A method for selecting refueling channels for CANDU reactor based on backtracking algorithm

Abstract

The present invention belongs to the field of nuclear power technology, and specifically relates to a CANDU reactor refueling channel selection method based on a backtracking algorithm. It comprises the following steps: Step 1: defining refueling channel selection constraints; Step 2: constructing a candidate refueling channel pool; Step 3: refueling channel search based on a backtracking algorithm; Step 4: evaluation and ranking of feasible refueling schemes; Step 5: using an existing core calculation program to carry out pre-simulation calculations and ranking of several feasible refueling schemes ranked high; Step 6: selecting the final refueling scheme based on the ranking. The beneficial effect is that: the present invention can search the entire solution space within an acceptable time, and can find all feasible solutions that meet the refueling channel selection constraints, thereby overcoming the limitations of manual channel selection by core management engineers and improving the standardization of refueling scheme design; by evaluating and ranking feasible solutions, the refueling design scheme can be optimized and the quality of the refueling scheme can be improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of nuclear power, and in particular relates to a CANDU reactor refueling channel selection method based on a backtracking algorithm. Background Art

[0002] The CANDU heavy water reactor adopts a horizontal pressure tube grid structure with a total of 380 relatively independent fuel channels (such as Figure 1 As shown in ① in the figure), it uses natural uranium as nuclear fuel and heavy water as coolant and moderator. From the perspective of core fuel management, the significant difference between the CANDU reactor and reactors that usually use shutdown method for refueling (such as pressurized water reactors) lies in its online refueling feature. The refueling direction of adjacent channels is opposite, and the refueling direction is along the flow direction of the coolant. Refueling is not only the main means to compensate for the reactivity consumption caused by daily operation, but also the main method to control the core to be in an ideal power distribution for a long time. Another unique feature is that 14 Liquid Zone Controller Units (LZCU) are arranged vertically in the core. Each unit is filled with light water, such as Figure 1 As shown in Figure ②, light water has a much larger absorption cross-section than heavy water. Therefore, when there is a reactivity disturbance in the core, such as refueling, by adjusting the water level of each LZCU, the thermal neutron utilization coefficient in the local area of ​​the reactor can be changed, thereby achieving the purpose of controlling reactivity and local area power.

[0003] The CANDU reactor utilizes a non-stop refueling system. During routine operation, the refueling plan (including channel selection and refueling sequence) must maintain the reactor's reactivity required for full power operation while also balancing fuel economy with the impact of refueling on reactor operation and thermal safety. Therefore, refueling plan design, particularly channel selection—selecting 7-8 fuel channels from the reactor's 380 channels at a time—is the greatest task and challenge facing CANDU core management engineers. While various refueling design and optimization methods and procedures have been developed for this typical multi-objective planning problem, their practical application has been less than ideal.

[0004] Currently, refueling plan design for CANDU reactors, both domestically and internationally, relies largely on manual labor. While a relatively mature set of expert criteria for selecting refueling channels has been established, and core management engineers have accumulated years of experience in refueling design, the large scale of the problem, the numerous optimization objectives, and the tight time constraints make manually designing a "good" refueling plan nearly impossible. Furthermore, refueling plans proposed by different engineers can vary significantly. Summary of the Invention

[0005] The purpose of the present invention is to provide a CANDU reactor refueling channel selection method based on a backtracking algorithm. The method uses the search, pruning, backtracking and other strategies of the backtracking algorithm to traverse the refueling solution space. During the traversal process, all feasible solutions or optimal solutions that meet the refueling design objectives and constraints are recorded and found.

[0006] The technical solution of the present invention is as follows: a method for selecting a CANDU reactor refueling channel based on a backtracking algorithm, comprising the following steps:

[0007] Step 1: Define the material change channel selection constraints;

[0008] Step 2: Build a candidate material exchange channel pool;

[0009] Step 3: Search for material change channel based on backtracking algorithm;

[0010] Step 4: Evaluation and ranking of feasible material replacement plans;

[0011] Step 5: Use the existing core calculation program to conduct preliminary simulation calculations and ranking of several feasible refueling schemes that are ranked high;

[0012] Step 6: Select the final material replacement plan based on the ranking.

