CN104751371A - Optimization method of CANDU reactor refueling scheme based on mixed integer programming and linear programming - Google Patents

Abstract

The invention discloses a method for optimizing the refueling scheme by utilizing an integer-linearity mixed programming. The problem is solved by two steps including: step one, giving consideration to the aftereffect of channel refueling, establishing a candidate channel selection model aiming at the least number of the refueling channels, continuously optimizing the refueling scheme for 16 weeks; and step two, providing a weekly refueling plan firstly by physics engineers of the reactor based on the running requirements of the reactor in the next week, then establishing a weekly refueling scheme optimization model aiming at the deepest average unloading burn-up, and synchronously adding corresponding restraint conditions into the model by giving consideration to various requirements for the running of the reactor. Considering the timeliness of designing the refueling scheme, a three-dimensional reactor core calculation model, i.e., a linearity sensitive matrix method, is provided for evaluating a mass of refueling schemes. The responses of the reactor core key parameters during the channel refueling can be quickly and precisely estimated, accordingly achieving quick evaluations to a mass of refueling schemes.

Description

Based on the CANDU reactor refuelling scheme optimization method of mixed integer programming linear programming

Technical field

Patent of the present invention belongs to CANDU reactor nuclear power station refuelling scheme design and optimization field, is specifically related to a kind of CANDU reactor refuelling scheme optimization method based on mixed integer programming linear programming.

Background technology

Bank 6 type heavy water reactors of shutting out have 380 fuel channels, different from the reactor (as presurized water reactor) adopting shutdown mode to carry out reloading, and CANDU reactor employing is reloaded mode online, and during Operation at full power, average every day will change two fuel channels.The design of daily refuelling scheme is piled physical engineering teacher by power station and is completed, and within usual 3 ~ 4 days, carries out once, picks out 6 ~ 7 at every turn and submit to operations staff to change from 380 fuel channels.The design of CANDU reactor refuelling scheme is the optimization problem of a complicated multiple goal, multiple constraint, the good usual demand fulfillment of refuelling scheme: maximize fuel discharge burnup, optimizing core power distribution makes it as far as possible close to desired value, reduce the passage superpower factor (CPPF) as far as possible, guarantee that passage/bundle power meets limit value requirement, optimize the operation characteristic etc. of liquid regions control device (liquid regions control device).In view of this complex nature of the problem, computer software completes refuelling scheme optimal design with assisted stack physical engineering teacher is introduced or is developed in each bank Du power station.

Similar with external a lot of homotype power station, the software package that reloads of current use, based on traditional expert system development, is marked to each passage by the multiple expert's criterion preset and evaluation function.Each criterion chooses an evaluating usually, and these parameters are closely related with the target optimized of reloading, as smallest passage margin of power in the largest passages superpower factor in the burnup of the passage that reloads, passage group, passage group etc.According to each criterion to after passage scoring, single evaluation of estimate is integrated thus obtains the final evaluation of estimate of passage, size and the experience of the comprehensive grading of heap physical engineering Shi Ze foundation passage select the passage that reloads, and finally determine good refuelling scheme.

Staff in use finds that this software package comes with some shortcomings gradually.First, this cover is based on the passage evaluation method of expert system, and the quality of its evaluation effect depends on the Experience norms chosen and preset of evaluating completely, is short of accurate core physics model.Secondly, the evaluation of passage, completely based on current reactor core state, is more paid close attention to local feature and the space distribution of the passage close region that reloads, and is lacked the assessment to aftereffect of reloading.Moreover the experience of the refuelling scheme heavy dependence heap physical engineering teacher that final design goes out, under same interpretational criteria, different personnel may design diverse refuelling scheme because of the difference of experience.

