AUTOMATED METHOD FOR DETERMINING LOADING PLANS FOR NUCLEAR REACTOR CORE TURBINES

Abstract

The invention proposes a computer-assisted method for determining an optimal loading plan for a nuclear reactor core. Respective positions of nuclear fuel assemblies are tested using this method to assign optimal positions to the assemblies and proceed with reactor loading. The reactor core comprises cells with symmetrical positions about axes of symmetry, and standard assemblies are intended to be inserted into each cell. These standard assemblies, intended to prepare for future loading, are distributed according to the number of production runs they have previously undergone. Furthermore, groups of cell positions that are symmetrical about the axes of symmetry are identified, and a number of symmetrical positions are counted in each group.Families of common assemblies are formed such that the common assemblies within the same family have at least similar burnup rates. Each family comprises a number of common assemblies corresponding to a number of positions within one of these groups. The loading plan consisting of the common assemblies at initial positions is tested by numerical simulation, and then the positions of the common assemblies are permuted while maintaining the previously formed families of assemblies. The loading plan formed by the common assemblies at the permuted positions is then tested by numerical simulation, relative to the predetermined criterion. This step is repeated until at least one candidate plan for reactor loading is obtained. (See Figure 2.)

Description

Title of the invention: AUTOMATED METHOD FOR DETERMINING LOADING PLANS FOR NUCLEAR REACTOR CORES Technical field

[0001] The present disclosure relates to a determination of loading plans for nuclear reactor cores. Prior art

[0002] It relates more particularly to the development of computer calculation methods and tools applicable to nuclear reactors. The application concerned here relates to one of the first stages of a core calculation chain for the design of loading plans.

[0003] Before each actual reloading of nuclear assemblies into a nuclear power plant reactor vessel, the operator must carry out a series of studies intended to assess the safety and operation of the future reactor core, which determines the actual restart of a nuclear unit.

[0004] To carry out these studies, the operator generally has a "core calculation chain", integrating an assembly reloading application for a new nuclear production campaign. These applications located at the start of the chain make it possible to design the loading plan for the cores in operation which must comply with all the safety criteria, as well as a set of constraints, called "operating constraints", which prohibit, for example, certain positions for certain assemblies.

[0005] Today, engineers solve this complex combinatorial problem "by hand" with dedicated applications.

[0006] The need is therefore to have a tool capable of automatically designing these reloading plans, taking into account in a configurable way the right safety criteria, the operating constraints and the quality of the assemblies available in reserve. This category of assemblies, stored in a pool, is called "management reserve". Management reserves are assemblies that are generally worn but still capable of carrying out an additional campaign.

[0007] From an operator's point of view, there is a need for a tool capable of managing the constraints of positioning assemblies in the core. Abstract

[0008] The present disclosure improves the situation.

[0009] A computer-assisted method is provided for determining a optimal loading plan for a nuclear reactor core. In this method in particular, respective positions of nuclear fuel assemblies are tested by said computer means according to at least one criterion before assigning optimal positions to the assemblies and proceeding with the loading of the reactor. The reactor core comprises (without the fuel assemblies) a multiplicity of cells having positional symmetries relative to a plurality of axes of symmetry, common assemblies being intended to be each introduced into a cell. The common assemblies for preparing a future loading are divided into at least three categories defined by the number of production campaigns they have carried out within the nuclear reactor: - a first category of assemblies not used in a previous production campaign and having a combustion rate lower than a first threshold (new or similar assemblies), - a second category of assemblies used in a previous production campaign and having a combustion rate between the first threshold and a second threshold, higher than the first threshold, and - a third category of assemblies having been used in at least two previous production campaigns and having a combustion rate higher than the second threshold. The method comprises in particular the steps: - identify groups of cell positions which are symmetrical with respect to said axes of symmetry, and count a number of symmetrical positions in each group, - constitute families of common assemblies, the common assemblies of the same family having at least similar combustion rates, said families each comprising a number of common assemblies corresponding to a number of positions of one of said groups, respectively (the term "respectively" meaning here that there is a bijection between the families of common assemblies and the groups of positions, each family of assemblies and each group of positions related by the bijection respectively comprising the same number of elements), - choose, from a database of valid loading standard plans, a loading standard plan whose assembly combustion rates, by family, are closest to the combustion rates of current assemblies, by family, and, within the framework of a numerical simulation, assign to the current assemblies respective initial positions corresponding to the positions of the assemblies in the chosen standard plan, - test by digital simulation the loading plan consisting of the current assemblies at said initial positions, relative to at least one predetermined criterion, - permute positions of current assemblies while retaining the families of assemblies previously constituted and test by digital simulation the loading plan loading formed from the current assemblies at said permuted positions, relative to said predetermined criterion, and - repeat the permutation and testing step until at least one candidate plan for loading the reactor is obtained, the candidate plan being the one that best meets the said predetermined criterion.

[0010] It is recalled here that the combustion rate (or "burn-up" hereinafter) is a fundamental quantity in the characterization of a fuel assembly and in the modeling of core calculations. It characterizes the energy that has been produced by a fuel assembly during its irradiation. It is expressed in MWj / t, the ratio of the total energy produced to the mass in tons of initial heavy metal invested. Knowing the combustion rate, the energy can be quickly calculated by multiplying the specific mass power by the number of calendar days of previous operation, for example. As a rough and general rule, the higher the combustion rate of a set of assemblies, the lower the power generated, compared to a set of new assemblies.

[0011] Here, the term "neighboring combustion rates", for the constitution of a family of assemblies, means combustion rates of assemblies whose values ​​do not deviate (in absolute value) from each other (or from an average per family) by more than a few percent for example. The criterion of "neighboring combustion rates" may not be the only one for grouping the assemblies by family. The assemblies of the same family may also be designed according to the same technology and / or include the same type of fuel, and / or others.

[0012] Similarly, the term "typical loading plan whose assembly combustion rates, by family, are closest to the combustion rates..." is understood above to mean the choice from a database of a typical plan whose burn-up values ​​are "closest" to those of the current assemblies, for example by choosing the typical plan which minimizes a calculation of the distance between the sum of the squares of the differences of the average burn-up values ​​by family of the typical plan and of the current assemblies.

[0013] The first and second “thresholds” mentioned above are also understood to mean thresholds which simply delimit ranges of combustion rates (for example between 0 and 200 MWj / t, then between 200 and 17,000 MWj / t, then between 17,000 and 33,000 MWj / t or more, etc.), these ranges being defined most often by the number of production campaigns already previously undergone by these current assemblies.

[0014] By "testing by numerical simulation" is meant neutron calculations (often in 3D) of the core operating with the current assemblies in the tested positions, in the absence or presence of control clusters, absorbing neutrons, to smother the nuclear fission reaction, and from which one extracts, by configuration in particular control clusters, at least values ​​of anti-reactivity margin and pencil powers or "hot spot factors Fxy and Fxy, g", respectively in the absence and presence of control clusters (these parameters being explained further on with reference to figures 50 and 51). Moreover, the aforementioned "criterion", to be fulfilled, can be based on a combination of these parameters, and in particular we seek not to exceed overall limit values ​​of these parameters for the selection of a candidate core.

[0015] By "permuting positions of current assemblies" is meant both permutations between assemblies of the same family ("intrafamily" permutations) and exchanges of positions between all the respective assemblies of two different families ("interfamily" permutations), these different families having the same number of members. In particular, the members of a family remain in the same family after permutation (and are not scattered).

[0016] Such an embodiment within the meaning of the present disclosure, with automated generation of plans then tested by the aforementioned computer means, by permutations or by cross-referencing with other plans as will be seen in an example of embodiment presented later, leads to plans of unsuspected quality for a person skilled in the art, and sometimes in a counterintuitive manner.

[0017] Such computerized generation makes it possible to produce quality plans, converging quickly (a few tens of minutes at most) to meet the aforementioned criterion (noted “EPC” and defined below).

[0018] Typically, the permutations can be carried out randomly (or pseudo-randomly because they are nevertheless controlled by the aforementioned computer means), while nevertheless respecting predetermined rules (such as the way in which the assembly positions can be permuted in particular).

