Reactor control method, reactor and calibration method

Abstract

The control method comprises a reactor control operation including the step of generating controls of an actuator using a digital model of the reactor, and an estimation operation for estimating at least one estimated digital coefficient belonging to a set of digital coefficients of the digital model, which is performed in parallel with the control operation, wherein the estimation operation includes the step of determining a simulated value of a group of operating parameters using the digital model for a sliding time window [t0 ; t0+T].

Description

Technology Field

[0001] The present invention generally relates to the control of a nuclear reactor. Background Technology

[0002] Patent applications filed in France under numbers FR 1850867 and FR 2103869 relate to reactor control methods that implement a predictive digital model configured to determine the change over time of a set of state parameters of a reactor using controls provided to an actuator from an initial state. This digital model makes it possible to determine optimal controls online, i.e., in real time, as a function of operating setpoints imposed on the operator.

[0003] Patent applications FR 1850867 and FR 2103869 use simple yet precise reactor modeling suitable for use in predictive control.

[0004] The predictive digital model must be as precise as possible to utilize all operating margins of the reactor and ensure a high level of performance. Since controls are updated periodically, for example at one-minute intervals, the predictive digital model must be fast. The predictive digital model is used multiple times within each time interval during control optimization operations.

[0005] In this context, the present invention aims to propose a more precise control method.

[0006] To this end, the present invention according to a first embodiment relates to a method for controlling a nuclear reactor, wherein the nuclear reactor comprises a pressure vessel, a core comprising a plurality of nuclear fuel assemblies arranged within the pressure vessel, a primary circuit for cooling the core in which a primary heat transfer fluid containing a neutron poison circulates, and a plurality of actuators acting on the core or the primary circuit, and the method comprises an operation for controlling the nuclear reactor comprising the following steps:

[0007] S10 / A step of acquiring current values ​​of a plurality of acquired operating parameters of a reactor;

[0008] S20 / A step of generating controls for an actuator using current values ​​of acquired operating parameters - at least some controls are determined using a digital model of the reactor, said digital model is configured to determine a change over time in a set of state parameters of the reactor using a set of controls and digital coefficients provided to the actuator -;

[0009] S30 / A step of controlling actuators using the generated controls;

[0010] Steps S10 / , S20 / and S30 / are repeatedly implemented,

[0011] The above method also includes an operation for estimating at least one estimated digital coefficient belonging to a set of digital coefficients and / or at least one estimated state parameter belonging to a set of state parameters, wherein the estimation operation is iteratively implemented at time tc in parallel with a control operation, and in each iteration includes the following steps:

[0012] S40 / A step of generating a generated value of at least one estimated digital coefficient and / or a generated initial value of at least one estimated state parameter;

[0013] For S50 / tc, for a time window [t0; t0+T] sliding with a time window width T located in the past, a step of determining simulated values ​​of a group of simulated driving parameters that form part of the driving parameters acquired using a digital model—the determination is performed by using the generated value of at least one estimated digital coefficient in the digital model and / or considering the generated initial value of at least one estimated state parameter at t0—;

[0014] S60 / A step of evaluating a cost function using the current values ​​and simulated values ​​of a group of simulated driving parameters;

[0015] Steps S40 / , S50 / and S60 / are repeated until the convergence criterion of the cost function is satisfied, and the generated value of at least one estimated digital coefficient and / or the generated initial value of at least one estimated state parameter that enables satisfying the convergence criterion is retained as an estimate of at least one estimated digital coefficient and / or at least one estimated state parameter at time tc.

[0016] Accordingly, the present invention makes it possible to periodically update digital coefficients of a digital model used to control a nuclear reactor and / or recalibrate specific state parameters. The operation for estimating digital coefficients and / or state parameters is performed in parallel, that is, simultaneously, with the operation for controlling the nuclear reactor.

[0017] In practice, in conventional technology, certain digital coefficients are obtained by calculation using hypotheses and simplifications that do not correspond to reality, or are constants calibrated for specific operating conditions. As these operating conditions change over the lifespan of the reactor, the digital coefficients no longer remain representative. For example, gradual wear occurs in the reactor's mechanical systems, particularly in the movement of the core's reactivity control bank. Furthermore, nuclear fuel assemblies are partially replaced every 18 months. During this period, fission products accumulate and affect the operation of the core.

[0018] The present invention makes it possible to ensure excellent representativeness of the digital model by periodically re-evaluating these digital coefficients.

[0019] This re-evaluation is performed by comparing the current recorded values ​​for specific driving parameters with simulated values ​​using a digital model.

[0020] Comparisons are performed over a sliding time window. In other words, the estimation operation uses an MHE-type (Moving Horizon Estimation) algorithm. This approach enables the rapid reconstruction of digital coefficients by converging to precise and realistic values ​​after a few iterations.

[0021] This method is adjusted to the time constant used for the operation to control the reactor. Reactor controls are typically updated at one-minute intervals. Digital counts can also be re-evaluated at one-minute intervals.

[0022] The present invention makes it possible to re-evaluate specific state parameters of a reactor in addition to or instead of digital coefficients. These state parameters are typically quantities that are not available for measurement, such as the concentration of xenon-135 or iodine-135 in a nuclear fuel assembly. These state parameters may be available or calculated by the reactor's instrumentation and control systems, but not always. They affect the controls determined by control operations, which are based on numerical results provided by digital models.

[0023] The control method may also have one or more of the following characteristics, considered individually or in all technically possible combinations:

[0024] - The cost function includes a term corresponding to the deviation between the current values ​​of a group of simulated driving parameters and the simulated values ​​over a time window;

[0025] - The cost function includes a term corresponding to the deviation between the generated value of at least one estimated digital coefficient and the estimate of at least one estimated digital coefficient obtained in the previous iteration;

[0026] - The cost function includes a term corresponding to the deviation between the generated initial value of at least one estimated state parameter and the estimate of at least one estimated state parameter obtained in the previous iteration;

[0027] - The digital model of the reactor includes a plurality of sub-models, each sub-model models one level of the reactor core and includes at least one equation describing the dynamics of the neutron density at that level and one equation describing the temperature of the primary heat transfer fluid at that level, and the digital model further includes equations describing the neutron exchange between levels and equations characterizing the reactivity at each level;

[0028] - The primary circuit comprises at least one primary loop having a hot branch and a cold branch connected respectively to the primary heat transfer fluid outlet and the primary heat transfer fluid inlet of the pressure vessel, and the reactor further comprises the following:

[0029] - Secondary circuit equipped with a turbine;

[0030] - A steam generator for each of the primary loops, having a first side interposed in the primary loop and a second side interposed in the secondary circuit;

[0031] - Neutron-absorbing control rod bank;

[0032] - A mechanism capable of selectively inserting or withdrawing a control rod bank into or out of the reactor core;

[0033] - A unit that enables the injection of neutron toxins into the primary heat transfer fluid; and

[0034] - Unit provided to inject water into the primary circuit;

[0035] The equations characterizing the reactivity at each level consider one or more of the following effects:

[0036] - Effects resulting from the temperature change of the primary heat transfer fluid at the corresponding level;

[0037] - Effects resulting from changes in output provided by the core at the corresponding level;

[0038] - Effects resulting from the movement of the control rod bank;

[0039] - Effects resulting from changes in neutron toxin concentration within the primary heat transfer fluid;

[0040] - Effects resulting from changes in the concentration of Xenon 135 within the nuclear fuel assembly at the relevant level;

[0041] - State parameters include one or more of the parameters in the list below:

[0042] - For each level of the core, the neutron density at the corresponding level, the concentration of Xenon 135 in the nuclear fuel assembly at the corresponding level, and the concentration of Iodine 135 in the nuclear fuel assembly at the corresponding level;

[0043] - For each level of the core, the temperature of the primary heat transfer fluid;

[0044] - Temperature of the primary heat transfer fluid at the inlet and outlet of the core;

