Method for estimating a future value of the axial power imbalance in a nuclear reactor

Abstract

Method for estimating an axial power imbalance in a nuclear reactor (11), comprising the following steps: - obtaining a reactor power setpoint (12), - for each variable of a plurality of reactor variables, determining a sequence of the variable (19), the sequence representing estimated future variations of the variable, - determining a sequence of the axial power imbalance (13), taking into account the sequences of the plurality of reactor variables (19), the determination of the axial power imbalance sequence (13) using a machine learning module (14) previously trained on historical reactor data (17). Figure for the abstract: Fig. 2

Description

Title of the invention: Method for estimating a future value of the axial power imbalance in a nuclear reactor. FIELD OF THE INVENTION

[0001] The invention relates to the estimation of a future value of the axial power imbalance in a nuclear reactor. STATE OF THE ART

[0002] Nuclear power plants, as "dispatchable" means of production, represent one of the main contributors to the balance of the electricity grid in France. Since electricity cannot (or can only be minimally) stored, the equality between the electrical power produced by the various means of production and the electrical power consumed by users must be verified at every moment.However, consumers and some means of production, particularly renewable electricity generation such as wind and solar, are uncontrollable and intermittent: a controllable generation method, such as nuclear power, is therefore necessary to compensate for fluctuations in consumption and uncontrollable production to ensure supply / demand balance. To achieve this, nuclear reactors in nuclear power plants must be technically capable of rapidly varying their electrical output according to demand, while remaining within their assigned operating and safety ranges. These operating ranges are determined, in particular, based on axial power imbalance and the Xenon oscillations now presented. Axial power imbalance in a reactor

[0003] Within a reactor, the thermal energy intended to be transformed into electrical energy is produced by fission. Nuclear fission is a phenomenon by which a heavy atomic nucleus, such as uranium or plutonium, splits into two (binary fission) or three (ternary fission) lighter nuclides, either spontaneously or after absorbing a neutron. The study of neutron movement in matter and the reactions they induce, particularly power generation by fission, is called neutronics. Neutronics is fundamental to the design of the cores of controlled fission nuclear reactors, such as pressurized water reactors.

[0004] With reference to Figure 1 illustrating a reactor 1, the axial direction z can be defined as the vertical direction given by a plumb line. This direction z is oriented vertically upwards in Figure 1. We are interested in characterizing a difference between a power P / , in the upper half of the reactor core and a power P / , in the lower half of the reactor core. Curve 5 represents the power as a function of the height z in the reactor.

[0005] This deviation varies under the effect of the control rods or clusters, the presence of neutron poisons such as fission products like xenon or samarium, the temperature of the fuel or its depletion rate which increases over time during the reactor's operating campaign.

[0006] The power difference between the top and bottom of the reactor can be characterized by two physical quantities: an axial offset (which can be designated by its English name "Axial Offset", abbreviated as AO) and an axial power imbalance, which can be designated by the notations "A!" or "DPAX"). These two quantities are defined by the following formulas:

[0007]

[0008] [)PAX =

[0009] with P„ the nominal power of the reactor.

[0010] The term P / , + = Pt denotes the total instantaneous power in the reactor. The Axial offset is a relative value of power compared to total power.

[0011] The axial imbalance “DPAX” is a relative value of power with respect to the nominal power Pn, nominal power which is not necessarily equal to the total instantaneous power Pt. Xenon Oscillation

[0012] Xenon-135 (135Xe) is a strong neutron-absorbing element that can be produced by fission but also, and especially, by the decay of Iodine-135 (135I), another product of the fission reaction. The presence of Xenon-135 in a reactor leads to a significant decrease in reactivity, making it a neutron poison that hinders the continuation of the chain reaction.

[0013] After a sufficiently long reactor operating time (approximately 60 hours) at constant reactor power, the concentration of Xenon-135 reaches an initial equilibrium in the reactor. This equilibrium is reached when the production of Xenon-135 becomes proportional to the reactor power and its destruction becomes proportional to the concentration of Iodine-135.

[0014] On a macroscopic scale, if the reactor power is reduced once this equilibrium is reached, the Iodine-135 concentration decreases exponentially until it reaches a new equilibrium value, while the Xenon-135 concentration first reaches a maximum (referred to as the xenon peak) before decreasing to a new equilibrium value. The time required to reach this peak (between 7 and 8 hours) and the corresponding antireactivity value depend on the reactor power before and after the reduction. The reactivity p is a quantity without unit expressed in pcm (parts per hundred thousand) which is defined as a relative variation of the effective multiplication coefficient of the neutron population keff itself defined as the ratio of the neutron population of the present generation and the neutron population of the previous generation:

[0015]

[0016] The sign of the reactivity p indicates whether the neutron population is stable (p= 0), increasing (p > 0), or decreasing (p < 0).

[0017] We will speak of antireactivity when p < 0

[0018] Conversely, if the power is increased, the concentration of Iodine-135 rises until it reaches a new equilibrium value, while the concentration of Xenon-135 first reaches a minimum (this is called Xenon depression) before increasing to a new equilibrium value. The time required to reach this minimum (between 2 and 3 hours) and the corresponding antireactivity value will depend on the power level before and after the increase.

[0019] Locally, a variation in power, by insertion of the clusters, results in an axial effect on the distribution of the neutron flux and leads to a modification of the distribution of Iodine 135 and Xenon 135.