[0013] The material change selection constraints in step 1 include:

[0014] Constraint on the number of refueling channels in each core area: The number of refueling channels in each core area is less than the preset threshold;

[0015] Material change channel direction balance constraint: The difference in the number of material change channels between side A and side C is less than the preset threshold;

[0016] Material change channel interval constraint: the distance between material change channels is greater than the preset threshold;

[0017] Liquid zone controller water level constraint: After channel material change, the LZC water level range and maximum absolute deviation are less than the preset threshold;

[0018] Reactivity constraint for material change introduction: The reactivity introduced by the material change channel is greater than the preset threshold.

[0019] In step 2, based on the unloading burnup, excess power factor, and residence time of each channel, fuel channels that simultaneously meet the following three conditions are selected from the 380 channels in the entire stack to form a candidate refueling channel pool:

[0020] Channel unloading fuel consumption: Channels with a relative unloading fuel consumption, i.e., a ratio of channel unloading fuel consumption to time-averaged fuel consumption greater than or equal to a specified value, are selected as candidates;

[0021] Channel overpower factor: Channels whose overpower factors of the channel itself and a surrounding gate element, i.e., the ratio of the current instantaneous power to the time-averaged reference power is less than or equal to the specified value, are selected as candidates;

[0022] Channel residence time: The channel itself and the surrounding gate cell channel whose residence time, that is, the difference from the last material change time, is greater than or equal to the specified value is selected as an alternative.

[0023] The step 3 includes:

[0024] Step 31: Define the backtracking algorithm state space

[0025] The state space is a complete representation of the intermediate decision states maintained by the algorithm during the search process. It records the selected channel set and candidate channel list in the current state. The initial state of the state space is: the selected channel set is empty and the candidate channel list is empty.

[0026] Step 32: Define the constraint pruning function

[0027] The constraint pruning function is a set of logical judgment rules used to terminate the branch search that does not meet the constraints early during the backtracking process. It includes the following rules:

[0028] Whether the constraints on the number of refueling channels in each area of ​​the core are met, whether the constraints on the direction balance of the refueling channels are met, and whether the constraints on the spacing of the refueling channels are met;

[0029] Step 33: Define the judgment conditions for material change channel selection

[0030] The selected refueling channel set meets the refueling plan; verify whether the LZC water level extreme difference value and the maximum absolute deviation value meet the constraints after refueling in all channels; verify whether the reactivity introduced by all refueling channels meets the constraints;

[0031] Step 34: Use the backtracking algorithm to search for the material change channel.

[0032] The step 34 includes:

[0033] Step 341: Initialize the state space, select a channel from the material change channel selection pool to add to the material change selected channel set, and the candidate channel list is the remaining channels in the selection pool;

[0034] Step 342: Select a channel from the candidate channel list based on the current state space;

[0035] Step 343: Update the state space, add the selected channel to the selected channel set, and remove the selected channel from the candidate channel list;

[0036] Step 344: Check whether the selected channel set in the current state space meets the material change constraint requirements according to the constraint pruning function;

[0037] Step 345: If satisfied, retain the current state space; if not satisfied, backtrack to the previous state space;

[0038] Step 346: Repeat steps 342 to 345 until the selected refueling channel set meets the refueling plan or there are no remaining channels in the candidate channel list;

[0039] Step 347: Based on the judgment conditions of the material exchange channel selection scheme, determine whether the selected material exchange channel set is a feasible solution, i.e., a feasible material exchange scheme;

[0040] Step 348: If it is a feasible solution, keep it; if it is an infeasible solution, discard it;

[0041] Step 349: Remove the channel selected in step 341 from the material change channel selection pool, and repeat steps 341 to 349 until the number of channels in the material change selection pool is less than the material change plan.

[0042] The step 4 includes:

[0043] Step 41: Definition and calculation of feasible solution evaluation indicators;

[0044] Evaluation index 1 is the maximum absolute deviation value of the LZC water level of the feasible solution. The smaller the evaluation index, the higher the ranking. Evaluation index 2 is the reactivity of the feasible solution. The larger the evaluation index, the higher the ranking.