[0045] - Temperature of the primary heat transfer fluid in the high-temperature branch and the low-temperature branch;

[0046] - Neutron toxicity concentration in the primary heat transfer fluid;

[0047] The above or each estimated digital coefficient is selected from the following list:

[0048] - : Conversion coefficient due to neutron absorption of Xenon 135 to Xenon 136;

[0049] - l * : Average lifetime of neutrons in the core;

[0050] - D: Neutron exchange coefficient between core levels;

[0051] - Kbor, Kbank, Kxenon: Efficiency factors characterizing the contribution to changes in reactivity at each level of the core—corresponding, respectively, to changes in neutron poison concentration in the primary heat transfer fluid, movement of the control rod bank, and changes in the concentration of Xenon-135 in the nuclear fuel assembly at the corresponding core level;

[0052] - : Time constant of temperature exchange between the primary and secondary circuits in a steam generator;

[0053] - : Time constant of the temperature change of the primary heat transfer fluid along a high-temperature branch;

[0054] - : Time constant of the temperature change of the primary heat transfer fluid along the low-temperature branch;

[0055] Each estimated state parameter is selected from the following list:

[0056] - For each level of the core, the concentration of Xenon 135 in the nuclear fuel assembly at the corresponding level;

[0057] - For each level of the core, the concentration of iodine-135 in the nuclear fuel assembly at the corresponding level;

[0058] In step S50 / , the simulated driving parameters are selected from the following list:

[0059] - Neutron flux at each level of the core;

[0060] - Axial distribution of neutron flux within the core;

[0061] - Temperature of the primary heat transfer fluid in the high-temperature branch and low-temperature branch of the primary circuit;

[0062] - Neutron toxicity concentration in the primary heat transfer fluid;

[0063] - Concentration of Xenon 135 in the nuclear fuel assembly at each level of the core, concentration of Iodine 135 in the nuclear fuel assembly at each level of the core;

[0064] The actuator controls used by the digital model are selected from the following list:

[0065] - Movement of control bank;

[0066] - Injection of neutron toxin into the primary circuit;

[0067] - Water injection into the primary circuit;

[0068] - Output provided by the turbine;

[0069] - In each iteration, the optimization operation is treated as an optimization problem aiming to minimize the cost function by implementing a numeric integrator and a numeric optimization solver.

[0070] According to a second aspect, the present invention relates to a reactor comprising a pressure vessel, a core comprising a plurality of nuclear fuel assemblies arranged within the pressure vessel, a primary circuit for cooling the core in which a primary heat transfer fluid containing a neutron poison circulates, a plurality of actuators acting on the core or the primary circuit, and a control assembly of the reactor, wherein the control assembly is configured to implement a control method having the above characteristics.

[0071] Nuclear reactors can also have the following characteristics:

[0072] - The primary circuit comprises at least one primary loop having a high-temperature branch and a low-temperature branch connected respectively to the primary heat transfer fluid outlet and the primary heat transfer fluid inlet of the pressure vessel, and the reactor further comprises the following:

[0073] - Secondary circuit equipped with a turbine;

[0074] - As a steam generator for the above or each primary loop, having a first side interposed in the primary loop and a second side interposed in the secondary circuit;

[0075] - Neutron-absorbing control rod bank;

[0076] - A mechanism capable of selectively inserting or withdrawing a control rod bank into or out of the reactor core;

[0077] - A unit that enables the injection of neutron toxins into the primary heat transfer fluid; and

[0078] - A unit provided to inject water into the primary circuit.

[0079] According to a third aspect, the present invention relates to a method for calibrating a digital model used to control a nuclear reactor, wherein the nuclear reactor comprises a pressure vessel, a core comprising a plurality of nuclear fuel assemblies arranged within the pressure vessel, a primary circuit for cooling the core in which a primary heat transfer fluid containing a neutron poison circulates, and a plurality of actuators acting on the core or the primary circuit, and the control of the nuclear reactor is performed according to a method comprising the following steps:

[0080] S10 / Acquisition of current values ​​of multiple operating parameters obtained from the reactor;

[0081] S20 / Generation of controls for an actuator using current values ​​of acquired operating parameters, at least some of the controls are determined using the digital model, and the digital model is configured to determine a change over time in a set of state parameters of a reactor using a set of controls and digital coefficients provided to the actuator;

[0082] S30 / Control actuators using the generated controls;

[0083] Steps S10 / , S20 / , and S30 / are implemented repeatedly;

[0084] The above calibration method comprises an operation for generating reference values ​​of a plurality of reference operating parameters of a reactor for a time interval I, and an operation for estimating at least one estimated digital coefficient belonging to a set of digital coefficients implemented for a time window [t0; t0+T] (where T is the width of the time window) within the time interval I, wherein the estimation operation comprises the following steps in each iteration:

[0085] S70 / Generation of a generated value of at least one estimated digital coefficient;

[0086] S80 / Determination of simulated values ​​of a group of simulated driving parameters forming part of reference driving parameters using a digital model for a time window [t0; t0+T] by using the generated value of at least one estimated digital coefficient in the digital model;

[0087] S90 / Evaluation of the cost function using reference values ​​and simulated values ​​of a group of simulated driving parameters;

[0088] Steps S70 / , S80 / and S90 / are repeated until the convergence criterion of the cost function is satisfied, and the generated value of at least one estimated digital coefficient that enables satisfying the convergence criterion is retained as an estimate of at least one estimated digital coefficient at time t0+T.

[0089] The calibration method may also have one or more of the following characteristics, considered individually or in all technically possible combinations:

[0090] - The estimation operation is implemented in a non-iterative manner, and the time window [t0; t0+T] corresponds to the time interval I;

[0091] - The estimation operation is implemented in an iterative manner, the time window [t0; t0+T] slides within the time interval I, and the time window moves in each iteration to sweep the time interval I. Brief explanation of the drawing

[0092] Other characteristics and advantages will become clear from the following detailed description, which is provided by example with reference to the attached drawings and is by no means limited, and among the said drawings FIG. 1 is a schematic representation of a nuclear reactor according to the present invention; FIG. 2 is a step diagram illustrating a control method of the present invention; FIG. 3 is a schematic representation of a digital model of a reactor core used in the method of FIG. 2; FIGS. 4 and 5 show coefficient D and determined by the estimation operation for an application example of the present invention and Curves representing as a function of time; FIGS. 6 to 9 show coefficients D, - determined by an estimation operation for other application examples of the present invention. , curves representing KBore and KXenon as a function of time; FIG. 10 is a curve illustrating another application example of the present invention, particularly aimed at determining state parameters. Specific details for implementing the invention

[0093] The reactor (1) depicted in FIG. 1 comprises a pressure vessel (2) and a core (3) arranged within the pressure vessel (2) in a conventional manner. The core (3) itself comprises a plurality of nuclear fuel assemblies (5).

[0094] The reactor (1) also includes a primary circuit (7) provided for cooling the core (3), where a primary heat transfer fluid containing a neutron poison circulates.

[0095] The primary circuit (7) includes at least one primary loop having a high-temperature branch (BC) and a low-temperature branch (BF) respectively connected to the primary heat transfer fluid outlet and the primary heat transfer fluid inlet of the pressure vessel (2).

[0096] Typically, the primary circuit (7) includes a plurality of primary loops as described above.

[0097] Each primary loop includes a primary pump (8).

[0098] The reactor (1) further includes a secondary circuit (9).

[0099] The secondary heat transfer fluid circulates in the secondary circuit (9).

[0100] The secondary circuit (9) includes a turbine (11).

[0101] The secondary circuit also includes a condenser (13), a water supply tank (15), and a secondary pump (17, 19).

[0102] The reactor (1) includes a steam generator (21) for each primary loop. The first side is interposed in the primary loop and the second side is interposed in the secondary circuit.