[0020] Fig. 1 illustrates the insertion and then the removal of a neutron poison bar or cluster 3 extending along the vertical direction z.

[0021] The effect of this bar 3 being inserted and then removed can be broken down into five phases corresponding to the letters A to E in [Fig. 1]. This maneuver notably impacts the concentration of Xenon 9 as a function of the height z in the reactor, and the concentration of Iodine 7 as a function of the height z in the reactor.

[0022] Inserting and then removing the bar 3 can lead to oscillations in the concentration of Xenon 9 between the upper and lower half of the reactor commonly called xenon oscillations.

[0023] This oscillation is broken down into five phases corresponding to the letters A to E represented in figures 1.

[0024] Phase A corresponds to a steady state in which the axial power distribution 3 and the concentrations 7 and 9 of Iodine 135 and Xenon 135 are in phase.

[0025] Phase B corresponds to the insertion of a group of clusters 3 into the reaction medium of reactor 1. This induces a modification of the axial power distribution: the power decreases in the upper half but remains approximately constant in the lower half. The equilibrium between the production, by radioactive decay of Iodine-135, and the disappearance of Xenon-135 by neutron capture or radioactive decay is disrupted. In the initial moments of this type of transient, the distributions of Iodine-135 and Xenon-135 remain unchanged while the power in the The lower part of the heart increases and the upper part decreases.

[0026] During phase C, in the upper part of the core, due to the decrease in neutron flux caused by the insertion of the cluster group, the concentration of Iodine-135 decreases and Xenon-135 disappears more slowly and begins to accumulate: the concentration of Xenon-135 increases, thus causing a decrease in reactivity. In the lower part of the core, due to the increase in flux, the concentration of Iodine-135 increases and the concentration of Xenon-135 decreases because Xenon-135 disappears more rapidly. Reactivity increases in the lower half. This redistribution of reactivity between the upper and lower parts of the core tends to amplify the disequilibrium phenomenon, with a maximum of axial disequilibrium reached after 7 to 8 hours, even if the inserted cluster group is removed.

[0027] Phase D corresponds to the period after the maximum axial imbalance has been reached. In the upper part of the heart, the decrease in the Iodine-135 concentration 7 leads to a deficit in Xenon-135 production, the concentration 9 of which begins to decrease, thus causing an increase in reactivity. In the lower part of the heart, the accumulation of Iodine-135 compensates for the depletion of Xenon-135, the concentration 9 of which begins to increase, thus leading to a decrease in reactivity. This process continues over time until a spatial distribution of power close to the initial situation is achieved after 17 to 18 hours. At this point, the Iodine-135 concentration 7 and the Xenon-135 concentration 9 are strongly unbalanced. The Xenon curve in phase D is in an intermediate position between the Xenon curve in phase C and the Xenon curve in phase E.

[0028] In phase E, the phenomenon reverses and the power peak shifts towards the top of the heart. The period of this oscillation is on the order of 35 hours.

[0029] Neutron flux distortions induced by the movement of the control rods and / or by Xenon oscillations can lead to the formation of hot spots inside the reactor, resulting in an excessive temperature rise in the fuel that can cause it to lose its integrity. To prevent this risk, the axial power imbalance must be controlled for reactor operation. Operators rely on a control diagram representing the axial imbalance as a function of the instantaneous total power. This diagram illustrates, in particular, a safety zone or reactor operating range, which is an area around a reference line. The reactor must operate in the area close to the reference line.To operate reactors safely and efficiently, operators therefore need tools capable of predicting the axial power imbalance (DPAX) based on the planned control strategy, allowing them to evaluate this strategy upstream and possibly consider another one that will further limit the axial power imbalance.

[0030] Current solutions for estimating the future state of the reactor do not provide satisfactory control assistance. Specifically, operators are required to modify power setpoints and monitor changes in the main key parameters of the nuclear reactor core in order to comply with operating constraints. As mentioned, these include power variations and other associated variations (variations in the average core temperature, control rod movements, changes in boric acid concentration in the reactor coolant, etc.).) generate disturbances whose effect is difficult to anticipate: the state of the reactor, and therefore its response to stresses, is constantly evolving; the phenomena involved are complex and characterized by very heterogeneous characteristic times, from a few seconds to several hours, and the evolution of certain key parameters, such as the concentration and spatial distribution of xenon in the reactor, are not measurable and therefore unknown to the operator.

[0031] Thus, in order for nuclear reactors in nuclear power plants to be technically able to vary the electrical power produced rapidly according to need, and more frequently than previous practices, while remaining within the operating and safety ranges assigned to them, there is a need for a reliable and rapid estimation tool to predict the future and delayed effects of each action of the operator, easily, in a context of tight planning. Description of the invention

[0032] One object of the invention is to propose a method for estimating a future value of an axial power imbalance in a nuclear reactor.

