Method for adjusting operating parameters of a nuclear reactor and corresponding nuclear reactor
阅读说明：本技术 用于调节核反应堆的操作参数的方法和对应的核反应堆 (Method for adjusting operating parameters of a nuclear reactor and corresponding nuclear reactor ) 是由 阿兰·格罗塞梯特 洛里·勒马聚里耶 菲力浦·谢弗雷尔 ***·亚勾比 于 2019-02-01 设计创作，主要内容包括：本发明的方法调节操作参数,这些操作参数至少包括堆芯的平均温度(T<Sub>m</Sub>)和轴向功率(AO)不平衡,该方法包括以下步骤：-通过监督器(31)实施预测控制算法来形成核反应堆的控制值的向量(U<Sub>S</Sub>)；-通过调节器(33)实施顺序增益控制算法来形成核反应堆的校正值的向量(u<Sub>K</Sub>)；-通过使用由监督器(31)产生的命令值向量(U<Sub>S</Sub>)和由调节器(33)产生的命令的校正值向量(u<Sub>K</Sub>),形成核反应堆命令的校正值向量(U)；以及-通过使用控制的校正值的向量(U)控制执行器,来调节核反应堆的操作参数。(The method of the invention adjusts operating parameters that include at least the average temperature (T) of the core m ) And an axial power (AO) imbalance, the method comprising the steps of: -forming a vector (U) of control values of the nuclear reactor by implementing a predictive control algorithm by means of a supervisor (31) S ) (ii) a -forming a vector (u) of correction values of the nuclear reactor by implementing a sequential gain control algorithm by means of a regulator (33) K ) (ii) a -by using a vector of command values (U) generated by a supervisor (31) S ) And a commanded correction value vector (u) generated by the regulator (33) K ) Forming a correction value vector (U) of the nuclear reactor command; and-adjusting an operating parameter of the nuclear reactor by controlling the actuator using the vector (U) of corrected values of the control.)
1. A method of adjusting operating parameters of a nuclear reactor, the operating parameters including at least an average core temperature (T;)m) And an axial power (AO) imbalance, the method comprising the steps of:
-obtainingTaking at least one input (D)U、DP) The current value of (a);
-obtaining a current value (Y) of an output vector, said output comprising at least said operating parameter;
-using said at least one input (D)U、DP) Forming a reference value (Y) of said vector of said outputref)；
-using at least one input (D)U、DP) And the current value (Y) of the vector of outputs, a vector of control values (U) of the nuclear reactor being formed by a supervisor (31) implementing a predictive control algorithmS)；
-using the current value (Y) of the vector of the output and the reference value (Y) of the vector of the outputref) Forming a correction value vector (u) for the nuclear reactor control by implementing a sequential gain control algorithm by a regulator (33)K)；
-said vector (U) of said values of said control by using said supervisor (31)S) And the vector (u) of the controlled correction values generated by the regulator (33)K) Forming a correction value vector (U) of said control of said nuclear reactor; and
-adjusting the operating parameter of the nuclear reactor by controlling an actuator using the vector (U) of the correction values of the control.
2. The method of claim 1, wherein the nuclear reactor (1) comprises:
-a tank (3);
-a core (5) comprising a plurality of nuclear fuel assemblies, placed in said tank (3);
-bundles (7) for controlling the reactivity of the core (5) and mechanisms (9), these mechanisms (9) being configured to move each bundle (7) in a direction of insertion into the core (5) or in a direction of extraction from the core (5);
-a primary circuit (10) for cooling the core (5) in which a primary coolant circulates, comprising a cold and a hot branch (11, 13) pierced in the tank (3) and through which the primary coolant enters the tank (3) and exits the tank (3), respectively;
-an injection circuit (15) configured to selectively inject a neutron poison or a diluent fluid without a neutron poison into the primary coolant fluid;
-said controlling comprises at least one movement rate of said control beam (7) and at least one injection rate of a neutron poison or diluent fluid.
3. The adjustment method according to claim 2, wherein the bundle (7) is moved in groups, one or more groups being grouped in a first set (Pbank, R, DCBA), the controlling comprising at least one rate of movement of the groups of the first set.
4. Adjustment method according to claim 3, wherein the other groups are grouped in a second set (Hbank), the control comprising at least one rate of movement of the groups of the second set in addition to the rate of movement of the groups of the first set.
5. Adjustment method according to claim 3 or 4, wherein the groups of the first set (Pbank, DCBA) are moved sequentially.
6. Adjustment method according to claim 3 or 4, wherein the first set has only one group (R).
7. Regulation method according to any one of claims 3 to 6, wherein the operating parameters also comprise the first set (P)bank) The insertion position of the group.
8. Method of regulation according to any one of claims 1 to 7, in which the nuclear reactor comprises a supply with the primary circuit (10) ofOne or more turbines (17) of steam, said at least one input (D)U、DP) Is the power required by the turbine (17) of the nuclear reactor.
9. Method of regulation according to claim 8, wherein the power supplied by the turbine (17) of the nuclear reactor comprises a programmed power (D) according to a predetermined program (for example a predetermined period of at least one day)U) And a power perturbation (dp), said reference value (Y) of said vector of said outputref) Using the programmed power (D) aloneU) To form the composite material.
10. The regulation method according to any one of claims 2 to 9, wherein said output comprises, in addition to said operating parameter, the temperature (T) of said primary coolant in said hot branchc) And the thermal power (P) of the coreK)。
11. The tuning method of claim 1, wherein the sequential gain control algorithm comprises a plurality of linear regulators, each linear regulator determined for a determined operating point of the nuclear reactor, the operating point preferably scaled to cover a nuclear reactor power range of 25% to 100% of rated nuclear reactor power.
12. Adjustment method according to claim 11, in combination with claim 3, wherein each operating point is defined by a determined insertion position (P) of the first set of groupsbank) And (5) characterizing.
13. The regulation method according to claim 11 or 12, wherein each linear regulator is expressed in the form of:
uK＝Kp(s)y1+Ki(s)y2wherein, y1Y and y2＝z
Wherein, KpAnd KiIs a gain matrix, s is a Laplace (Laplace) variable, y is the current of the vector of the outputAn output deviation vector between a value and the reference value of the output vector, z is an operating parameter vector deviation between the current value of the vector of the operating parameter to be checked and the reference value of the vector of the operating parameter to be checked, and uKIs the vector of the correction values of the control.