Summary of the invention

The object of the invention is the many deficiencies existed for improving the current software package that reloads, improve quality, the work efficiency of the design of heap physical engineering teacher refuelling scheme, power station is run there is higher security and economy, propose a kind of CANDU reactor refuelling scheme optimization method based on MILP (Mixed Integer Linear Programming).This patent adopts MILP (Mixed Integer Linear Programming) method to solve this refuelling scheme optimization problem, using economic index (number of active lanes of reloading is minimum or passage discharge burn-up is the highest) as objective function during modeling, other target and requirement are all as constraint condition, two steps are become to solve whole PROBLEM DECOMPOSITION, each step is set up the mathematical model of MILP (Mixed Integer Linear Programming) (MILP) respectively and adopts commercial solver to solve, and finally obtains refuelling scheme optimum in a week.The first step is consider the passage aftereffect of reloading, and sets up candidate's channel selecting model for target, carry out the refuelling scheme optimization of continuous 16 weeks so that number of active lanes of reloading is minimum.Add the constraint to reactor core built-in reactivity and region reactivity distribution during modeling, make region reactivity distribution as far as possible close to desired value.Reactor core parameter calculates and adopts zero dimension linear response model, and when supposing that reactor core maintains, equal power distribution is constant.The combination of channels of reloading in each week is obtained by solving candidate's channel selecting model, and candidate's passage that the combination of channels of reloading of two weeks is above optimized as second step.Second step, heap physical engineering Shi Shouxian provides according to the reactor service requirement of following a week plan of reloading in week, then with average discharge burn-up the most deeply for target sets up all refuelling scheme Optimized models, consider many requirements of reactor operation simultaneously, add corresponding constraint condition in a model.Consider the ageing requirement that refuelling scheme designs, in order to the refuelling scheme that Fast Evaluation is a large amount of, propose a three-dimensional reactor core computation model-linear sensitive matrix method.It solves without the need to three-dimensional ore body model consuming time by preformed sensitive matrix, just can comparatively accurately and fast calculate main reactor core parameter, complete the evaluation of refuelling scheme merely through simple algebraic operation.By solving all refuelling scheme Optimized models, finally obtain the combination of channels of reloading of each day of reloading in one week.

To achieve these goals, technical scheme of the present invention is: a kind of CANDU reactor refuelling scheme optimization method based on mixed integer programming linear programming, comprises the following steps:

Step 1, candidate's channel selecting: the difference utilizing interchannel burnup characteristics, sets up and considers to reload the mathematic optimal model of aftereffect, thus determine the time sequencing that passage reloads; When determining candidate's passage, core physics model is mainly based on following two hypothesis: 1) to maintain target power distribution all the time constant for core power; 2) reactor core reactivity available " zero dimension linear response model " represents;

Step 1.1, builds core physics model, for determining reactor core built-in reactivity:

Step 1.1.1, determines entirely to pile built-in reactivity ρ _core:

Wherein, ρ _ifor the reactivity of fuel channel i, it is passage average burn-up ω _ifunction, funtcional relationship is obtained by the matching of lattice cell calculation procedure; Burnup ω _iwhen being multiplied by by residence time, equal power obtains; f _ifor the time equal power fraction of fuel channel i, distributed by the time equal power of reactor core and obtain;

Step 1.1.2, in step 1.1.1 simultaneously, determines radial 7 liquid regions control device built-in reactivities; For region j, its built-in reactivity ρ _{zone, j}can be expressed as:

${\mathrm{\ρ}}_{\mathrm{zone},j}=\underset{i=1}{\overset{N_{\mathrm{zone},j}}{\mathrm{\Σ}}}{f}_i^{\′}{\mathrm{\ρ}}_i\left({\mathrm{\ω}}_i\right),j=1,...,7---\left(2\right)$

Wherein, N _{zone, j}for the fuel channel number that region j comprises, f _i' for fuel channel i relative to region j time equal power power fraction, ρ _i, ω _ithe same formula of meaning (1);

Step 1.2, builds candidate's channel selecting model: the time point that passage reloads determined by candidate's channel selecting model in units of week, specifies that the passage that reloads weekly enters reactor core simultaneously simultaneously, and the time span of candidate's channel selecting model is taken as 16 weeks:

The objective function of objective function---candidate's channel selecting model is that 16 weeks total number of active lanes of reloading are minimum, and formula is:

$\mathrm{Minimize}\underset{i=1}{\overset{16}{\mathrm{\Σ}}}{X}_i---\left(3\right)$

In formula, X _i={ x _j} _j=1...380, to be length be 380 vector, wherein each element x _jbe all 0-1 variable, represent a certain passage j and whether reload;

Constraint condition---the constraint condition considered in model comprises:

1) in 16 weeks, each fuel channel reloads 1 time at the most;

2) control of the minimum discharge burn-up of single channel: flow assists passage discharge burn-up will not reload lower than this passage hourly value 80% of reloading, non-flow assists passage discharge burn-up will not reload lower than this passage hourly value 95% of reloading;

3) control of the average discharge burn-up of all passages that reload: total average discharge burn-up is greater than the given limit value of user;

4) reload in each week passage discreteness require: reload interchannel and be interposed between more than 2 passages;

5) reload between adjacent two weeks passage discreteness require: the passage that reloads the last week must not be adjacent with the passage that reloads this week;

6) burn-up equilibrium of the radial A side, each region of reactor core and C wing passage controls: the burnup difference of all passages in A side, each region and C side is less than the given limit value of user;