[0033] The objective is achieved within the framework of the present invention by means of a method for estimating a future value of an axial power imbalance in a nuclear reactor, the method comprising the following steps:

[0034] - obtaining a sequence of successive values ​​of a power setpoint of the reactor,

[0035] - for each variable of a plurality of reactor variables, determination of a sequence of successive values ​​of the variable, the sequence representing future variations of the variable, the variations being estimated by taking into account the power setpoint, the plurality of reactor variables including a xenon concentration in an upper half of the reactor and a xenon concentration in a lower half of the reactor,

[0036] - determination of a sequence of successive values ​​of the axial imbalance of power, taking into account the sequences of the plurality of reactor variables,

[0037] the determination of the axial power imbalance sequence using a machine learning module previously trained on historical reactor data, and

[0038] Determining the sequence of xenon concentration in the upper half of the reactor and determining the sequence of xenon concentration in the lower half of the reactor using a model of the evolution of iodine concentration and xenon concentration as a function of neutron flux

[0039] Such a process is advantageously and optionally complemented by the following various features taken alone or in combination:

[0040] - for at least one variable of the plurality of variables, the determination of the time sequence of the variable includes a measure of the variable;

[0041] - the plurality of reactor variables includes at least one of a position of a device configured to absorb neutrons in the reactor, an average measured temperature of the reactor vessel, a flow rate of a heat transfer fluid circulating in the reactor, a concentration of a chemical species in the heat transfer fluid, the chemical species being configured to absorb neutrons in the reactor, and a burn-up rate of a nuclear fuel contained in the reactor;

[0042] - the determination of the sequence of the axial power imbalance also takes includes at least one of the following: a mean reference temperature of the reactor vessel, a type of fuel management corresponding to a fractionation of a reactor core during a fuel renewal, an enrichment of fissile nuclei of the reactor and a type of heavy nuclei of the reactor;

[0043] - the determination of the sequence of the plurality of reactor variables and the determination The calculation of the axial power imbalance sequence takes into account a reactor control scenario corresponding to a sequence of successive values ​​of at least one variable controllable by an operator;

[0044] - a step of determining a score for the control scenario, the score being preferably a value of a quantity chosen from a volume of effluent produced, an average deviation from the reference axial imbalance, and an average distance to the limits of a reactor operating range; and

[0045] - the command scenario is a first command scenario, the steps of the process being carried out a second time by replacing the first scenario with a second reactor control scenario corresponding to another sequence of successive values ​​of at least one controllable variable, the process preferably including a step of comparing the scores of the first scenario and the second scenario.

[0046] The invention also relates to a computer program comprising instructions adapted to the implementation of at least one of the steps of the process as described above when said program is executed on a computer.

[0047] The invention also relates to a device for estimating a future value of an axial power imbalance in a nuclear reactor, the device comprising a computing module configured to implement the method as described above, the computing module being configured to

[0048] - obtain a sequence of successive values ​​of a power setpoint of the reactor,

[0049] - determine, for each variable of a plurality of reactor variables, a sequence of successive values ​​of the variable, the sequence representing future variations of the variable, the variations being estimated by taking into account the power setpoint, the plurality of reactor variables including a xenon concentration in an upper half of the reactor, and a xenon concentration in a lower half of the reactor,

[0050] - determine a sequence of successive values ​​of the axial power imbalance taking into account the sequence of the plurality of reactor variables,

[0051] the calculation module comprising a machine learning module previously trained on historical reactor data, and

[0052] the calculation module using a model of the evolution of an iodine concentration and a xenon concentration as a function of a neutron flux, so as to determine the sequence of the xenon concentration in the upper half of the reactor and the sequence of the xenon concentration in the lower half of the reactor. DESCRIPTION OF THE FIGURES

[0053] Other features and advantages of the invention will become apparent from the following description, which is purely illustrative and not limiting, and should be read in conjunction with the accompanying drawings on which:

[0054] [Fig.l] the [Fig.l], already mentioned, is a schematic illustration in relation to a Xenon oscillation phenomenon;

[0055] [Fig.2] [Fig.2] is a schematic illustration relating to an embodiment of a method for estimating an axial power imbalance in a reactor;

[0056] [Fig.3]

[0057] [Fig.4]

[0058] [Fig.5]

[0059] [Fig.6]

[0060] [Fig.7]

[0061] [Fig. 8]

[0062] Figures 3 and 6 schematically illustrate an axial power imbalance as a function of time, Figures 4 and 7 schematically illustrate a setpoint of power as a function of time, and figures 5 and 8 schematically illustrate a power setpoint as a function of an axial power imbalance. DETAILED DESCRIPTION OF THE INVENTION

[0063] Method for estimating a future value of an axial power imbalance

[0064] In relation to [Fig. 2], a method for estimating the future value of a die Axial power balance in a nuclear reactor 11 is proposed.

[0065] The axial power imbalance in a nuclear reactor has previously been introduced under the notation "DPAX", it is a relative power value with respect to the nominal power Pw of the reactor.

[0066] DPAX— —.¾ Ph

[0067] In a first step, a sequence 12 of successive values ​​of a reactor power setpoint P is obtained. A sequence of successive values ​​taken by a quantity is also referred to below as a "time series".

[0068] This step corresponds in particular to the situation where an operator controlling a nuclear reactor must perform a power transient 12 of that reactor. The operator enters a load program, that is to say, an evolution of the electrical power P of the reactor as a function of time t. This evolution can notably be given in the form of a time series of values ​​of a power to be maintained, that is to say, values ​​of a power setpoint, as a function of time. A power setpoint is therefore understood here as a physical quantity with the dimensions of power, and which is the power to be maintained.