14. The adjustment method according to claim 13, wherein the method comprises the steps of: obtaining linear regulators, the step comprising, for each linear regulator, the sub-steps of:
-forming a linearized model of the nuclear reactor by linearizing a non-linearized model of the nuclear reactor at the corresponding operating point, the linearized model relating:
-said output deviation vector (y) and said operating parameter deviation vector (z) of an aspect and
-on the other hand the at least one input disturbance (dp), the disturbance of the vector of control values (dU), the disturbance of the vector of output deviations (y) (dy), and the vector of correction values (u) of the control (d)K) At least one of the above-mentioned (b),
-whereby said linearized model and said linear actuator form a loop system for said insertion position;
-determining an operating constraint of the nuclear reactor to be observed for a predetermined disturbance (dp) of the at least one input or a predetermined disturbance (dU) of the vector of the values of the predetermined control or a disturbance (dy) of the deviant vector output (y);
-translating each operational constraint into a numerical condition to be observed for a transfer function between:
-on the one hand, the disturbance (dp) of the at least one input, or the disturbance (dU) of the vector of control values, or the disturbance (dy) of the vector of output deviations (y), with
-on the other hand, one of the difference between the current value of one of the operating parameters and the reference value of the operating parameter, or the difference between the current value of one of the outputs and the reference value of the output, or the correction value of the control;
-determining the gain matrix KpAnd KiIs determined by an optimization algorithm to at least stabilize the loop system for the corresponding operating point and to satisfy the digital condition corresponding to all the operating constraints.
15. The regulation method according to claim 14, wherein the linear regulator to be observed is obtained at least for disturbances which are power steps of ± P% of the nominal power PN of the nuclear reactor demanded by the turbine, P being between 5% and 15%, taking into account one or more of the following operating constraints:
-Tmof said current value and said reference value Tm，refDifference T betweenmIn that
-said current value of AO and said reference value AOrefThe difference therebetween being- Δ AOmaxAnd Δ AOmaxTo (c) to (d);
-the beam moving speed is less than
Variation of neutron poison concentration less than
16. The tuning method of claim 15, wherein the one or more operational constraints translate into one or more of the following numerical conditions:
-wherein the content of the first and second substances,is the power step and TmA transfer function between, wherein,ΔPmax＝P％.PN；
-wherein the content of the first and second substances,is a transfer function between said power step and the AO, wherein,ΔPmax＝P％.PN；
-wherein the content of the first and second substances,
-
17. method of regulation according to any one of claims 14 to 16, in combination with claim 3, in which the linear regulator to be observed is obtained at least for disturbances which are power steps of ± P% of the nominal power PN of the nuclear reactor demanded by the turbine, P being between 5% and 15%, taking into account the following operating constraints:
-Pbankwith said current value of Pbank，refIs in the range ofAndin the meantime.
18. The adjustment method of claim 17, wherein the operational constraints translate into the following numerical conditions:
-
19. the adjustment method according to any one of claims 14 to 18, wherein the linear adjuster is obtained taking into account the following operational constraints:
-a minimum variation of said operating parameter is caused by a disturbance which is a power step of ± P% of the nominal power PN of said nuclear reactor demanded by said turbine, P being between 5% and 15%;
-said constraints translate into the following numerical conditions:
-wherein K represents the gain matrix KpAnd KiΩ denotes a set of gain matrices to stabilize the loop system,
20. The conditioning method of any of claims 14 to 19, wherein each linearization model considers the delay associated with the injection of the neutron poison using the equation:
wherein, CbIs the concentration of said neutron poison in the or each primary loop; u. ofQIs used at a flow rate QborThe command to increase the concentration of neutron poison in the primary loop resulting from a command to inject neutron poison;is the delay command to increase the neutron poison concentration in the primary loop; s is the laplace variable; h is the value of the delay considered, typically between 100 and 500 seconds; n is an integer between 3 and 15.
21. The adjustment method according to any one of claims 14 to 20, wherein the gain matrix K is determined by the optimization algorithm at a determined operating pointpAnd KiTo stabilize the loop system for the determined operating point and to stabilize the loop system for at least two adjacent determined operating points while satisfying the digital condition corresponding to all of the operating constraints.
22. The regulation method according to any one of the preceding claims, in combination with claim 11, wherein the supervisor predictive control algorithm (31) uses the non-linear model of the nuclear reactor.
23. A nuclear reactor comprising a core (5) and an assembly (25) for adjusting operating parameters of the core, including at least the mean temperature (T) of the corem) And an axial power (AO) imbalance, the nuclear reactor (1) further comprising:
-means (27) for acquiring at least one input (D)U、DP) The current value of (a);
-means (29) for obtaining a current value (Y) of a vector of outputs, said outputs comprising at least said operating parameters;
the adjustment assembly (25) comprises:
-a module (35) for using said at least one input (D)U、DP) Forming a reference value (Y) of said vector of said outputref)；
-a supervisor (31) programmed to use at least one input (D)U、DP) And the current value (Y) of the vector of outputs, forming a vector of control values (U) of the nuclear reactor by implementing a predictive control algorithmS)；
-a regulator (33) programmed to use said current value (Y) of said vector of said output and said reference value (Y) of said vector of said outputref) Forming a correction value vector (u) for said control of said nuclear reactor by implementing a sequential gain control algorithmK)；
-a module (37) for using said vector (U) of control values formed by said supervisor (31)S) And the controlled correction value vector (u) generated by the regulator (33)K) Forming a correction value vector (U) for the nuclear reactor control; and
-a module (39) for adjusting said operating parameters of said nuclear reactor by controlling actuators using said vector (U) of said correction values of said control.
24. The nuclear reactor of claim 23, wherein the nuclear reactor comprises:
-a tank (3);
-a core (5) comprising a plurality of nuclear fuel assemblies, placed in said tank (3);
-bundles (7) for controlling the reactivity of the core and mechanisms (9), these mechanisms (9) being configured to move each bundle (7) in a direction of insertion into the core (5) or in a direction of extraction from the core (5);
-a primary circuit (10) for cooling the core (5) in which a primary coolant circulates, comprising a cold and a hot branch (11, 13) pierced in the tank (3) and through which the primary coolant enters the tank (3) and exits the tank (3), respectively;
-an injection circuit (15) configured to selectively inject a neutron poison or a diluent fluid without a neutron poison into the primary coolant fluid;
the controlling comprises at least one moving rate of the control beam (7) and at least one injection rate of a neutron poison or diluent fluid.
25. The nuclear reactor of claim 24 wherein the adjustment assembly (25) is configured to move the bundles (7) in groups, one or more groups being grouped in a first set (Pbank, R, DCBA), the controlling comprising at least one rate of movement of the groups of the first set.
26. The nuclear reactor of claim 25 wherein the other groups are grouped in a second set (Hbank), the control comprising at least one rate of movement of the groups of the second set in addition to the rate of movement of the groups of the first set.
[ technical field ] A method for producing a semiconductor device
The invention relates to the regulation of operating parameters of a nuclear reactor.
[ background of the invention ]
Considering the large share of nuclear energy in a french energy structure, the massive introduction of renewable energy sources (wind and solar) into the electrical grid creates an additional need for energy production flexibility, thereby affecting nuclear reactors. The flexibility reflects the ability of the power production unit to adapt to its production. Renewable energy sources have the property of being intermittent over time or depending on climate uncertainty. This increase in flexibility without a large capacity energy storage system has led to an increased need to regulate the power available to conventional generators, including nuclear reactors in france.