7) control of each week reactor core built-in reactivity: the built-in reactivity of reactor core is greater than the given limit value of user;

8) control of radial each region built-in reactivity weekly: the ratio of each region built-in reactivity and reactor core built-in reactivity fluctuates in the given scope of user;

9) according to current reactor core state and the history of reloading of the last week, increase constraint condition, the passage namely reloaded the last week to the selection of first week passage that reloads, the passage around it can not reload at first week;

Above-mentioned constraint condition mathematical linguistics is expressed as equation or inequality, gets final product founding mathematical models;

Step 2, all refuelling scheme optimization

Step 2.1, builds core physics model, for Fast Evaluation refuelling scheme:

Step 2.1.1, the disturbance affecting reactor core state parameter mainly comprise reload, liquid regions control device SEA LEVEL VARIATION, burnup accumulation, generate sensitive matrix in advance for above-mentioned different disturbance respectively; The method for making of sensitive matrix is described for the sensitive matrix of channel power to disturbance of reloading below:

Step 2.1.1.1, to selected reference reactor core state, utilize RFSP-IST process simulation when do not reload and immobile liquid body region control device water level reactor core burnup behavior, obtain the power P of T each fuel channel in the full power world _i ^t, t ∈ [0, T];

Step 2.1.1.2, reloads to a certain selected j passage under with reference to reactor core state, and the burnup utilizing RFSP-IST program to carry out T full power sky equally calculates, and obtains the fuel channel power P after reloading _i ^j,t;

Step 2.1.1.3, utilizes following formula to carry out the calculating of sensitive matrix:

$S_{j\→i}^t=({P_i}^{j,t}-{P_i}^t)/{\mathrm{\Δk}}_j---\left(6\right)$

Wherein, Δ k _jfor this passage k reloading caused by j passage under reference reactor core state _∞transient change amount, can calculate according to reactivity-burnup curve; Repeat said process 380 times, just can obtain the sensitive matrix that i channel power reloads to the arbitrary passage of reactor core; By same mode, channel power and the built-in reactivity variable quantity sensitive matrix to liquid regions control device SEA LEVEL VARIATION and burnup accumulation can be obtained;

Step 2.1.2, the power calculation of the arbitrary fuel channel i of heap in-core can be expressed as:

$P_i\≈P_{i,0}+\underset{p}{\mathrm{\Σ}}\underset{r}{\mathrm{\Σ}}{S}_{p,r\→i}{\mathrm{\Δ}}_{p,r},i=1,...,380---\left(4\right)$

Wherein, P _{i, 0}represent the power with reference to i passage under reactor core state, S _{p, r → i}i.e. sensitive matrix, represents with reference on reactor core basis, by the variable quantity of the i channel power in heap caused by the disturbance of r position p type unit; And Δ _p,rthen represent the disturbance quantity of certain refuelling scheme r position p type reality; Can adopt uses the same method calculates bundle power, area power;

Step 2.1.3, the reactor core built-in reactivity variable quantity introduced that reloads can be expressed as:

$\mathrm{\Δk}\≈\underset{p}{\mathrm{\Σ}}\underset{r}{\mathrm{\Σ}}{S}_{p,r\→k}{\mathrm{\Δ}}_{p,r}---\left(5\right)$

In formula, S _{p, r → k}for the sensitive matrix produced in advance, represent with reference on reactor core basis, by the variable quantity of the reactor core built-in reactivity in heap caused by the disturbance of r position p type unit;

Step 2.2, builds all refuelling scheme Optimized models: in all refuelling scheme Optimized models, and one week reload concentrates on four day time and complete, and namely reload Monday, Tuesday, Thursday, Friday, all the other times do not reload;

Objective function---all refuelling scheme Optimized models are the darkest in objective function with one week average discharge burn-up, and formula is:

$\mathrm{Maximize}\underset{i=1}{\overset{7}{\mathrm{\&Sigma;}}}<\mathrm{Bu}\&CenterDot;X^{\&prime;}{>}_i/\underset{i=1}{\overset{7}{\mathrm{\&Sigma;}}}{N}_i---\left(7\right)$

In formula, N _ifor known constant, represent the port number that reloads of every day; Bu and X' to be all length be 380 vector, whether wherein the element of X' is 0-1 variable, represent each passage and reload; The element of Bu represents the discharge burn-up of each passage;

Constraint condition---the constraint condition considered in all refuelling scheme Optimized models comprises:

1), within one week, the number of active lanes of reloading of every day equals planned value;