[0019] In one embodiment (for most cores, typically pressurized water cores), the aforementioned plurality of axes of symmetry comprises four axes of symmetry of the core, passing through the center of the core and comprising two axes, one vertical, the other horizontal, and two other axes of slope respectively of 45 degrees and 135 degrees relative to a horizontal line (all these axes being intersecting at the center of the core plane). We then consider groups of N cell positions located on said axes of symmetry, and groups of M cell positions not being located on said axes of symmetry (with typically M>N for pressurized water reactor cores). For example, for a core of 157 assemblies, we have M=8 and N=4.

[0020] In one embodiment, the aforementioned method may comprise, within the framework of the aforementioned digital simulation: - place an assembly chosen from said current assemblies in a central position, and - placing the assemblies of said families around the central assembly in groups of positions symmetrical with respect to the plurality of axes of symmetry, the assemblies positioned in the same group of positions being members of the same family of assemblies (and therefore having similar combustion rates).

[0021] The central assembly can typically be chosen based on its burnup rate. In general, it can be the one with the highest burnup rate and which is capable of carrying out an additional campaign in the core without exceeding a prescribed burnup. The central assembly is not in a family and is therefore not affected by any permutation. Furthermore, it may be preferred to place new or similar assemblies at the periphery of the core in order to flatten (or homogenize) the radial power distribution due to their high reactivity, i.e. their high capacity to generate nuclear fissions. This also makes it possible to compensate for neutron leaks at the edge of the vessel. As illustrated in [Fig.50], in general, the aim is to avoid local peaks in power P (dotted curves) and to flatten the power distribution as much as possible (solid line).

[0022] It will thus be understood that these heart predispositions can be given initially by the aforementioned standard plan, for example.

[0023] Among the predefined permutation rules, the permutations within the same family modify each assembly position of the family.

[0024] Thus, during intrafamily permutations, all assemblies are moved by permutations within the family.

[0025] Such an embodiment is illustrated as an example in [Fig. 19].

[0026] Among the predefined permutation rules, in order to test permutations between families (inter-family), the process may include: - swap the positions of current assemblies between two distinct families having the same number of members, and test by numerical simulation the loading plan consisting of the current assemblies at said swapped positions, relative to said predetermined criterion.

[0027] Such an embodiment is illustrated as an example in [Fig.20].

[0028] In an embodiment for the creation of “crossing plans” as mentioned previously, the permutations and testing step can be: - performed a predetermined number of iterations, until a first candidate plan was identified, then - repeated a predetermined number of iterations, until a second candidate plan is identified, the method further comprising at least one step of testing a crossing plan between the first and second plans.

[0029] We can of course repeat this step, with two, then three, four, etc. pairs of candidate plans successively, which makes it possible to gradually converge towards an ideal plan, as illustrated in [Fig.21] described later, this ideal plan respecting the aforementioned predetermined criterion.

[0030] In one embodiment, the constitution of a crossing plane can be carried out as follows: - the positions of a subset of the assembly families of the first candidate plan are preserved, and the remaining assembly families are: * assigned to positions which coincide with the positions of these same families in the second plan, if these positions are still available in the crossing plan, or * (otherwise) assigned to other groups of available positions, the number of members of said other groups being equal to the number of members of the families remaining to be placed.

[0031] Such an embodiment is illustrated in [Fig.19].

[0032] In this case, families of four assemblies are always assigned to sets each consisting of four positions (locations called above "cells") and / or families of eight assemblies are assigned to sets each consisting of eight positions.

[0033] To further comply with said predefined permutation rules, the assemblies generally comprise a face facing a predetermined observation point, and after permutations, the permuted assemblies retain this same face facing the observation point (for example, the north face of an assembly is, after permutation, still facing north).

[0034] As regards the verification of the achievement of the aforementioned predetermined criterion, a numerical simulation by neutron calculations of each core plane tested can be carried out, under conditions with and without insertion of neutron absorbing clusters, stifling the chain reaction, to estimate quantities specific to the core plane tested, these quantities including in particular hot spot factors without cluster FxyÇplan) and with clusters ! xy, giplan), as well as an antireactivity margin Marge(plan).

[0035] These estimated quantities can be compared to limit values ​​in the calculation of a loading plan evaluation expression, noted EPC, and it is then possible to select, from among possible plans, a candidate plan which has the smallest EPC evaluation expression, thus fulfilling the predetermined criterion, mentioned above.

[0036] In an exemplary embodiment, the EPC evaluation expression of a plan is given by: EPC=Cxmax(MargeIUr-Margin(plan) ;0) + ( + Margin x (777V xg(pliai)-FxyMg ;0) ) Or : - Margej is a limit value of antireactivity margin, - Fxy^ , g is a hot spot limit value in the presence of clusters, - Fxy is a hotspot limit value in the absence of clusters, - C is a positive real coefficient, and ' represents the sum of terms over a set of clusters, whose expression of a term, for a given cluster g is: [ jrr— x maxfFxv, g( plane ) - Fxy,. , g ; 0 ) | '

[0037] For example, in the EPC evaluation expression, the two terms: (Margin \ / , . \ ef T—“ x max Fxx( plane ) - Fxy,. ; 0 Margeljm xx max^ / 7xy, g(plane} Fxy g, O) j can be of the same order of magnitude, and the coefficient C can then be initially chosen so that the term C x max (Margin-Margin (plan); 0) is also of the same order of magnitude as one of the two aforementioned terms.

[0038] Typically, the coefficient C can be between 0.5 and 1 (and be worth, for example, 0.75).

[0039] Alternatively, the coefficient C can be between 1 and 10 for example.

[0040] The present disclosure also relates to a configuration of a nuclear reactor core, resulting from the implementation of the above method.

[0041] For example, a core plan thus obtained by the method can typically be distinguished from a “conventional” configuration of the prior art, in which the assemblies of the first category are generally found in a first peripheral zone of the core, the assemblies of the second category in a second intermediate zone of the core and the assemblies of the third category in a third central zone. In a core obtained by implementing the above method, these assemblies can be more “mixed” than in a conventional configuration, for example.

[0042] The present disclosure also relates to a computer program comprising instructions for implementing the above method, when these instructions are executed by a processor. According to another aspect, there is provided a non-transitory recording medium, readable by a computer, on which such a program is recorded.

[0043] The present disclosure also relates to a computer device comprising at least one processor for implementing the above method.

[0044] [Fig.52] illustrates an exemplary embodiment of such a DIS device, comprising ty a memory MEM capable of storing at least the instructions of a computer program of the aforementioned type and a processor PROC cooperating with the memory MEM to execute these instructions. The device DIS may further comprise an input interface IN with which the processor PROC cooperates to receive, for example, data relating to the assemblies (total number, combustion rate, data from standard plans, etc.), and an output interface OUT with which the processor PROC cooperates to deliver, for example, the data of a candidate plan. Brief description of the drawings

[0045] Other characteristics, details and advantages will appear on reading the detailed description below, and on analyzing the attached drawings, in which: Fig.l

[0046] [Fig.l] shows a fuel assembly of a reactor core in an exemplary embodiment. Fig. 2

[0047] [Fig.2] shows a sectional plan of a 157-assembly core in an example of realization. Fig. 3

[0048] [Fig.3] shows two calculation modules involved in a method according to an embodiment of the present disclosure: a module M0D1 for the constitution of plans according to predefined rules (in particular core permutation and crossing rules) and a module M0D2 for the evaluation according to the aforementioned EPC criterion of the plan thus constituted by the module M0D1. Fig. 4 to Fig. 8

[0049] [Fig.4], [Fig.5], [Fig.6], [Fig.7], [Fig.8] show intrafamily permutations possible for a family of four. Fig. 9 to Fig. 15

[0050] [Fig.9], [Fig.10], [Fig.11], [Fig.12], [Fig.13], [Fig.14], [Fig.15] show the per possible intrafamily mutations for a family of eight members. Fig. 16

[0051] [Fig. 16] shows an example of a possible realization of a permutation between two families (inter-family permutations) of four members each (permutation of two families 4 placed in positions of symmetry 4). Fig. 17

[0052] [Fig. 17] shows an example of a possible realization of a permutation between two families (inter-family permutations) of eight members each (permutation of two families 8 placed in symmetrical positions 8). Fig. 18

[0053] [Fig. 18] shows an example of crossing two parent planes, according to one embodiment, to generate a child plane. Fig. 19