[0045] Step 42: Perform multi-level sorting on the feasible solutions according to evaluation index 1 and evaluation index 2 respectively.

[0046] The step 5 comprises:

[0047] Step 51: Preliminary simulation calculation of feasible material replacement scheme;

[0048] Step 52: Calculate the core power margin of each feasible solution based on the pre-simulation results, and define it as evaluation index 3. The larger the evaluation index, the higher the ranking.

[0049] Step 53: Perform multi-level sorting on the simulated feasible solutions according to evaluation index 3, evaluation index 1 and evaluation index 2 respectively.

[0050] The beneficial effects of the present invention are:

[0051] (1) Improve the design quality of material replacement scheme

[0052] The CANDU reactor refueling scheme selection method based on backtracking algorithm proposed in the present invention can search the entire solution space within an acceptable time and find all feasible solutions that meet the refueling channel selection constraints, thereby overcoming the limitations of manual channel selection by core management engineers and improving the standardization of refueling scheme design; through the evaluation and ranking of feasible solutions, the refueling design scheme is optimized and the quality of the refueling scheme is improved.

[0053] (2) Improving the thermal safety margin of reactors

[0054] Typically, only one refueling scenario is manually selected for pre-simulation calculations to assess the core power margin. Even if the margin is low, the candidate may be forced to accept it for various reasons (such as timeliness and lack of skills). However, the method proposed in this invention can find all feasible solutions and evaluate as many feasible scenarios as needed, completely avoiding the selection of scenarios with low core power margins, thereby improving the reactor's thermal safety margin. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 This is a simplified diagram of the CANDU reactor core structure;

[0056] In the figure, ① represents a fuel channel, also known as a grid cell. The distance between the centers of two adjacent channels is called a grid pitch. Each fuel channel can be numbered using row and column coordinates. For example, channel A09 is shown in ①. ② represents the LZC zone number. 1 and 8 together represent coaxial zones 1 and 8. The LZC water level range represents the difference between the highest and lowest water levels, and the maximum absolute deviation represents the maximum absolute deviation between the water level in the 14 zones and the average water level.

[0057] Figure 2 This is a flow chart of a CANDU reactor refueling channel selection method based on a backtracking algorithm provided by the present invention;

[0058] Figure 3 The process diagram of the material change channel is searched using the backtracking algorithm. DETAILED DESCRIPTION

[0059] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0060] Backtracking algorithms, similar to enumeration, systematically search for solutions in a depth-first fashion and are commonly used to solve large-scale, constrained combinatorial problems. Refueling channel selection also falls into this category. This paper provides a CANDU reactor refueling channel selection method based on a backtracking algorithm. This method leverages well-established engineering refueling expert criteria to efficiently optimize the design of refueling solutions, replacing manual optimization.

[0061] A CANDU reactor refueling channel selection method based on a backtracking algorithm comprises the following steps:

[0062] Step 1: Define the material change channel selection constraints

[0063] In engineering practice, a combination of material change channels that simultaneously satisfies the following constraints is a feasible material change solution.

[0064] The material change selection constraints include:

[0065] Constraint on the number of refueling channels in each core area: The number of refueling channels in each core area is less than the preset threshold;

[0066] Material change channel direction balance constraint: The difference in the number of material change channels between side A and side C is less than the preset threshold;

[0067] Material change channel interval constraint: the distance between material change channels is greater than the preset threshold;

[0068] Liquid Zone Controller (LZC) water level constraint: The LZC water level range and maximum absolute deviation after channel refueling are less than the preset threshold;

[0069] Reactivity constraint for material change introduction: The reactivity introduced by the material change channel is greater than the preset threshold.

[0070] Step 2: Build a pool of candidate material exchange channels

[0071] Based on the unloading burnup, excess power factor, and residence time of each channel, fuel channels that meet the following three conditions are selected from the 380 channels in the entire reactor to form the candidate refueling channel pool:

[0072] Channel unloading fuel consumption: Channels with a relative unloading fuel consumption (i.e., the ratio of channel unloading fuel consumption to time-averaged fuel consumption) greater than or equal to the specified value are selected as candidates;

[0073] Channel overpower factor: Channels whose overpower factors (i.e., the ratio of the current instantaneous power to the time-averaged reference power) of the channel itself and a surrounding gate cell channel are less than or equal to the specified value are selected as candidates;

[0074] Channel residence time: Channels whose residence time (i.e., the difference from the last material change time) of the channel itself and a surrounding gate element channel is greater than or equal to the specified value are selected as candidates;

[0075] Considering that the CANDU nuclear power plant has a strong timeliness requirement for the design of the refueling plan, the main purpose of this step is to reduce the scale of the problem.