2), within one week, the port number that reloads in radial each region is less than 3;

3), within one week, A side differs with the number of the passage that reloads of C side and is less than 5;

4) passage that reloads in 10 days must not be adjacent;

5) had when continuous two days when reloading, reload channel spacing beyond 2 passages;

6) every day reload channel spacing beyond 3 passages;

7) control of the minimum discharge burn-up of passage: for FAF passage, relative discharge burn-up will not reload lower than hourly value 80%, FARE passage is then set to 95%;

8), after reloading Tuesday and Friday, the deviation of 14 relative mean waters of liquid regions control device water level is less than 20%, and after reloading Monday and Thursday, water level deviation is less than 25%;

9), within one week, the power of all passages is all less than each self-operating limit value;

10), within one week, the power of each passage No. 6 and No. 7 clusters is less than operation limit value;

11), within one week, the axial power tilt in radial each region is less than 2.5%;

12) reactor core built-in reactivity was greater than and limited the use of the given limit value in family next Monday;

13) when the superpower factor of CPPF regional channel is greater than 1.045, all passages be adjacent can not reload;

Above-mentioned constraint condition mathematical linguistics is expressed as equation or inequality, gets final product founding mathematical models; By solving all refuelling scheme Optimized models, obtain the combination of channels of reloading of each day of reloading.

Beneficial effect of the present invention comprises: when carrying out every one-step optimization, and the feature all in conjunction with particular problem to be solved proposes rational core physics model.When the first step determines candidate's passage, based on time equal power distribution and the hypothesis of zero dimension reactivity model, while ensureing higher average discharge burn-up, determine from the angle optimizing the distribution of reactor core long reaction the approximate time that passage reloads, effectively consider passage and to reload the aftereffect brought to reactor core.When carrying out all refuelling schemes and optimizing, propose the physical model of linear sensitive matrix, it can the response of reactor core key parameter when prediction path reloads quickly and accurately, thus realizes the Fast Evaluation to magnanimity refuelling scheme.Therefore, this patent method has more solid theoretical foundation relative to traditional expert system.Moreover, mathematically also verified, solve Mixed integer linear programming and finally can obtain theoretic optimum solution.In other words, under the prerequisite of reasonable assumption, heap physical engineering teacher can obtain optimum refuelling scheme, decreases the dependence to its personal experience.Meanwhile, also can export a lot of feasible solution when solving mathematical model, these feasible programs can provide different options for the decision-making of staff.

Embodiment

Below in conjunction with embodiment, the present invention is described further.

The present embodiment adopts MILP (Mixed Integer Linear Programming) method to solve CANDU reactor refuelling scheme design and optimization problem in two steps, and concrete steps are as follows:

Step 1, candidate's channel selecting; Consider the precision of physical model, candidate's passage that the combination of channels of reloading of getting two weeks is above optimized as next step, candidate's CHANNEL OPTIMIZATION model is gained the name thus;

On long terms, one of target that under equilibrium core, CANDU reactor runs is exactly that core power is distributed close to reference value, the distribution of instant all power; There is the heap in-core of ideal power distribution, the fuel channel that current burnup is substantially identical can present different burnup rules in future, utilize the difference of interchannel burnup characteristics, set up and consider to reload the mathematic optimal model of aftereffect, thus determine the time sequencing that passage reloads; When determining candidate's passage, core physics model is mainly based on following two hypothesis: 1) to maintain target power distribution all the time constant for core power; 2) reactor core reactivity available " zero dimension linear response model " represents;

Step 1.1, builds core physics model, for determining reactor core built-in reactivity:

Step 1.1.1, determines entirely to pile built-in reactivity ρ _core:

Wherein, ρ _ifor the reactivity of fuel channel i, it is passage average burn-up ω _ifunction, funtcional relationship is obtained by the matching of lattice cell calculation procedure; Burnup ω _iwhen being multiplied by by residence time, equal power obtains; f _ifor the time equal power fraction of fuel channel i, distributed by the time equal power of reactor core and obtain;

Step 1.1.2, in step 1.1.1 simultaneously, determines radial 7 liquid regions control device built-in reactivities; For region j, its built-in reactivity ρ _{zone, j}can be expressed as:

${\mathrm{\&rho;}}_{\mathrm{zone},j}=\underset{i=1}{\overset{N_{\mathrm{zone},j}}{\mathrm{\&Sigma;}}}{f}_i^{\&prime;}{\mathrm{\&rho;}}_i\left({\mathrm{\&omega;}}_i\right),j=1,...,7---\left(2\right)$

