Method for controlling a nuclear reactor, nuclear reactor and calibration method

Abstract

Method for controlling a nuclear reactor, nuclear reactor and calibration method. The control method comprises a nuclear reactor control operation with a step of generating actuator commands using a numerical model of the nuclear reactor, and an operation of estimating at least one estimated numerical coefficient belonging to the set of numerical coefficients of the numerical model, implemented in parallel with the control operation. This estimation operation includes a step of determining simulated values ​​of a group of operating parameters using the numerical model, for a sliding time window [t0; t0+T]. Figure for the abstract: 3

Description

Title of the invention: Method for controlling a nuclear reactor, nuclear reactor and calibration method

[0001] The invention relates generally to the control of nuclear reactors.

[0002] The patent applications filed in France under numbers FR 1850867 and FR 2103869 relate to methods for controlling nuclear reactors implementing a predictive digital model configured to determine the evolution over time of a set of state parameters of the nuclear reactor from an initial state, using the commands provided to the actuators. This digital model makes it possible to determine online, i.e., in real time, the best commands according to the operational instructions imposed on the operators.

[0003] Patent applications FR 1850867 and FR 2103869 use a simple and accurate model of the nuclear reactor, suitable for use in predictive control.

[0004] The predictive numerical model must be as accurate as possible to take full advantage of the nuclear reactor's operational margins and ensure a high level of performance. It must be fast, since the controls are updated periodically, for example, at one-minute intervals. The predictive numerical model is used several times during each time interval during the control optimization operation.

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

[0006] To this end, the invention, according to a first aspect, relates to a method for controlling a nuclear reactor, the nuclear reactor having a pressure vessel, a core comprising a plurality of nuclear fuel assemblies arranged in the pressure vessel, a primary core cooling circuit 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, the method comprising a nuclear reactor control operation with the following steps:

[0007] S10 / Acquisition of current values ​​of a plurality of operating parameters acquired from the nuclear reactor;

[0008] S20 / generation of actuator commands using the current values ​​of the operating parameters acquired, at least some commands being determined using a numerical model of the nuclear reactor, the numerical model being configured to determine a time evolution of a set of state parameters of the nuclear reactor using the commands supplied to the actuators and a set of numerical coefficients;

[0009] S30 / control of actuators using generated commands;

[0010] steps S10 / , S20 / and S30 / being implemented iteratively;

[0011] the method also comprising an estimation operation of at least one estimated numerical coefficient belonging to the set of numerical coefficients and / or at least one estimated state parameter belonging to the set of state parameters, implemented iteratively at times tc, in parallel with the control operation, this estimation operation comprising at each iteration the following steps:

[0012] S40 / generation of a generated value of at least one estimated numerical coefficient and / or an initial value generated from at least one estimated state parameter;

[0013] S50 / determination of simulated values ​​of a group of operating parameters simulated as part of the operational parameters acquired, using the numerical model, for a sliding time window [t0 ; t0+T] with tc, T being the width of the time window, the time window being located in the past with respect to tc, using in the numerical model the generated value of at least one estimated numerical coefficient and / or considering at t0 the initial generated value of at least one estimated state parameter;

[0014] S60 / evaluation of a cost function using current values ​​and values simulated from the simulated operating parameter group;

[0015] steps S40 / , S50 / and S60 / being repeated until a convergence criterion of the cost function is satisfied, the generated value of at least one estimated numerical coefficient and / or the generated initial value of at least one estimated state parameter allowing the convergence criterion to be satisfied being retained as an estimate of at least one estimated numerical coefficient and / or at least one estimated state parameter at time tc.

[0016] Thus, the invention makes it possible to periodically update the numerical coefficients of the numerical model used for controlling the nuclear reactor and / or to recalibrate certain state parameters. The operation of estimating the numerical coefficients and / or state parameters is carried out in parallel with the operation of controlling the nuclear reactor, that is to say, concurrently.

[0017] Indeed, in the prior art, certain numerical coefficients are constants obtained by calculation, using assumptions and simplifications that do not correspond to reality, or that are calibrated for specific operating conditions. During the life of the nuclear reactor, these operating conditions change such that the numerical coefficients are no longer representative. For example, there is progressive wear of the nuclear reactor's mechanical systems, particularly for the movement of the core reactivity control units. By Elsewhere, nuclear fuel assemblies are partially renewed every 18 months. Fission products accumulate during this period, which impacts the core's operation.

[0018] The invention makes it possible to periodically re-evaluate these numerical coefficients, so as to guarantee excellent representativeness of the numerical model.

[0019] This re-evaluation is carried out by comparing the current values ​​recorded for certain operating parameters with the values ​​simulated using the numerical model.

[0020] The comparison is performed over a moving time window. In other words, the estimation operation uses a Moving Horizon Estimation (MHE) algorithm. This approach allows the numerical coefficients to be reconstructed quickly, converging after a few iterations to accurate and realistic values.

[0021] This method is adapted to the time constant used for the nuclear reactor control operation. The nuclear reactor commands are typically refreshed at one-minute intervals. The numerical coefficients can also be re-evaluated at one-minute intervals.

[0022] The invention allows for the re-evaluation, in addition to or instead of numerical coefficients, of certain state parameters of the nuclear reactor. These state parameters are typically quantities not available for measurement, such as the concentration of Xenon-135 or Iodine-135 in the nuclear fuel assemblies. These state parameters may be available in, or calculated by, the reactor's instrumentation and control system, but this is not always the case. They affect the numerical results provided by the numerical model, and therefore the commands determined by the control operation.

[0023] The piloting method may also have one or more of the following characteristics, considered individually or according to all technically possible combinations: - the cost function includes a term corresponding to the difference between the actual values ​​and the simulated values ​​of the group of simulated operating parameters over the time window; - the cost function includes a term corresponding to the difference between the generated value of at least one estimated numerical coefficient and the estimate of at least one estimated numerical coefficient obtained in the previous iteration; - the cost function includes a term corresponding to the difference between the initial generated value of at least one estimated state parameter and the estimate of at least one estimated state parameter obtained in the previous iteration; - The numerical model of the nuclear reactor comprises several sub-models, each sub-model modeling a level of the nuclear reactor core and including at least one equation describing the kinetics of a neutron density at said level and an equation describing the temperature of the primary heat transfer fluid at said level, the numerical model further including equations describing neutron exchanges between levels and equations characterizing a reactivity at each level; - the primary circuit comprises at least one primary loop having a hot branch and a cold branch connected respectively to a primary heat transfer fluid outlet and a primary heat transfer fluid inlet of the pressure vessel, the nuclear reactor further comprising:

[0024] - a secondary circuit equipped with a turbine;

[0025] - a steam generator for the primary loop or each primary loop, having a first side one side inserted in the primary loop and a second side inserted in the secondary circuit;

[0026] - groups of neutron-absorbing control bars;

[0027] - a mechanism capable of selectively inserting or extracting groups of bars control in the core of the nuclear reactor;

[0028] - a unit for injecting neutron poison into the heat transfer fluid primary; and - a unit designed to inject water into the primary circuit; - The equations characterizing reactivity at each level take into account one or more of the following effects:

[0029] - effect due to a variation in the temperature of the primary heat transfer fluid level ;

[0030] - effect due to a variation in the power supplied by the heart at said level;

[0031] - effect due to the movement of control bar groups;

[0032] - effect due to a variation in the concentration of neutron poison in the ca fluid primary locomotor;

[0033] - effect due to a variation in the concentration of Xenon 135 in the assemblies of nuclear fuel audit level; - The state parameters include one or more of the parameters from the list below:

[0034] - for each level of the core, neutron density at said level, concentration in Xenon 135 in nuclear fuel assemblies at said level, concentration of Iodine 135 in nuclear fuel assemblies at said level;

[0035] - for each level of the core, temperature of the primary heat transfer fluid;

[0036] - temperature of the primary heat transfer fluid at the inlet and outlet of the core;