[0054] [Fig. 19] shows a concrete example of intrafamily permutation according to one embodiment. Fig. 20

[0055] [Fig.20] shows a concrete example of interfamily permutation according to one embodiment. Fig. 21

[0056] [Fig.21] shows the performances achieved in terms of convergence towards an optimum core plan, respecting the aforementioned EPC criterion, according to a concrete example of realization (reactor 1 of the Dampierre power plant (France) for campaign 36). Fig. 22

[0057] [Fig.22] is a schematic flowchart of the method presented above, according to an exemplary embodiment. Fig. 23 to Fig. 33

[0058] [Fig.23], [Fig.24], [Fig.25], [Fig.26], [Fig.27], [Fig.28], [Fig.29], [Fig.30], [Fig.31], [Fig.32], [Fig.33] illustrate possible positions for families of four assemblies in a 157-assembly core. Fig. 34 to Fig. 47

[0059] [Fig.34], [Fig.35], [Fig.36], [Fig.37], [Fig.38], [Fig.39], [Fig.40], [Fig.41], [Fig.42], [Fig.43], [Fig.44], [Fig.45], [Fig.46], [Fig.47] illustrate possible positions for families of eight assemblies in a 157-assembly core. Fig. 48

[0060] [Fig.48] shows a 193-assembly core plan produced by implementing the method. Fig. 49

[0061] [Fig.49] shows a 205-assembly core plan produced by implementing the method. Fig. 50

[0062] [Fig.50] schematically illustrates a radial power sheet generated by a core, in the absence of a control cluster, the sheet being homogeneous (solid line curve), or inhomogeneous (dotted line curve) favoring the presence of a PC hot spot (Fxy factor mentioned above). Fig. 51

[0063] [Fig.51] schematically illustrates a radial power sheet generated by a heart, here in the presence of control clusters g, the sheet being homogeneous (curve in solid line), or inhomogeneous (dotted line curve) favoring the presence of PC hot spots in the presence of clusters (Fxy factor, g mentioned above). Fig. 52

[0064] [Fig.52] schematically illustrates a device for implementing the above method, in an exemplary embodiment. Description of the embodiments

[0065] The present disclosure provides a new tool that improves the current situation through an approach according to a method that reduces the speeds of realization of reloading plans while designing cores optimized from the point of view of safety and operation.

[0066] As presented previously, the present disclosure provides a method using permutations of assemblies in families, or exchanges of families of assemblies in groups of positions having the same number of elements.

[0067] Below, a description is given of three particular steps implementing permutations of assemblies in the positions of a nuclear reactor core, in order to arrive at a configuration whose neutronic characteristics are located in a predefined safety zone.

[0068] However, before describing the above process in detail, it is important to define some concepts of combustible core.

[0069] With reference to [Fig.l], in each assembly of a reactor core, CC tubes (called "fuel rods") are assembled using in particular GR holding grids. An assembly is the elementary fuel unit present in a nuclear reactor core, which is made up of a plurality of assemblies, called "fuel assemblies" by misuse of language. Passages are also provided in at least part of the assemblies to introduce one or more G clusters in order to smother the nuclear fission reaction, if necessary. In each fuel rod, a plurality of fuel pellets are threaded into a cladding. The fuel pellets are for example made of uranium dioxide UO2. The assembly of [Fig.l] is shown relative to the z axis of heights. The core itself, made up of a plurality of assemblies like that illustrated in [Fig.l], is shown as an example in [Fig.2], seen “in section” in the x,y plane. .

[0070] In particular, [Fig. 2] shows four axes of symmetry intersecting the center of the core plane, one parallel to the x axis, the other parallel to the y axis, and two axes inclined respectively by 45° and 135° relative to the x axis. The symmetry of the assemblies can be observed relative to each of these axes, in particular in terms of respective values ​​of combustion rate or "bum-up" hereinafter.

[0071] We can appreciate in [Fig.2] the symmetry of positions of the assemblies having neighboring burn-ups. For example, the assemblies in H2 and H14 (symmetrical with respect to the horizontal axis) have respective burn-ups of 14548 and 14561 (values ​​appearing in the second line of each box in [Fig.l]). We can also appreciate that the assemblies in J3 and G3 (symmetrical with respect to the vertical axis) have respective rates of 32415 and 32536. We can also note that their respective symmetrical C9 and C7 with respect to the 45° axis have neighboring combustion rates, which are 32262 and 32453. We can note that the same is true for their other symmetrical N7, N9 and J13, G13. All these assemblies, J3, G3, C7, C9, N7, N9, J13 and G13 then have combustion rates between approximately 32000 and 32500, and are therefore very close, relative to the combustion rates of the other assemblies. These assemblies J3, G3, C7, C9, N7, N9, J13 and G13 constitute a family occupying here a group of symmetrical positions with respect to all the axes.Their number is eight, per group of symmetrical positions, in the example illustrated in [Fig.2] of a core formed of 157 assemblies. This number of groups of symmetrical positions can be greater in a core comprising a greater number of assemblies.

[0072] To take the example of the H2 and H14 assemblies having respective burn-ups of 14548 and 14561, their symmetrical members in the same family are P8 and B8 and their rates are 14599 and 14482. It can be appreciated again that these combustion rates are very similar for assemblies thus occupying a group of four symmetrical positions with respect to all the axes. This group in fact comprises only four members of positions), and not eight members as previously, because these positions are themselves located on axes of symmetry.

[0073] It can also be noted in [Fig.2] that in addition to the assemblies in R7, R8, R9, J1, H1, G1, A7, A8, A9, J15, H15, G15 which have high combustion rates to protect the vessel housing the core, the periphery of the core preferably comprises new assemblies in P5 to P11, L14-E14, B11-B5, E2-L2 whose combustion rates are low, likely to make these assemblies very reactive in a neutron flux. However, these assemblies, placed in these peripheral positions which correspond to areas with low neutron flux due to their leaks towards the outside of the core, will produce fewer neutrons, therefore will produce a lower power than the average of the assemblies. Again, such an arrangement makes it possible to "flatten" (or homogenize) the radial power distribution as illustrated in [Fig.50].

[0074] It is recalled that, in general, we seek to avoid local power peaks and to flatten the power distribution as much as possible. Typically, we also seek to avoid hot spots (factor Fx>y explained later).

[0075] An explanation of the principle of “anti-reactivity margin” is set out below.

[0076] To control the nuclear reaction in the reactor core, the operator has two main means.

[0077] A first means consists of adjusting the boron concentration in the water of the primary circuit, boron having the property of absorbing the neutrons produced by the nuclear fission reaction. Dilution of boron is then understood to mean the operation consisting of injecting water into the primary circuit to reduce the boron concentration, and thus promote the increase in the neutron flux. Conversely, borication is understood to mean the addition of boron to the water of the primary circuit to promote the boron concentration and therefore reduce the neutron flux.

[0078] A second means consists of introducing the control clusters (reference G of [Fig.l]) into the core or removing them from it. These control clusters, gathered in groups, contain neutron-absorbing materials. Their position at a given height in the core makes it possible to introduce more or less anti-reactivity into the core of the reactor, having defined that the reactivity expressed in pcm (per hundred thousand, 10-5) is the quantity which measures a relative increase in the neutron flux induced by a control means (movement of the control clusters, variation in the boron concentration, etc.).

[0079] In normal operation, the position of certain clusters is regulated by a computer according to a reactor power setpoint. However, it is appropriate to maintain certain clusters at a sufficient height, set by the technical operating specifications, so that their fall into the core can effectively smother the nuclear fission reaction in the event of an automatic shutdown of the reactor. This height makes it possible to maximize the antireactivity that will be introduced if necessary. This arrangement makes it possible to guarantee a sufficient “antireactivity margin” to allow automatic shutdown of the reactor.

[0080] Referring again to [Fig.2], a “loading plan” corresponds to the definition of a refill (an inventory of fuel assemblies) coupled with a matrix (defining the arrangement of these assemblies in the tank).

[0081] The number of assemblies per type of nuclear reactor core is predetermined.