Wherein, N _{zone, j}for the fuel channel number that region j comprises, f _i' for fuel channel i relative to region j time equal power power fraction, ρ _i, ω _ithe same formula of meaning (1);

Step 1.2, build candidate's channel selecting model: consider the degree of approximation of core physics model and the complexity of mathematical modeling, the time point that passage reloads determined by candidate's channel selecting model in units of week, specify that the passage that reloads weekly enters reactor core simultaneously simultaneously, and the time span of candidate's channel selecting model be taken as 16 weeks:

The objective function of objective function---candidate's channel selecting model is that 16 weeks total number of active lanes of reloading are minimum, and formula is:

$\mathrm{Minimize}\underset{i=1}{\overset{16}{\mathrm{\&Sigma;}}}{X}_i---\left(3\right)$

In formula, X _i={ x _j} _j=1...380, to be length be 380 vector, wherein each element x _jbe all 0-1 variable, represent a certain passage j and whether reload;

Constraint condition---the constraint condition considered in model comprises:

1) in 16 weeks, each fuel channel reloads 1 time at the most;

2) control of the minimum discharge burn-up of single channel: flow assists passage discharge burn-up will not reload lower than this passage hourly value 80% of reloading, non-flow assists passage discharge burn-up will not reload lower than this passage hourly value 95% of reloading;

3) control of the average discharge burn-up of all passages that reload: total average discharge burn-up is greater than the given limit value of user;

4) reload in each week passage discreteness require: reload interchannel and be interposed between more than 2 passages;

5) reload between adjacent two weeks passage discreteness require: the passage that reloads the last week must not be adjacent with the passage that reloads this week;

6) burn-up equilibrium of the radial A side, each region of reactor core and C wing passage controls: the burnup difference of all passages in A side, each region and C side is less than the given limit value of user;

7) control of each week reactor core built-in reactivity: the built-in reactivity of reactor core is greater than the given limit value of user;

8) control of radial each region built-in reactivity weekly: the ratio of each region built-in reactivity and reactor core built-in reactivity fluctuates in the given scope of user;

9) according to current reactor core state and the history of reloading of the last week, increase constraint condition, the passage namely reloaded the last week to the selection of first week passage that reloads, the passage around it can not reload at first week;

Above-mentioned constraint condition mathematical linguistics is expressed as equation or inequality, commercial mathematical optimization software founding mathematical models can be utilized;

Step 2, all refuelling scheme optimization

Step 2.1, build core physics model, for Fast Evaluation refuelling scheme: suppose when there being multiple disturbance introducing reactor core, caused effect can linear superposition, namely various disturbance is mutually independent, and the response of reactor core to disturbance and the amplitude proportional of disturbance;

Step 2.1.1, the disturbance affecting reactor core state parameter mainly comprise reload, liquid regions control device SEA LEVEL VARIATION, burnup accumulation, generate sensitive matrix in advance for above-mentioned different disturbance respectively; The method for making of sensitive matrix is described for the sensitive matrix of channel power to disturbance of reloading below:

Step 2.1.1.1, to selected reference reactor core state, utilize RFSP-IST process simulation when do not reload and immobile liquid body region control device water level reactor core burnup behavior, obtain the power P of T each fuel channel in the full power world _i ^t, t ∈ [0, T];

Step 2.1.1.2, reloads to a certain selected j passage under with reference to reactor core state, and the burnup utilizing RFSP-IST program to carry out T full power sky equally calculates, and obtains the fuel channel power P after reloading _i ^j,t;

Step 2.1.1.3, utilizes following formula to carry out the calculating of sensitive matrix:

$S_{j\&RightArrow;i}^t=({P_i}^{j,t}-{P_i}^t)/{\mathrm{\&Delta;k}}_j---\left(6\right)$

Wherein, Δ k _jfor this passage k reloading caused by j passage under reference reactor core state _∞transient change amount, can calculate according to reactivity-burnup curve; Repeat said process 380 times, just can obtain the sensitive matrix that i channel power reloads to the arbitrary passage of reactor core; By same mode, channel power and the built-in reactivity variable quantity sensitive matrix to liquid regions control device SEA LEVEL VARIATION and burnup accumulation can be obtained;

Step 2.1.2, the power calculation of the arbitrary fuel channel i of heap in-core can be expressed as:

Wherein, P _{i, 0}represent the power with reference to i passage under reactor core state, S _{p, r → i}i.e. sensitive matrix, represents with reference on reactor core basis, by the variable quantity of the i channel power in heap caused by the disturbance of r position p type unit; And Δ _p,rthen represent the disturbance quantity of certain refuelling scheme r position p type reality; Can adopt uses the same method calculates bundle power, area power;