[0103] The high-temperature branch (BC) connects the outlet of the pressure vessel to the inlet of the first side of the steam generator (21). The low-temperature branch (BF) connects the discharge port of the primary pump (8) to the inlet of the pressure vessel (2).

[0104] The primary heat transfer fluid transfers heat to the secondary fluid in the steam generator (21) or each steam generator (21).

[0105] The secondary heat transfer fluid is vaporized in the steam generator (21) under the influence of the heat transferred by the primary heat transfer fluid.

[0106] The secondary heat transfer fluid in steam form is circulated from the steam generator (21) to the turbine (11) and then condensed in the condenser (13). It is then returned to the steam generator (21) in liquid form.

[0107] The valve (23) is interposed in the steam line connecting the steam generator (21) to the turbine (11) and enables the flow rate of steam supplied to the turbine (11).

[0108] The turbine (11) mechanically drives the alternator (25).

[0109] The electricity generated by the alternator (25) is supplied to the electric distribution network (29).

[0110] The reactor (1) further includes a unit (31) that enables the injection of a neutron poison into the primary heat transfer fluid. The neutron poison is typically boron.

[0111] A container (32) containing a concentrated neutron poison solution, for example boric acid, is connected to the primary circuit (7) by a conduit (33). A pump (35) and a valve (37) are interposed in the conduit (33).

[0112] Unit (31) enables selectively increasing the concentration of neutron poison in the primary liquid.

[0113] The reactor further includes a unit (39) provided to inject water into the primary circuit.

[0114] The unit (39) includes a vessel (41) connected to the primary circuit (7) by a line (43). A pump (45) and a valve (47) are interposed in the line (43).

[0115] The water is typically pure desalinated water.

[0116] Unit (39) is provided to inject water into the primary circuit (7), which results in a reduction of the concentration of neutron toxins in the primary heat transfer fluid.

[0117] In a conventional manner, the reactor (1) further includes a control rod bank (49) and a mechanism (51) that can selectively insert or withdraw the control rod bank (49) into or out of the reactor core (3).

[0118] Control rods are made of neutron-absorbing material.

[0119] The control rod bank (49) is moved to selectively change the reactivity inside the core (3).

[0120] Accordingly, the reactor (1) includes a plurality of actuators acting on the core (3) or primary circuit (7).

[0121] In the example described above, these actuators include a control rod bank (49), a unit (31) that enables the injection of neutron poison into the primary heat transfer fluid, a unit (39) provided for injecting water into the primary circuit, and a valve (23) that enables the control of the flow rate of steam supplied to the turbine (11).

[0122] The valve (23) regulates the output provided by the turbine (11), which acts indirectly on the output provided by the core through the control members of the core (3).

[0123] The reactor (1) also includes a measuring instrument (53) that enables direct measurement or determination of multiple operating parameters of the reactor.

[0124] These driving parameters include, for example, the following parameters:

[0125] - Output provided by the turbine (11);

[0126] - Temperature of the primary heat transfer fluid at the inlet and outlet of the core (3);

[0127] - Temperature of the primary heat transfer fluid in the high-temperature branch (BC) and the low-temperature branch (BF);

[0128] - Location of the control rod bank (49);

[0129] - Output provided by the core (3) of the reactor;

[0130] - Neutron flux at different levels of the core (3);

[0131] - Distribution of neutron flux within the core (3);

[0132] - Neutron toxicity concentration in the primary heat transfer fluid.

[0133] Advantageously, the current flow rate of the neutron poison and the current flow rate of water injected into the primary heat transfer fluid are also measured or determined.

[0134] The measuring instrument (53) includes neutron detectors that are positioned outside the core (3) and distributed over the entire height of the core. These detectors are known as ex-core chambers.

[0135] The output provided by the core is obtained by calculation based on information provided by detectors measuring, for example, the neutron flux outside the core.

[0136] As a variation, the output provided by the core is determined using the measured value of the output provided by the turbine.

[0137] Parameters characterizing the distribution of neutron flux within the core are, for example, the axial power distribution or axial offset (AO). The axial offset is calculated using the following formula:

[0138] AO = (Φh-Φb) / (Φh+Φb)

[0139] Here, Φh is the neutron flux of the upper half of the core, and Φb is the neutron flux of the lower half of the core.

[0140] Neutron flux in the upper and lower halves of the core is typically obtained by neutron detectors placed outside the core (3). As a variation, it is obtained by probes placed inside the core (3), called in-core probes.

[0141] As a variation, the parameter characterizing the distribution of neutron flux within the core is Φh-Φb or another suitable parameter.

[0142] The measuring instrument (53) includes temperature measuring probes arranged to measure the temperature of the heat transfer fluid in the high-temperature branch and the low-temperature branch and the pressure vessel.

[0143] The measuring instrument (53) advantageously includes a sensor that measures the mechanical output provided by the turbine directly or indirectly.

[0144] The position of the control rod bank (49) is typically determined from information provided by the mechanism (51) for moving the control rods.

[0145] The reactor (1) also includes a reactor control assembly (55).

[0146] The control assembly is configured to implement a method for controlling the reactor to be described now.

[0147] As illustrated in FIG. 2, the method comprises an operation for reactor control including the following steps:

[0148] S10 / Acquisition of current values ​​of multiple acquired operating parameters of a reactor;

[0149] S20 / Generation of controls for an actuator using current values ​​of acquired operating parameters - at least some controls are determined using a digital model of the reactor, said digital model is configured to determine the change over time of a set of state parameters of the reactor using a set of controls and digital coefficients provided to the actuator -;

[0150] S30 / Control actuators using the generated controls.

[0151] Steps S10 / , S20 / and S30 / are implemented iteratively.

[0152] Advantageously, steps S20 / and S30 / are repeated at intervals of less than 60 minutes, preferably less than 20 minutes, for example, at intervals such as 1 minute.

[0153] Step S10 / is repeated with the same period. As a variation, Step S10 / is repeated with a larger period. This period may vary depending on the acquired operating parameters.

[0154] Controls are determined to adjust a certain number of controlled operating parameters of the reactor to set values.

[0155] The controlled operating parameters are, for example, the temperature Tmoy of the primary heat transfer fluid, the axial offset AO, and the output provided by the turbine.

[0156] The actuator controls generated in step S20 / are selected from the following list:

[0157] - Movement of control bank;

[0158] - Injection of neutron toxin into the primary circuit;

[0159] - Water injection into the primary circuit;

[0160] - Output provided by the turbine.

[0161] Typically, all controls in the above list are generated in step S20 / .

[0162] Digital models are used, for example, to determine all controls in a list.

[0163] As a variation, the digital model is used to determine only specific controls in the list. Other controls are fixed manually or determined in step S20 / using control loops independent of the digital model.

[0164] Each control loop is provided to adjust one of the controlled driving parameters using one of the controls in this case.

[0165] For example, reactors operating in mode A include a control loop for the temperature of the primary heat transfer fluid. The loop receives the current average temperature Tmoy of the primary heat transfer fluid in the reactor core (3) as input.

[0166] This value corresponds, for example, to the average of the temperature measured at the reactor inlet and the temperature measured at the core outlet.

[0167] The above loop also receives the set value temperature.

[0168] The average temperature Tmoy of the primary heat transfer fluid in the core is controlled by moving the control rod bank (49) as a function of the difference between the current temperature and the setpoint temperature. Four rod banks, called groups A, B, C, and D, can be moved to control the temperature Tmoy.

[0169] In FR1850867, a digital model is used to determine the movement of the control bank, neutron toxicity injection, and water injection. In FR2103869, a digital model is used to determine neutron toxicity injection and water injection.

[0170] The digital model in step S20 / can be used in various ways.

[0171] In FR1850867, digital models are used in combination with gain-scheduled control algorithms. Digital models are used to determine the controls. Gain-scheduled control algorithms are used to develop modification controls. The controls actually applied to control the actuators are the sum of the controls and the modification controls.

[0172] In FR2103869, a digital model is used to determine the optimized injection sequence of neutron poison or water during the power transient.