[0082] For example, in the case of square-section assemblies, the following arithmetic properties are verified: - Always counting a central assembly, the total number A of assemblies is always odd for any reactor, and - For reasons of symmetry known as "one quarter" or "one eighth" as mentioned previously, and to ensure a minimum splitting of the core by three during fuel renewal, A-1 is an integer divisible by 3 and 4.

[0083] Towards the end of an N campaign of operation of a nuclear unit, the operator must anticipate the next N+l campaign of operation, and have a loading plan for the N+L campaign. The industrial challenge is to minimize, at the end of the N campaign, the period of temporary shutdown of operation known as "unit shutdown" for possible maintenance of equipment and / or unloading / reloading of nuclear fuels. Each day of shutdown represents a real loss of earnings for the operator. As soon as the unit shutdown phase begins, all the fuel assemblies from campaign N are unloaded from the vessel into a storage pool, called the "fuel building" near the reactor building. The assemblies from the upcoming N+1 campaign are transferred from a fuel building pool to the reactor building pool. The spent assemblies, which are not recovered, i.e. not reloaded in the upcoming campaign, remain in the fuel building pool for several years before being removed for reprocessing. The assemblies that can still be recovered for the next unit loading plans are added to the management reserve and are also stored in the fuel building pool.To give an idea and an order of magnitude, they are those which have a combustion rate approximately within the intervals of [8000; 14500] MWJ / t, [20000; 25000], and [32000; 35000], etc., in the example of [Fig.2], whereas the “new” assemblies have a combustion rate close to 100 MWj / t for example.

[0084] It should be noted that the number of burnup ranges referred to above depends on the fractionation by which the nuclear fuel is renewed. In the example above, this is a fractionation by thirds, hence three burnup ranges, not including new or similar assemblies. For a core with “quarter-core” fractionation, four burnup ranges would have been observed. This is not a rule but an observation that results from core management.

[0085] Permanently worn assemblies are stored temporarily before being removed for reprocessing.

[0086] At this point, the loading of the fuel assemblies can begin. They are physically positioned in the position specified by the loading plan.

[0087] For the design of the loading plan as such, the technology of pressurized water reactors requires reloading the cores with new fuel assemblies according to a known periodicity. It is the type of fuel (Uranium, Plutonium, etc.), the enrichment in fissile material of the pellets (U, Pu) of the rods of the fuel assemblies, and the fractionation of the renewed part, which dictate the maximum achievable natural campaign length.

[0088] For example, for a 900 MWe REP (pressurized water reactor) type reactor, the number of assemblies A is 157 and has the following options, having considered that Al assemblies are split: - A split by 1 / 3 meaning that the refill will be 52 assemblies, - A split by 1 / 4 meaning that the refill will be 40 assemblies, actually leading to the following partition 3x40 +36 = 156

[0089] Thus, with identical material invested and enrichment, a so-called quarter-heart campaign will be shorter than a so-called third-heart campaign, because the former provides less responsiveness than the latter.

[0090] A strategy linked to the availability of the slices favors long campaigns of 14 to 18 months, or even more, leading to a combination of a 1 / 3 core fractionation and a high Uranium enrichment, at more than 4% for example within the limits of the acceptability criteria previously validated by the nuclear safety authorities, including the behavior of the fuel assemblies, the antireactivation margins, and various envelope criteria (in particular the radial power sheet generated).

[0091] Today, the search for loading plans is carried out manually by operations engineers.

[0092] By "manually" is meant in a first step the initial positioning of the A assemblies, although this step can be automated by carrying out for example a mimicry based on the knowledge of loading plans of previous campaigns consisting of reducing the differences in combustion rates for an assembly occupying a given "naval battle" place. Such a loading plan listed in "naval battle" is of the type illustrated in [Fig.2].

[0093] In a second step, after evaluation of the loading plan thus established, the engineer modifies the location of certain families of assemblies to correct effects causing the acceptability criteria to fall outside the admissible safety and operating zones. The new plan is evaluated by neutron calculation in turn and so on until the above-mentioned criteria are met. The plan obtained is then the final plan on the basis of which the unloading / loading operations can actually be carried out.

[0094] This approach follows a set of compromises aimed at satisfying safety criteria and economic criteria while taking into account possible operating hazards.

[0095] As a general rule, we seek to place the new assemblies rather on the periphery of the reactor (fixed position according to management) to minimize the radial power peaks (noted Fxy) of the fuel assembly rods by flattening the radial power sheet, as illustrated by the solid line curve in [Fig.50]. The total power of a rod, normalized to 1 being defined, the so-called "hot spot" factor Fxy is the maximum power of such a rod which must not exceed a limit value (for example Fxy = 1.44, which means 44% more power than the average power of 1, due to the normalization). For example, the threshold Ps of [Fig.50] can be 1.44 and the inhomogeneous dotted line curve is likely to exceed this limit at point PC.

[0096] Next, we look for possible symmetries in the placement of the assemblies in limiting hotspot factors (by setting an allowable Fxymax limit).

[0097] The same compromises are also sought with the achievement of core performance in the presence of control clusters, as illustrated in [Fig.51]. In particular, in the presence of control clusters g, their introduction must be sufficiently effective to stifle the nuclear fission reaction in the core, beyond or at the level of an antireactivity margin (reference "Margin" in [Fig.51]). Furthermore, it is also sought to further limit the hot spots in the presence of clusters g, noted "Fxy, g" in [Fig.51] (appearing on the curve in dotted lines).

[0098] Loading plan optimization requires experience to quickly propose solutions on complex plans. Indeed, finding an optimized plan corresponds to a combinatorial problem of searching for a hundred plans among a colossal number of possible matrices. This number is obtained by circular permutations between families and members within each family. Typically, based for example on a core with 193 predetermined assemblies, comprising 12 families of 4 assemblies, 18 families of 8 assemblies, it is theoretically possible to place them in approximately 3 1030 matrices, the central assembly being fixed (with 3 1030 ~ 12! x4! x 18! x8!).

[0099] The resolution of this problem is not unique. Indeed, several plans can respond favorably to the safety requirements of the nuclear unit.

[0100] Nevertheless, such an approach is tedious and the present disclosure proposes a particular use of computer means, as explained below.

[0101] More particularly, it proposes to carry out a search for plans using a digital simulator linking two modules intended to quickly evaluate the criteria of the candidate loading plan and to modify it. The first module for constructing a loading plan is coupled with a second module evaluating the safety and operating criteria of the plan found. This is a method which can therefore be provided in two stages implemented by two modules M0D1, M0D2, as shown diagrammatically in [Fig. 3]. The first module M0D1 proposes a “correct” core plan (initially derived from a base of standard plans but with possible permutations respecting predetermined permutation rules) and the second module M0D2 proposes an evaluation in particular by digital neutronic calculations of the quality of the core thus constituted, in relation to a criterion called “EPC” hereinafter (for “core plan evaluation”).

[0102] The process can be iterated a plurality of times, the candidate core plan which can be retained being the one which best fulfills the aforementioned EPC criterion (i.e. the one which minimizes it as presented in the example below).

[0103] From the characteristics calculated for a given core plane by the neutron calculation means of the M0D2 module, a value is in fact determined whose unit is the pcm (per hundred thousand), thanks to the following function, giving the Evaluation of the Heart Plan “EPC”:

[0104] EPC-QJSxmax^Marge,.'"-Margin) plan); 0J + { C) xmiix^Fxy^pian') - Fxy^o) + Margin / im

[0105] EPC being greater than or, at best, equal to 0, by construction.

[0106] We are in fact seeking to minimize this function to reach the value of 0. As the terms constituting the formula are positive, this means that they are each zero, in this case, and therefore that each of the criteria relating to them would be respected.

[0107] For example, for a 900 Mwe REP type reactor: - the limit value of the antireactivity margin Margin^ is set at 1800 pcm, - the hot spot limit value Fxy is set to 1.44, - the hot spot limit values ​​in the presence of control clusters Fxy^, g correspond to the radial power limit peaks when clusters g are inserted into the core (by cluster group or combinations of cluster groups): the values ​​are between 1.44 and 1.8 in reference to the current specifications set by the safety authorities in France; these values ​​may vary from one country to another, depending in particular on the type of nuclear reactor core.

[0108] The values ​​of Marge(plan), Fxy(plan) and Fxy, g(plan) are calculated for a given core plan by a neutron calculation code which is more precisely a nuclear reactor physics code whose main principles are now explained.