Step 2.1.3, the reactor core built-in reactivity variable quantity introduced that reloads can be expressed as:

$\mathrm{\&Delta;k}\&ap;\underset{p}{\mathrm{\&Sigma;}}\underset{r}{\mathrm{\&Sigma;}}{S}_{p,r\&RightArrow;k}{\mathrm{\&Delta;}}_{p,r}---\left(5\right)$

In formula, S _{p, r → k}for the sensitive matrix produced in advance, represent with reference on reactor core basis, by the variable quantity of the reactor core built-in reactivity in heap caused by the disturbance of r position p type unit; Once have sensitive matrix and actual disturbance quantity, carry out channel power by formula (4) and (5) and just become simple algebraic operation with the calculating that reactor core built-in reactivity changes, the three-dimensional reactor core neutron diffusion problem of demand solution just can not complete refuelling scheme appraisal, very efficient and convenient;

Step 2.2, builds all refuelling scheme Optimized models: in all refuelling scheme Optimized models, and one week reload concentrates on four day time and complete, and namely reload Monday, Tuesday, Thursday, Friday, all the other times do not reload.

Objective function---all refuelling scheme Optimized models are the darkest in objective function with one week average discharge burn-up, and formula is:

$\mathrm{Maximize}\underset{i=1}{\overset{7}{\mathrm{\&Sigma;}}}<\mathrm{Bu}\&CenterDot;X^{\&prime;}{>}_i/\underset{i=1}{\overset{7}{\mathrm{\&Sigma;}}}{N}_i---\left(7\right)$

In formula, N _ifor known constant, represent the port number that reloads of every day; Bu and X' to be all length be 380 vector, whether wherein the element of X' is 0-1 variable, represent each passage and reload; The element of Bu represents the discharge burn-up of each passage;

Constraint condition---the constraint condition considered in all refuelling scheme Optimized models comprises:

1), within one week, the number of active lanes of reloading of every day equals planned value;

2), within one week, the port number that reloads in radial each region is less than 3;

3), within one week, A side differs with the number of the passage that reloads of C side and is less than 5;

4) passage that reloads in 10 days must not be adjacent;

5) had when continuous two days when reloading, reload channel spacing beyond 2 passages;

6) every day reload channel spacing beyond 3 passages;

7) control of the minimum discharge burn-up of passage: for FAF passage, relative discharge burn-up will not reload lower than hourly value 80%, FARE passage is then set to 95%;

8), after reloading Tuesday and Friday, the deviation of 14 relative mean waters of liquid regions control device water level is less than 20%, and after reloading Monday and Thursday, water level deviation is less than 25%;

9), within one week, the power of all passages is all less than each self-operating limit value;

10), within one week, the power of each passage No. 6 and No. 7 clusters is less than operation limit value;

11), within one week, the axial power tilt in radial each region is less than 2.5%;

12) reactor core built-in reactivity was greater than and limited the use of the given limit value in family next Monday;

13) when the superpower factor of CPPF regional channel is greater than 1.045, all passages be adjacent can not reload;

Above 1) ~ 5) firm constraints are all experiences with reference to heap physical engineering teacher, can contribute to reducing search volume, improve model solution speed.Above-mentioned constraint condition mathematical linguistics is expressed as equation or inequality, commercial mathematical optimization software founding mathematical models can be utilized; By solving all refuelling scheme Optimized models, obtain the combination of channels of reloading of each day of reloading.

For the CANDU reactor refuelling scheme optimization method based on MILP (Mixed Integer Linear Programming) that assessment the present embodiment proposes, by off-line numerical simulation, backtracking is done to unit operation history and calculated.Compared with the actual operating data adopting the former software package that reloads to obtain, the refuelling scheme of this patent method design, under the prerequisite meeting whole security requirement, has higher economy, as shown in the table; The radial and axial power distribution of reactor core is more close to target distribution simultaneously.

Above embodiments of the invention are explained in detail, above-mentioned embodiment is only optimum embodiment of the present invention, but the present invention is not limited to above-described embodiment, in the ken that those of ordinary skill in the art possess, various change can also be made under the prerequisite not departing from present inventive concept.