[0173] Other uses of digital models can be considered.

[0174] The digital model uses all the controls in the list above. As a variation, it uses only some of the controls in the list above.

[0175] The digital model of the reactor core is a so-called predictive model.

[0176] The digital model of a nuclear reactor core is a nonlinear model. As a variation, the digital model is linear. This digital model is obtained by linearizing, for example, the nonlinear model described below.

[0177] This digital model is schematically illustrated in Fig. 3.

[0178] The digital model of the core includes multiple sub-models, and each sub-model models one level of the core (3).

[0179] In other words, the core is divided into multiple slices along the vertical direction, and each sub-model models one of the core slices.

[0180] Typically, the digital model of the core includes 2 to 20 sub-models, preferably 2 to 10 sub-models, and for example, 6 sub-models.

[0181] Each submodel includes at least one equation describing the dynamics of the neutron density at the corresponding level, and one equation describing the temperature of the primary heat transfer fluid at the corresponding level.

[0182] The temperatures T2 to T7 at the exit of each level are derived from the neutron flux at each level.

[0183] The equations are shown below:

[0184] Level 1:

[0185]

[0186]

[0187] Level i:

[0188]

[0189]

[0190] Highest Level:

[0191]

[0192]

[0193] - ni : Neutron density at level i;

[0194] - ρi : Reactivity at level i;

[0195] - D : Neutron exchange coefficient;

[0196] - l * : Average lifetime of neutrons (immediate and delayed);

[0197] - KT / H : Temperature / enthalpy conversion coefficient;

[0198] - Kn : Output / neutron flux conversion coefficient;

[0199] - Qp: Mass flow rate of the primary heat transfer fluid in the core;

[0200] - T1, T7: Temperatures at the inlet and outlet of the core;

[0201] - Ti: Temperature of the primary heat transfer fluid at each level.

[0202] Here, the temperature at each level corresponds to the temperature at the inlet of that level.

[0203] Therefore, each level of the core is modeled using a single-group approximation of point neutron kinetics by adding a coefficient D to account for neutron exchange between levels.

[0204] Delayed neutrons and precursors having faster kinetics than those expected by the above method or operator are not modeled. These neutrons typically have kinetics of 10 seconds for a computational time interval of approximately 60 seconds.

[0205] The digital model also includes equations that characterize the reactivity at each level.

[0206] These equations consider one or more of the following effects:

[0207] - Effect due to temperature change of the primary heat transfer fluid at the corresponding level (also called the moderator effect);

[0208] - Effects resulting from changes in output provided by the core at the corresponding level (Doppler effect);

[0209] - Effects resulting from the movement of the control rod bank;

[0210] - Effects resulting from changes in neutron toxin concentration within the primary heat transfer fluid;

[0211] - Effects resulting from changes in the concentration of Xenon 135 within the nuclear fuel assembly at the relevant level.

[0212] The equations are as follows:

[0213]

[0214]

[0215]

[0216]

[0217]

[0218]

[0219]

[0220]

[0221] - ρi0 : Initial reactivity at level i determined in the previous time interval;

[0222] - Pi: Thermal output provided by core level i, assumed to be proportional to neutron density;

[0223] - Xei: Concentration of Xenon 135 in the nuclear fuel assembly at level i;

[0224] - Ii: Concentration of iodine-135 in the nuclear fuel assembly at level i;

[0225] - Γl : Production coefficient of iodine-135 by nuclear fission;

[0226] - λl : Decay constant of iodine-135 to xenon-135;

[0227] - ΓXe : Production coefficient of Xenon 135 by nuclear fission;

[0228] - λXe : Decay constant of xenon 135;

[0229] - : Conversion coefficient due to neutron absorption of Xenon 135 to Xenon 136;

[0230] - Kmod, Kdop, Kbor, Kbank, Kxenon: Efficiency coefficients that respectively characterize the contribution to changes in reactivity at each level of the core - corresponding to changes in temperature, changes in the output provided by the core, changes in the concentration of neutron poison in the primary heat transfer fluid, movement of the control rod bank, and changes in the concentration of Xenon 135 in the nuclear fuel assembly at the corresponding core level.

[0231] In the equations above, Δ represents the change with respect to the previous time interval.

[0232] The effect resulting from changes in the output provided by the core makes it possible to characterize the effect of changes in nuclear fuel temperature, also known as the Doppler effect.

[0233] The change in Xenon 135 at each level is modeled using conventional equations that consider the following:

[0234] - Production of Iodine-135 by nuclear fission;

[0235] - Radioactive decay of Iodine-135 to Xenon-135;

[0236] - Production of Xenon 135 by nuclear fission;

[0237] - Radioactive decay of Xenon 135;

[0238] - Conversion of Xenon 135 to Xenon 136 by neutron absorption.

[0239] ΔPbanki corresponds to the movement of the entire control bank within level i expressed in the steps. This parameter corresponds to the sum of the changes in the number of insertion steps at level i of all control banks.

[0240] ΔPi is obtained by the following equation:

[0241] ΔPi = Kn x Δni, where Kn is a predetermined constant.

[0242] Furthermore, digital models include the following general equations:

[0243]

[0244] P is the total output provided by the core.

[0245] The change over time in the total output provided by the core is typically imposed by the manager of the electrical distribution network.

[0246] The value of ΔPbanki is determined by the digital model as a function of the change in the average temperature Tmoy of the primary heat transfer fluid within the core. The digital model first determines the value of Tmoy according to the following equation:

[0247] Tmoy = (T1 + T7) / 2.

[0248] Then, the digital model determines the reference average temperature Tref as a function of parameters such as the desired reactor output. This data is available in the reactor control assembly. This is typically imposed by the operator of the electrical distribution network (29).

[0249] The digital model then determines the difference ΔTmoy between Tmoy and the reference average temperature Tref.

[0250] When Tmoy goes out of the temperature dead band, that is, when ΔTmoy exceeds a predetermined threshold, the digital model determines that it is necessary to set the value of Tmoy to the dead band limit and shift the control bank. The digital model calculates the value of ΔPbank as a function of ΔTmoy that enables the achievement of criticality.

[0251] Reference temperature values ​​and the width of the temperature dead zone as a function of reactor output are recorded in a digital model as predetermined values ​​or are provided by the control assembly (55).

[0252] ΔCpn is obtained by integrating the amount of neutron poison and / or water injected into the primary heat transfer fluid. Digital models use the following equations for this purpose:

[0253] For water injection: dCpn / dt = - Cpn x Qw / Mt

[0254] For neutron toxin injection: dCpn / dt = (Crea - Cpn) x Qpn / Mt

[0255] Here, Mt is the total mass of water in the primary circuit (e.g., 260 tons for an N4 unit), Crea is the neutron poison concentration in the injected neutron poison solution, Cpn is the current neutron poison concentration in the primary heat transfer fluid, Qw is the flow rate of the injected deionized water, and Qpn is the flow rate of the injected neutron poison solution.

[0256] Delay is considered to evaluate the effect of demineralized water or neutron toxin injection.

[0257] The value of Qp, that is, the flow rate of the primary heat transfer fluid in the core, is a predetermined value.

[0258] As a variation example, this is retrieved from the control assembly (55).

[0259] The digital model also includes equations that model the temperature changes of the low-temperature and high-temperature branches:

[0260]

[0261]

[0262]

[0263] - Tbf and Tbc are the temperatures of the primary heat transfer fluid in the low-temperature branch and the high-temperature branch;

[0264] - is the derivative with respect to time Tbf, Tbc, and T1;

[0265] - K is a constant and;

[0266] - Pvap is the output extracted by the steam generator;

[0267] - : Time constant of temperature exchange between the primary and secondary circuits in a steam generator;

[0268] - : Time constant of the temperature change of the primary heat transfer fluid along a high-temperature branch;

[0269] - : Time constant of the temperature change of the primary heat transfer fluid along a low-temperature branch.