[0069] In a second step 18 of the process, the load program is processed to determine future variations 19 of a plurality of reactor variables. These different variables are called explanatory variables in the sense that they are used to estimate the values ​​of another variable, namely the axial power imbalance. Hypothetical values ​​are thus determined for each of the explanatory variables. In other words, for each variable in a plurality of reactor variables, a time series is determined representing future variations of the variable estimated by taking into account the power setpoint. The time series may also include past variations of the variable.

[0070] Among the explanatory variables are the xenon concentration in the upper half of the reactor and the xenon concentration in the lower half of the reactor. These two variables are calculated using a model of the evolution of iodine and xenon concentrations as a function of neutron flux. This model is based in particular on the following equations for the evolution of iodine and xenon concentrations: 100711 100721 ​​TF = Wr

[0073] declined for each half, upper and lower, of the reactor.

[0074] In these equations, ο denotes the neutron flux, Q denotes the iodine concentration, CXe denotes the xenon concentration, yj denotes the fission yield of iodine and Ÿxe the fission yield of xenon respectively. A fission yield of a product corresponds to the probability or rate of production of that product when fission occurs. Ey denotes the macroscopic fission cross section, that is, the macroscopic probability of fission of heavy nuclei related to the probability per unit time that a neutron encounters a heavy nucleus and that fission occurs, / / denotes the radioactive decay rate of iodine and ^xe the radioactive decay rate of xenon. Finally, (7^ denotes the microscopic neutron absorption cross section of Xenon related to the probability per unit time that a neutron encounters a Xenon 135 nucleus and is captured (which does not generate fission).

[0075] yfifÿ is a term representing the production of iodine 135.

[0076] - ^ / Czest is a term representing the disappearance in iodine 135.

[0077] + ÀjCjqsI a term representing the production in xenon 135.

[0078] ■ ^Xe^Xe' is a term representing the disappearance in xenon 135.

[0079] In a third step of the process, a time series 13 of the axial power imbalance DPAX is determined by taking into account the time series of the plurality of reactor variables. The time series represents, as a function of time t, future variations of the axial power imbalance estimated by taking into account the time series of the plurality of reactor variables and the load program.

[0080] This determination of the time series of the axial power imbalance is carried out using a machine learning module 14 previously trained on historical reactor data 15. It should be noted that the learning module can be retrained at the end of a reactor operating cycle to take into account more recent operating data in the training. This training of the model over the entire database takes less than 4 hours.

[0081] The historical reactor data 15 are structured during an extraction step 16 to obtain structured historical operating data 17. In particular, during this extraction step, the data can be enriched with historical values ​​of axial shift AO and / or axial imbalance DPAX. It may be useful, in particular, to determine the axial imbalance DPAX from the axial shift AO when it is the only available variable, as measurements of the axial shift AO are generally noisier than those of the axial imbalance DPAX. particularly when the instantaneous power of the reactor is low.

[0082] The machine learning module 14 is configured to be trained on historical datasets 15 from one or more reactors. This machine learning module may include, in particular, two sub-modules.

[0083] The first sub-module is configured to learn a relationship between a set of explanatory variables and the axial power imbalance. After learning this relationship from historical reactor operating data, the first sub-module processes the values ​​of recent and hypothetical explanatory variables to provide an initial forecast of the axial power imbalance over the next few hours. Several algorithms can be used to implement this first sub-module.

[0084] In a first option, decision tree forests are used, such as random forests (also referred to by the English expression "Random Forest"), or boosting algorithms and gradient boosting algorithms (also referred to by the English expression "Boosting algorithm" or "Gradient Boosting algorithms").

[0085] In a second option, generalized additive models are used (also referred to by the English expression "generalized additive model" or "GAM").

[0086] In a third option, neural networks are used.

[0087] The second submodule implements a correction to the estimate produced by the first submodule. In particular, the second submodule can implement a simple correction for a prediction bias at an initial time, that is, a difference between the predicted imbalance and the measured imbalance at the initial time of the forecast. The second submodule can also implement a more complex model trained to predict the prediction error of the first submodule based on the latest predicted and measured values ​​of the axial power imbalance. The second submodule can then, in particular, use an autoregressive model or autoregressive process, which is a regression model for time series in which the series is explained by its past values ​​rather than by other variables.Alternatively, the second sub-module can use a Long Short Terni Memory (LSTM) neural network, which is a specific neural network architecture.

[0088] The use of a machine learning module, and a model of the evolution of an Iodine concentration in the reactor and a Xenon concentration in the reactor as a function of a neutron flux in the reactor makes it possible to estimate the axial power imbalance reliably and quickly.

[0089] The main advantages of this process are as follows.

[0090] First, the process allows for greater ease of use: the model does not It requires no calibration beyond the learning phase, which is carried out prior to deployment. In other words, this step is not the responsibility of the operator who controls the reactor, and more generally, the user of the model.

[0091] Furthermore, the accuracy achieved in the axial imbalance estimates is satisfactory over a time range on the order of the observed power transients, from a few hours to about twelve hours. Applying the method to data from EDF's (Électricité de France) nuclear fleet between 2008 and 2021 allows for comparison of the estimates with historical measurements. The absolute error observed between the axial imbalance predictions (DPAX) made by the tool according to the present invention and the actual values ​​of the axial imbalance (DPAX) is less than 2% for 95% of the data.