[0037] - temperature of the primary heat transfer fluid in the hot branch and in the cold branch; - concentration of neutron poison in the primary heat transfer fluid; - The estimated numerical coefficient(s) is / are chosen from the following list:

[0038] - : neutron absorption transmutation coefficient of Xenon 135 Xenon 136;

[0039] -1* : average lifetime of neutrons in the heart;

[0040] - D: neutron exchange coefficient between core levels;

[0041] - Kbor, Kbank, Kxenon: efficiency coefficients characterizing the contribution in the variation of reactivity at each level of the core respectively of the variation of concentration of neutron poison in the primary coolant, of the displacements of the control rod groups, of the variation of the concentration of Xenon 135 in the nuclear fuel assemblies at said level of the core;

[0042] - 1 gv; time constant of the temperature exchange between the primary circuit and the se secondary within the steam generator;

[0043] - Tbc; time constant for the evolution of the temperature of the heat transfer fluid primary along the warm branch;

[0044] - Thf: time constant for the evolution of the temperature of the heat transfer fluid primary along the cold branch; - The estimated state parameter(s) is / are chosen from the following list:

[0045] - for each core level, concentration of Xenon 135 in the assemblies of nuclear fuel audit level;

[0046] - for each level of the core, concentration of Iodine 135 in the assemblies of nuclear fuel audit level - at step S50 / , the simulated operating parameters are chosen from the following list:

[0047] - neutron flux at each level of the core;

[0048] - axial distribution of neutron flux in the heart;

[0049] - temperature of the primary heat transfer fluid in the hot branch and in the cold branch of the primary circuit;

[0050] - neutron poison concentration in the primary heat transfer fluid;

[0051] - concentration of Xenon 135 in nuclear fuel assemblies each core level, concentration of Iodine 135 in the nuclear fuel assemblies at each core level; - The actuator commands used by the digital model are chosen from the following list:

[0052] - displacement of control groups;

[0053] - injection of neutron poison into the primary circuit;

[0054] - injection of water into the primary circuit;

[0055] - power supplied by the turbine;

[0056] - at each iteration, the optimization operation is treated as a problem optimization aimed at minimizing the cost function, by implementing a numerical integrator and a numerical optimization solver.

[0057] According to a second aspect, the invention relates to a nuclear reactor comprising a pressure vessel, a core comprising a plurality of nuclear fuel assemblies arranged in the pressure vessel, a primary core cooling circuit in which circulates a primary heat transfer fluid containing a neutron poison, a plurality of actuators acting on the core or the primary circuit, and a nuclear reactor control assembly, the control assembly being configured to implement the control method having the above characteristics.

[0058] The nuclear reactor may also have the following characteristics:

[0059] - the primary circuit comprises at least one primary loop having a hot branch and cold branch connected respectively to a primary heat transfer fluid outlet and a primary heat transfer fluid inlet of the pressure vessel, the nuclear reactor further comprising:

[0060] - a secondary circuit equipped with a turbine;

[0061] - a steam generator for the primary loop or each primary loop having a first side one side inserted in the primary loop and a second side inserted in the secondary circuit;

[0062] - groups of neutron-absorbing control bars;

[0063] - a mechanism capable of selectively inserting or extracting groups of bars control in the core of the nuclear reactor;

[0064] - a unit for injecting neutron poison into the heat transfer fluid primary; and

[0065] - a unit intended to inject water into the primary circuit.

[0066] According to a third aspect, the invention relates to a method for calibrating a numerical model used for controlling a nuclear reactor, the nuclear reactor having a pressure vessel, a core comprising a plurality of nuclear fuel assemblies arranged in the pressure vessel, a primary core cooling circuit 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, the control of the nuclear reactor being carried out according to a method comprising the following steps:

[0067] S10 / acquisition of current values ​​of a plurality of operating parameters acquired from the nuclear reactor;

[0068] S20 / generation of actuator commands using the current values ​​of the acquired operating parameters, at least some commands being determined using said numerical model, the numerical model being configured to determine a time evolution of a set of state parameters of the nuclear reactor using the commands supplied to the actuators and a set of nu- coefficients mériques;

[0069] S30 / control of actuators using generated commands;

[0070] steps S10 / , S20 / and S30 / being implemented iteratively;

[0071] The calibration method comprising an operation of generating reference values ​​for a plurality of reference operating parameters of the nuclear reactor for a time interval I, and an operation of estimating at least one estimated numerical coefficient belonging to the set of numerical coefficients, implemented for a time window [t0; t0+T] within the time interval I, T being the width of the time window, this estimation operation comprising at each iteration the following steps:

[0072] S70 / generation of a generated value of at least one estimated numerical coefficient;

[0073] S80 / Determination of simulated values ​​of a group of operating parameters simulated as part of the reference operating parameters, using the numerical model, for the time window [to ; t0+T] using in the numerical model the generated value of at least one estimated numerical coefficient;

[0074] S90 / evaluation of a cost function using reference values ​​and the simulated values ​​of the simulated operating parameter group;

[0075] steps S70 / , S80 / and S90 / being repeated until a convergence criterion of the cost function is satisfied, the generated value of at least one estimated numerical coefficient allowing satisfaction of the convergence criterion being retained as an estimate of at least one estimated numerical coefficient at time to+T.

[0076] The calibration method may also have one or more of the following characteristics, considered individually or in all technically possible combinations:

[0077] - the estimation operation is implemented in a non-iterative manner, the window of time [t0 ; t0+T] corresponding to the time interval I;

[0078] - the estimation operation is implemented iteratively, the time window [tO ; tO+T] sliding inside the time interval I, the time window moving at each iteration and sweeping through the time interval I.

[0079] Other features and advantages will become apparent from the detailed description given below, by way of example and not limitation, with reference to the attached figures, including:

[0080] [Fig-1] [Fig.1] is a schematic representation of a nuclear reactor according to the invention;

[0081] [Fig.2] [Fig.2] is a step diagram illustrating the piloting process of the invention;

[0082] [Fig.3] [Fig.3] is a schematic representation of the digital model of the core of the reactor used in the process of [Fig.2];

[0083] [Fig.4][Fig.5] Figures 4 and 5 are curves, showing for example application of the invention the coefficients D and ^Xe determined by the estimation operation, as a function of time;

[0084] [Fig.6][Fig.7][Fig.8][Fig.9] Figures 6 to 9 are curves, showing for another example of application of the invention the coefficients D, &Xe KBorej and KXenon determined by the estimation operation, as a function of time; and.

[0085] [Fig. 10] The [Fig. 10] is a curve illustrating yet another example of application of the invention, aimed at determining, among other things, a state parameter.

[0086] The reactor 1 shown in [Fig.1] comprises, in a conventional manner, a pressure vessel 2 and a core 3 arranged in the pressure vessel 2. The core 3 itself comprises a plurality of nuclear fuel assemblies 5.

[0087] The nuclear reactor 1 also includes a primary circuit 7, intended for cooling the core 3, in which a primary heat transfer fluid containing a neutron poison circulates.

[0088] The primary circuit 7 includes at least one primary loop having a hot branch BC and a cold branch BF connected respectively to a primary heat transfer fluid outlet and a primary heat transfer fluid inlet of the pressure vessel 2.

[0089] Typically, the primary circuit 7 comprises several primary loops as described above.

[0090] Each primary loop includes a primary pump 8.

[0091] The nuclear reactor 1 still includes a secondary circuit 9.

[0092] A secondary heat transfer fluid circulates in the secondary circuit 9.

[0093] The secondary circuit 9 includes a turbine 11.

[0094] The secondary circuit also includes a condenser 13, a reservoir supply pump 15, and secondary pumps 17, 19.

[0095] The nuclear reactor 1 comprises a steam generator 21 for each primary loop. Its first side is intercalated in said primary loop and its second side in the secondary circuit.