In addition, the adjustment of the operating parameters of the nuclear reactor must be carried out according to very restrictive multi-objective specifications. In particular, the adjustment system must minimize changes in operating parameters and minimize stress on the actuator. Currently, the regulation systems of nuclear reactors are based on PID. However, they can only take these last constraints into account in a very incomplete way.
[ summary of the invention ]
In this case, according to a first aspect, the present invention aims to propose a method of adjusting operating parameters of a nuclear reactor which offers additional flexibility while allowing compliance with very restrictive multi-objective specifications.
To this end, the invention relates to a method of regulating operating parameters of a nuclear reactor, these operating parameters including at least the mean temperature of the core and the axial power imbalance, the method comprising the steps of:
-obtaining a current value of at least one input;
-obtaining a current value of an output vector, the output comprising at least an operating parameter;
-forming a reference value of the vector of outputs using the current value of the at least one input;
-forming a vector of control values for the nuclear reactor by a supervisor implementing a predictive control algorithm using at least the current values of at least one input and the current values of a vector of outputs;
-implementing a sequential gain control algorithm by the regulator using the current value of the output vector and the reference value of the output vector to form a vector of correction values for the nuclear reactor command;
-forming a correction value vector for the nuclear reactor command using the command value vector formed by the supervisor and the correction value vector for the command formed by the regulator; and
-adjusting an operating parameter of the nuclear reactor by controlling the actuator using the vector of commanded correction values.
The regulation process may also have one or more of the following characteristics considered alone or in any technically possible combination:
-the nuclear reactor comprises:
a groove;
a core including a plurality of nuclear fuel assemblies disposed in a trough;
core reactivity control bundles and mechanisms configured to move each bundle in a direction of insertion into the core or in a direction of withdrawal from the core;
primary core cooling circuit in which primary coolant circulates, the primary core cooling circuit including a cold branch and a hot branch pierced in the slot, and the primary coolant entering and exiting the slot through the cold branch and the hot branch, respectively;
an injection circuit configured to selectively inject a neutron poison or a diluent fluid without a neutron poison into the primary heat transfer fluid;
controlling includes controlling at least one rate of movement of the beam and at least one rate of injection of a neutron poison or diluent fluid;
-bundle packet movement, one or more groups being grouped in a first group, commanding at least one rate of movement of the groups comprising the first group;
-the other groups are grouped together in a second set, the command comprising, in addition to the moving rate of the group of the first set, at least one moving rate of the group of the second set;
-the groups of the first set move sequentially;
-the first set has only one group;
-the operating parameters further comprise the insertion positions of the groups of the first set;
-the nuclear reactor comprises one or more turbines supplied with steam through a primary circuit, at least one input being the power required by the turbines of the nuclear reactor;
the power supplied by the turbines of the nuclear reactor comprises a power and a power disturbance programmed according to a predetermined program (for example, a predetermined period of at least one day), the reference value of the vector of outputs being determined by using said programmed power alone;
-the output comprises, in addition to the operating parameters, the temperature of the primary coolant in the hot branch and the thermal power of the core;
-the sequential gain control algorithm comprises a plurality of linear regulators, each linear regulator being determined for a specific operating point of the nuclear reactor, said operating points being preferably staggered so as to cover a power range of the nuclear reactor ranging from 25% to 100% of the nominal power of the nuclear reactor;
-each operating point is characterized by a determined insertion position of the first set of groups;
-each linear regulator is expressed in the form:
uK＝Kp(s)y1+Ki(s)y2wherein, y1Y and y2＝z
Wherein, KpAnd KiIs a gain matrix, s is a Laplace (Laplace) variable, y is an output offset vector between a current value of the output vector and a reference value of the output vector, z is an operating parameter offset vector between a current value of the operating parameter vector to be checked and a reference value of the operating parameter vector to be checked, and u isKIs a vector of commanded correction values;
-the method comprises the steps of: obtaining linear regulators, the step comprising, for each linear regulator, the sub-steps of:
forming a linearized model of the nuclear reactor by linearizing a non-linear model of the nuclear reactor at corresponding operating points, the linearized model correlating:
■ an output offset vector and an operating parameter offset vector of an aspect
■ interference of at least one of the input at least one of the control value vectors, interference of the output offset vector and interference of the correction value vector of the control value elsewhere;
whereby the linearized model and the linear actuator form a loop system for the insertion location;
determining a predetermined disturbance for a vector of values of at least one input predetermined disturbance or command or a predetermined disturbance of an output deviation vector to be observed for an operating constraint of the nuclear reactor;
translating each operational constraint into a numerical condition to be observed for a transfer function between:
■ on the one hand, interference of at least one input or control value vector or output deviation vector, with
■ on the other hand, the difference between the current value of one of the operating parameters and the reference value of said operating parameter, or the difference between the current value of one of the outputs and the reference value of said output, or
One of the commanded correction values;
determining a gain matrix KpAnd KiIs determined by an optimization algorithm to at least stabilize the loop system for the corresponding operating point and to satisfy a digital condition corresponding to all operating constraints;
-obtaining a linear regulator to be observed at least for disturbances which are power steps of ± P% of the nominal power PN of the nuclear reactor demanded by the turbine, P being between 5% and 15%, taking into account one or more of the following operating constraints:
*Tmcurrent value and reference value T ofm,refThe difference between them is located
current value and reference value AO of AOrefThe difference AO between them is located at- Δ AOmaxAnd Δ AOmaxTo (c) to (d);
the moving speed of beam is less than
Variation in neutron poison concentration less thanIs measured by the flow rateThe rate of increase of the concentration of neutron poison in the primary loop caused by injection of neutron poison;
-said one or more operational constraints translate into one or more of the following numerical conditions:
wherein the content of the first and second substances,is a transfer function between the power step and the rate of movement of the beam, wherein,
-obtaining a linear regulator to be observed at least for disturbances which are power steps of ± P% of the nominal power PN of the nuclear reactor requested by the turbine, P being between 5% and 15%, taking into account the following operating constraints:
*Pbankcurrent value of and Pbank,refIs measured by the difference P between the reference valuesbankIs located atAnd
-said operational constraints translate into the following numerical conditions:
-obtaining a linear regulator taking into account the following operating constraints:
interference causes a minimum change of the operating parameter, the interference being a power step of ± P% of the nominal power PN of the nuclear reactor demanded by the turbine, P being between 5% and 15%;
-said constraints translate into the following numerical conditions:
wherein K represents a gain matrix KpAnd KiAnd Ω denotes a set of gain matrices of the stable loop system,is a transfer function between the power step and an operating parameter deviation vector, WzIs a predetermined frequency weighting matrix;
-each linearization model takes into account the delay associated with the injection of neutron poison using the following equation:
wherein, CbIs the concentration of neutron poison in the or each primary loop; u. ofQIs used at a flow rate QborA command to increase the concentration of neutron poison in the primary loop resulting from a command to inject neutron poison;
-determining the gain matrix K by means of an optimization algorithm at the determined operating pointpAnd KiTo stabilize the loop system for said determined operating point and to stabilize the loop system for at least two adjacent determined operating points while satisfying digital conditions corresponding to all operating constraints;
-a predictive control algorithm of the supervisor using said non-linear model of the nuclear reactor.