[0076] Step 3: Material change channel search based on backtracking algorithm

[0077] Step 31: Define the backtracking algorithm state space

[0078] The state space is a complete representation of the intermediate decision states maintained by the algorithm during the search process. It records the selected channel set and candidate channel list in the current state. The initialization state of the state space is: the selected channel set is empty and the candidate channel list is empty.

[0079] Step 32: Define the constraint pruning function

[0080] The constraint pruning function is a set of logical judgment rules used to terminate the branch search that does not meet the constraints early during the backtracking process. It contains the following rules:

[0081] Whether the number constraints of refueling channels in each area of ​​the core are met, whether the direction balance constraints of the refueling channels are met, and whether the spacing constraints of the refueling channels are met.

[0082] Step 33: Define the judgment conditions for material change channel selection

[0083] The selected refueling channel set meets the refueling plan; verify whether the LZC water level range and maximum absolute deviation value meet the constraints after refueling in all channels; verify whether the reactivity introduced by all refueling channels meets the constraints.

[0084] Step 34: Use backtracking algorithm to search for material change channel:

[0085] Step 341: Initialize the state space, select a channel from the material change channel selection pool to add to the material change selected channel set, and the candidate channel list is the remaining channels in the selection pool.

[0086] Step 342: Select a channel from the candidate channel list based on the current state space;

[0087] Step 343: Update the state space, add the selected channel to the selected channel set, and remove the selected channel from the candidate channel list;

[0088] Step 344: Check whether the selected channel set in the current state space meets the material change constraint requirements according to the constraint pruning function;

[0089] Step 345: If satisfied, retain the current state space; if not satisfied, backtrack to the previous state space;

[0090] Step 346: Repeat steps 342 to 345 until the selected refueling channel set meets the refueling plan or there are no remaining channels in the candidate channel list;

[0091] Step 347: Based on the judgment conditions of the material exchange channel selection scheme, determine whether the selected material exchange channel set is a feasible solution, i.e., a feasible material exchange scheme;

[0092] Step 348: If it is a feasible solution, keep it; if it is an infeasible solution, discard it;

[0093] Step 349: Remove the channel selected in step 341 from the material change channel selection pool, and repeat steps 341 to 349 until the number of channels in the material change selection pool is less than the material change plan.

[0094] Step 4: Evaluation and ranking of feasible material replacement plans:

[0095] Step 41: Definition and calculation of feasible solution evaluation indicators.

[0096] Evaluation index 1 is the maximum absolute deviation value of the LZC water level of the feasible solution. The smaller the evaluation index, the higher the ranking. Evaluation index 2 is the reactivity of the feasible solution. The larger the evaluation index, the higher the ranking.

[0097] Step 42: Perform multi-level sorting on the feasible solutions according to evaluation index 1 and evaluation index 2 respectively.

[0098] Step 5: Use the existing core calculation program to perform pre-simulation calculations and rank the top-ranked feasible refueling schemes. Since core pre-simulation calculations are relatively time-consuming, users can select the top-ranked schemes to enter this step based on their actual needs.

[0099] Step 51: Preliminary simulation calculation of feasible material replacement scheme;

[0100] Step 52: Calculate the core power margin of each feasible solution based on the pre-simulation results, and define it as evaluation index 3. The larger the evaluation index, the higher the ranking.

[0101] Step 53: Perform multi-level sorting on the simulated feasible solutions according to evaluation index 3, evaluation index 1 and evaluation index 2 respectively.

[0102] Step 6: The user selects the final material replacement plan based on the ranking.