[0270] Therefore, the digital coefficients used in the digital model are KT / H, Kn, Kmod, Kdop, Kbor, Kbank, Kxenon, D, ΓI, Γxe and , l * ,λl, λXe, , , am.

[0271] The driving parameters for which current values ​​are obtained in step S10 / are selected from the following list:

[0272] - Neutron flux at each level ni of the core;

[0273] - Axial distribution of neutron flux within the core;

[0274] - Temperature of the primary heat transfer fluid in the high-temperature branch and low-temperature branch of the primary circuit;

[0275] - Neutron toxicity concentration in the primary heat transfer fluid;

[0276] - Concentration of Xenon 135 in the nuclear fuel assembly at each level of the core, concentration of Iodine 135 in the nuclear fuel assembly at each level of the core.

[0277] Typically, the current values ​​of all the above parameters are obtained.

[0278] As a variation, only the current values ​​of some of these parameters are obtained.

[0279] The neutron flux at each level of the core is provided directly by neutron detectors of the instruments (53) distributed across the height of the core. As a variation, it is calculated from the information provided by the neutron detectors.

[0280] The axial distribution of the neutron flux within the core is provided by the measuring instrument (53). This distribution corresponds, for example, to an axial offset.

[0281] The temperature of the primary heat transfer fluid in the high-temperature branch and low-temperature branch of the primary circuit and the concentration of neutron toxins in the primary heat transfer fluid are provided directly by the measuring instrument (53).

[0282] The concentrations of Xenon-135 and Iodine-135 at each level of the core within the nuclear fuel assembly are typically retrieved from the control assembly (55). In certain reactors, this control assembly (55) includes an expert system configured specifically to determine these concentrations of Xenon-135 and Iodine-135. This expert system is designated by the acronym CMS (Core Monitoring System, or Core Monitoring System). If these concentrations are not available, it is preferable that they be estimated by an estimation operation as described below.

[0283] State parameters include one or more of the parameters in the list below:

[0284] - For each level of the core, the neutron density ni at the corresponding level, the concentration of Xenon 135 in the nuclear fuel assembly at the corresponding level Xei, and the concentration of Iodine 135 in the nuclear fuel assembly at the corresponding level Ii;

[0285] - For each level of the core, the temperature Ti of the primary heat transfer fluid;

[0286] - Temperatures T1, T7 of the primary heat transfer fluid at the inlet and outlet of the core;

[0287] - Temperatures of the primary heat transfer fluid in the high-temperature branch and low-temperature branch TBC, TBF;

[0288] - Neutron toxicity concentration Cpn in the primary heat transfer fluid.

[0289] Typically, all of the above parameters are state parameters.

[0290] As a variation, only some of the above parameters are state parameters.

[0291] In step S30 / , the controls generated in step S20 / are used to control the corresponding actuators.

[0292] Step S30 / is fully automatic, and the actuators are controlled by a computer without operator intervention.

[0293] As a variation, at least some actuators are manually controlled in step S30 / . The controls generated in step S20 / constitute decision aids, i.e., recommendations, for operators controlling the reactor.

[0294] The above method also includes an operation to estimate at least one estimated digital coefficient belonging to a set of digital coefficients and / or at least one estimated state parameter belonging to a set of state parameters, wherein the estimation operation is repeatedly implemented at time tc in parallel with the control operation.

[0295] This estimation operation includes the following steps in each iteration:

[0296] S40 / Generation of a generated value of at least one estimated digital coefficient and / or a generated initial value of at least one estimated state parameter;

[0297] For a time window [t0; t0+T] sliding with a time window width T located in the past for S50 / tc, the determination of simulated values ​​of a group of simulated driving parameters forming part of the driving parameters acquired using a digital model, said determination is performed by using the generated value of at least one estimated digital coefficient in the digital model and / or considering the generated initial value of at least one estimated state parameter at t0;

[0298] S60 / Evaluation of the cost function using current values ​​and simulated values ​​of simulated driving parameters.

[0299] Steps S40 / , S50 / and S60 / are repeated until the convergence criterion of the cost function is satisfied, and the generated value of at least one estimated digital coefficient and / or the generated initial value of at least one estimated state parameter that enables satisfying the convergence criterion is retained as an estimate of at least one estimated digital coefficient and / or at least one estimated state parameter at time tc.

[0300] Estimation operations are performed simultaneously with control operations. Estimation operations enable real-time modification of digital coefficients or state variables used in the digital model for operations to control the reactor.

[0301] The estimation operation is performed repeatedly at a cycle of less than 60 minutes, preferably less than 20 minutes, for example, at a cycle of 1 minute.

[0302] The estimation operation aims to estimate, for example, at least one digital coefficient.

[0303] Alternatively, the estimation operation aims to estimate both at least one digital coefficient and at least one state parameter.

[0304] In practice, the precision of digital models depends in part on precise knowledge of state parameters. There are cases where specific state parameters are not available even through instruments, or more generally, through the reactor's control assembly.

[0305] In this case, one or more of these state parameters are determined favorably during the estimation operation.

[0306] According to a less frequent alternative, only one or more state parameters are determined by the estimation operation.

[0307] Each estimated digital coefficient is preferably selected from the following list:

[0308] - : Conversion coefficient due to neutron absorption of Xenon 135 to Xenon 136;

[0309] - l * : Average lifetime of (immediate and delayed) neutrons in the core;

[0310] - D: Neutron exchange coefficient between core levels;

[0311] - Kbor, Kbank, Kxenon: Efficiency factors characterizing the contribution to changes in reactivity at each level of the core, respectively—corresponding to changes in neutron poison concentration in the primary heat transfer fluid, movement of the control rod bank, and changes in the concentration of Xenon-135 in the nuclear fuel assembly at the corresponding core level—;

[0312] - : Time constant of temperature exchange between the primary and secondary circuits within a steam generator;

[0313] - : Time constant of the temperature change of the primary heat transfer fluid along a high-temperature branch;

[0314] - : Time constant of the temperature change of the primary heat transfer fluid along a low-temperature branch.

[0315] The above or each estimated state parameter is preferably selected from the following list:

[0316] - For each level of the core, the concentration of Xenon 135 Xei in the nuclear fuel assembly at that level,

[0317] - For each level of the core, the concentration of Iodine 135 in the nuclear fuel assembly at the corresponding level is Ii.

[0318] Typically, the estimation operation is configured to estimate all digital coefficients in the list above and all state parameters in the list above.

[0319] In a variant example, to limit computation time, the estimation operation is configured to estimate the following:

[0320] - Only 1 to 9 of the above digital coefficients, preferably 1 to 7, more preferably 1 to 4; or

[0321] - Only 1 to 35 of the above state parameters, preferably 1 to 8, more preferably 1 to 4;

[0322] - All of the above digital coefficients from 1 to 9 and the above state parameters from 1 to 35, preferably 1 to 7 of the above digital coefficients and 1 to 24 of the above state parameters, more preferably 1 to 4 of the above digital coefficients and 1 to 12 of the above state parameters.

[0323] In step S50 / , the simulated driving parameters are selected from the following list:

[0324] - Neutron flux at each level ni of the core;

[0325] - Axial distribution of neutron flux within the core;

[0326] - Temperature of the primary heat transfer fluid in the high-temperature branch and low-temperature branch of the primary circuit;

[0327] - Neutron toxicity concentration in the primary heat transfer fluid;

[0328] - Concentration of Xenon 135 in the nuclear fuel assembly at each level of the core, concentration of Iodine 135 in the nuclear fuel assembly at each level of the core.

[0329] Typically, in step S50 / , the group of simulated driving parameters includes all driving parameters in the above list. As a variation, the group of simulated driving parameters includes only some of the driving parameters in the above list.

[0330] The digital model is used to determine the change over time of simulated values ​​over a time window [t0; t0+T].