According to a second aspect, the invention relates to a nuclear reactor comprising:
-a core and an assembly for adjusting operating parameters of the core, the operating parameters including at least an average temperature and an axial power imbalance of the core, the nuclear reactor further comprising:
an acquisition unit having at least one current value of an input;
means for obtaining current values of the output vectors, the output including at least operating parameters;
-the adjustment assembly comprises:
a module for forming a reference value of the vector of outputs using the current value of the at least one input;
a supervisor programmed to form a vector of control values for the nuclear reactor by implementing a predictive control algorithm using at least the current values of at least one input and the current values of the vector of outputs;
a regulator programmed to form a vector of correction values for nuclear reactor control by implementing a sequential gain control algorithm using a current value of the vector of outputs and a reference value of the vector of outputs;
a module for forming a correction value vector for a nuclear reactor command using the command value vector formed by the supervisor and the correction value vector for the command formed by the regulator; and
a module for adjusting an operating parameter of the nuclear reactor by controlling the actuator using a vector (U) of the commanded correction values.
The nuclear reactor may also have one or more of the following characteristics considered alone or in any technically possible combination:
-the nuclear reactor comprises:
a groove;
a core including a plurality of nuclear fuel assemblies disposed in a trough;
core reactivity control bundles and mechanisms configured to move each bundle in a direction of insertion into the core or in a direction of withdrawal from the core;
primary core cooling circuit in which primary coolant circulates, the primary core cooling circuit including a cold branch and a hot branch pierced in the slot, and the primary coolant entering and exiting the slot through the cold branch and the hot branch, respectively;
an injection circuit configured to selectively inject a neutron poison or a diluent fluid without a neutron poison into the primary heat transfer fluid; the command includes controlling at least one rate of movement of the beam and at least one rate of injection of a neutron poison or diluent fluid;
-the adjusting component is configured to move the bundle groups, the one or more groups being grouped in a first group, controlling at least one rate of movement of the groups comprising the first group;
-the other groups are grouped together in a second set, the command comprising, in addition to the moving rate of the group of the first set, at least one moving rate of the group of the second set;
-the groups of the first set move sequentially;
-the first set has only one group;
-the operating parameters further comprise the insertion positions of the groups of the first set;
-the nuclear reactor comprises one or more turbines supplied with steam through a primary circuit, at least one input being the power required by the turbines of the nuclear reactor;
the power supplied by the turbines of the nuclear reactor comprises a power and a power disturbance programmed according to a predetermined program (for example, a predetermined period of at least one day), the reference values of the vector of outputs being calculated by using said programmed power alone;
-the output comprises, in addition to the operating parameters, the temperature of the primary coolant in the hot branch and the thermal power of the core;
-the sequential gain control algorithm comprises a plurality of linear regulators, each linear regulator being determined for a specific operating point of the nuclear reactor, said operating point being scaled to cover a power range of the nuclear reactor ranging from 25% to 100% of the nominal power of the nuclear reactor;
-each operating point is characterized by a determined insertion position of the first set of groups;
-each linear regulator is expressed in the form:
uK＝Kp(s)y1+Ki(s)y2wherein, y1Y and y2＝z
Wherein, KpAnd KiIs a gain matrix, s is a laplace variable, y is an output offset vector between a current value of the output vector and a reference value of the output vector, z is an operating parameter offset vector between a current value of the operating parameter vector to be checked and a reference value of the operating parameter vector to be checked, and u isKIs a vector of the commanded correction values.
[ description of the drawings ]
Further characteristics and advantages of the invention will emerge from the detailed description given below, purely by way of indication and without limitation, with reference to the accompanying drawings, in which:
FIG. 1 is a schematic representation of the conditioning method of the present invention;
FIG. 2 is a schematic representation of a nuclear reactor in which the method of FIG. 1 may be implemented;
FIG. 3 is a schematic representation of a sequence for inserting groups of the first set for a variant of the adaptation method from the T-mode adaptation;
FIG. 4 schematically illustrates the difference between a sequential gain adjuster and a supervisor;
FIG. 5 is a schematic representation of a sequential gain control algorithm;
FIG. 6 is a schematic representation of the steps for obtaining a linear regulator of a sequential gain control algorithm;
FIG. 7 is a graphical representation of a step disturbance signal used to obtain the steps of the linear regulator of FIG. 6;
FIG. 8 is a schematic representation illustrating an alternative embodiment of a linear actuator determination by region;
FIG. 9 is a schematic representation of a supervisor;
FIG. 10 is a graphical representation of the evolution of the power demanded by the turbine when the reactor is operating under frequency control;
FIG. 11 is a graphical representation of the performance achieved by the supervisor alone in the operational scenario of FIG. 10;
FIGS. 12-19 are graphical representations of the results obtained with the method of the present invention for the power required by the turbine to form a 100% -60% -100% PN ramp at 5% PN/min;
FIGS. 20-26 are graphical representations of the results obtained with the method of the present invention for the power required by the turbine to form a step-down power of 100% -90% PN;
fig. 27-33 are graphical representations of the results obtained with the method of the present invention for the power required by the turbine to form a 100% -70% PN ramp at 5% PN/min with frequency adjustment.
[ detailed description ] embodiments
The method schematically represented in fig. 1 is intended to adjust the operating parameters of the nuclear reactor 1 diagrammatically represented in fig. 2.
The nuclear reactor 1 includes:
-a tank 3;
a core 5 comprising a plurality of nuclear fuel assemblies, placed in the tank 3;
bundles 7 for controlling the reactivity of the core and mechanisms 9, these mechanisms 9 being configured to move each bundle 7 in the direction of insertion into the core 5 or in the direction of extraction from the core 5;
a primary circuit 10 for cooling the core 5, in which a primary coolant circulates, comprising a
an injection circuit 15 configured to selectively inject a neutron poison or a diluent fluid without a neutron poison into the primary heat transfer fluid.
The neutron poison is typically boron. The diluent fluid is typically water.
Generally, the primary loop 10 includes one or more loops, each having a hot leg and a cold leg.
The nuclear reactor 1 comprises one or more turbines 17 supplied with steam by the primary circuit 10.
The nuclear reactor 1 is typically a PWR (pressurized water reactor). It comprises a steam generator 19 for each loop of the primary circuit 10. Each loop connects a tank 3 in a closed circuit to the primary side of an associated steam generator 19. Furthermore, the nuclear reactor 1 comprises a secondary circuit 21 connecting the secondary side of the or each steam generator 19 to the associated turbine 17 in a closed circuit. The turbine 17 drives an alternator 23.
Alternatively, the primary heat transfer fluid may directly drive each turbine.
