suitable for handling numerical calculations related to the three-dimensional transient neutron diffusion equation.

5. The method for measuring the value of control rods in a nuclear reactor based on parameter inversion according to claim 1, characterized in that, The control rod to be tested is inserted into the reactor core in a free-fall manner, or in a controlled-propulsion manner.

6. The method for measuring the value of control rods in a nuclear reactor based on parameter inversion according to claim 1, characterized in that, The calculation of the value parameters of the control rod under test based on the determined core cross-section parameters includes: obtaining the corresponding core cross-section parameters for each depth of the control rod under test in the core, thereby performing static calculations of the core to obtain the static reactivity of the core, and calculating the value parameters of the control rod under test based on the static reactivity of the core.

7. The method for measuring the value of control rods in a nuclear reactor based on parameter inversion according to claim 1, characterized in that, The value parameters include integral value and / or differential value.

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