[0109] The term "nuclear reactor physics code" applies to software capable of calculating the three-dimensional distribution of power (in Watts) in a nuclear reactor core from structural data (geometry, chemical composition, heavy nuclei composition, etc.). To do this, the software must be able, for example, in 3D geometry: - Calculate the distribution of coolant temperatures in the reactor core. The coolant is the fluid that removes the heat produced by nuclear fission. This calculation is carried out by a module of the code called the “thermohydraulic module”; - Calculate the temperature distribution of the nuclear fuel. This calculation is carried out by a module of the code called “thermal module” or “thermomechanical module” if mechanical aspects are also covered (e.g. pellet-cladding interaction); - Calculate the distribution of the neutron flux from which the power is derived, by a module called the “neutron module”.

[0110] It is the coupled interaction of these three modules above which makes it possible to calculate the 3D power in the reactor core.

[0111] Neutronics modifies the temperatures of the coolant, the temperature of the ca- The moderator modifies the fuel temperatures. The temperatures of the moderator and the fuel modify the neutronics. Indeed, fission (nuclear physics) is caused by an interaction of a heavy nucleus with neutrons (managed by the neutronic module), said fission producing heat which propagates in the matter (managed by the thermal module), the latter transmitting its calories to the water, the coolant, which transports them by raising its temperature (managed by the thermohydraulic module) and consequently modifies the temperature of the fuel.

[0112] We then observe counter-reaction phenomena. Since the coolant water is also the moderator by which the neutrons are slowed down to promote fissions, its temperature variation will modify its density and therefore the neutron slowing down, which therefore impacts the future generation of fissions. At the same time, a change in the fuel temperature increases the neutron absorption reactions, particularly in Uranium 238, which modifies the neutron.

[0113] Here neutronics is the central branch of nuclear reactor physics because it governs the generation of the aforementioned phenomena. It allows the characterization of the neutron population distributed spatially and temporally according to an energy spectrum which will depend on the interaction with matter. These interactions are absorption (fissile, fertile and sterile), diffusion, reflection, neutron leaks. To this must be added a kinetic component linked to the effective production of neutrons by fission divided into prompt neutrons and delayed neutrons. The latter, in the minority and born several seconds after the prompt neutrons, are essential to allow the control of a nuclear reactor. Other phenomena such as poisoning by Xenon, a product of fission, will also modify neutronics.

[0114] Thus, the aforementioned physical phenomena which occur within a nuclear reactor are of great complexity, which requires the use of core physics calculation codes of the so-called "COCCINELLE" type with which the Applicant is equipped.

[0115] It is understood that several iterations are necessary to evaluate the whole at equilibrium. Once convergence is obtained, the reactor physics code can produce results necessary for the operation and safety of the reactor: - location of the hot spot (Fxy), - “intelligent” power distribution, - calculated responses of various core instrumentation, - reactor control and stability over time, - irradiation of nuclear fuels (burn-up assessment), etc.

[0116] The most classic use of a reactor physics code lies in the calculation of the loading plan, namely the optimal arrangement of bare fuels which make it possible to satisfy the numerous safety criteria (efficiency of the control rods or "clusters" above), hot spot (Fxy), flattening of the power sheet, anti-reactivity margin, etc.).

[0117] The COCCINELLE calculation code, the official code of the calculation chain in operation in the French fleet of electric generating reactors to date, falls into the class of “reactor physics codes”. It includes: - An axial 1D thermohydraulic module in the channel containing the water heat transfer fluid; - A radial 1D thermal module in the cylindrical fuel rod; - A 3D neutronics module in neutron scattering theory.

[0118] Neutron scattering is a theoretical model widely used throughout the world to treat a simplified form of the Boltzmann equation that governs the behavior of neutrons in matter. Descriptions of the theoretical models, which are far too complex to be detailed here, used in COCCINELLE can be found in the French-language references "La physique des broyeurs nucléaires, 3ème édition" (author Serge Marguet, ISBN 978-2-7430-1105-5, Lavoisier edition) and in the English-language references "The physics of nuclear reactors" (author Serge Marguet, ISBN 978-3-319-59558-7, Springer edition).

[0119] Other older reference works present the fundamental principles of nuclear reactor physics, such as the “Treatise on Neutronics” by Jean Bussac and Paul Reuss, published by HERMANN ISBN 2-705-6011-9 - second edition, 1985.

[0120] In the following, the method according to the present disclosure is explained for cores of the 900 MWe REP type comprising 157 fuel assemblies, and this in a non-limiting manner because the same method can be applied in principle to all other cores such as the 1300 MWe REP comprising 193 assemblies, the 1450 Mwe REP comprising 205 assemblies, and the “EPR” reactor which is a 1650 Mwe pressurized water reactor comprising 241 assemblies.

[0121] We seek to position 157 assemblies in the 157 positions (or "cells") of a nuclear reactor core in such a way that the neutron criteria determined by the calculation chain are lower than a limit threshold (hot spot factors without control cluster Fxy or with clusters g: Fxy,g) or higher than a limit threshold (anti-reactivity margin Margin). These different criteria are combined in an evaluation function defined above which gives a numerical value to each core plan (noted EPC for "Core Plan Evaluation").

[0122] As a general rule, it is well known that it is preferable to place the assemblies by substantially decreasing combustion rate starting from the center of the core. This is a general principle that the person skilled in the art tries to follow during operations carried out “manually” as explained above. The method according to the present disclosure, based in particular on random permutations, does not follow this approach, although it appears that the plans found by the method according to the present disclosure substantially respect this principle. Nevertheless, the present method differs from the non-automated manual approach.

[0123] As previously indicated, the method comprises three steps: - Step 1: partition of the assemblies by respective combustion rates to constitute families (or “categories” in the definition of the process given above); - Step 2: selection from a database of a standard plan having assembly combustion rates closest to those partitioned in step 1, and evaluating the EPC (by numerical simulation) of a core made up of the assemblies partitioned in step 1 and positioned in assembly positions of the standard plan having the closest combustion rates; - Step 3: consider groups of symmetrical positions with respect to the core's axes of symmetry and numerically simulate the effect of assembly permutations according to predefined rules (permutations within the same group and / or between groups, the assembly face always remaining opposite a given observation point), then evaluate the EPC (by numerical simulation) of a core whose assemblies have thus permuted, this step 3 can be iterated several times to test whether the EPC is reduced compared to previous configurations. If this is the case, a candidate core configuration can be determined for the next campaign (the one with the lowest EPC).

[0124] We now detail each of these steps.

[0125] In step 1, we rely on an example of core management, called “core third” of a 900 MWe REP type reactor comprising 157 assemblies.

[0126] At the end of campaign cycle N, the 157 assemblies are composed for example of: - 52 assemblies irradiated around 10,000 MWj / t (i.e. 1 cycle): these assemblies are kept and they are recharged in campaign N+1 for a second cycle, - 52 assemblies irradiated around 25,000 MWj / t (i.e. 2 cycles): these assemblies are kept and they are recharged in campaign N+1 for a third cycle, - 52 assemblies irradiated around 33,000 MWj / t (i.e. 3 cycles): these assemblies are not kept and they are stored in a pool for later reprocessing, - 1 assembly irradiated around 40,000 MWj / t (at least 4 cycles), the central assembly, which is also not kept: it is stored in a pool for further reprocessing.

[0127] For the following campaign N+l at the start of the cycle, 157 assemblies are elected: - 52 new assemblies, having a bum-up of 0 MWj / t (or residual, close to 0 and typically less than 200), - 52 irradiated assemblies of around 10,000 MWj / t (from previous campaigns, see above), - 52 irradiated assemblies of around 25,000 MWj / t (from previous campaigns, see above), and - 1 irradiated assembly of around 33,000 MWj / t (from the pool of previous campaigns).

[0128] On this basis, the 157 assemblies elected above for the N+1 campaign are classified by families defined as follows: - families of 4 assemblies, having similar combustion rates in the same family, - families of 8 assemblies, having similar combustion rates within the same family, and - a family of 1 assembly, generally the most irradiated assembly as given in the example above.

[0129] “Neighboring combustion rates” mean burn-ups such that their mutual differences are, in absolute value, lower than a predefined threshold (1000 MWj / t for example).