[0103] Example:

[0104] Taking the refueling channel selection of a domestic heavy water reactor nuclear power plant as an example, the objectives, technical solutions, and beneficial effects of the present invention are further explained in detail. When implementing the refueling channel selection, the refueling plan has been determined to be 7 according to the production and operation requirements of the nuclear power plant, that is, 7 refueling channels need to be selected this time.

[0105] The specific implementation is as follows:

[0106] Define the material change channel selection constraints.

[0107] Constraints on the number of refueling channels in each core area: The number of refueling channels in each core area is less than 3; Refueling channel direction balance constraint: The difference in the number of refueling channels between side A and side C is less than 5; Refueling channel spacing constraint: The distance between refueling channels is greater than 3 grid pitches; Liquid Zone Controller (LZC) water level constraint: After channel refueling, the LZC water level extreme difference value is less than 40%, and the LZC water level maximum absolute deviation value is less than 25%; Refueling introduction reactivity constraint: The single-channel reactivity introduced by the refueling channel is greater than 0.165mk.

[0108] Build a pool of candidate material exchange channels.

[0109] From the 380 channels in the entire reactor, channels with relative unloading fuel consumption ≥80%, channel overpower factor ≤1.045, and residence time in surrounding adjacent channels ≥8 days were selected to form a candidate refueling channel pool, totaling 20 channels.

[0110] The backtracking algorithm-based material change channel selection program module was executed. The program ran for about 1 minute and finally gave 5 material change channel selection schemes, as follows:

[0111] [D12, K11, L04, P18, R11, V10, V14]

[0112] [D12, K11, L04, P18, R11, V14, W09]

[0113] [D12, K11, L04, P18, R07, S11, V14]

[0114] [D12, K11, L04, P18, R07, U10, V14]

[0115] [D12, K11, L04, P18, R07, S11, W09]

[0116] All feasible refueling plans are evaluated and ranked as follows:

[0117] [D12, K11, L04, P18, R07, S11, W09]

[0118] Water level: 16.40%, reactivity: 0.169mk

[0119] [D12, K11, L04, P18, R11, V14, W09]:

[0120] Water level: 17.15%, reactivity: 0.166mk

[0121] [D12, K11, L04, P18, R07, S11, V14]

[0122] Water level: 17.47%, reactivity: 0.175mk

[0123] [D12, K11, L04, P18, R07, U10, V14]

[0124] Water level: 17.82%, reactivity: 0.169mk

[0125] [D12, K11, L04, P18, R11, V10, V14]:

[0126] Water level: 18.2%, reactivity: 0.171mk

[0127] The core calculation program was used to carry out preliminary simulation calculations and ranking of all five refueling plans.

[0128] [D12, K11, L04, P18, R11, V10, V14]:

[0129] Power margin: 3.11%, water level: 18.2%, reactivity: 0.171mk

[0130] [D12, K11, L04, P18, R11, V14, W09]:

[0131] Power margin: 3.11%, water level: 17.15%, reactivity: 0.166mk

[0132] [D12, K11, L04, P18, R07, S11, V14]

[0133] Power margin: 3.08%, water level: 17.47%, reactivity: 0.175mk

[0134] [D12, K11, L04, P18, R07, U10, V14]

[0135] Power margin: 3.05%, water level: 17.82%, reactivity: 0.169mk

[0136] [D12, K11, L04, P18, R07, S11, W09]

[0137] Power margin: 2.28%, water level: 16.40%, reactivity: 0.169mk

[0138] The user selects the final material replacement plan based on the sorting as [D12, K11, L04, P18, R11, V10, V14].

[0139] At this point, the material change channel selection has been completed.