[0331] The width T of the time window is 0 hours 15 minutes to 24 hours, preferably 0 hours 30 minutes to 1 hour 30 minutes, for example, 1 hour.

[0332] Time t0+T corresponds to time tc, for example.

[0333] As a variation, time t0+T is shifted back with respect to tc, typically by a few minutes.

[0334] The time window slides in the sense that it moves within time with time tc. The time window always has the same time offset for time tc.

[0335] As shown above, the digital model uses the generated value of at least one estimated digital coefficient in step S50 / or considers the generated initial value of at least one estimated state parameter in t0.

[0336] The other digital coefficients used are predetermined constants.

[0337] The initial values ​​of other state parameters are typically the values ​​obtained from the simulation in the previous iteration.

[0338] The digital model in step S50 / uses the values ​​of the controls actually applied during the time window [t0; t0+T].

[0339] The cost function used in step S60 / includes a term corresponding to the deviation between the current values ​​of the group of simulated driving parameters and the simulated values ​​over a time window.

[0340] Advantageously, the cost function also includes a term corresponding to the deviation between the generated value of at least one estimated digital coefficient and the estimate of at least one estimated digital coefficient obtained in the previous iteration.

[0341] This term is useful only when the estimation operation aims to estimate at least one digital coefficient.

[0342] The cost function preferably includes a term corresponding to the deviation between the generated initial value of at least one estimated state parameter and the estimate of at least one estimated state parameter obtained in the previous iteration.

[0343] This term is useful only when the estimation operation aims to estimate at least one state parameter.

[0344] For example, the cost function is as follows:

[0345]

[0346] Here, J is the cost function and;

[0347] x is a vector of state parameters;

[0348] is a vector of state parameters containing the estimated state parameters or generated initial values ​​for the parameters and the values ​​at t0 estimated in the previous iteration for other state parameters;

[0349] is an estimated digital coefficient or a vector of coefficients obtained in the previous iteration;

[0350] p is a vector containing estimated digital coefficients or generated values ​​of coefficients;

[0351] y(τ) is a vector of current values ​​of a group of measured driving parameters;

[0352] h(x(τ)) is a vector of simulated values ​​of a group of simulated driving parameters;

[0353] and Norms such as, where a is a vector with n components and Sx is an nxn matrix.

[0354] Sx, Sp, and R are matrices used to weight the contributions of different terms in the cost function. When Sx is large, deviations between the state parameters determined in the current problem-solving and previously calculated state parameters are strongly penalized (used when there is confidence in this estimate). If confidence in the previous estimate is low, the weight may be less significant. Sp plays the same role for the digital coefficients of the digital model. R penalizes deviations between the operating parameters simulated by the digital model and the measured operating parameters. R is generally selected based on considerations related to the nature of measurement uncertainty (such as the precision of the instrumentation). Sx and Sp are adjusted by the designer to obtain the best possible estimation result.

[0355] As shown above, steps S40 / , S50 / , and S60 / are repeated until the convergence criterion of the cost function is satisfied.

[0356] More specifically, in each iteration, the optimization operation is treated as an optimization problem aiming to minimize the cost function J by implementing a numeric integrator and a numeric optimization solver.

[0357] Optimization problems are first converted into non-linear programming (NLP) problems by the discretization method.

[0358] This discretization method is a single-shooting method, a multi-shooting method, or a direct placement method.

[0359] Nonlinear programming problems are solved using numerical integrators capable of handling so-called stiff systems by implementing suitable methods: collocation, linear multi-step methods, Euler methods, Range-Kutta methods, Dorman-Price methods.

[0360] Numerical optimization solvers use the interior point method or sequential quadratic programming (SQP).

[0361] The cost function is optimized by a numerical optimization solver. However, the calculation of the cost function requires simulating the model with a digital model. This simulation calls a numerical integrator.

[0362] The control assembly (55) will now be described (see also FIG. 1).

[0363] This control assembly (55) includes the following:

[0364] a / Acquisition unit (57) that repeatedly acquires current values ​​of acquired driving parameters;

[0365] b / A computational member (59) configured to generate controls of actuators using current values ​​of acquired operating parameters, at least some of the controls determined using a digital model of the reactor;

[0366] c / Unit for controlling actuators using generated controls (61).

[0367] The acquisition unit (57) is a computer or part of a computer.

[0368] Typically, the acquisition unit (57) is configured to implement step S10 / .

[0369] The calculation member (59) is configured to implement step S20 / .

[0370] The digital model is what was explained above.

[0371] The control unit (61) is configured to implement step S30 / .

[0372] The control assembly (55) also includes at least one estimated digital coefficient belonging to a set of digital coefficients and / or at least one estimated state parameter belonging to a set of state parameters, and an estimation unit (63) of at least one estimated state parameter belonging to a set of state parameters.

[0373] The estimation unit (63) is a computational component. The estimation unit (63) is integrated into the computational component (59). As a variation, the estimation unit (63) is independent.

[0374] The estimation unit (63) is configured to implement the estimation operation described above.

[0375] A first example of the control method of the present invention is illustrated in FIGS. 4 and 5.

[0376] In this example, the digital model includes six levels, i.e., six sub-models. For eight operating parameters, the digital model compares the values ​​simulated by the digital model with the measured values ​​of the same operating parameters: neutron density at the six levels, the temperature of the primary heat transfer fluid in the high-temperature branch of the primary circuit, and the temperature of the primary heat transfer fluid in the low-temperature branch.

[0377] The width of the time window is 1 hour.

[0378] The optimization operation aims to determine two digital coefficients:

[0379] - D: Neutron exchange coefficient between core levels (expressed in Fig. 4);

[0380] - : Conversion coefficient due to neutron absorption of Xenon 135 to Xenon 136 (expressed in Fig. 5).

[0381] The horizontal curve R corresponds to the actual value of the digital coefficient. The curve E corresponds to the continuous estimates obtained using the method of the present invention.

[0382] The scenario considered here corresponds to a transition from 100% output to 70% followed by maintaining that output. This is followed by a return to 100% output and maintaining the output. Finally, the load is reduced to 50% output.

[0383] The two digital coefficients are initialized to values ​​that are very far removed from the actual values, but they are of a plausible magnitude.

[0384] The figures show that the estimates converge rapidly toward the actual values. Variations in the reactor's rated power cause small-amplitude disturbances, but the estimates quickly return to the actual values.

[0385] A second application example of the control method of the present invention is illustrated in FIGS. 6 to 9.

[0386] In this example, the digital model includes six levels, i.e., six sub-models. For 20 operating parameters, the digital model compares the values ​​simulated by the digital model with the measured or simulated values ​​of these operating parameters: neutron density at the six levels, the concentration of Xenon-135 in the nuclear fuel assembly at each level of the core, the concentration of Iodine-135 in the nuclear fuel assembly at each level of the core, the temperature of the primary heat transfer fluid in the high-temperature branch of the primary circuit, and the temperature of the primary heat transfer fluid in the low-temperature branch.

[0387] The width of the time window is 1 hour.

[0388] The optimization operation aims to determine four digital coefficients:

[0389] - D: Neutron exchange coefficient between core levels (expressed in Fig. 6);

[0390] - : Conversion coefficient due to neutron absorption of Xenon 135 to Xenon 136 (expressed in Fig. 7);

[0391] - Kbor and Kxenon (Figs. 8 and 9).

[0392] The horizontal curve R corresponds to the actual value of the digital coefficient. The curve E corresponds to the continuous estimates obtained using the method of the present invention.

[0393] The scenario considered here is the same as in Figures 4 and 5.

[0394] The four digital coefficients are initialized to values ​​that are very far removed from the actual values, but they are of plausible magnitude.

[0395] The figures show that the estimates converge rapidly toward the actual values. Variations in the reactor's rated power cause small-amplitude disturbances, but the estimates quickly return to the actual values.

[0396] A third application example of the control method of the present invention is illustrated in FIG. 10.