[0092] Finally, the method reduces computation time, particularly compared to the computation time required by 3D calculation codes: a forecast covering several hours is generated in a fraction of a second by the method, versus several minutes for a 3D code. The tool's computational speed allows it to process a very large amount of data; for example, about thirty minutes are sufficient to evaluate the tool's forecasts on 11,700 power transients. Advantageously, in operation, for evaluating the strategy to follow during a transient, the processing time is on the order of a tenth of a second. Advantageously, during a power transient that has undergone an initial estimation of the evolution of the axial power imbalance, the operator can launch a second estimation process before the end of the horizon chosen for the first estimation.The operator can thus have a second estimate, which helps to reduce forecast discrepancies.

[0093] Figures 3, 4 and 5 on the one hand and Figures 6, 7 and 8 on the other hand illustrate an application of the process.

[0094] Figures 3 and 6 relate to the axial imbalance DPAX as a function of time t: curves 31 and 61 represent the measured axial imbalance DPAX, and curves 32 and 62 represent the axial imbalance DPAX estimated according to the method. The time interval over which curves 31 and 61 are plotted is identical to the time interval over which curves 32 and 62 are plotted. This interval is graduated in hours of the day, with the value 00:00 corresponding to midnight, which separates the end of the first day on the left and the beginning of the following day on the right.

[0095] Figures 4 and 7 represent the thermal power supplied by the core as a function of time t: curves 41 and 71 represent the power setpoint. The time interval over which curve 41 is plotted is identical to the time interval over which curve 71 is plotted. This interval is graduated in daylight hours, with the value 00:00 corresponding to midnight, which separates the end of the first day on the left and the beginning of the following day on the right. This time interval is also identical to the time interval over which curves 31, 32, 61 and 62 are plotted.

[0096] Curves 41 and 71 show a power transient with successively in time a decrease in power from a high value to a low value, followed by a power plateau at the low value and finally a rise in power from the low value to the high value.

[0097] Figures 5 and 8 represent the evolution of the axial imbalance DPAX, measured and estimated when the reactor's thermal power follows a transient according to a programmed profile. This is a parametric relationship between two variables, each a function of time. More precisely, the plots in [Fig. 5] are the paths traveled by a point (Pth(t), DPAX(t)) from a time origin 55. These paths are derived from Figures 3 and 4, which share the same time origin (34, 42). The curves in Figures 3 and 4 represent the functions Pth = Pth(t) and DPAX = DPAX(t); time-domain variables.

[0098] Similarly, the paths of [Fig.8] are the paths traveled by a point (Pth(t), DPAX(t)) from a time origin 85, paths being deduced from figures 6 and 7 of the same time origin (63,73) and whose respective curves are representative of the functions Pth= Pth(t) and DPAX= DPAX(t); time variables.

[0099] Trace 51 in [Fig. 5] and trace 81 in [Fig. 8] represent the evolution of the axial imbalance DPAX measured during the evolution of the thermal power according to a programmed profile transient. The arrows indicate the path of traces 51 and 81 in chronological order.

[0100] Similarly, curve 53 in [Fig.5] and trace 83 in [Fig.8] represent the axial imbalance DPAX estimated according to the method of the present invention during the evolution of the thermal power according to a programmed profile transient.

[0101] Figures (3,4,5) and (6,7,8) correspond to representations in a control diagram available to operators in the control room.

[0102] The method allows for the estimation of future values ​​of the axial imbalance DPAX for a number of hours that can be set upstream of the method, according to a desired time horizon. Figures 3 to 8 correspond to a time horizon of 8 hours. Therefore, in [Fig. 3], curve 32, corresponding to the estimated axial imbalance DPAX, stops at time 33, at the end of the transient. The estimation corresponding to curve 32 extends over 8 hours, from approximately 9:30 PM until 5:30 AM the following morning.

[0103] It should be noted that the number of hours of estimation can be decreased or increased by the operator.

[0104] The progression through time is illustrated in [Fig. 3] by cursor 34, in [Fig. 4] by cursor 42, in [Fig. 6] by cursor 63 and in [Fig. 7] by cursor 73. In Figures 3 and 4, cursors 34 and 42 are positioned temporally upstream of the transient, while in Figures 6 and 7 cursors 63 and 73 are positioned temporally on the power plateau at the low value and upstream of the power rise from the low value to the high value.

[0105] During process implementation, the operator stores the power transient in memory to perform the first step of the process. The sequence of successive reactor power setpoint values ​​obtained can be displayed as a graph as illustrated in Figures 4 and 7.

[0106] When the third step of the process is carried out, the time series of the determined axial power imbalance DPAX can also be displayed as illustrated by curves 32 and 62. It should be noted that if several estimations are launched successively, in particular during a transient, the different curves of the estimated axial power imbalance DPAX can be displayed simultaneously.

[0107] The example in figures 3 to 8 corresponds to a real transient that was carried out in the past on one of the reactors in the French nuclear fleet.

[0108] Curves 32 and 62 estimating the axial power imbalance DPAX can be compared to curves 31 and 61 of the axial power imbalance DPAX actually measured during this transient.

[0109] In this example, the hypothetical values ​​are in fact the true measured values ​​of the plurality of variables during the transient, that is to say that the historical data actually measured on site during the transient in question were used.

[0110] Optionally, the method may include a measurement step for at least one variable from the plurality of variables. Determining the time sequence of this variable or these variables then includes a measurement of the variable or variables. The time series then comprises past variations of the variable.

[0111] Among the plurality of variables of the reactor, the following variables can be used in particular.