Claims

1. A CANDU reactor refueling channel selection method based on backtracking algorithm, characterized in that: The following steps are involved: Step 1: Define the material change channel selection constraints; The material change channel selection constraints in step 1 include: Constraint on the number of refueling channels in each core area: The number of refueling channels in each core area is less than the preset threshold; Material change channel direction balance constraint: The difference in the number of material change channels between side A and side C is less than the preset threshold; Material change channel interval constraint: the distance between material change channels is greater than the preset threshold; Liquid zone controller water level constraint: After channel material change, the LZC water level range and maximum absolute deviation are less than the preset threshold; Reactivity constraint introduced by material change: the reactivity introduced by the material change channel is greater than the preset threshold; Step 2: Build a candidate material exchange channel pool; In step 2, based on the unloading burnup, excess power factor, and residence time of each channel, fuel channels that simultaneously meet the following three conditions are selected from the 380 channels in the entire stack to form a candidate refueling channel pool: Channel unloading fuel consumption: Channels with a relative unloading fuel consumption, i.e., a ratio of channel unloading fuel consumption to time-averaged fuel consumption greater than or equal to a specified value, are selected as candidates; Channel overpower factor: Channels whose overpower factors of the channel itself and a surrounding gate element, i.e., the ratio of the current instantaneous power to the time-averaged reference power is less than or equal to the specified value, are selected as candidates; Channel residence time: The residence time of the channel itself and the surrounding gate element channel, that is, the channel whose difference from the last material change time is greater than or equal to the specified value, is selected as a candidate; Step 3: Search for material change channel based on backtracking algorithm; The step 3 includes: Step 31: Define the backtracking algorithm state space The state space is a complete representation of the intermediate decision states maintained by the algorithm during the search process. It records the selected channel set and candidate channel list in the current state. The initial state of the state space is: the selected channel set is empty and the candidate channel list is empty. Step 32: Define the constraint pruning function The constraint pruning function is a set of logical judgment rules used to terminate the branch search that does not meet the constraints early during the backtracking process. It includes the following rules: Whether the constraints on the number of refueling channels in each area of ​​the core are met, whether the constraints on the direction balance of the refueling channels are met, and whether the constraints on the spacing of the refueling channels are met; Step 33: Define the judgment conditions for material change channel selection The selected refueling channel set meets the refueling plan; verify whether the LZC water level extreme difference value and the maximum absolute deviation value meet the constraints after refueling in all channels; verify whether the reactivity introduced by all refueling channels meets the constraints; Step 34: Use the backtracking algorithm to search for the material change channel; Step 4: Evaluation and ranking of feasible material replacement plans; The step 4 includes: Step 41: Definition and calculation of feasible solution evaluation indicators; Evaluation index 1 is the maximum absolute deviation value of the LZC water level of the feasible solution. The smaller the evaluation index, the higher the ranking. Evaluation index 2 is the reactivity of the feasible solution. The larger the evaluation index, the higher the ranking. Step 42: Perform multi-level sorting on the feasible solutions according to evaluation index 1 and evaluation index 2 respectively; Step 5: Use the existing core calculation program to conduct preliminary simulation calculations and ranking of several feasible refueling schemes that are ranked high; The step 5 comprises: Step 51: Preliminary simulation calculation of feasible material replacement scheme; Step 52: Calculate the core power margin of each feasible solution based on the pre-simulation results, and define it as evaluation index 3. The larger the evaluation index, the higher the ranking. Step 53: performing multi-level sorting on the simulated feasible solutions according to evaluation index 3, evaluation index 1, and evaluation index 2 respectively; Step 6: Select the final material replacement plan based on the ranking.

2. The method for selecting a CANDU reactor refueling channel based on a backtracking algorithm according to claim 1, wherein: The step 34 includes: Step 341: Initialize the state space, select a channel from the material change channel selection pool to add to the material change selected channel set, and the candidate channel list is the remaining channels in the selection pool; Step 342: Select a channel from the candidate channel list based on the current state space; Step 343: Update the state space, add the selected channel to the selected channel set, and remove the selected channel from the candidate channel list; Step 344: Check whether the selected channel set in the current state space meets the material change constraint requirements according to the constraint pruning function; Step 345: If satisfied, retain the current state space; if not satisfied, backtrack to the previous state space; Step 346: Repeat steps 342 to 345 until the selected refueling channel set meets the refueling plan or there are no remaining channels in the candidate channel list; Step 347: Based on the judgment conditions of the material exchange channel selection scheme, determine whether the selected material exchange channel set is a feasible solution, i.e., a feasible material exchange scheme; Step 348: If it is a feasible solution, keep it; if it is an infeasible solution, discard it; Step 349: Remove the channel selected in step 341 from the material change channel selection pool, and repeat steps 341 to 349 until the number of channels in the material change selection pool is less than the material change plan.

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