[0096] The hot branch BC connects the outlet of the pressure vessel to the inlet of the first side of the steam generator 21. The cold branch BF connects the discharge of the primary pump 8 to the inlet of the pressure vessel 2.

[0097] The primary heat transfer fluid transfers its heat to the secondary fluid in the steam generator or each steam generator 21.

[0098] The secondary heat transfer fluid is vaporized in the steam generator 21, under the effect of the heat given off by the primary heat transfer fluid.

[0099] The secondary heat transfer fluid in the form of vapor circulates from the steam generator 21 to the turbine 11 and is then condensed in the condenser 13. It is then returned in liquid form to steam generator 21.

[0100] A valve 23 is interposed on the steam line connecting the steam generator 21 to the turbine 11, and allows the flow rate of steam supplying the latter to be regulated.

[0101] The turbine 11 mechanically drives an alternator 25.

[0102] The electricity generated by the alternator 25 supplies an electrical distribution network 29.

[0103] Nuclear reactor 1 further includes a unit 31 for injecting neutron poison into the primary coolant. The neutron poison is typically boron.

[0104] A tank 32 containing a concentrated solution of neutron poison, for example boric acid, is connected to the primary circuit 7 via conduit 33. A pump 35 and a valve 37 are interposed on conduit 33.

[0105] Unit 31 selectively allows the concentration of neutron poison in the primary liquid to be increased.

[0106] The nuclear reactor still includes a unit 39 designed to inject water into the primary circuit.

[0107] Unit 39 includes a tank 41 connected by a line 43 to the primary circuit 7. A pump 45 and a valve 47 are intercalated in the line 43.

[0108] The water is typically pure demineralized water.

[0109] Unit 39 is designed to inject water into the primary circuit 7, which has the effect of reducing the concentration of neutron poison in the primary heat transfer fluid.

[0110] In a conventional manner, the nuclear reactor 1 also includes groups 49 of control rods and a mechanism 51 capable of selectively inserting or extracting the groups of control rods 49 into the core 3 of the nuclear reactor.

[0111] The control bars are made of a neutron-absorbing material.

[0112] The control bar groups are 49 moved so as to selectively modify the reactivity within core 3.

[0113] The nuclear reactor 1 thus comprises a plurality of actuators acting on the core 3 or the primary circuit 7.

[0114] In the example described above, these actuators include the control rod groups 49, the unit 31 for injecting neutron poison into the primary heat transfer fluid, the unit 39 for injecting water into the primary circuit, and the valve 23 for regulating the flow of steam supplying the turbine 11.

[0115] The valve 23 regulates the power supplied by the turbine 11, which indirectly affects the power supplied by the core through the core control devices 3.

[0116] The nuclear reactor 1 also includes instrumentation 53 allowing for the direct measurement or determination of a plurality of operating parameters of the nuclear reactor.

[0117] These operating parameters include, for example, the following parameters:

[0118] - power supplied by the turbine 11;

[0119] - temperature of the primary heat transfer fluid at the inlet and outlet of core 3;

[0120] - temperature of the primary heat transfer fluid in the hot branch BC and in the cold branch BF;

[0121] - position of control bar groups 49;

[0122] - power supplied by the core 3 of the nuclear reactor;

[0123] - neutron flux at different levels of the core 3;

[0124] - distribution of neutron flux in the heart 3;

[0125] - neutron poison concentration in the primary heat transfer fluid.

[0126] Advantageously, the current flow rate of neutron poison and the current flow rate of water injected into the primary heat transfer fluid are also measured or determined.

[0127] The instrumentation 53 includes, in particular, neutron detectors, placed outside the core 3, and distributed along the entire height of the core. These detectors are known as ex-core chambers.

[0128] The power supplied by the core is obtained for example by calculation, based on information provided by detectors measuring neutron fluxes outside the core.

[0129] Alternatively, the power supplied by the core is determined using the measurement of the power supplied by the turbine.

[0130] The parameter characterizing the distribution of neutron flux in the core is, for example, the axial power distribution, or axial offset AO. The axial offset is calculated using the following formula:

[0131] AO = (OM>b) / (Oh+Ob)

[0132] where <e>h is the neutron flux from the upper half of the heart, and <e>b the neutron flux of the lower half of the heart.

[0133] The neutron fluxes of the upper and lower halves of the heart are typically obtained by neutron detectors placed outside the heart 3. Alternatively, they are obtained by probes placed in the heart 3, called in-core probes.

[0134] Alternatively, the parameter characterizing the distribution of neutron flux in the core is <e> h- <e>b, or any other suitable parameter.

[0135] The instrumentation 53 includes temperature measuring probes, arranged to measure the temperature of the heat transfer fluid in the hot and cold branches and in the pressure vessel.

[0136] The instrumentation 53 advantageously includes a sensor measuring directly or indirectly the mechanical power supplied by the turbine.

[0137] The position of the control bar groups 49 is typically determined from information provided by the control bar movement mechanism 51.

[0138] The nuclear reactor 1 also includes a nuclear reactor control unit 55.

[0139] The control assembly is configured to implement the nuclear reactor control process which will now be described.

[0140] As illustrated in [Fig.2], the process comprises a nuclear reactor control operation with the following steps:

[0141] S10 / acquisition of current values ​​of a plurality of operating parameters acquired from the nuclear reactor;

[0142] S20 / generation of actuator commands using the current values ​​of operating parameters acquired, at least some commands being determined using a numerical model of the nuclear reactor, the numerical model being configured to determine a time evolution of a set of state parameters of the nuclear reactor using the commands supplied to the actuators and a set of numerical coefficients;

[0143] S30 / control of actuators using generated commands.

[0144] Steps S10 / , S20 / and S30 / are implemented iteratively.

[0145] Advantageously, steps S20 / and S30 / are repeated with a period of less than sixty minutes, preferably less than twenty minutes, and worth, for example, one minute.

[0146] Step S10 / is repeated with the same period. Alternatively, it is repeated with a longer period. This period may differ depending on the acquired operating parameters.

[0147] The controls are determined to regulate a number of regulated operating parameters of the nuclear reactor to setpoint values.

[0148] The regulated operating parameters are for example the temperature of the primary heat transfer fluid Tmoy, the axial offset AO, the power supplied by the turbine, etc.

[0149] The actuator commands generated in step S20 / are selected from the following list:

[0150] - displacement of control groups;

[0151] - neutron poison injection into the primary circuit;

[0152] - injection of water into the primary circuit;

[0153] - power supplied by the turbine.

[0154] Typically, all commands in the above list are generated at step S20 / .

[0155] The numerical model is used for example to determine all the orders in the list.

[0156] Alternatively, the numerical model is used to determine only certain commands from the list. The other commands are fixed manually, or de completed at step S20 / using control loops independent of the digital model.

[0157] Each control loop is provided in this case to regulate one of the regulated operating parameters, using one of the commands.

[0158] For example, nuclear reactors operating in mode A include a primary coolant temperature control loop. The loop receives as input the current average temperature Tmoy of the primary coolant in the reactor core 3.

[0159] This value corresponds, for example, to the average of the temperature measured at the reactor inlet and the temperature measured at the core outlet.

[0160] The loop also receives the setpoint temperature.

[0161] The average temperature of the primary heat transfer fluid Tmoy in the core is controlled by moving control rod groups 49, according to the difference between the current temperature and the setpoint temperature. Four rod groups, called groups A, B, C, D, can be moved to control the temperature Tmoy.

[0162] In FR1850867, the numerical model is used to determine the displacement of control groups, the injection of neutron poison, and the injection of water. In FR2103869, the numerical model is used to determine the injection of neutron poison and the injection of water.

[0163] The digital model in step S20 / can be used in multiple ways.

[0164] In FR1850867, it is used in combination with a sequenced-gain control algorithm. The numerical model is used to determine the commands. The sequenced-gain control algorithm is used to develop corrective commands. The commands actually applied for driving the actuators are the sum of the commands and the corrective commands.