[0130] In the following and by abuse of language, we will designate by “family 4”, “family 8”, and “family 1”, these families comprising 4 assemblies, 8 assemblies, or 1 assembly, respectively.

[0131] The families of assemblies thus constituted by such a partition have, for a given family, close Burn-Up (BU) values, i.e. whose differences are for example around 1000 MWj / t (or less than a few percent typically), and moreover have identical technological characteristics (type of fuel, or others). These families are called in the following “families of the future core plan”.

[0132] The term "loading" refers to the set of 157 fuel assemblies which, once positioned in the reactor vessel, will form what is called the "core" of the nuclear reactor.

[0133] Step 2 is described below, which identifies a plan in a database containing numerous standard loading plans from different nuclear reactors (and not just the one currently being reloaded).

[0134] The base contains a set of plans, some of which have the same characteristics as that to be constituted for the present core, for campaign N+1 which comprises, according to the example introduced in step 1, plans formed of 157 assemblies partitioned into three batches of 52 assemblies and a central assembly.

[0135] Among these plans, the comparison with the plans in the database identifies the one hereinafter called the “typical plan”, whose assembly combustion rates are closest to the combustion rates of the assemblies predefined in step 1. previous and elected for the N+l campaign whose respective positions in the heart must be determined.

[0136] For this purpose, a "burn-up distance" is determined between the assemblies of the standard plan and those of the future core plan. The distances between families of the same species are determined, i.e. between families 4, on the one hand, and between families 8, on the other hand.

[0137] One embodiment may consist of comparing the average of the burn-ups of a first family 4 included in the loading constituted in step 1 with the average burn-up of all the families 4 of the standard plan, and choosing the correspondence with the family of the standard plan whose average is closest.

[0138] Then, a comparison can be made of the average of the bum-ups of a second family 4 included in the loading constituted in step 1 with the average burn-up of all the families 4 of the plan, deprived of the one which has already been matched. The process continues until all the families 4 of the future core plan have been matched with one and only one family 4 of the standard plan.

[0139] The same sub-steps are carried out in the same order as for families 4 but this time with families 8 of the future plan and families 8 of the standard plan.

[0140] At the end of the two previous sub-steps, all the families of the future plan are each in correspondence with one and only one family of the standard plan. The sum of the squares of the differences between average burn-ups of these matched families is then calculated. The final value is an indicator of the "distance" between these two sets of families. The definition of this indicator is not limiting, and it can be defined for example as the sum of the absolute values, therefore positive, of the differences between average burn-ups of the matched families. The process is repeated on all the standard plans. At the end of these iterations, each standard plan is associated with a distance to the families of the future core plan.

[0141] The standard plan with the minimum distance indicator is then selected. This is then the standard reference plan for constructing the plan for the future campaign.

[0142] Once this standard plan has been selected, each family of the future plan is placed in the same position of symmetry as that occupied by the family of the reference standard plan with which it was matched during the previous processes.

[0143] The core plane thus formed is thus an initial core plane (which must then undergo the permutations of step 3 described in detail below). It can be noted that the central assembly positioned at H8 in the plane of [Fig.2], has an imposed position and does not undergo the aforementioned permutations.

[0144] Step 3 is described below.

[0145] In the 157-assembly core considered in this example, there are eleven positions of symmetry 4 (numbered from 1 to 11) and 14 symmetry 8 positions (numbered from 12 to 25), plus a central position.

[0146] With reference to [Fig.2], these symmetry positions 4 are the positions placed on the diagonals R1-A15 and R15-A1 and the medians H1-H15 and R8-A8. The central assembly is excluded.

[0147] All other positions are of 8 symmetry: none of the assemblies of the 8 families concerned are positioned on a diagonal or a median as defined above.

[0148] Figures 23 to 33 illustrate the 11 positions of symmetry 4 and Figures 34 to 47 illustrate the 14 positions of symmetry 8.

[0149] The fuel assemblies are therefore partitioned into 11 families 4, 14 families 8, and one family 1 containing only one assembly: - so: 4xll + 8xl4+l = 157 assemblies

[0150] Thus the plan formed from these positions leads to a total of 157 assemblies.

[0151] There are of course a greater number of positions in a core comprising more than 157 assemblies, but always families 4, families 8, and family 1, respecting these position symmetries.

[0152] The sequence of calculation steps is described below.

[0153] The neutron calculation code is launched and the parameters Margin(plane), Fxy(plane) and Fxy,g(plan) are extracted from the results to evaluate the EPC criterion defined above.

[0154] If this EPC criterion has reached a target value between 0 and / or close to 0 during a maximum number of permutations reached, then the plan having this target value becomes the elected plan for the future campaign.

[0155] During these permutations, reassignments of positions are carried out while respecting for each family 4 and family 8, the symmetry 4 and the symmetry 8. Permutations of assembly positions are thus carried out, and following each or several permutations, a new neutron calculation is carried out to determine the new EPC criterion. This process continues and the core having an EPC of zero or close to zero can be selected as a candidate.

[0156] The permutations within families 4 and families 8 are described below.

[0157] A "configuration of a family" is an order of placement of the assemblies of the family in the positions of the symmetry position to which it is assigned. Each assembly position of a given symmetry family has a rank in accordance with [Fig.4] and [Fig.5].

[0158] Note that figures 4 and 5 are not an image of the heart as represented in [Fig.2], but a symbolic representation of positions in 4 symmetry or 8 symmetry as defined above.

[0159] The four assemblies of a family 4 being placed in the 4 positions of a symmetry position 4, it is possible to swap them according to one of the three possibilities described below.

[0160] In permutation 4.a, the assembly located in position 4 is placed in position 1. The assembly located in position 1 is placed in position 2. The assembly located in position 2 is placed in position 3. The assembly located in position 3 is placed in position 4.

[0161] During permutation 4.b, the assemblies change position in the symmetrical position, relative to the axes of symmetry on which they are located, as illustrated in [Fig.7].

[0162] During permutation 4.c, the assemblies change position by rotating in the opposite direction to permutation 4.a, in accordance with [Fig.8].

[0163] We can therefore count four possible configurations for the four assemblies of a family 4 in the cells of a symmetrical position 4 (the initial configuration plus the three obtained by the three permutations).

[0164] For families 8 and symmetry positions 8, there are seven possible permutations, i.e. eight possible configurations (the initial configuration plus the seven configurations obtained by the seven permutations. These seven permutations are described below.

[0165] In permutation 8.a (illustrated in [Fig.9]), the assembly located in position 1 is placed in position 2. The assembly located in position 2 is placed in position 1. The assembly located in position 3 is placed in position 4. The assembly located in position 4 is placed in position 3. The assembly located in position 5 is placed in position 6. The assembly located in position 6 is placed in position 5. The assembly located in position 7 is placed in position 8. The assembly located in position 8 is placed in position 7.

[0166] In permutation 8.b, the assemblies change position to the symmetrical position, as shown in [Fig. 10].

[0167] In permutation 8.c, the assemblies change position to the symmetrical position, as shown in [Fig. 11].

[0168] In permutation 8.d, the assemblies change position to the symmetrical position, as shown in [Fig. 12].

[0169] In permutation 8.e, the assemblies change position to the symmetrical position, as shown in [Fig. 13].

[0170] During the permutation 8.f the assemblies change position in the symmetrical position, in accordance with [Fig. 14].

[0171] In the permutation 8.g, the assemblies change position in the symmetrical position, according to [Fig. 15].

[0172] In the above, the permutations were carried out within the same family, these are so-called “intrafamily” permutations.

[0173] However, one or more permutations between two families may also be provided, one taking the place of the other. The configuration of a family is therefore changed by moving from one of the four configurations of a family 4 to another configuration of the same family 4, or by moving from one of the eight configurations of a family 8 to another configuration of the same family 8.

[0174] A permutation of families 4 is defined by the exchange of two different families 4 located in two different symmetrical positions 4 of the core plane. The assemblies placed in position 1 of the two symmetrical positions 4 exchange their position. The assemblies placed in position 2 of the two symmetrical positions 4 exchange their position. The assemblies placed in position 3 of the two symmetrical positions 4 exchange their position. The assemblies placed in position 4 of the two symmetrical positions 4 exchange their position. This is illustrated in [Fig. 16].