Claims (1)

1., based on a CANDU reactor refuelling scheme optimization method for mixed integer programming linear programming, it is characterized in that comprising the following steps:

Step 1, candidate's channel selecting: the difference utilizing interchannel burnup characteristics, sets up and considers to reload the mathematic optimal model of aftereffect, thus determine the time sequencing that passage reloads; When determining candidate's passage, core physics model is mainly based on following two hypothesis: 1) to maintain target power distribution all the time constant for core power; 2) reactor core reactivity available " zero dimension linear response model " represents;

Step 1.1, builds core physics model, for determining reactor core built-in reactivity:

Step 1.1.1, determines entirely to pile built-in reactivity ρ _core:

${\mathrm{\&rho;}}_{\mathrm{core}}=\underset{i=1}{\overset{380}{\mathrm{\&Sigma;}}}{f}_i{\mathrm{\&rho;}}_i\left({\mathrm{\&omega;}}_i\right)---\left(1\right)$

Wherein, ρ _ifor the reactivity of fuel channel i, it is passage average burn-up ω _ifunction, funtcional relationship is obtained by the matching of lattice cell calculation procedure; Burnup ω _iwhen being multiplied by by residence time, equal power obtains; f _ifor the time equal power fraction of fuel channel i, distributed by the time equal power of reactor core and obtain;

Step 1.1.2, in step 1.1.1 simultaneously, determines radial 7 liquid regions control device built-in reactivities; For region j, its built-in reactivity ρ _{zone, j}can be expressed as:

${\mathrm{\&rho;}}_{\mathrm{zone},j}=\underset{i=1}{\overset{N_{\mathrm{zone},j}}{\mathrm{\&Sigma;}}}{f}_i^{\&prime;}{\mathrm{\&rho;}}_i\left({\mathrm{\&omega;}}_i\right),j=1,...,7---\left(2\right)$

Wherein, N _{zone, j}for the fuel channel number that region j comprises, f _i' for fuel channel i relative to region j time equal power power fraction, ρ _i, ω _ithe same formula of meaning (1);

Step 1.2, builds candidate's channel selecting model: the time point that passage reloads determined by candidate's channel selecting model in units of week, specifies that the passage that reloads weekly enters reactor core simultaneously simultaneously, and the time span of candidate's channel selecting model is taken as 16 weeks:

The objective function of objective function---candidate's channel selecting model is that 16 weeks total number of active lanes of reloading are minimum, and formula is:

$\mathrm{Minimize}\underset{i=1}{\overset{16}{\mathrm{\&Sigma;}}}{X}_i---\left(3\right)$

In formula, X _i={ x _j} _j=1...380, to be length be 380 vector, wherein each element x _jbe all 0-1 variable, represent a certain passage j and whether reload;

Constraint condition---the constraint condition considered in model comprises:

1) in 16 weeks, each fuel channel reloads 1 time at the most;

2) control of the minimum discharge burn-up of single channel: flow assists passage discharge burn-up will not reload lower than this passage hourly value 80% of reloading, non-flow assists passage discharge burn-up will not reload lower than this passage hourly value 95% of reloading;

3) control of the average discharge burn-up of all passages that reload: total average discharge burn-up is greater than the given limit value of user;

4) reload in each week passage discreteness require: reload interchannel and be interposed between more than 2 passages;

5) reload between adjacent two weeks passage discreteness require: the passage that reloads the last week must not be adjacent with the passage that reloads this week;

6) burn-up equilibrium of the radial A side, each region of reactor core and C wing passage controls: the burnup difference of all passages in A side, each region and C side is less than the given limit value of user;

7) control of each week reactor core built-in reactivity: the built-in reactivity of reactor core is greater than the given limit value of user;

8) control of radial each region built-in reactivity weekly: the ratio of each region built-in reactivity and reactor core built-in reactivity fluctuates in the given scope of user;

9) according to current reactor core state and the history of reloading of the last week, increase constraint condition, the passage namely reloaded the last week to the selection of first week passage that reloads, the passage around it can not reload at first week;

Above-mentioned constraint condition mathematical linguistics is expressed as equation or inequality, gets final product founding mathematical models;

Step 2, all refuelling scheme optimization

Step 2.1, builds core physics model, for Fast Evaluation refuelling scheme:

Step 2.1.1, the disturbance affecting reactor core state parameter mainly comprise reload, liquid regions control device SEA LEVEL VARIATION, burnup accumulation, generate sensitive matrix in advance for above-mentioned different disturbance respectively; The method for making of sensitive matrix is described for the sensitive matrix of channel power to disturbance of reloading below:

Step 2.1.1.1, to selected reference reactor core state, utilize RFSP-IST process simulation when do not reload and immobile liquid body region control device water level reactor core burnup behavior, obtain the power P of T each fuel channel in the full power world _i ^t, t ∈ [0, T];