[0165] In FR2103869, the numerical model is used to determine, during power transients, optimized sequences for injecting neutron poison or water.

[0166] Other uses of the digital model can be envisaged.

[0167] The digital model uses all the commands from the list above. Alternatively, it uses only some of the commands from the list above.

[0168] The numerical model of the core of the nuclear reactor is a so-called predictive model.

[0169] The numerical model of the nuclear reactor core is a non-linear model. In Alternatively, the numerical model is linear. This numerical model is then obtained, for example, by linearizing the non-linear model described below.

[0170] This digital model is illustrated schematically in [Fig.3].

[0171] The digital model of the heart comprises several sub-models, each sub- modeling a level of core 3.

[0172] In other words, the core is divided, along the vertical direction, into several slices, each sub-model modeling one of the core slices.

[0173] Typically, the numerical model of the core comprises between two and twenty sub-models, preferably between two and ten sub-models, and includes, for example, six sub-models.

[0174] Each sub-model includes at least one equation describing the kinetics of a neutron density in said level, and one equation describing a temperature of the primary heat transfer fluid in said level.

[0175] The temperatures T2 to T7 at the outlet of each level are deduced from the neutron flux in each level.

[0176]

[0177]

[0178] The equations are shown below: Level 1: T -T in A2— Qp nl

[0179] dn, Pt D

[0180]

[0181] Level i: T — T + KtihKv nh - L-1+ Qp n / -l

[0182] dn, P; -r = - n,-1 + ni+1 dt i > i \ ti 1+1 /

[0183]

[0184] Highest level: T7 = T6+-q— n6

[0185] ,D„ ~ --n6+-n5

[0186]

[0187]

[0188]

[0189]

[0190]

[0191]

[0192]

[0193]

[0194]

[0195]

[0196] with: - n; : neutron density at level i ; -p;: reactivity at level i - D : neutron exchange coefficient ; -1* : mean lifetime of neutrons (prompt and delayed) ; - Kt / h : temperature / enthalpy conversion coefficient ; - Kn : power / neutron flux conversion coefficient ; - Qp : mass flow rate of primary heat transfer fluid in the core.- Tl, T7: temperature at the inlet and outlet of the core; - Ti: temperature of the primary heat transfer fluid at each level; The temperature at each level corresponds here to the temperature at the inlet of that level.

[0197] Thus, each level of the core is modeled using a one-group approximation of point neutron kinetics with, in addition, a coefficient D for . to account for neutron exchanges between levels.

[0198] Delayed neutrons and precursors, which have a faster dynamic range than expected by the process or the operator, are not modeled. These neutrons have a typical dynamic range of 10 seconds, for a computation time step of approximately 60 seconds.

[0199] The numerical model also includes equations characterizing the reactivity at each level

[0200] These equations take into account one or more of the following effects:

[0201] - effect due to a variation in the temperature of the primary heat transfer fluid level (also called moderating effect);

[0202] - effect due to a variation in the power supplied by the heart at said level (effect Doppler);

[0203] - effect due to the movement of the control bar groups;

[0204] - effect due to a variation in neutron poison concentration in the ca fluid primary locomotor;

[0205] - effect due to a variation in the concentration of Xenon 135 in the assemblies of Nuclear fuel audit level.

[0206] The equations are as follows:

[0207] p. — p.. + A p ,+ A p, + A p, , 4- A p + A p LJ i iP 1 mod ' dop bank 1 bor ' xenon

[0208] with

[0209] ^p^k^at,

[0210] Ap dop = K dop AP i

[0211] A pbank = Kbank A Pbanki

[0212] A pbor = Kbor A Cpn

[0213] A Pxenon — K xenon A Xi^

[0214] Al — pp _ J j dt ~LIri AIli [02151 =rXep.+(4,,+^.)¾.

[0216] where

[0217] - pio: initial reactivity at level i, determined at the previous time step;

[0218] - P; : thermal power supplied by level i of the core, assumed to be proportional to neutron density;

[0219] - Xe; : concentration of Xenon 135 in nuclear fuel assemblies at level i;

[0220] - P: Iodine-135 concentration in nuclear fuel assemblies at level i;

[0221] - Ti: coefficient of production of Iodine 135 by fission;

[0222] - Xi: decay constant of Iodine 135 in Xenon 135;

[0223] - TXe: Xenon 135 production coefficient by fission;

[0224] - XX: decay constant of Xenon 135;

[0225] - ^Xe ■ neutron absorption transmutation coefficient of Xenon 135 in Xenon 136

[0226] - Kmod, Kdop, Kbor, Kbank, Kxenon: efficiency coefficients characterizing the contribution in the variation of reactivity at each level of the core respectively of the variation of temperature, variation of the power supplied by the core, of the variation of the concentration of neutron poison in the primary coolant, of the displacements of the control rod groups, of the variation of the concentration of Xenon 135 in the nuclear fuel assemblies at said level of the core.

[0227] In the equations above, A denotes a variation with respect to the previous time step.

[0228] The effect due to the variation of the power supplied by the core makes it possible to characterize the effect of a variation in the temperature of the nuclear fuel, also called the Doppler effect.

[0229] The evolution of Xenon 135 at each level is modeled using classical equations taking into account:

[0230] - the production of Iodine 135 by fission;

[0231] - the radioactive decay of Iodine 135 into Xenon 135;

[0232] - the production of Xenon 135 by fission;

[0233] - the radioactive decay of Xenon 135;

[0234] - the transmutation of Xenon 135 into Xenon 136 by neutron absorption.

[0235] APbanki corresponds to the displacement of all control groups within level i, expressed in steps. This parameter corresponds to the sum of the variations in the number of insertion steps in level i for all control groups.

[0236] AP; is obtained by the following equation:

[0237] AP; = Kn x An;, where Kn is a predetermined constant.

[0238] Furthermore, the numerical model incorporates the following general equation:

[0239] P=KnEni

[0240] P being the total power supplied by the core.

[0241] The evolution over time of the total power supplied by the core is typically imposed by the electricity distribution network manager.

[0242] The value of the APbank is determined by the numerical model, as a function of the evolution of the average temperature Tmoy of the primary heat transfer fluid in the core. The numerical model first determines the value of Tmoy according to the following equation:

[0243] Tmoy = (Tl + T7) / 2.

[0244] Then, the numerical model determines a reference mean temperature Tref, based on parameters such as the desired reactor power. This data is available in the reactor control system. It is typically imposed by the electricity distribution network operator 29.

[0245] The numerical model then determines the difference ATmoy between Tmoy and the average reference temperature Tref.

[0246] If Tmoy falls outside the temperature dead band, i.e., if ATmoy exceeds a predetermined threshold value, the numerical model sets the value of Tmoy at the dead band limit and determines that it is necessary to move the control groups. It calculates a value of APbank as a function of ATmoy, allowing criticality to be reached.

[0247] The reference temperature values ​​and the temperature deadband width as a function of reactor power are predetermined values, recorded in the numerical model, or are provided by the control assembly 55.

[0248] ACpn is obtained by integrating the quantities of neutron poison and / or water injected into the primary heat transfer fluid. The numerical model uses the following equations for this purpose:

[0249] dCpn / dt = - Cpn x Qw / Mt for a water injection;

[0250] dCpn / dt = (Crea - Cpn) x Qpn / Mt for a neutron poison injection,

[0251] with Mt total mass of water in the primary circuit, for example 260 tonnes for a tranche N4, Créa neutron poison concentration in the injected neutron poison solution, Cpn current neutron poison concentration in the primary heat transfer fluid, Qw injected demineralized water flow rate, Qpn injected neutron poison solution flow rate.

[0252] A delay is considered to evaluate the effect of the injection of demineralized water or neutron poison.

[0253] The value of Qp, i.e. the flow rate of primary heat transfer fluid in the core, is a predetermined value.

[0254] Alternatively, it is retrieved from pilot assembly 55.