[0175] As regards families 8, a permutation of families 8 is defined by the exchange of two different families 8 located in two different symmetrical positions 8 of the core plane. The assemblies placed in position 1 of the two symmetrical positions 8 exchange their position. The assemblies placed in position 2 of the two symmetrical positions 8 exchange their position. The assemblies placed in position 3 of the two symmetrical positions 8 exchange their position. The assemblies placed in position 4 of the two symmetrical positions 8 exchange their position. The assemblies placed in position 5 of the two symmetrical positions 8 exchange their position. The assemblies placed in position 6 of the two symmetrical positions 8 exchange their position. The assemblies placed in position 7 of the two symmetrical positions 8 exchange their position.The assemblies placed in position 8 of the two symmetrical positions 8 exchange their position. This is illustrated in [Fig. 17].

[0176] We now define with reference to [Fig.18] a crossing of two core planes by the construction of a “child” core plane, from two “parent” core planes, as follows: - The parent plan with the smallest EPC is parent 1, - the parent plan with the largest EPC of the two parents is parent 2.

[0177] If the two parent plans have the same EPC, an equiprobable random draw allows parent plan 1 to be chosen.

[0178] We select P4 positions of symmetry 4 and P8 positions of symmetry 8, by equiprobable random drawing, from among the 11 positions of symmetry 4 and the 14 positions of symmetry 8, where P4 is between 1 and 11 and P8 is between 1 and 14.

[0179] In practice, P4 and P8 are close to a third of the number of symmetry positions 4 and 8 respectively.

[0180] In the child core plane, in the 9 (P4 + P8) symmetry positions thus selected, the assembly families which are located in the corresponding symmetry positions of the parent core plane 1 are positioned, each family remaining in the same configuration as in the parent 1.

[0181] In the parent core 2, the symmetry positions 4 and the symmetry positions 8 which were not selected in the previous step are scanned. If these symmetry positions 4 and 8 contain assembly families 4 and 8 which have not yet been positioned in the child core plane, then they are positioned in the corresponding symmetry positions of the child core plane, each assembly family then remaining in the same configuration as in the parent core 2.

[0182] If there are unoccupied 4-symmetry positions in the child core plane, there also remains an equivalent number of 4-families not yet positioned in this child plane. In this case, a 4-symmetry position is randomly (or pseudo-randomly according to possible rules) drawn from among the remaining 4-symmetry positions, and a 4-families from among the remaining 4-families, and assemblies of this 4-families are placed in this 4-symmetry position, then the configuration is randomly drawn from among the 4 possible configurations. This process is repeated until all the remaining 4-families have been placed in a 4-symmetry position.If no random selection is required, for example, then at each step of this process one can choose the 4-symmetry position closest to the center of the core, and the 4-family with the lowest average burn-up among the remaining 4-families, the family remaining in the same configuration as in the parent 2-core, and repeat this process until all remaining 4-families have been placed in a 4-position.

[0183] If there are unoccupied 8-symmetry positions in the child core plane, there also remains an equivalent number of 8 families not yet positioned in this child plane. In this case, one can randomly draw an 8-symmetry position from the remaining 8-symmetric positions, and an 8-family from the remaining 8-families, and place the assemblies of this 8-family in this 8-symmetric position, then randomly draw the configuration from the 8 possible configurations and repeat this process until all the remaining 8-families have been placed in an 8-symmetry position.If no random selection is required, then one can choose at each step of this process the symmetric 8 position closest to the center of the core, and the 8 family with the lowest average burn-up among the remaining 8 families, the family remaining in the same configuration as in the parent core 2, and repeat this process until all remaining 8 families have been placed in a symmetric 8 position.

[0184] In summary, there are three types of assembly placement / permutation: - Placement by crossing two core planes as illustrated in [Fig. 18], - Permutation within the same family (rotation for example) as illustrated in [Fig.19], - Permutation between two families of the same number of members as illustrated in [Fig.20].

[0185] With reference to [Fig.22], to test the different plans thus obtained, we define the (positive) integers K, Kl, K2 where K= K1+K2. We can create K core plans from the initial core plan obtained in step 2, according to the following operations carried out in any order, with reference to block S2 of [Fig.22] (which follows a start step SI during which we can observe the burn-ups of the assemblies to be placed for example).

[0186] Kl core plans are created by inter-family permutation (i.e. within the same family), each of the plans being created by applying PKI,8 (PKI,8 chosen from the integers 1,2...) permutations of two families 8 and / or PKI,4 (PKI,4 chosen from the integers 1, 2...) permutations of two families 4.

[0187] Pki,8 and PKi,4 are fixed beforehand, for example by drawing lots from the set of integers from 1 to 10.

[0188] The Pki, 8 pairs of families 8, and the PKi, 4 pairs of families 4 are chosen by equiprobable random drawing among the 14 families 8 and the 11 families 4.

[0189] [Fig.20] illustrates an example where PKi,8= L

[0190] We then proceed to the creation of K2 core plans by inter-family permutation. This is a permutation to move from one configuration to another for PK2>8 (PK2,8 = 1,2...) families 8 and / or a permutation to move from one configuration to another for PK2j4 (Pk2,4 chosen from the integers 1,2...) families 4. The PK2>8 families 8 and the P K2>4 families 4 are chosen by random drawing from the 14 families 8, and the 11 families 4. The type of permutation applied to each of these families is chosen by equiprobable random drawing (one from 8 possible configurations for families 8 and one from 4 possible configurations for families 4).

[0191] These K core plans constitute the set of core plans called here “generation 0”.

[0192] Having predefined the (positive) integers Cl, C2, C3 where K= C1+ C2+ C3, we then proceed to apply the following procedure N times (block S6 of [Fig.22]), to constitute the set of core plans of generation n from the generation of core plans of generation n-1 (n going from 1 to N).

[0193] The following three sub-steps refer to block S4 of [Fig.22].

[0194] The creation of Cl heart plans is carried out in the following manner: - choice by equiprobable random drawing of a core plan from the set of K plans from the previous step n-1, and - application of the permutations of PCi,8 (Pci,8 chosen from the integers 1,2...) pairs of families 8 and / or PCi,4 (Pci,4 chosen from the integers 1,2...) pairs of families 4.

[0195] We then proceed to create C2 heart plans in the following manner: - choice by equiprobable random drawing of a core plan from the set of K core plans remaining from step n-1, and - application of permutations of PC2j8 (PC2,8 chosen from the integers 1,2...) pairs of families 8 and PC2j4 (Pc2,4 chosen from the integers 1,2...) pairs of families 4.

[0196] Finally, we proceed to the creation of C3 core plans by crossing two core plans among the K plans of step n-1. The pair of core plans is chosen randomly by equiprobable random drawing among the core plans of the set of K plans of step n-1.

[0197] Referring again to [Fig.22], in the plan evaluation step S3, the evaluation is determined according to the EPC criterion presented previously, for the K core plans of the previous step n-1 and for the K plans created in step n as explained above.

[0198] In step S5, K plans having the smallest EPC evaluation are selected from these 2xK plans. These K selected plans constitute the core plans of step n.

[0199] These N applications of the above procedure are repeated i times (block S7) by modifying the parameters PCi,s, Pci,4, Pc2,s, Pc2,4- • •

[0200] We obtain a result similar to that presented in [Fig.21] illustrating an example of evolution of the criteria Fxy, Fxy,g and MAR over 100 generations.

[0201] The method then makes it possible to obtain plans optimized in Fxy (hot spot factor), Fxy>g (hot spot factor in the presence of clusters), and MAR (anti-reactivity margin), thus best meeting the simultaneous consideration of these three criteria. It will be noted here that from generation 65, there is at least one plan that has reached the minimum of the EPC, therefore respecting all of these criteria. It can typically be noted that at generation 67 for example, there is a reduction in the hot spot factors (as expected for a "good" core) and this to the detriment of a very slight reduction in the anti-reactivity margin which remains within an acceptable measure. Such an observation clearly shows that a convergence towards a compromise between these three criteria at the same time is sought, and not on each of these criteria taken successively as a person skilled in the art would typically think.