[0112] A first variable is the position of a device configured to absorb neutrons in the reactor. More precisely, it is the axial position of this device, which can be maintained above the zone where the neutrons circulate or lowered into this zone. The lower the device is positioned in the structure, the more neutrons it captures.

[0113] Such a device may comprise different units or groups of bars.

[0114] A first group of bars forms a power compensation group (which can be designated by the abbreviation PCG). The purpose of the PCG is to compensate for the power defect, that is to say, the anti-reactivity due to the power variation. The PCG is composed of four groups of rods that are inserted into the core one after the other according to the following sequence: in a first sequence, the first group is inserted until it reaches a certain depth, then in a In the second sequence, the second group inserts itself to a certain depth before, in a third sequence, the third group inserts itself to a certain depth, and finally, in a fourth sequence, the fourth group inserts itself to a certain depth. Each sequence cannot occur before the preceding sequence is complete. Thus, the clusters exhibit a relative overlap between any two distinct clusters at any given time. The GCP group may include a group of gray clusters, which are relatively low-absorbing compared to the "black" clusters defined below. The gray clusters help to limit the impact on power imbalance.

[0115] Such a device may include a second group of bars, which is a temperature control group (which may be designated by the abbreviation group R) of black absorbent bars. The R group is another group that allows for regulation in combination with variations in boron concentration.

[0116] With respect to the first variable, it is possible to determine its future variations in the following manner.

[0117] For the power compensation group (PCG), the position of this group can be linked to the reactor's thermal power by a relationship. This relationship is established during a dedicated periodic test in which the reactor power is varied to determine the PCG position that effectively compensates for the power variations. A misalignment situation can be chosen by requiring that the actually controlled position of the PCG rods is not exactly the position given by the relationship. In particular, the position of the PCG rods can be controlled by a constant misalignment.

[0118] For the temperature control group, or group R, the position of the bars in this group R can be chosen to be constant. In this case, criticality in the reactor is achieved by adjusting the boron concentration in the heat transfer fluid.

[0119] Criticality is related to the neutron population in the reactor. When criticality is reached, that is, when the regime is critical, the neutron population remains constant over time. Reaching criticality sustains the exothermic reaction in the reactor.

[0120] It should be noted that since the first variable is controllable, the future variations determined can be freely modified by the user.

[0121] A second variable is the average measured temperature of the reactor vessel. To determine future variations of this second variable, the average measured temperature of the vessel is assumed to be equal to the reference temperature.

[0122] A third variable is the average reference temperature of the tank. The average reference temperature corresponds to the temperature that should prevail within of the reactor vessel, taking into account the power supplied by the reactor, while the average measured temperature corresponds to the actual measured temperature of the vessel. To determine future variations of this third variable, the average reference temperature is determined from a relationship based on the future thermal power of the reactor.

[0123] A fourth variable is the flow rate of the heat transfer fluid circulating in the reactor. The heat transfer fluid is the primary fluid that enables the thermalization of neutrons and the transfer of heat from the reactor core to the secondary circuit. To determine future variations of this fourth variable, the primary flow rate can be established based on the future thermal power of the reactor. More precisely, a "nominal" value from the beginning to the start of the cycle is defined during a dedicated periodic test. This "nominal" value then varies with the thermal power according to an empirical linear law.

[0124] A fifth variable is the concentration of a chemical species in the heat transfer fluid, the chemical species being configured to absorb neutrons in the reactor. For example, this chemical species is boron. Future values ​​of the concentration of the chemical species, such as boron, can be determined using a second statistical model that takes as input the xenon concentration and the position of the device configured to absorb neutrons in the reactor. This second statistical model is similar to the first model for estimating future values ​​of the axial power imbalance, except that, in the first model, the boron concentration is an explanatory variable, and in the second model, the boron concentration is the explained or response variable.

[0125] When future variations of the fifth variable, and in particular the boron concentration, are imposed, then it is necessary to use another adjustment variable, such as in particular group R.

[0126] If the concentration of Boron is not provided by the operator, the forecasting model does not use Boron as an explanatory variable.

[0127] A sixth variable is the burnup of nuclear fuel contained in the reactor. To determine future variations of this sixth variable, the future burnup of the fuel is considered to be equal to the product of the thermal power and the operating time, which is then divided by the initial mass of fuel. Alternatively, the integral of the thermal power over the operating time can be used, which is then divided by the initial mass of fuel.

[0128] Furthermore, the determination of the time series of the axial power imbalance can also be carried out by taking into account a type of fuel management corresponding to a fractionation of a reactor core during a refueling of the Fuel, reactor fissile nuclei enrichment, and reactor heavy nuclei type: The fuel management type and the heavy nuclei type are categorical variables and remain constant throughout a cycle. For example, the reactor heavy nuclei type corresponds to the categories enriched uranium, reprocessed uranium, plutonium, etc.

[0129] The determination of the time series of the plurality of reactor variables and the determination of the time series of the axial power imbalance can also take into account a reactor control scenario corresponding to a sequence of at least one variable controllable by an operator.

[0130] A controllable variable may be the position of a device configured to absorb neutrons in the reactor or the concentration of a chemical species in the heat transfer fluid.

[0131] The operator can define a control scenario, that is, the different actions he plans to carry out. These actions relate to controllable variables such as the positions of the control bars or the boron concentration. The operator chooses, for at least one controllable variable, a sequence of successive values ​​that the variable will take over the next few hours.