The nuclear reactor 1 also includes a set of 25 control operating parameters of the core, commonly referred to as core control (CoreControl). The conditioning assembly 25 includes an information processing unit formed, for example, by a processor and a memory (not shown) associated with the processor. As a variant, the conditioning component 25 is produced in the form of a programmable logic component, such as an FGPA (field programmable gate array), or in the form of an application-specific integrated circuit, such as an ASIC (application-specific integrated circuit).
The adjustment assembly 25 is configured to move the beam 7 through the functional group. The beams of the same group move together and are always all in the same insertion position.
Advantageously, the groups are divided into one or more sets. The distribution of the groups and their use depends on the control mode of the nuclear reactor.
In some control modes, several groups are grouped in a first group.
In this case, the groups of the first set are typically moved sequentially. This means that they are inserted one after the other with a predetermined overlap, as described below. Alternatively, the overlap may be variable.
According to an alternative embodiment, all groups of the first set move together. This is understood to mean that they are always all in the same insertion position and move together.
In other control modes, the first set has only one group.
In some control modes, other groups are grouped in a second group.
In this case, the groups of the second subset typically move together.
In other control modes, all groups are aggregated in a first set and there is no second set.
In other control modes, certain groups are grouped in a third set in addition to the first and second sets.
In all cases, the adjustment assemblies move the same group of assemblies in a coordinated manner (sequentially, collectively, etc.). The adjustment assembly moves the assembly or each group of assemblies to control the operation of the reactor, in particular to adjust operating parameters.
Several examples of control modes are described in detail below, inspired by modes T, G and A, respectively.
In the control mode, inspired by the T mode, which is particularly suitable for European Pressurized Reactors (EPR), the groups are divided into two sets:
-a first set, called Pbank;
a second set, called Hbank.
The first set is particularly suitable for checking the mean temperature Tm. The second set Hbank is particularly suitable for checking the axial offset AO.
The first and second sets have variable compositions, as follows.
For example, the control bundles 7 are grouped into 5 groups P1 to P5.
As shown in FIG. 3, groups P1 through P5 constitute the Pbank and Hbank groups as follows:
at 100% nominal power PN of the reactor, Pbank consists of P1, and Hbank consists of P2 to P5. Pbank is inserted slightly more than Hbank.
-inserting Pbank when the power is reduced to 85% PN, in order to control the average temperature to its reference value. The decrease in potency results in a change in AO controlled by Hbank.
The power continues to decrease. When the distance between P1 and P2 is equal to the maximum separation between the two sets of bundles (half the core height), P2 separates from the Hbank set and passes into the Pbank set. P1 was then inserted.
Pbank continues to be inserted as the power continues to decrease. When the maximum distance between P2 and P3 is reached, P3 passes into Pbank and is inserted, and so on P4.
If the control bundles are grouped into a different number of bundles, the sequence will be the same.
Thus, the groups of the first set Pbank move sequentially. The groups of the second Hbank set move together.
The term "position of the first Pbank set" is understood herein to mean the cumulative position of the groups belonging to the first set. The position is denoted as Pbank。
For example, the position is calculated using the following equation:
Pbank＝min(P4,214)+min(P3,214)+min(P2,214)+P1
wherein, P1、P2、P3And P4The positions of groups P1 to P4 are indicated, respectively. A value 214 is selected for the mid-core position (mid-core position) of the bundle. This position is expressed in number of extraction steps from the maximum insertion position of the group.
The position of the second set Hbank is here meant to be the position of the group P5, which group is never integrated into the first Pbank set.
In a second control mode inspired by G-mode, the groups are divided into two sets:
the first set comprises a single group formed by black beams (i.e. beams that are very absorbing), group R;
the second set of PCGs, called the set for power compensation, consists of groups G1 and G2(G for the grey beam) and groups N1 and N2(N for the black beam). The absorption of the gray beam is relatively lower than that of the black beam.
The groups of the second subset are inserted sequentially. Advantageously, they are inserted according to the electrical power required by the turbine.
In this second control mode, AO is advantageously controlled primarily by injection of neutron poison or diluent.
In a third control mode inspired by mode a, the functional groups are all grouped together in a first set, here denoted by the acronym DCBA.
This typically consists of four sets A, B, C and D, which are fitted in sequence like Pbank.
The first set is particularly suitable for controlling the average temperature Tm.
In this third control mode, AO is advantageously controlled primarily by injection of neutron poison or diluent fluid.
The operating parameters to be controlled include at least the average temperature Tm of the core and the axial power AO imbalance.
The average core temperature Tm is defined herein as TfAnd TcMean value between, TfAnd TcThe temperature of the primary coolant at the outlet of the core 3 and at the inlet of the core 3 (i.e., at the hot leg 13 and the cold leg 11).
When the primary circuit has several loops, for example, the average temperature of the hot and cold branches of the primary circuit is taken into account.
The axial power imbalance AO is expressed by the following relation:
AO＝(FH-FB)/(FH+FB)
where FH and FB are the neutron fluxes in the upper and lower core, respectively.
Advantageously, the operating parameters to be checked also comprise the position P of the group of the first setbank。
This is typically the case at least for the first mode of controlling the reactor.
This corresponds to controlling the operating parameter Pmax, i.e. the maximum power that can be reached by rapidly extracting the groups to their maximum extraction position.
In fact Pmax is advantageously translated to the reference position of the Pbank group, which makes it possible to compensate for power failures. Thus, controlling Pmax corresponds to controlling the position of the Pbank group according to an insertion curve determined as a function of the power of the core and the power that the operator wishes to be able to return. For example, Pmax for 100% PN means that the position of the Pbank group is such that the return to 100% PN can be made by simply extracting the Pbank group.
For the second and third modes of controlling the reactor, the position of the group of the first set is typically not part of the operating parameter to be controlled. These parameters include only Tm and AO.
As shown in fig. 1, the adjustment process takes into account at least one input and several outputs.
The input is defined as a predicted path or as an additional constraint or constraint modification applied to the control process.
The at least one input is typically the power required by the turbines of the nuclear reactor.
Generally, the power supplied by the turbine 17 of a nuclear reactor comprises two components: programming power D according to a predetermined programUAnd power interference dp. For example, the programming power is predetermined for a period of at least one day. The power disturbance corresponds, for example, to a regulation performed in the operation of the primary or secondary loop, a charge reserve step, or the like.
According to an alternative embodiment, the term power required by the turbine or nuclear power reactor is understood to mean the programmed power DU。
According to another variant embodiment, the term "power requested from the turbine of the nuclear reactor" is understood to mean the power D suppliedPWherein D isP＝DU+dp。
In addition to or instead of the power required by the turbine, the at least one alternative input comprises one or more of the following inputs:
-maximum programming insertion for Pbank group;
-widening the authorized variation range of a physical parameter, such as the average core temperature or the axial power AO imbalance;
degradation of the actuator performance (insertion speed of the control unit, injection rate of boron or distilled water).
This list is not exhaustive.