[0397] In this example, the digital model includes six levels, i.e., six sub-models. For eight operating parameters, the digital model compares the values ​​simulated by the digital model with the measured values ​​of these operating parameters: neutron density at the six levels, the temperature of the primary heat transfer fluid in the high-temperature branch of the primary circuit, and the temperature of the primary heat transfer fluid in the low-temperature branch.

[0398] The width of the time window is 1 hour.

[0399] The optimization operation aims to determine the xenon 135 densities in each sub-model of the digital model, namely the six xenon densities.

[0400] The scenarios considered are the same as those in Figures 4 and 5. The estimates of these driving parameters are initialized to values ​​that are out of order (15% error) but are of a plausible size.

[0401] Figure 10 illustrates the error in the estimation of Xenon 135 density, that is, the deviation between the value estimated by the digital model and the actual value. This deviation is expressed as a percentage of the actual value. The value shown in Figure 10 is the average of the errors for the six levels of the model. The error is plotted on the vertical axis, and time on the horizontal axis.

[0402] Figure 10 shows that in this case, the normalized estimation error for all xenon densities after only one optimization is of order 1 percent and decreases further over time, so the estimates converge quickly.

[0403] According to another aspect, the present invention relates to a method for calibrating a digital model used to control a nuclear reactor.

[0404] The digital model is what was explained above.

[0405] Calibration is performed independently of reactor control. This means that calibration operations are separated from reactor control and can be performed at any time, for example, before the commissioning of the digital model or while the reactor is shut down.

[0406] The digital model is calibrated using simulated values, referred to as reference values ​​below, instead of current values ​​acquired using sensors mounted on the reactor.

[0407] This calibration method typically aims to determine digital coefficients used by digital models at different operating points of the reactor, particularly during power transients.

[0408] More specifically, the calibration method includes an operation for generating reference values ​​of a plurality of reference operating parameters of a reactor for a time interval I, and an operation for estimating at least one estimated digital coefficient belonging to a set of digital coefficients implemented for a time window [t0; t0+T] (T is the width of the time window) within the time interval I.

[0409] For example, the estimation operation is iteratively implemented for a time window [t0; t0+T] sliding within a time interval I, where T is the width of the time window, and the time window moves in each iteration to sweep the time interval I.

[0410] The generated reference values ​​correspond to the time-dependent changes in the values ​​of the reference driving parameters over the entire time interval I.

[0411] The reference driving parameters are identical to the driving parameters acquired above in relation to step S10, for example.

[0412] Time interval I has a duration of several hours, for example, 24 hours, preferably 12 hours.

[0413] Reference values ​​are generated by an expert system containing software for simulating the operation of the reactor. This expert system is frequently designated by the acronym CMS (Core Monitoring System). This type of CMS, called ARGOS, is integrated into specific reactors. As this expert system is well known, it will not be described in detail here.

[0414] Reference values ​​are generated by considering scenarios for controlling the reactor during time interval I, such as power transient, operation at constant power, or other scenarios.

[0415] At least one estimated digital coefficient is as described above.

[0416] The estimation operation is implemented by repeatedly sliding the time window [t0; t0+T] within the time interval I. The time window moves in each iteration by a time interval of less than 60 minutes, preferably less than 20 minutes, for example, 1 minute.

[0417] The width T of the time window is as described above.

[0418] If the time interval starts at time T1 and ends at time T2, in the first iteration, t0 preferably coincides with T1. In the last iteration, t0+T preferably coincides with T2.

[0419] In other words, the time window sweeps the entire interval I.

[0420] The estimation operation includes the following steps in each iteration:

[0421] S70 / Generation of a generated value of at least one estimated digital coefficient;

[0422] S80 / Determination of simulated values ​​of a group of simulated driving parameters forming part of reference driving parameters using a digital model for a time window [t0; t0+T] by using the generated value of at least one estimated digital coefficient in the digital model;

[0423] S90 / Evaluation of the cost function using reference values ​​and simulated values ​​of a group of simulated driving parameters;

[0424] Steps S70 / , S80 / and S90 / are repeated until the convergence criterion of the cost function is satisfied, and the generated value of at least one estimated digital coefficient that enables satisfying the convergence criterion is retained as an estimate of at least one estimated digital coefficient at time t0+T.

[0425] Step S70 / is performed as in Step S40 / described above.

[0426] Step S80 / is performed as in Step S50 / described above.

[0427] Step S90 / is performed as described above in Step S60 / , using reference values ​​instead of the current values ​​of the group of simulated driving parameters.

[0428] Therefore, the estimation operation makes it possible to determine the change of at least one estimated digital coefficient over the time interval [T1+T; T2], that is, substantially the entire time interval I.

[0429] The value of at least one estimated digital coefficient retained to calibrate the digital model is typically the value determined in the last iteration, i.e., for time T2.

[0430] As a variation, the estimation operation is implemented in a non-repetitive manner, and the time window [t0; t0+T] corresponds to the time interval I.

[0431] In other words, t0 corresponds to T1, t0+T corresponds to T2, and the width T of the time window is equal to the duration of the time interval I.