[0132] For example, the operator can base himself on a first estimate of the evolution of the axial power imbalance without specifying a scenario and on the basis of this simulation, he determines a scenario and launches a second estimate of the evolution of the axial power imbalance which this time takes into account the determined scenario.

[0133] The method may further include a step for determining a score for the control scenario. This score may be, for example, a value of a quantity chosen from among a volume of effluent produced, a mean deviation from the reference axial imbalance, and a mean distance or mean margin to the limits of a reactor operating range. Other formulas for calculating the score may be used.

[0134] The reference axial imbalance corresponds to the reference line in the control diagram which represents the reference axial imbalance as a function of the total instantaneous power.

[0135] The reactor's operating range, and therefore its limits, are also defined in relation to the control diagram. This operating range is a safety zone located around the reference line. It can, for example, be defined by limiting axial imbalance lines in the diagram. The average distance to the limits can be evaluated as the distance to one of these limiting axial imbalance lines.

[0136] The scenario score provides the operator with an evaluation of the scenario estimated in relation to effluent production criteria that will require special treatment or reactor stability criteria.

[0137] It is possible to implement an estimation of two scenarios which the operator then compares based on their respective scores. In this case:

[0138] - the command scenario mentioned above is then a first scenario of order,

[0139] - a second scenario is obtained and transmitted as input to the process, this second scenario corresponds to a sequence of at least one variable controllable by an operator, a sequence different from that which corresponds to the first scenario, and

[0140] - the steps of the process are carried out a second time by replacing the first scenario by the second scenario.

[0141] Advantageously, the process includes a step of comparing the scores of the first scenario and the second scenario.

[0142] It should be noted that the different curves corresponding to the different estimated scenarios can be displayed on the same graph so that they can be compared visually by the operator.

[0143] When the method includes a step of comparing the scores of the first scenario and the second scenario, the method may further provide a ranking of the scenarios in ascending order for the selected criterion or if several criteria have been calculated each of these criteria.

[0144] With reference to [Fig.2], it is the decision support device 20 which can provide this classification of scenarios.

[0145] For example, in relation to the criterion of the volume of effluents produced, a first scenario in which it is estimated that 20 m3 of effluents are produced is ranked better than a second scenario in which it is estimated that 60 m3 of effluents are produced.

[0146] For example, with regard to the criterion of deviation from the reference axial imbalance, a first scenario in which the deviation from the reference axial imbalance is estimated to be on average equal to 2% is ranked better than a second scenario in which the deviation from the reference axial imbalance is on average equal to 4%.

[0147] For example, in relation to the margin criterion at the limits of the operating domain and where appropriate to limiting axial imbalance lines, a first scenario in which the margin at the limits of the operating domain is estimated to be on average equal to 5% is ranked better than a second scenario in which the margin at the limits of the operating domain is on average equal to 3%.

[0148] The decision support device 20 can also determine an overall scenario score that takes into account a plurality of scores. The device 20 can then provide a suggested scenario that optimizes the different criteria taken into account in the overall score.

[0149] Once the scenario is selected by the operator and the various instructions are actually imposed on the reactor, it is possible to make successive estimations over time. Thus, the process can be repeated every minute so as to provide a new estimate of the temporal evolution of the axial imbalance DPAX every minute. The repetition frequency of the process can be determined in advance by the operator.

[0150] The method can also be used to list different "acceptable" scenarios or control strategies. This involves finding acceptable scenarios, in the sense of sequences of actions to be performed by the operator, meaning scenarios that respect the insertion and extraction limits of the control groups and allow the core to remain critical (keff = 1). The idea is to test different possible control solutions, which are determined, for example, by disrupting one or more scenarios previously identified as acceptable. The method can also rank these different scenarios.

[0151] The method can also be used to evaluate the impact on the axial imbalance DPAX of a possible need for a rapid increase in reactor power.

[0152] To achieve this, additional hypothetical power transients simulating rapid increases in reactor power can be determined. This involves creating sequences of successive reactor power values. These sequences take as their initial values ​​the values ​​of the power setpoint sequence imposed on the reactor. Subsequently, the steps of the axial imbalance estimation process are carried out based on these additional transients. A stability parameter can be determined based on the deviation from the reference axial imbalance, the distance to the reference line, or the margin at the limits of the operating range. An alert can be issued to the operator when the stability parameter crosses a threshold, particularly in the event of a risk of exceeding the operator's margin relative to the operating limits, or of a reduced margin.The operator can then adapt its strategy accordingly, particularly if it wishes to be able to meet a potential need for a rapid increase in reactor power. This estimation can be carried out at a constant frequency, for example every half hour.

[0153] Finally, the method presented so far can be used to assess the potential impact of remote control on the axial imbalance DPAX. Remote control is understood as a secondary adjustment of the electrical power produced by the installation and consequently of the thermal power produced by the reactor, which has the dual objective of, on the one hand, restoring the primary reserve to its nominal value and, on the other hand, of To restore the planned power levels at the interconnection points with the rest of the network, for example, the European electricity grid, a remote control signal is sent by the electricity transmission system operator. This signal can take values ​​between -1 and +1. The remote control signal is sent to a group of power plants that constitute a secondary reserve so that they can adjust the power they were initially designed to produce: a value of -1 in the remote control signal corresponds to a reduction in the total reserve power. A power plant's reserve power is approximately 5% of its nominal power; a value of +1 in the remote control signal corresponds to an increase in the total reserve power.