In addition to the operating parameters, the output preferably also includes the temperature T of the primary coolant in the hot branch 13cAnd thermal power P of the corek。
To allow regulation, the nuclear reactor 1 comprises:
-a unit 27 for obtaining the current value of at least one input;
an acquisition unit 29 of the current value of the output vector.
The nuclear reactor 1 comprises a control system equipped with a set of sensors, which make it possible to access the current values of the following quantities: t isc、TfPower P of AO, coreKAnd Pbank。
The control system may also provide DUAnd is equipped with a means for accessing DPThe sensor of (1).
The acquisition unit 27 is configured to acquire the current value of the power required by the turbine directly from the control system.
The acquisition unit 29 is configured to acquire the current values of certain outputs, in particular T, directly from the control systemc、AO、PKAnd Pbank. The acquisition unit 29 is configured to calculate the current value of the other output from the value provided by the control system, in particular Tm.
The acquisition units 27 and 29 are, for example, modules of the regulating assembly 25 or directly inform the regulating assembly 25.
During the adjustment, the operating parameters are adjusted by giving commands to the actuators.
These commands advantageously comprise controlling at least one movement rate V of the beambarresAnd at least one injection rate of a neutron poison or diluent fluid.
In some control modes (e.g. a first control mode), the beam is controlledAt least one moving rate VbarresTypically including the rate of movement of the group of the first Pbank set and the rate of movement of the group of the second Pbank set.
These rates correspond to the first P as defined abovebankThe position of the set and the derivative over time of the position of the second Hbank set as defined above.
Annotating these rates vP separatelybankAnd vHbank。
In other control modes (e.g., second and third control modes), at least one moving rate V of the beam is controlledbarresTypically corresponding to the rate of movement of the first set of groups.
The rate of neutron poison or diluent fluid injection is generally expressed as the rate of change of the concentration of neutron poison in the primary coolant, expressed as uQ. In other cases, it is expressed in terms of the mass flow rate injected into the primary coolant, denoted as QborOr Qdil。
The command is generated by the adjustment assembly 25, which transmits the command to the actuator. The actuators are the drive mechanism 9 of the beam, and the injection circuit 15 of the neutron poison or diluent fluid.
The adjustment process is designed to meet specifications, i.e., multiple objectives. These constraints will be described only for the first control mode.
Core control is constrained by an authorized operating domain in which deviations of operating parameters from their references must be maintained. This domain is defined by the Limit Condition Operation (LCO), i.e., each controlled operating parameter (i.e., T)mAO and Pbank) Relative to their referenced upper and lower limits.
We define these references by:
Tm,refis an average temperature reference
AOrefIs AO reference
Pbank,refPosition reference for Pbank group
The deviation of the parameters to be checked against their reference is given by:
ΔTmmean temperature deviation from its reference
Δ AO is the deviation of AO from its reference
ΔPbankIs the difference in position of Pbank from its reference.
Then we define the limits of the operational domain, such as:
ΔAO∈[-ΔAOmax,ΔAOmax]
typical values for these parameters are for example:
ΔAOmax＝5％AO
core control must help achieve flexibility requirements for the reactor, such as:
adaptation to daily changes in demand (load monitoring)
Load slope: PN between 25% and 100% of + -5%/min PN
Adaptation to real-time demand variations (frequency control)
Once: + -5% PN at 1%/s
Plus or minus 5% PN at second 1%/min
Adaptation to network interference (backup capacity)
Step change: + -10% PN between 30% PN and 100% PN
The purpose of core control is to keep the output controlled within the authorized operating range defined above, regardless of the power variations specified above.
The maximum grant requirement is defined as follows:
controlling the saturation of the beam at the following positions:
minimum position:
maximum position
Minimum speed:
maximum speed:
maximum and minimum rates of neutron poison injection/dilution:
minimum neutron poison flow rate:
maximum neutron poison flow rate:
minimum diluent fluid flow rate:
maximum flow rate of diluent fluid:
minimum concentration:
the regulator must have a guarantee of robustness:
minimum modulus margin, margin: mm＝0.5
The reference of the output to be controlled depends on the operation of the core. They are defined as follows:
reference temperature Tm,refIs a function of nuclear reactor power. It is read directly on a predetermined curve as a function of the power requested by the turbine. Here, we consider the current value of at least one input.
Reference axial power imbalance AOrefAre periodically updated, for example once a month, to account for the depletion of the core. It is provided directly by the operator of the nuclear reactor and is considered constant between two updates.
Reference position P of Pbank subassemblybank,refIs a function of the power of the nuclear reactor. It is read directly on a predetermined curve as a function of the power required by the turbine. The reference position is given as a cumulative position.
The method of adjusting the operating parameters for the first control mode will now be described in detail.
The process is designed to take into account the fact that control of the nuclear reactor core has specific characteristics.
Reactors have different kinetics, both slow and fast. The kinetics associated with xenon are very slow (on the order of hours), while the kinetics associated with power and temperature are rather fast (on the order of ten seconds).
Throughout the operational domain, the behavior of the core is highly non-linear, primarily due to the insertion of the bundle groups into the core. The effect of the beam set on the various operating parameters to be controlled varies greatly between the maximum power (100% PN) and the intermediate power (e.g., 60% PN). We even observe a reversal of the effect of the actuators in certain regions of the core.
Neutron poison actuators considered in the control problem have significant delays: for 300 seconds. Although the systems one tries to control are relatively slow (overall order of magnitude: 10 seconds), delays of this order are significant for the regulation.
The above specifications contain a number of constraints, including time constraints, which are often difficult to consider by conventional control techniques.
Currently, each power generation unit receives a daily load change program. Therefore, the procedure is known in advance. However, we currently do not utilize this signal to predict future commands. In the present control method, future changes of the signal may be taken into account for the formation of the command.
To cope with the difficulties indicated above, the regulation method implements a hierarchical control strategy.
The method comprises the following steps:
-obtaining a current value D of at least one inputU、DP；
-obtaining a current value Y of the output vector;
using the current value D of at least one input signalU、DPForming a reference value Y of the output vectorref；
-using at least the current value D of at least one inputU、DPAnd the current value Y of the vector output, forming a vector U of command values for the nuclear reactor by implementing a predictive control algorithm by means of the supervisor 31S；
Using the current value Y of the output vector and the reference value Y of the output vectorrefThe sequential gain control algorithm is implemented by the regulator 33 to form a correction value vector u for nuclear reactor controlK；
Using a vector U of command values generated by the supervisor 31SAnd a commanded correction value vector u generated by regulator 33KForming a correction value vector U of the nuclear reactor command; and
vector u of correction values by use of controlsKControlling an actuator to adjust an operating parameter of the nuclear reactor.
As mentioned above, the at least one input is typically the power required by the turbine. This typically corresponds to the programming power provided by, for example, a previously known load monitoring program.
Alternatively, it is the actual power of the turbine given by the equation below, here denoted as DP：DP＝Du+dP。
The at least one alternative input includes one or more of the inputs listed above in addition to or instead of the power required by the turbine.