[0202] Such an implementation makes it possible to randomly draw plans, the intersections of which with other plans or permutations lead to plans of unsuspected quality for a person skilled in the art, and sometimes counterintuitively. The random generation thus automated, then tested, makes it possible to lead to quality plans, converging quickly (a few tens of minutes at most) to meet the EPC criterion.

[0203] The method according to the meaning of the present disclosure makes it possible to test several reloading strategies for an effective campaign or a series of campaigns to a balance in terms of finding a compromise between several criteria, without mobilizing human resources. In particular, campaigns that must include test assemblies that depart from a standard nomenclature, forming a technological novelty, is no longer a difficulty.

[0204] On average, the time saved in mobilizing human resources, per loading plan, is therefore around 4 days.

[0205] Of course, the present disclosure is not limited to the description of the exemplary embodiments presented above as examples, but extends to other variants.

[0206] The achievement of a compromise for a core of 157 assemblies has been described above. However, the above principles can of course be applied to other types of core, distinguished here by the size of the core and therefore by the number of assemblies. Thus the number of families 4 and families 8 increases. The principles stated in terms of authorized permutations and more generally in the flowchart of [Fig.22] are retained.

[0207] [Fig.48] also illustrates a core of 193 assemblies, presenting a central position and 192 positions which are distributed as follows: - 12 families of 4 assemblies, - and 18 families of 8 assemblies (with 48 +144 +1 = 193).

[0208] Here again, we can appreciate the neighboring burn-up rates by family of assemblies (for example 31875 MWj / t and 31763 MWj / t in P13 and N14).

[0209] The one in [Fig.49], with 205 assemblies, has a central position and 204 positions which are distributed as follows: - 13 families of 4 assemblies, - and 19 families of 8 assemblies (13x4 + 19x8 +1 = 205).

[0210] These principles also apply to cores having different assembly shapes, for example and not limited to hexagonal, triangular, or rectangular section, instead of a square section shape as presented above. In this case, the axes of symmetry are different and the numbers of families differ, but the same principles as those set out above can remain.

[0211] Furthermore, an EPC criterion was presented above in the form of a sum of three terms for taking into account three parameters. Of course, other parameters can be taken into account, thus possibly increasing the number of terms in the aforementioned sum.

[0212] Furthermore, a grouping of assemblies by families has been presented above, essentially based on their respective burn-up values. As indicated elsewhere in the description above, other parameters, in addition to the combustion rate, can be used to constitute the families (assembly technology, type of fuel, etc.).

Claims

1. Claims A computer-assisted method for determining an optimal loading plan for a nuclear reactor core, in which method respective positions of nuclear fuel assemblies are tested by said computer means according to at least one criterion before assigning optimal positions to the assemblies and proceeding with the loading of the reactor, the reactor core comprising a multiplicity of cells having positional symmetries relative to a plurality of axes of symmetry, current assemblies being intended to be each introduced into a cell, the current assemblies for preparing a future loading being distributed according to at least three categories defined by the number of production campaigns of the nuclear reactor: - a first category of assemblies not used in a previous production campaign and having a combustion rate lower than a first threshold, - a second category of assemblies having been used in a previous production campaign and having a combustion rate between the first threshold and a second threshold, higher than the first threshold, and - a third category of assemblies having been used in at least two previous production campaigns and having a combustion rate higher than the second threshold, the method comprising the steps: - identify groups of cell positions which are symmetrical with respect to said axes of symmetry, and count a number of symmetrical positions in each group, - constitute families of common assemblies, the common assemblies of the same family having at least similar combustion rates, and said families each comprising a number of common assemblies corresponding to a number of positions of one of said groups, respectively, - choose, from a database of valid loading plan types, a loading plan type whose assembly combustion rates, by family, are closest to the combustion rates of current assemblies, by family, and, within the framework of a numerical simulation, assign to current assemblies respective initial positions corresponding to the positions of the assemblies in the chosen standard plan, - testing by digital simulation the loading plan consisting of the current assemblies at said initial positions, relative to at least one predetermined criterion, - permuting the positions of current assemblies while retaining the families of assemblies previously constituted and testing by digital simulation the loading plan formed of the current assemblies at said permuted positions, relative to said predetermined criterion, and - repeating the permutations and testing step until at least one candidate plan for loading the reactor is obtained, the candidate plan best fulfilling said predetermined criterion.

2. Method according to claim 1, in which the permutations are carried out randomly, while respecting predetermined rules.

3. Method according to one of the preceding claims, in which said plurality of axes of symmetry comprises four axes of symmetry of the core, passing through the center of the core and comprising two axes, one vertical axis, the other horizontal, and two axes respectively of slope of 45 degrees and 135 degrees relative to a horizontal line, and in which groups of N positions of cells located on said axes of symmetry are considered, and groups of M positions of cells not being located on said axes of symmetry.

4. Method according to one of the preceding claims, comprising, within the framework of said digital simulation: - placing an assembly chosen from said current assemblies in a central position, and - placing the assemblies of said families around the central assembly in groups of positions symmetrical with respect to the plurality of axes of symmetry, the assemblies positioned in the same group of positions being members of the same family of current assemblies.

5. Method according to one of the preceding claims, in which the permutations within the same family modify each assembly position of the family.

6. Method according to one of the preceding claims, comprising, for testing permutations between families: - swap the positions of current assemblies between two distinct families having the same number of members, and test by numerical simulation the loading plan consisting of the current assemblies at said swapped positions, relative to said predetermined criterion.

7. Method according to one of the preceding claims, in which the permutation and testing step is: - carried out a predetermined number of iterations, until a first candidate plan is identified, then - repeated a predetermined number of iterations, until a second candidate plan is identified, the method further comprising at least one step of testing a crossing plan between the first and second plans.

8. Method according to claim 7, comprising the constitution of a crossing plan in which the positions of a subset of the assembly families of the first candidate plan are preserved, and the remaining assembly families are: - assigned to positions which coincide with the positions of these same families in the second plan, if these positions are still available in the crossing plan, or - assigned to other groups of available positions, the number of members of said other groups being equal to the number of members of the families remaining to be placed.

9. Method according to one of the preceding claims, in which the assemblies comprise a face facing a predetermined observation point, and after permutations, the permuted assemblies retain said face facing the observation point.

10. Method according to one of the preceding claims, in which a numerical simulation is carried out by neutron calculations of each core plane tested, under conditions with and without insertion of nuclear fission reaction smothering clusters, to estimate quantities specific to the core plane tested, said quantities comprising hot spot factors without clusters Fxyiplan) and with clusters Fxy, g(plan), as well as an antireactivity margin Marge(plan).

11. Method according to claim 10, in which said estimated quantities are compared with limit values ​​in the calculation of a loading plan evaluation expression, denoted EPC, and a candidate plan is selected from among possible plans which has the expression smallest EPC assessment meeting the said predetermined criterion.

12. The method of claim 11, wherein the EPC evaluation expression of a plan is given by: EPC = Cx Margin)plan) ;0 ) + [ ' jx max] F.xylplan j - + Margin x £s ( xmax^Fxy, g (plan)- Fxy^. g ;0j 'J where: - Margin^ is a limit value of antireactivity margin, - Fxy>j , g is a limit value of hot spot in the presence of clusters, - Fxyj is a limit value of hot spot in the absence of clusters, - C is a positive real coefficient, and - IL represents the sum over the set of clusters of the expression given for a cluster g: ( Fxy..^ * max ( * W s (plan ) - Fxy^ g ; 0 ) )

13. Method according to claim 12, in which, in the EPC evaluation expression, the terms: ( Fxy^' )xmAX(Fxy(plan) - Fxylin>°) MargeHm xx max (Fxy. g(plan) - Fxy^ g ; 0) j are of the same order of magnitude, and the coefficient C is chosen so that the term C xm^[Margehfn-Marge(plan) ; 0) is also of the same order of magnitude as one of the two aforementioned terms.

14. Method according to one of claims 12 and 13, in which the coefficient C is between 0.5 and 1.

15. Method according to one of claims 12 and 13, in which the coefficient C is between 1 and 10.

16. Computer program comprising instructions for implementing the method according to one of claims 1 to 15, when said instructions are executed by a processor of a processing circuit.

17. Computer device comprising a processing circuit for implementing the method according to one of claims 1 to 15.

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