[0154] To assess the potential impact of remote control on a reactor, the method can estimate a power variation corresponding to remote control using steps similar to those described previously in relation to assessing the impact on the axial imbalance DPAX of a possible need for a rapid increase in reactor power. The method can include a step that alerts the operator if there is a risk of exceeding the operator's available margin relative to the operating limits. The operator can then adapt their strategy accordingly.

[0155] An object of the invention is a computer program comprising instructions adapted to the implementation of at least one of the steps of the process as it has been presented so far when said program is executed on a computer.

[0156] An object of the invention is a device for estimating a future value of an axial power imbalance in the nuclear reactor, the device comprising a computing module configured to implement the method as described so far, the computing module being configured to

[0157] - obtain a sequence of successive values ​​of a power setpoint of the reactor,

[0158] - determine, for each variable of a plurality of reactor variables, a sequence of successive values ​​of the variable, the sequence representing future variations of the variable, the variations being estimated by taking into account the power setpoint, the plurality of reactor variables including a xenon concentration in an upper half of the reactor, and a xenon concentration in a lower half of the reactor,

[0159] - determine a sequence of successive values ​​of the axial power imbalance taking into account the sequence of the plurality of reactor variables,

[0160] the calculation module comprising a machine learning module previously trained on historical reactor data, and

[0161] the calculation module using a model of the evolution of an iodine concentration and of a xenon concentration as a function of a neutron flux, so as to determine the sequence of xenon concentration in the upper half of the reactor and the sequence of xenon concentration in the lower half of the reactor.

Claims

Demands

1. A method for estimating a future value of an axial power imbalance in a nuclear reactor (11), the method comprising the following steps: - obtaining a sequence of successive values ​​of a reactor power setpoint (12), - for each variable of a plurality of reactor variables, determining a sequence of successive values ​​of the variable (19), the sequence representing future variations of the variable, the variations being estimated taking into account the power setpoint, the plurality of reactor variables comprising a xenon concentration in an upper half of the reactor and a xenon concentration in a lower half of the reactor, - determining a sequence of successive values ​​of the axial power imbalance (13), taking into account the sequences of the plurality of reactor variables (19),the determination of the axial power imbalance sequence (13) using a machine learning module (14) previously trained on historical reactor data (17), and the determination of the xenon concentration sequence in the upper half of the reactor and the determination of the xenon concentration sequence in the lower half of the reactor using a model of the evolution of an iodine concentration and a xenon concentration as a function of a neutron flux.

2. A method according to claim 1 wherein for at least one variable of the plurality of variables, the determination of the time sequence of the variable includes a measurement of the variable.

3. A method according to any one of claims 1 to 2, wherein the plurality of reactor variables comprises at least one of the following: - a position of a device configured to absorb neutrons in the reactor, - a measured average temperature of the reactor vessel, - a flow rate of a heat transfer fluid circulating in the reactor, - a concentration of a chemical species in the heat transfer fluid, the chemical species being configured to absorb neutrons in the reactor, and - a burnup rate of nuclear fuel contained in the reactor.

4. A method according to claim 3 wherein the determination of the axial power imbalance sequence also takes into account at least one of the following: a mean reference temperature of the vessel, a type of fuel management corresponding to a fractionation of a reactor core during a refueling, an enrichment of fissile reactor nuclei and a type of heavy reactor nuclei.

5. A method according to any one of claims 1 to 4 wherein the determination of the sequence of the plurality of reactor variables and the determination of the sequence of the axial power imbalance takes into account a reactor control scenario corresponding to a sequence of successive values ​​of at least one variable controllable by an operator.

6. A method according to claim 5 further comprising a step of determining a score of the control scenario, the score preferably being a value of a quantity chosen from a volume of effluent produced, an average deviation from the reference axial imbalance and an average distance to limits of a reactor operating domain.

7. A method according to any one of claims 5 to 6, wherein the control scenario is a first control scenario, the steps of the method being carried out a second time by replacing the first scenario with a second reactor control scenario corresponding to another sequence of successive values ​​of at least one controllable variable, the method preferably comprising a step of comparing the scores of the first scenario and the second scenario.

8. Computer program comprising instructions adapted to carry out at least one of the steps of the process according to any one of claims 1 to 7 when said program is executed on a computer.

9. Device for estimating a future value of an axial power imbalance in a nuclear reactor, the device comprising a calculation module configured to implement the method according to any one of claims 1 to 7, the calculation module being configured to: - obtain a sequence of successive values ​​of a reactor power setpoint, - determine, for each variable of a plurality of variables of the reactor, a sequence of successive values ​​of the variable, the sequence representing future variations of the variable, the variations being estimated by taking into account the power setpoint, the plurality of variables of the reactor including a concentration of xenon in an upper half of the reactor, and a concentration of xenon in a lower half of the reactor, - determine a sequence of successive values ​​of the axial power imbalance, taking into account the sequence of the plurality of reactor variables, the calculation module including a machine learning module previously trained on historical reactor data, and the calculation module using a model of the evolution of an iodine concentration and a xenon concentration as a function of a neutron flux, so as to determine the sequence of the xenon concentration in the upper half of the reactor and the sequence of the xenon concentration in the lower half of the reactor.

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