Advantageously, the reference value Y of the output vectorrefBy programming power D onlyuAnd (4) determining. Thus, the reference value YrefIs not considered to be random (i.e. by d)PGiven) is modified by a change in power.
Reference value Y of output vectorrefThe following were used:
zTc,refis the reference thermal branch temperature. It reads on a predetermined curve, directly giving T as a function of the current value of at least one inputc,ref。
Tm,ref、AOrefAnd Pbank,refAs determined as described above.
Is the baseline core power. It is considered to be equal to the power required by the turbine.
The vector U of correction commands (i.e. commands given to the actuators) passes through the vector U of command values to be generated by the supervisor 31SAnd a commanded correction value vector u generated by regulator 33KAdding to obtain: u is equal to US+uK
The current value Y of the output vector is as follows:
Y＝(TcTmAO PKPbank)T
y is obtained as described above.
The supervisor 33 takes the vector Y as input, being defined as the current value Y of the output vector and the reference value Y of the output vectorrefThe difference between:
y＝Y-Yrefwherein y ═ TcTmAO PKPbank)T。
The sequential gain adjuster 33 solves the following problems:
ensuring a fine control of the system by ensuring a good performance around the various operating points a priori, in particular for counteracting the disturbances associated with the frequency adjustment.
Controlling the reactor over the entire operating range by adapting the gains of the constituent reactors as operation proceeds.
Ensuring robustness locally around the operating point (multi-objective approach).
Consider a large number of command constraints imposed in the specification.
However, for systems that exhibit such large non-linearities as is the case here, the sequential gain adjuster may exhibit poor performance. In fact, it is synthesized at various operating points on the basis of a linearized model. However, the use of linearized models may lack the representativeness of a global nonlinear model. A disadvantage is that the trajectory taken by the regulator may be far from the optimal path of the overall behaviour. Fig. 4 compares the path taken by the sequential gain adjuster (dashed line) with the path taken by the predictive control algorithm (solid line). It illustrates the fact that the sequential gain adjuster does not take into account the overall constraints of the tracking path, which the predictive control will take into account.
The sequential gain adjuster is a structured adjuster, preferably of the multivariable PI type.
The order of the actuators is advantageously located at the position of the first Pbank subset. In other words, the adjuster 31 comprises a set of linear adjusters, each linear adjuster being determined for a predetermined operating point, i.e. for a predetermined insertion position of the first Pbank set.
A nuclear reactor model for synthesizing linear regulators, also known as LTI (linear time invariant), is a nonlinear point model that is linearized around a predetermined operating point. It does not mimic xenon. In fact, since xenon is very slow in the face of other state changes, the multi-target regulator will not have the task of predicting it, which is specific to the supervisor.
In addition, the model is synthesized on a set of local LTI modulators. Therefore, the model does not benefit from good representation of the non-linear model for high power amplitude variations (e.g., load variations).
The supervisor 31 implements a predictive control algorithm using the same non-linear point model as that of the reactor for the linear regulator of the synthesis regulator 33, this control technique coping with the above-mentioned numerous problems:
it combines the ability to control the system regardless of its dynamics (slow: xenon, and/or fast: temperature) by using a potentially non-linear model of the system.
It allows to take into account delays, even long delays, in particular the injection of neutron poisons.
In addition, if the load monitoring program is known in advance, it anticipates the behavior by calculating the best path given the program.
Finally, the path of the regulator will be optimized over the overall behavior of the system, rather than locally as is the case with a regulator having only sequential gains.
However, like any finite time domain nonlinear predictive control algorithm:
it does not have any robustness guarantees.
It calculates the fixed command within a defined time frame called "no sample". The sampling interval may be large depending on the available computational power, the prediction time domain, and the complexity of the model used. In this case, the supervisor does not have the ability to adapt its commands to counteract any unplanned disturbances. In fact, if these disturbances are faster than the sampling step, the supervisor with fixed commands at that step will not be able to adapt its commands fast enough to reject the disturbances. In this case, power variation due to frequency setting may cause a problem. In fact, the power variation is random and fast.
Thus, the central idea of the present invention is to combine a predictive control algorithm with a multi-target regulator with sequential gains. The advantages of one make it possible to compensate, at least in part, for the weaknesses of the other, as highlighted in the following table.
Thus, the sequential gain control algorithm of the regulator 33 includes a plurality of linear regulators, each linear regulator being determined for a particular operating point of the nuclear reactor.
The operating points are staggered to cover a nuclear reactor power range from 25% to 100% of the nominal power of the nuclear reactor.
In the first control mode, each operating point is defined by the determined insertion position P of the first set of groupsbankCharacterised, typically by position PbankAre uniquely characterized.
Alternatively, the determined insertion positions P of the first set of groups are added to or replaced bybankEach operating point may also be characterized by one or more of the following physical parameters:
-a power level of the reactor;
-insertion position of Hbank group;
-a boron concentration;
-the temperature of the primary coolant at the inlet and outlet of the core;
-a primary fluid flow.
For example, each linear regulator is expressed in the following form illustrated in fig. 5:
uK＝K(s).y＝Kp(s)y1+Ki(s)y2wherein, y1Y and y2＝z
Wherein, KpAnd KiIs the gain matrix, s is the Laplace variable, Y is the current value of the output vector Y and the reference value of the output vector YrefZ is an operating parameter deviation vector between a current value of the operating parameter vector to be checked and a reference value of the operating parameter vector to be checked, and ukIs a vector of the commanded correction values.
The different vectors are composed as follows:
thus, we define the matrix KPAnd KIThe following were used:
and is
The method comprises the following steps: obtaining linear regulators, the step comprising, for each linear regulator, the sub-steps of:
-forming a linearized model of the nuclear reactor by linearizing a non-linear model of the nuclear reactor at corresponding operating points, the linearized model relating:
-an output deviation vector on the one hand and an operating parameter deviation vector,
on the other hand, at least one input disturbance dpDisturbance d of the correction value vector of the commandUDisturbance dy of output deviation vector y, and correction value vector u of commandKA linearization model and a linear regulator form a loop system for the insertion location (illustrated in FIG. 6);
-determining an operating constraint of the nuclear reactor to be observed for a predetermined disturbance dU of a vector U of at least one input predetermined disturbance dp or commanded correction value or a predetermined disturbance dy of an output deviation vector y;
-translating each operational constraint into a numerical condition to be observed for a transfer function between:
on the one hand, at least one input DUThe interference dp of (d), the interference dU of the corrected command vector U, or the interference dy of the output deviation vector y
-on the other hand, one of a difference between a current value of one of the operating parameters and a reference value of said operating parameter, or a difference between a current value of one of the outputs and a reference value of said output, or a commanded correction value;
-determining a gain matrix KpAnd KiIs determined by an optimization algorithm to at least stabilize the loop system for the corresponding insertion position and to satisfy all operational constraintsCorresponding numerical conditions.
The optimization algorithm is typically not smooth.