Claims

Claim 1 A method for controlling a nuclear reactor, wherein the nuclear reactor (1) comprises a pressure vessel (2), a core (3) comprising a plurality of nuclear fuel assemblies (5) arranged within the pressure vessel (2), a primary circuit (7) for cooling the core (3) in which a primary heat transfer fluid containing a neutron poison circulates, and a plurality of actuators acting on the core (3) or the primary circuit (7); the method comprises: acquiring current values ​​of a plurality of acquired operating parameters of the nuclear reactor (S10 / ); generating controls for the actuators using the current values ​​of the acquired operating parameters (S20 / ) - at least some of the controls are determined using a digital model of the nuclear reactor, said digital model is configured to determine the evolution over time of a set of state parameters of the nuclear reactor using a set of controls and digital coefficients provided to the actuators -; The method comprises operations for controlling a reactor through the step (S30 / ) of controlling actuators using the generated controls, wherein the steps (S10 / , S20 / and S30 / ) are implemented iteratively, and the method also comprises an operation for estimating at least one estimated digital coefficient belonging to a set of digital coefficients and / or at least one estimated state parameter belonging to a set of state parameters, wherein the estimation operation is implemented iteratively at time tc in parallel with the control operation, and in each iteration the estimation operation comprises: a step (S40 / ) of generating a generated value of at least one estimated digital coefficient and / or a generated initial value of at least one estimated state parameter; a time window [t0] sliding with tc;A reactor control method comprising the step (S50 / ) of determining simulated values ​​of a group of simulated operating parameters that form part of the operating parameters obtained by using a generated value of at least one estimated digital coefficient in a digital model and / or considering a generated initial value of at least one estimated state parameter at t0 for [t0+T], wherein T is a time window width and the time window is located in the past for tc; and the step (S60 / ) of evaluating a cost function using the current values ​​of the group of simulated operating parameters and the simulated values, wherein the steps (S40 / , S50 / and S60 / ) are repeated until a convergence criterion of the cost function is satisfied, and the generated value of at least one estimated digital coefficient and / or the generated initial value of at least one estimated state parameter that enables satisfying the convergence criterion is retained as an estimate of at least one estimated digital coefficient and / or at least one estimated state parameter at time tc.; Claim 2 A reactor control method according to claim 1, wherein the cost function includes a term corresponding to the deviation between the current values ​​of a group of simulated operating parameters and the simulated values ​​over a time window. Claim 3 A reactor control method according to claim 1 or 2, wherein the cost function comprises a term corresponding to the deviation between the generated value of at least one estimated digital coefficient and the estimate of at least one estimated digital coefficient obtained in a previous iteration. Claim 4 A reactor control method according to any one of claims 1 to 3, wherein the cost function comprises a term corresponding to the deviation between the generated initial value of at least one estimated state parameter and the estimate of at least one estimated state parameter obtained in a previous iteration. Claim 5 A method for controlling a reactor according to any one of claims 1 to 4, wherein the digital model of the reactor comprises a plurality of sub-models, each sub-model models one level of the reactor core and includes at least one equation describing the dynamics of the neutron density at said level and an equation describing the temperature of the primary heat transfer fluid at said level, and the digital model further comprises equations describing the neutron exchange between levels and equations characterizing the reactivity at each level. Claim 6 A method for controlling a reactor, wherein the primary circuit (7) comprises at least one primary loop having a high-temperature branch (BC) and a low-temperature branch (BF) respectively connected to the primary heat transfer fluid outlet and the primary heat transfer fluid inlet of the pressure vessel (2), and the reactor (1) further comprises: - a secondary circuit (9) having a turbine (11); - a steam generator (21) for each of the primary loops having a first side interposed in the primary loop and a second side interposed in the secondary circuit; - a control rod bank (49) for absorbing neutrons; - a mechanism (51) capable of selectively inserting or withdrawing the control rod bank (49) into or from the core (3) of the reactor; - a unit (31) capable of injecting a neutron poison into the primary heat transfer fluid; and - a unit (39) provided for injecting water into the primary circuit. Claim 7 A reactor control method according to claim 6, wherein the equations characterizing the reactivity at each level take into account one or more of: - effects due to a change in the temperature of the primary heat transfer fluid at the level; - effects due to a change in the output provided by the core at the level; - effects due to a movement of the control rod bank; - effects due to a change in the concentration of neutron poison in the primary heat transfer fluid; and - effects due to a change in the concentration of Xenon 135 in the nuclear fuel assembly at the level. Claim 8 A reactor control method according to claim 6 or 7, wherein the state parameters comprise: - for each level of the core, a neutron density at said level, a concentration of xenon 135 in the nuclear fuel assembly at said level, a concentration of iodine 135 in the nuclear fuel assembly at said level; - for each level of the core, a temperature of the primary heat transfer fluid; - a temperature of the primary heat transfer fluid at the inlet and outlet of the core; - a temperature of the primary heat transfer fluid at the high-temperature branch and the low-temperature branch; - a concentration of neutron poison in the primary heat transfer fluid, one or more of the parameters. Claim 9 In any one of paragraphs 6 through 8, each estimated digital coefficient is - : Conversion coefficient due to neutron absorption of Xenon 135 to Xenon 136; - l * : Average lifetime of (immediate and delayed) neutrons within the core;- D: Neutron exchange coefficient between core levels;- Kbor, Kbank, Kxenon: Efficiency coefficients characterizing the contribution to changes in reactivity at each core level, respectively - corresponding to changes in neutron poison concentration in the primary heat transfer fluid, movement of the control rod bank, and changes in the concentration of Xenon-135 in the nuclear fuel assembly at the core level, respectively - ;- : Time constant for temperature exchange between the primary and secondary circuits in a steam generator;- : Time constant of the temperature change of the primary heat transfer fluid along a high-temperature branch;- : Time constant of the temperature change of the primary heat transfer fluid along the low-temperature branch. A reactor control method selected from a list of Claim 10 A reactor control method according to any one of claims 6 to 9, wherein each estimated state parameter is selected from: - for each level of the core, the concentration of xenon 135 in the nuclear fuel assembly at said level, and - for each level of the core, the concentration of iodine 135 in the nuclear fuel assembly at said level. Claim 11 A reactor control method according to any one of claims 6 to 10, wherein at step S50 / , the simulated operating parameters are selected from a list of: - neutron flux at each level of the core; - axial distribution of neutron flux within the core; - temperature of the primary heat transfer fluid in the high-temperature branch and low-temperature branch of the primary circuit; - neutron toxicity concentration in the primary heat transfer fluid; - concentration of xenon 135 in the nuclear fuel assembly at each level of the core, and concentration of iodine 135 in the nuclear fuel assembly at each level of the core. Claim 12 A reactor control method according to any one of claims 6 through 11, wherein the controls of the actuators used by the digital model are: - movement of the control bank; - injection of neutron poison into the primary circuit; - injection of water into the primary circuit; - selection from a list of outputs provided by the turbine. Claim 13 A reactor control method according to any one of claims 1 to 12, wherein in each iteration, the optimization operation is treated as an optimization problem aimed at minimizing a cost function by implementing a numeric integrator and a numeric optimization solver. Claim 14 A reactor comprising a pressure vessel (2), a core (3) comprising a plurality of nuclear fuel assemblies (5) arranged within the pressure vessel (2), a primary circuit (7) for cooling the core (3) in which a primary heat transfer fluid containing a neutron poison circulates, a plurality of actuators acting on the core (3) or the primary circuit (7), and a control assembly (55) of the reactor, wherein the control assembly (55) is configured to implement a control method according to any one of claims 1 to 13. Claim 15 In claim 14, the primary circuit (7) comprises at least one primary loop having a high-temperature branch (BC) and a low-temperature branch (BF) respectively connected to the primary heat transfer fluid outlet and the primary heat transfer fluid inlet of the pressure vessel (2), and the reactor (1) comprises: - a secondary circuit (9) having a turbine (11); - a steam generator (21) for the primary loop or each primary loop, having a first side interposed in the primary loop and a second side interposed in the secondary circuit; - a control rod bank (49) for absorbing neutrons; - a mechanism (51) capable of selectively inserting or withdrawing the control rod bank (49) into or from the core (3) of the reactor; - a unit (31) capable of injecting a neutron poison into the primary heat transfer fluid; and - a unit (39) provided for injecting water into the primary circuit, the reactor. Claim 16 A method for calibrating a digital model used to control a reactor, wherein the reactor (1) comprises a pressure vessel (2), a core (3) comprising a plurality of nuclear fuel assemblies (5) arranged within the pressure vessel (2), a primary circuit (7) for cooling the core (3) in which a primary heat transfer fluid containing a neutron poison circulates, and a plurality of actuators acting on the core (3) or the primary circuit (7); the control of the reactor comprises the steps of: acquiring current values ​​of a plurality of acquired operating parameters of the reactor (S10 / ); and generating controls for the actuators using the current values ​​of the acquired operating parameters (S20 / ) - at least some controls are determined using the digital model, and the digital model is configured to determine a change over time in a set of state parameters of the reactor using a set of controls and digital coefficients provided to the actuators -; The method is performed by a method including the step (S30 / ) of controlling actuators using the generated controls, wherein the steps (S10 / , S20 / and S30 / ) are implemented iteratively, and the calibration method includes an operation for generating reference values ​​of a plurality of reference operating parameters of a reactor for a time interval I, and an operation for estimating at least one estimated digital coefficient belonging to a set of digital coefficients implemented for a time window [t0; t0+T] (T is the width of the time window) within the time interval I, wherein the estimation operation in each iteration comprises: a step (S70 / ) of generating a generated value of at least one estimated digital coefficient; and a step (S80 / ) of determining simulated values ​​of a group of simulated operating parameters that form part of the reference operating parameters using a digital model for a time window [t0; t0+T] by using the generated value of at least one estimated digital coefficient in a digital model.A digital model calibration method used to control a nuclear reactor, comprising the step (S90 / ) of evaluating a cost function using reference values ​​and simulated values ​​of a group of simulated operating parameters, wherein the steps (S70 / , S80 / and S90 / ) are repeated until a convergence criterion of the cost function is satisfied, and the generated value of at least one estimated digital coefficient that enables satisfying the convergence criterion is retained as an estimate of at least one estimated digital coefficient at time t0+T.; Claim 17 A digital model calibration method used to control a reactor, wherein the above-mentioned estimation operation is implemented in a non-repetitive manner, and the time window [t0; t0+T] corresponds to a time interval I. Claim 18 A digital model calibration method used to control a reactor, wherein, in paragraph 16, the estimation operation is implemented in an iterative manner, the time window [t0; t0+T] slides within time interval I, and the time window moves in each iteration to sweep time interval I.

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