[0255] The numerical model also includes equations modeling the evolution of temperatures in the cold and hot branches: [°2561 "L = (T^-K x Pvilp-Tbf ) [°2571 T^CTa-T,) [°2581 =

[0259] - Tbf and Tbc are the temperatures of the primary heat transfer fluid in the branches cold and hot;

[0260] -Tbf, Tbc and T| are the time derivatives of Tbf, Tbc and Ti;

[0261] - K is a constant;

[0262] - Pvap is the power extracted by the value generators;

[0263] - 1 gv; time constant of the temperature exchange between the primary circuit and the se secondary within the steam generator;

[0264] - Tbc; time constant for the evolution of the temperature of the heat transfer fluid primary along the warm branch;

[0265] - Thf: time constant for the evolution of the temperature of the heat transfer fluid primary along the cold branch.

[0266] The numerical coefficients used in the numerical model are therefore KT / H, Kn K mod, Kdop, Kbor, Kbank, Kxenon, D, G, Txe and 1*, Tq, , Tbc, Tbf.

[0267] The operating parameters whose current values ​​are acquired in step S10 / are chosen from the following list:

[0268] - neutron flux at each level n; of the core;

[0269] - axial distribution of neutron flux in the heart;

[0270] - temperature of the primary heat transfer fluid in the hot branch and in the cold branch of the primary circuit;

[0271] - neutron poison concentration in the primary heat transfer fluid;

[0272] - Xenon-135 concentration in nuclear fuel assemblies at each level of the core, concentration of Iodine 135 in the nuclear fuel assemblies at each level of the core.

[0273] Typically, the current values ​​of all the above parameters are acquired.

[0274] Alternatively, only the current values ​​of a part of these parameters are acquired.

[0275] The neutron flux at each level of the core is provided directly by the neutron detectors of instrumentation 53 distributed along the height of the core. Alternatively, it is calculated from the information provided by the neutron detectors.

[0276] The axial distribution of the neutron flux in the core is provided by the instrumentation 53. This distribution corresponds, for example, to the axial offset.

[0277] The temperature of the primary heat transfer fluid in the hot branch and in the cold branch of the primary circuit and the concentration of neutron poison in the primary heat transfer fluid are provided directly by the instrumentation 53.

[0278] The Xenon-135 concentration and the Iodine-135 concentration in the nuclear fuel assemblies at each core level are typically retrieved in the control unit 55. This control unit 55, in some nuclear reactors, includes an expert system configured to determine, among other things, these Xenon-135 and Iodine-135 concentrations. This expert system is designated by the acronym CMS (Core Monitoring System). When these concentrations are not available, they are preferably estimated by operation estimation, as described below.

[0279] The state parameters include one or more of the parameters from the list below:

[0280] - for each level of the core, neutron density at said level n, concentration in Xenon 135 Xe; in nuclear fuel assemblies at said level, concentration of Iodine 135 h in nuclear fuel assemblies at said level;

[0281] - for each level of the core, temperature of the primary heat transfer fluid T; ;

[0282] - temperature of the primary heat transfer fluid at the inlet and outlet of the T7 core;

[0283] - temperature of the primary heat transfer fluid in the hot branch and in the cold branch TBc, TBF;

[0284] - neutron poison concentration in the primary heat transfer fluid Cpn.

[0285] Typically, all the above parameters are state parameters.

[0286] Alternatively, only some of the above parameters are state parameters.

[0287] At step S30 / , the commands generated at step S20 / are used to control the corresponding actuators.

[0288] The S30 / step is completely automatic, the actuators being controlled by a computer without intervention from an operator.

[0289] Alternatively, at least some of the actuators are manually controlled at step S30 / . The commands generated at step S20 / constitute decision aids, i.e. recommendations, for the operators controlling the nuclear reactor.

[0290] The method also includes an estimation operation of at least one estimated numerical coefficient belonging to the set of numerical coefficients and / or at least one estimated state parameter belonging to the set of state parameters, implemented iteratively at times tc, in parallel with the control operation.

[0291] This estimation operation includes the following steps at each iteration:

[0292] S40 / generation of a generated value of at least one estimated numerical coefficient and / or an initial value generated from at least one estimated state parameter;

[0293] S50 / determination of simulated values ​​of a group of operating parameters simulated as part of the operational parameters acquired, using the numerical model, for a sliding time window [t0 ; t0+T] with tc, T being the width of the time window, the time window being located in the past with respect to tc, using in the numerical model the generated value of at least one estimated numerical coefficient and / or considering at t0 the initial generated value of at least one estimated state parameter;

[0294] S60 / evaluation of a cost function using current values ​​and values simulated operating parameters.

[0295] Steps S40 / , S50 / and S60 / are repeated until a convergence criterion of the cost function is satisfied, the generated value of at least one estimated numerical coefficient and / or the generated initial value of at least one estimated state parameter that satisfies the convergence criterion being retained as an estimate of at least one estimated numerical coefficient and / or at least one estimated state parameter at time tc.

[0296] The estimation operation is performed simultaneously with the control operation. It allows for real-time correction of the numerical coefficients or state variables used in the numerical model for the control operation of the nuclear reactor.

[0297] The estimation operation is carried out iteratively, with a period of less than sixty minutes, preferably less than twenty minutes, and worth, for example, one minute.

[0298] The estimation operation aims to estimate, for example, only at least one numerical coefficient.

[0299] Alternatively, it aims to estimate belonging to both at least one numerical coefficient and at least one state parameter.

[0300] Indeed, the accuracy of the numerical model relies in part on a detailed knowledge of the state parameters. It sometimes happens that certain state parameters are not available, either through the instrumentation or more generally in the nuclear reactor control system.

[0301] In this case, one or more of these state parameters are advantageously determined during the estimation operation.

[0302] According to another, less frequent alternative, only one or more state parameters are determined by the estimation operation.

[0303] The estimated numerical coefficient or coefficients are preferably chosen from the following list:

[0304] - ^Xe: neutron absorption transmutation coefficient of Xenon 135 in Xenon 136;

[0305] -1* : average lifetime of neutrons (prompt and delayed) in the heart;

[0306] - D: neutron exchange coefficient between core levels;

[0307] - Kbor, Kbank, Kxenon: efficiency coefficients characterizing the contribution in the variation of reactivity at each level of the core respectively of the variation of concentration of neutron poison in the primary coolant, of the displacements of the control rod groups, of the variation of the concentration of Xenon 135 in the nuclear fuel assemblies at said level of the core;

[0308] - tgv ; time constant of the temperature exchange between the primary circuit and the se secondary within the steam generator;

[0309] - rix; time constant for the evolution of the temperature of the heat transfer fluid primary along the warm branch;

[0310] - Tbf: time constant for the evolution of the temperature of the heat transfer fluid primary along the cold branch.

[0311] The estimated state parameter(s) is preferably chosen from the following list:

[0312] - for each core level, concentration of Xenon 135 Xe; in the assemblies nuclear fuel audit level

[0313] - for each level of the core, concentration of Iodine 135 f in the assemblies of Nuclear fuel audit level.

[0314] Typically, the estimation operation is configured to estimate all the numeric coefficients from the above list and all the state parameters from the above list.

[0315] To limit computation time, the variant estimation operation is configured to estimate:

[0316] - only between 1 and 9 of the numerical coefficients above, preferably between 1 and 7, preferably between 1 and 4; or

[0317] - only between 1 and 35 of the above state parameters, preferably between 1 and 8, preferably between 1 and 4;

[0318] - both between 1 and 9 of the numerical coefficients above and between 1 and 35 of the pa state parameters above, preferably between 1 and 7 of the numerical coefficients above and between 1 and 24 of the state parameters above, again preferably between 1 and 4 of the numerical coefficients above and between 1 and 12 of the state parameters above.