Step 2.1.1.2, reloads to a certain selected j passage under with reference to reactor core state, and the burnup utilizing RFSP-IST program to carry out T full power sky equally calculates, and obtains the fuel channel power P after reloading _i ^j,t;

Step 2.1.1.3, utilizes following formula to carry out the calculating of sensitive matrix:

$S_{j\&RightArrow;i}^t=({P_i}^{j,t}-{P_i}^t)/{\mathrm{\&Delta;k}}_j---\left(6\right)$

Wherein, Δ k _jfor this passage k reloading caused by j passage under reference reactor core state _∞transient change amount, can calculate according to reactivity-burnup curve; Repeat said process 380 times, just can obtain the sensitive matrix that i channel power reloads to the arbitrary passage of reactor core; By same mode, channel power and the built-in reactivity variable quantity sensitive matrix to liquid regions control device SEA LEVEL VARIATION and burnup accumulation can be obtained;

Step 2.1.2, the power calculation of the arbitrary fuel channel i of heap in-core can be expressed as:

$P_i\&ap;P_{i,0}+\underset{p}{\mathrm{\&Sigma;}}\underset{r}{\mathrm{\&Sigma;}}{S}_{p,r\&RightArrow;i}{\mathrm{\&Delta;}}_{p,r},i=1,...,380---\left(4\right)$

Wherein, P _{i, 0}represent the power with reference to i passage under reactor core state, S _{p, r → i}i.e. sensitive matrix, represents with reference on reactor core basis, by the variable quantity of the i channel power in heap caused by the disturbance of r position p type unit; And Δ _p,rthen represent the disturbance quantity of certain refuelling scheme r position p type reality; Can adopt uses the same method calculates bundle power, area power;

Step 2.1.3, the reactor core built-in reactivity variable quantity introduced that reloads can be expressed as:

$\mathrm{\&Delta;k}\&ap;\underset{p}{\mathrm{\&Sigma;}}\underset{r}{\mathrm{\&Sigma;}}{S}_{p,r\&RightArrow;k}{\mathrm{\&Delta;}}_{p,r}---\left(5\right)$

In formula, S _{p, r → k}for the sensitive matrix produced in advance, represent with reference on reactor core basis, by the variable quantity of the reactor core built-in reactivity in heap caused by the disturbance of r position p type unit;

Step 2.2, builds all refuelling scheme Optimized models: in all refuelling scheme Optimized models, and one week reload concentrates on four day time and complete, and namely reload Monday, Tuesday, Thursday, Friday, all the other times do not reload;

Objective function---all refuelling scheme Optimized models are the darkest in objective function with one week average discharge burn-up, and formula is:

$\mathrm{Maximize}\underset{i=1}{\overset{7}{\mathrm{\&Sigma;}}}<\mathrm{Bu}\&CenterDot;X^{\&prime;}{>}_i/\underset{i=1}{\overset{7}{\mathrm{\&Sigma;}}}{N}_i---\left(7\right)$

In formula, N _ifor known constant, represent the port number that reloads of every day; Bu and X' to be all length be 380 vector, whether wherein the element of X' is 0-1 variable, represent each passage and reload; The element of Bu represents the discharge burn-up of each passage;

Constraint condition---the constraint condition considered in all refuelling scheme Optimized models comprises:

1), within one week, the number of active lanes of reloading of every day equals planned value;

2), within one week, the port number that reloads in radial each region is less than 3;

3), within one week, A side differs with the number of the passage that reloads of C side and is less than 5;

4) passage that reloads in 10 days must not be adjacent;

5) had when continuous two days when reloading, reload channel spacing beyond 2 passages;

6) every day reload channel spacing beyond 3 passages;

7) control of the minimum discharge burn-up of passage: for FAF passage, relative discharge burn-up will not reload lower than hourly value 80%, FARE passage is then set to 95%;

8), after reloading Tuesday and Friday, the deviation of 14 relative mean waters of liquid regions control device water level is less than 20%, and after reloading Monday and Thursday, water level deviation is less than 25%;

9), within one week, the power of all passages is all less than each self-operating limit value;

10), within one week, the power of each passage No. 6 and No. 7 clusters is less than operation limit value;

11), within one week, the axial power tilt in radial each region is less than 2.5%;

12) reactor core built-in reactivity was greater than and limited the use of the given limit value in family next Monday;

13) when the superpower factor of CPPF regional channel is greater than 1.045, all passages be adjacent can not reload;

Above-mentioned constraint condition mathematical linguistics is expressed as equation or inequality, gets final product founding mathematical models; By solving all refuelling scheme Optimized models, obtain the combination of channels of reloading of each day of reloading.