[0319] At step S50 / , the simulated operating parameters are chosen from the following list: - neutron flux at each level n; of the heart; - axial distribution of neutron flux in the heart; - temperature of the primary heat transfer fluid in the hot branch and in the cold branch of the primary circuit; - concentration of neutron poison in the primary heat transfer fluid; - Xenon-135 concentration in nuclear fuel assemblies at each level of the core, Iodine-135 concentration in nuclear fuel assemblies at each level of the core.

[0320] Typically, at step S50 / , the group of simulated operating parameters includes all the operating parameters from the list above. Alternatively, the group of simulated operating parameters includes only some of the operating parameters from the list above.

[0321] The numerical model is used to determine the evolution over time of the simulated values ​​over the time window [t0 ; to+T].

[0322] The width T of the time window is between 15 and 24 hours, preferably between Oh3O and lh30, and is equal for example to Ih.

[0323] The instant to+T corresponds for example to the instant tc.

[0324] Alternatively, the time t0+T is shifted in the past relative to tc, typically by a few minutes.

[0325] The time window is sliding in the sense that it moves in time with the instant tc. It always has the same time offset with respect to the instant tc.

[0326] As indicated above, the numerical model uses at step S50 / the generated value of at least one estimated numerical coefficient and / or considers at t0 the generated initial value of at least one estimated state parameter.

[0327] The other numerical coefficients used are predetermined constants.

[0328] The initial values ​​of the other state parameters are typically those obtained by the simulation at the previous iteration.

[0329] The numerical model at step S50 / uses the values ​​of the commands actually applied during the time window [to ; t0+T].

[0330] The cost function used in step S60 / includes a term corresponding to the difference between the actual values ​​and the simulated values ​​of the group of simulated operating parameters over the time window.

[0331] Advantageously, the cost function also includes a term corresponding to the difference between the generated value of the at least one estimated numerical coefficient and the estimate of the at least one estimated numerical coefficient obtained in the previous iteration.

[0332] This term is only useful when the estimation operation aims to estimate at least one numerical coefficient.

[0333] The cost function preferably includes a term corresponding to the difference between the initial generated value of at least one estimated state parameter and the estimate of at least one estimated state parameter obtained in the previous iteration.

[0334] This term is only useful when the estimation operation aims to estimate at least one state parameter.

[0335] For example, the cost function is as follows: [03361 to do+^ n He "H Ib'Mh(x(r)) He R Dr.

[0337] Where J is the cost function;

[0338] x is the state parameter vector;

[0339] X is the state parameter vector, containing the initial value generated for the or the estimated state parameters and the value at t0 estimated at the previous iteration for the other state parameters;

[0340] p is the vector of the estimated numerical coefficient(s) obtained in the previous iteration;

[0341] p is the vector containing the generated values ​​of the estimated numerical coefficient(s);

[0342] y(r) is the vector of current values ​​of the group of measured operating parameters;

[0343] h(x(r)) is the vector of simulated values ​​of the group of operating parameters simulated;

[0344] || a || $ , || a || , and || a || R are norms such that || £ || — tl ■> °where a is a vector with n components and Sx is a matrix of size nxn.

[0345] Sx, Sp, and R are matrices used to weight the contribution of the different terms in the cost function. For large Sx, the difference between the state parameters determined in the current solution of the problem and the previously calculated state parameters is heavily penalized (used if there is confidence in this estimate). If little confidence is placed in the previous estimate, the weighting can be less significant. Sp plays the same role for the numerical coefficients of the numerical model. R penalizes the differences between the operational parameters simulated by the numerical model and the measured operational parameters. R is generally chosen based on considerations relating to the nature of the measurement uncertainties (accuracy of the instrumentation devices, etc.). Sx and Sp are adjusted by the designer to obtain the best possible estimation results.

[0346] As stated above, steps S40 / , S50 / and S60 / are repeated until a convergence criterion of the cost function is satisfied.

[0347] More precisely, at each iteration, the optimization operation is treated as an optimization problem aimed at minimizing the cost function J, by implementing a numerical integrator and a numerical optimization solver.

[0348] The optimization problem is first transcribed into a non-linear programming (NLP, Non Linear Programming) problem by a discretization method.

[0349] This discretization method is a single-shot method, a multiple-shot method, or a direct collocation method.

[0350] The nonlinear programming problem is solved using a digital integrator capable of processing so-called stiff systems by implementing an appropriate method: collocation, multistep linear method, Euler method, Range-Kutta method, Dormand-Price method.

[0351] The numerical optimization solver uses the interior point method or sequenced quadratic programming (SQP).

[0352] The cost function is optimized by the numerical optimization solver. However, calculating the cost function requires simulating the model with the numerical model. This simulation uses the digital integrator.

[0353] The control assembly 55 will now be described (see also [Fig.1]).

[0354] This control assembly 55 includes:

[0355] a / an acquisition unit 57 iteratively acquiring the current values ​​of the acquired operating parameters;

[0356] b / a computing unit 59 configured to generate actuator commands using current values ​​of acquired operating parameters, at least some commands being determined using the numerical model of the nuclear reactor;

[0357] c / a unit 61 for controlling the actuators using the generated commands.

[0358] The acquisition unit 57 is a computer, or part of a computer.

[0359] Typically, the acquisition unit 57 is configured to implement step S10 / .

[0360] The computing unit 59 is configured to implement step S20 / .

[0361] The numerical model is that described above.

[0362] The control unit 61 is configured to implement step S30 / .

[0363] The control assembly 55 also includes an estimation unit 63 of at least one estimated numerical coefficient belonging to the set of numerical coefficients and / or of at least one estimated state parameter belonging to the set of state parameters.

[0364] The estimation unit 63 is a calculating element. It is integrated into the calculating element 59. Alternatively, it is independent.

[0365] Estimation unit 63 is configured to implement the estimation operation described above.

[0366] A first example of application of the control method of the invention has been shown in Figures 4 and 5.

[0367] In this example, the numerical model has six levels, i.e. six sub-models. It compares the values ​​simulated by the numerical model of eight operating parameters with the measurements of these same operating parameters: the neutron densities at the six levels, the temperature of the primary heat transfer fluid in the hot branch and the temperature of the primary heat transfer fluid in the cold branch of the primary circuit.

[0368] The width of the time window is one hour.

[0369] The optimization operation aims to determine two numerical coefficients:

[0370] - D: neutron exchange coefficient between core levels (represented on the [Fig.4]);

[0371] - &xe: neutron absorption transmutation coefficient of Xenon 135 in Xenon 136 (shown in [Fig.5]).

[0372] The horizontal curve R corresponds to the actual value of the numerical coefficient. The curve E corresponds to the successive estimates obtained using the method of the invention.

[0373] The scenario considered here corresponds to a decrease from 100% power to 70% with a plateau at this power level. Then a return to 100% power and a plateau at this power level. Finally, a decrease in load to 50% power.

[0374] The two numerical coefficients are initialized to values ​​very far from the real values, but of a plausible order of magnitude.

[0375] The figures show that the estimates converge rapidly to the actual values. Variations in the reactor's rated power induce small perturbations, but the estimates quickly return to the actual values.

[0376] A second example of application of the control method of the invention has been shown in Figures 6 to 9.

[0377] In this example, the numerical model has six levels, i.e. six sub-models. It compares the values ​​simulated by the numerical model of twenty operating parameters with the measurements or simulation of these operating parameters: the neutron densities at the six levels, the concentrations of Xenon 135 in the nuclear fuel assemblies at each level of the core, the concentrations of Iodine 135 in the nuclear fuel assemblies at each level of the core, the temperature of the primary coolant in the hot branch and the temperature of the primary coolant in the cold branch of the primary circuit.

[0378] The width of the time window is one hour.

[0379] The optimization operation aims to determine four numerical coefficients:

[0380] - D: neutron exchange coefficient between core levels (represented on the [Fig.6])

[0381] - ^Xe: neutron absorption transmutation coefficient of Xenon 135 in Xenon 136 (represented in [Fig.7]);

[0382] - Kbor and Kxenon (figures 8 and 9).

[0383] The horizontal curve R corresponds to the actual value of the numerical coefficient. The curve E corresponds to the successive estimates obtained using the method of the invention.

[0384] The scenario considered here is the same as in Figures 4 and 5.

[0385] The four numerical coefficients are initialized to values ​​very far from the real values, but of plausible orders of magnitude.

[0386] The figures show that the estimates converge rapidly to the actual values. Variations in the reactor's rated power induce small perturbations, but the estimates quickly return to the actual values.

[0387] A third example of application of the control method of the invention is illustrated in [Fig. 10].

[0388] In this example, the numerical model has six levels, i.e., six sub-models. It compares the values ​​simulated by the numerical model of eight operating parameters with the measurements of these operating parameters: the neutron densities at the six levels, the temperature of the primary heat transfer fluid in the hot branch and the temperature of the primary heat transfer fluid in the cold branch of the primary circuit.

[0389] The width of the time window is one hour.

[0390] The optimization operation aims to determine the xenon 135 densities in each sub-model of the numerical model, i.e. six xenon densities.

[0391] The scenario considered is the same as in Figures 4 and 5. The estimates of these operating parameters are initialized to values ​​that are wide (15% error) but of a plausible order of magnitude.

[0392] Figure 10 illustrates the error in estimating the density of xenon-135, that is, the difference between the value estimated by the numerical model and the actual value. This difference 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 on the y-axis, and time is on the x-axis.

[0393] Fig. 10 shows in this case that the estimates converge rapidly since after a single optimization, the normalized estimation error for all xenon densities is on the order of one percent, and decreases further over time.

[0394] According to another aspect, the invention relates to a method for calibrating a numerical model used for controlling a nuclear reactor.

[0395] The numerical model is that described above.

[0396] Calibration is performed independently of the control of the nuclear reactor. This means that the calibration operation is decoupled from the control of the nuclear reactor and can be carried out at any time, for example before the commissioning of the numerical model, or while the nuclear reactor is shut down.

[0397] The numerical model is calibrated using simulated values, referred to below as reference values, instead of actual values ​​acquired using sensors equipping the nuclear reactor.

[0398] This calibration process typically aims to determine the numerical coefficients used by the numerical model at different operating points of the nuclear reactor, particularly during power transients.

[0399] More specifically, the calibration method comprises an operation of generating reference values ​​for a plurality of reference operating parameters of the nuclear reactor for a time interval I, and an operation of estimating at least one estimated numerical coefficient belonging to the set of numerical coefficients, implemented for a time window [t0; t0+T] within the interval of time I, T being the width of the time window.

[0400] For example, the estimation operation is implemented iteratively for a sliding time window [t0 ; t0+T] within the time interval I, T being the width of the time window, the time window moving at each iteration and sweeping through the time interval I.

[0401] The reference values ​​generated correspond to the evolution over time of the values ​​of the reference operating parameters over the entire time interval I.

[0402] The reference operating parameters are for example the same as the acquired operating parameters described above with reference to step S10 / .

[0403] The time interval I has a duration of several hours, for example 24 hours and preferably 12 hours.

[0404] The reference values ​​are generated by an expert system, comprising software for simulating the operation of the nuclear reactor. This expert system is frequently referred to by the acronym CMS (Core Monitoring System). A CMS of this type, called ARGOS, is integrated into some nuclear reactors. This expert system is well-known and will not be described in detail here.

[0405] The reference values ​​are generated by considering a nuclear reactor control scenario during the time interval I, for example a power transient, or constant power operation, or any other scenario.

[0406] The at least one estimated numerical coefficient is such as described above.

[0407] The estimation operation is implemented by iteratively sliding the time window [t0 ; t0+T] in the time interval I. The time window moves at each iteration by a time step less than 60 minutes, preferably less than 20 minutes, for example worth 1 minute.

[0408] The width T of the time window is as described above.

[0409] If the time interval starts at time T1 and ends at time T2, at the first iteration t0 preferably coincides with TL. At the last iteration, t0+T preferably coincides with T2.

[0410] In other words, the time window sweeps the entire interval I.

[0411] The estimation operation comprising the following steps at each iteration:

[0412] S70 / generation of a generated value of at least one estimated numerical coefficient;

[0413] S80 / determination of simulated values ​​of a group of operating parameters simulated as part of the reference operating parameters, using the numerical model, for the time window [to ; t0+T], using in the numerical model the generated value of at least one estimated numerical coefficient;

[0414] S90 / evaluation of a cost function using reference values ​​and the simulated values ​​of the simulated operating parameter group;

[0415] steps S70 / , S80 / and S90 / being repeated until a convergence criterion of the cost function is satisfied, the generated value of at least one estimated numerical coefficient allowing to satisfy the convergence criterion being retained as an estimate of at least one estimated numerical coefficient at time to+T.

[0416] Step S70 / is performed as step S40 / described above.

[0417] Step S80 / is performed as step S50 / described above.

[0418] Step S90 / is performed as step S60 / described above, using the reference values ​​instead of the current values ​​of the simulated operating parameter group.

[0419] The estimation operation therefore makes it possible to determine the evolution of at least one numerical coefficient estimated in the time interval [T1+T; T2], that is to say practically over the entire time interval I.

[0420] The value of at least one estimated numerical coefficient retained to calibrate the numerical model is typically the value determined at the last iteration, i.e. for now T2.

[0421] Alternatively, the estimation operation is implemented in a non-iterative manner, the time window [t0 ; t0+T] corresponding to the time interval I.

[0422] In other words, t0 coincides with T1, t0+ T coincides with T2, the width T of the time window being equal to the duration of the time interval I.< / e> < / e> < / e> < / e>

Claims

Demands

1. A method for controlling a nuclear reactor, the nuclear reactor (1) having a pressure vessel (2), a core (3) comprising a plurality of nuclear fuel assemblies (5) arranged in the pressure vessel (2), a primary circuit (7) for cooling the core (3) through which circulates a primary coolant containing a neutron poison, and a plurality of actuators acting on the core (3) or the primary circuit (7), the method comprising a nuclear reactor control operation with the following steps: S10 / acquisition of current values ​​of a plurality of operating parameters acquired from the nuclear reactor; S20 / generation of actuator commands using current values ​​of acquired operating parameters, at least some commands being determined using a numerical model of the nuclear reactor, the numerical model being configured to determine a time evolution of a set of state parameters of the nuclear reactor using the commands supplied to the actuators and a set of numerical coefficients; S30 / control of the actuators using the generated commands; steps S10 / , S20 / and S30 / being implemented iteratively; the method also comprising an estimation operation of at least one estimated numerical coefficient belonging to the set of numerical coefficients and / or at least one estimated state parameter belonging to the set of state parameters, implemented iteratively at times tc, in parallel with the control operation, this estimation operation comprising at each iteration the following steps: S40 / generation of a generated value of at least one estimated numerical coefficient and / or an initial generated value of at least one estimated state parameter; S50 / Determination of simulated values ​​of a group of simulated operating parameters that are part of the acquired operating parameters, using the numerical model, for a sliding time window [t0; t0+T] with tc, where T is the width of the time window, the time window being located in the past relative to tc, using in the numerical model the generated value of at least one estimated numerical coefficient and / or considering at t0 the initial generated value of at least an estimated state parameter; S60 / evaluation of a cost function using current values ​​and simulated values ​​of the simulated operating parameter group; steps S40 / , S50 / and S60 / being repeated until a convergence criterion of the cost function is satisfied, the generated value of at least one estimated numerical coefficient and / or the generated initial value of at least one estimated state parameter that satisfies the convergence criterion being retained as an estimate of at least one estimated numerical coefficient and / or at least one estimated state parameter at time tc.

2. A control method according to claim 1, wherein the cost function includes a term corresponding to the difference between the actual values ​​and the simulated values ​​of the group of simulated operating parameters over the time window.

3. A piloting method according to claim 1 or 2, wherein the cost function includes a term corresponding to the difference between the generated value of at least one estimated numerical coefficient and the estimate of at least one estimated numerical coefficient obtained in the previous iteration.

4. A control method according to any one of claims 1 to 3, wherein the cost function includes a term corresponding to the difference between the initial generated value of at least one estimated state parameter and the estimate of at least one estimated state parameter obtained in the previous iteration.

5. A control method according to any one of the preceding claims, wherein the numerical model of the nuclear reactor comprises several sub-models, each sub-model modeling a level of the nuclear reactor core and comprising at least one equation describing a kinetics of a neutron density at said level and an equation describing a temperature of the primary coolant at said level, the numerical model further comprising equations describing neutron exchanges between levels and equations characterizing a reactivity at each level.

6. A control method according to claim 5, wherein the primary circuit (7) comprises at least one primary loop having a hot branch (BC) and a cold branch (BF) connected respectively to a primary heat transfer fluid outlet and a primary heat transfer fluid inlet of the pressure vessel (2), the reactor

7.

8. nuclear (1) further comprising: - a secondary circuit (9) equipped with 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; - groups of control bars (49) absorbing neutrons; - a mechanism (51) capable of selectively inserting or extracting the control rod groups (49) into the core (3) of the nuclear reactor; - a unit (31) for injecting neutron poison into the primary heat transfer fluid; and - a unit (39) intended for injecting water into the primary circuit. A control method according to claim 6, wherein the equations characterizing the reactivity at each level take into account one or more of the following effects: - effect due to a variation in the temperature of the primary heat transfer fluid at said level; - effect due to a variation in the power supplied by the heart at that level; - effect due to the movement of control bar groups; - effect due to a variation in the concentration of neutron poison in the primary heat transfer fluid; - effect due to a variation in the concentration of Xenon 135 in nuclear fuel assemblies at that level. A control method according to claim 6 or 7, wherein the state parameters comprise one or more of the parameters in the list below: - for each level of the core, neutron density at said level, Xenon 135 concentration in the nuclear fuel assemblies at said level, Iodine 135 concentration in the nuclear fuel assemblies at said level; - for each level of the core, temperature of the primary heat transfer fluid; - temperature of the primary heat transfer fluid at the inlet and outlet of the core; - temperature of the primary heat transfer fluid in the hot branch and in the cold branch; - concentration of neutron poison in the heat transfer fluid primary.

9. A control method according to any one of claims 6 to 8, wherein the estimated numerical coefficient(s) is / are selected from the following list: - &Xe: neutron absorption transmutation coefficient of Xenon-135 to Xenon-136; -1*: mean lifetime of neutrons (prompt and delayed) in the core; - D: neutron exchange coefficient between core levels; - Kbor, Kbank, Kxenon: efficiency coefficients characterizing the contribution to the variation in reactivity at each core level of the variation in neutron poison concentration in the primary coolant, the displacements of the control rod groups, and the variation in Xenon-135 concentration in the nuclear fuel assemblies at said core level, respectively; - tgv: time constant of the temperature exchange between the primary and secondary circuits within the steam generator; - Tbc;- Tbf: time constant for the evolution of the temperature of the primary heat transfer fluid along the hot branch; - Tbf: time constant for the evolution of the temperature of the primary heat transfer fluid along the cold branch.

10. A control method according to any one of claims 6 to 9, wherein the estimated state parameter or parameters is selected from the following list: - for each core level, Xenon 135 concentration in the nuclear fuel assemblies at said level, - for each core level, Iodine 135 concentration in the nuclear fuel assemblies at said level.

11. A control method according to any one of claims 6 to 10, wherein at step S50, the simulated operating parameters are chosen from the following list: - neutron flux at each core level; - axial distribution of the neutron flux in the core; - temperature of the primary coolant in the hot and cold branches of the primary circuit; - neutron poison concentration in the primary coolant; - Xenon-135 concentration in the fuel assemblies nuclear at each level of the core, concentration of Iodine 135 in the nuclear fuel assemblies at each level of the core.

12. A control method according to any one of claims 6 to 11, wherein the actuator commands used by the digital model are selected from the following list: - displacement of control groups; - injection of neutron poison into the primary circuit; - injection of water into the primary circuit; - power supplied by the turbine.

13. A piloting method according to any one of the preceding claims, wherein at each iteration, the optimization operation is treated as an optimization problem aimed at minimizing the cost function, by implementing a numerical integrator and a numerical optimization solver.

14. A nuclear reactor comprising a pressure vessel (2), a core (3) comprising a plurality of nuclear fuel assemblies (5) arranged in the pressure vessel (2), a primary circuit (7) for cooling the core (3) through which circulates a primary coolant containing a neutron poison, a plurality of actuators acting on the core (3) or the primary circuit (7), and a nuclear reactor control assembly (55), the control assembly (55) being configured to implement the control method of any one of claims 1 to 13

15. A nuclear reactor according to claim 14, wherein the primary circuit (7) comprises at least one primary loop having a hot branch (BC) and a cold branch (BF) connected respectively to a primary heat transfer fluid outlet and a primary heat transfer fluid inlet of the pressure vessel (2), the nuclear reactor (1) further comprising: - a secondary circuit (9) equipped with a turbine (11); - a steam generator (21) for the primary loop or loops having a first side intercalated in the primary loop and a second side intercalated in the secondary circuit; - control rod groups (49) absorbing neutrons; - a mechanism (51) capable of selectively inserting or extracting the control rod groups (49) into the core (3) of the nuclear reactor; - a unit (31) for injecting neutron poison into the primary heat transfer fluid; and - a unit (39) designed to inject water into the primary circuit.

16. A method for calibrating a numerical model used for controlling a nuclear reactor, the nuclear reactor (1) having a pressure vessel (2), a core (3) comprising a plurality of nuclear fuel assemblies (5) arranged in the pressure vessel (2), a primary circuit (7) for cooling the core (3) through which circulates a primary coolant containing a neutron poison, and a plurality of actuators acting on the core (3) or the primary circuit (7), the control of the nuclear reactor being carried out according to a method comprising the following steps: S10 / acquisition of current values ​​of a plurality of operating parameters acquired from the nuclear reactor; S20 / generation of actuator commands using current values ​​of acquired operating parameters, at least some commands being determined using said numerical model, the numerical model being configured to determine a time evolution of a set of state parameters of the nuclear reactor using the commands supplied to the actuators and a set of numerical coefficients; S30 / actuator control using generated commands; steps S10 / , S20 / and S30 / being implemented iteratively; the calibration process comprising an operation to generate reference values ​​for a plurality of reference operating parameters of the nuclear reactor for a time interval I, and an operation to estimate at least one estimated numerical coefficient belonging to the set of numerical coefficients, implemented for a time window [t0 ; t0+T] within the time interval I, T being the width of the time window, this estimation operation comprising at each iteration the following steps: S70 / generation of a generated value of at least one estimated numerical coefficient; S80 / determination of simulated values ​​of a group of simulated operating parameters forming part of the reference operating parameters, using the numerical model, for the time window [t0 ; t0+T] using in the numerical model the generated value of at least one estimated numerical coefficient; S90 / Evaluation of a cost function using the values ​​of reference and the simulated values ​​of the group of simulated operating parameters; steps S70 / , S80 / and S90 / being repeated until a convergence criterion of the cost function is satisfied, the generated value of at least one estimated numerical coefficient allowing satisfaction of the convergence criterion being retained as an estimate of at least one estimated numerical coefficient at time t0+T.

17. Calibration method according to claim 16, wherein the estimation operation is carried out in a non-iterative manner, the time window [t0 ; t0+T] corresponding to the time interval I.

18. Calibration method according to claim 16, wherein the estimation operation is carried out iteratively, the time window [t0 ; t0+T] sliding within the time interval I, the time window moving at each iteration and sweeping through the time interval I.

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