The nonlinear model of a nuclear reactor is as follows:
ρ(t)＝ρdop(t)+ρbarres(t)+ρmod(t)+ρbore(t)+ρXe(t)
wherein the content of the first and second substances,
and d ═ Pturb
The delay for neutron poison is expressed by the following relationship:
τAOIs AO time constant
τbcIs the thermal branch time constant
τbfIs cold branch time constant
τcoIs the time constant of the core
τGVIs GV whenConstant of room
c is the precursor concentration in the core
CbIs boron concentration
CPIs the specific heat capacity of the water in the primary circuit
KnIs the power conversion coefficient
n is the neutron density in the core
QPIs a primary loop water flow
Is the cold branch temperature at the GV level
ρ is reactivity
KdopKcKfKPKHKCBIs a coefficient that varies according to the core condition and introduces nonlinearity.
Linearization is performed according to any suitable method, for example by performing a Taylor (Taylor) expansion on an equation that includes the non-linearity around the operating point in question.
The linearized model around the operating point looks like this:
ρ(t)＝ρdop(t)+ρbarres(t)+ρmod(t)+ρbore(t)
ρmod(t)＝KcTc(t)+KfTf(t)
ρbarres(t)＝KPPb(t)+KHHb(t)
ρbore(t)＝KCBCb(t)
PK(t)＝Kn.n(t)
where the bold face coefficients are identified at each operating point.
These equations constitute G shown in FIG. 6LPVAnd (4) modeling.
We approximate the neutron poison injection delay by the Laguerre approximation defined as follows:
And LPV model GLPVIn combination, these equations constitute the model GR of fig. 6, i.e. the linearized model of the nuclear reactor at the operating point in question.
GLPVThe model may be expressed in the following form:
wherein the content of the first and second substances,
D11(π)＝D11＝θ3×1D21(π)＝D21＝θ3×1
D12(π)＝D12＝θ5×3D22(π)＝D22＝θ5×3
wherein the state x is defined by
The input vector is defined by:
u＝(vPbankvHbankuQ)T
interference vector is defined by d ═ PturbAnd (4) defining.
The interferences and constraints to be observed are those in the specifications defined above.
Translating operational constraints into digital conditions that can be used to determine the gain matrix involves specifically translating time constraints into frequency constraints. To this end, we seek a transfer function responsive to known requirementsIs calculated from the approximation of the maximum amplitude of the output signal y. Then, we use the transfer Ty→dNorm H of∞The norm characterizes its worst-case gain. From this gain, the maximum amplitude of the output signal is characterized as a function of the amplitude of the square wave signal for a defined stable initial state.
In general, consideration of time criteria is a difficult problem for control issues. In the present case, this is a major constraint of the control problem. The specification specifies certain time constraints that must be adhered to. For example, in any scenario, the average temperature should not exceed 1.5 ℃, i.e.
In the present invention, the maximum overshoot of certain parameters is characterized under known requirements, taking into account a stable initial state. The possible requirements are given by the following specifications: power steps of even up to 10% PN are adjusted in frequency with a 5% PN/min ramp. According to the expert knowledge of the Framatome (Framatome), the most unfavorable scenario (the most constraining regulation scenario) is a power step of P% of the nominal power PN of the nuclear reactor required by the turbine, P being between 5% and 15%, P being for example 10%.
Thus, it is assumed here that if the loop system complies with the specifications for the scenario: p% PN power step, it complies with the control target in all cases discussed.
Let us consider the excitation signal dP％This signal represents the worst case (power step of P%). The signal consists of a period T and an amplitude Δ PmaxThe square wave signal of P% PN is approximated, assuming it adequately represents a square wave. Such a signal has been shown in fig. 7 with a power step of 10% PN, where T is 100 seconds.
Let us decompose the Fourier series signal dp％Denoted s. We obtained known results for the following niches:
wherein
assuming a zero initial state (y (t-0) ═ 0), the amplitude of the output signal y is equal to the sum of the amplitudes of the harmonics times the gain of the transfer evaluated at the pulse of each harmonic.
The maximum amplification of the input signal s by the worst-case transfer function provides the maximum amplitude y of the output signal ymaxA good approximation of. Then we get:
||Ty→d||∞×smax～ymax
wherein s ismaxIs the most important of sA large amplitude. Now, due to the signal dP％So we obtain s-dP％And it follows that: smax～ΔPmax. Since we seek DmaxSo that y ismax≤DmaxWe found that:
||Ty→d||∞×ΔPmax≤Dmax
this equation is then used to express various criteria that reflect the constraints on the command. It is for this reason that we reformulate the requirements with mathematical criteria.
Wherein the content of the first and second substances,
du＝(dvPdvHduQ)Tis a disturbance of the vector of command values, and u ═ v (vP)bankvHbankuQ)TIs a vector of correction command values;
WRis a target modulus margin, this value being predetermined and equal to 0.5, for example;
is the power step and TmA transfer function between, wherein,ΔPmax＝P％.PN；
wherein the content of the first and second substances,
wherein the content of the first and second substances,is a transfer function between the power step and the rate of movement of the beam, wherein,
wherein the content of the first and second substances,is a transfer function between the power step and the neutron poison injection rate, wherein,
the linear regulator is preferably obtained also taking into account the following operating constraints:
a disturbance dp, which is a power step of ± P% of the nominal power PN of the nuclear reactor demanded by the turbine, P being between 5% and 15%, causes a minimum variation of the operating parameter.
The constraints translate into the following numerical conditions:
wherein K represents a gain matrix KpAnd KiAnd Ω denotes a set of gain matrices of the stable loop system,
As specified above, z ═ TmAO Pbank)TIs a vector of variation of the operating parameter to be controlled.
In general, WzThe frequency weighting matrix is defined by:
the weight selected for each channel is defined by:
frequency weighting for average temperature output
Frequency weighting for position output of Pbank
They are defined as follows:
where K1, K2, K3, τ 1, τ 2, and τ 3 are predetermined coefficients.
In the above equation, | | | | non-conducting phosphor∞Symbol H∞Norm, and | | | | luminance2Symbol H2And (4) norm. These norms are defined, for example, in j.m. maciejowski. multivariable Feedback design. addison-Wesley, 1989.
For at least the first control mode, the linear regulator is obtained taking into account the following operating constraints:
current value PbankWith reference value Pbank,refDifference P betweenbankIn thatAnd
The operating constraints translate into the following numerical conditions:
wherein the content of the first and second substances,is the power step and PbankA transfer function between, wherein,
further, in the first control mode, the operational constraint on the rate of movement of the beam is
gain matrix KpAnd KiThe determination of gain (c) is performed using a non-smooth optimization method well suited to solve the control problem. The tool used is for example Systune from matrix laboratories (Matlab). The tool has a complete integration environment, which allows the expression of the constraint H as described above2And H∞。
According to an advantageous variant, at a determined Pbank insertion position, the gain matrix K is determined by means of an optimization algorithmpAnd KiIn order to stabilize the loop system for said determined insertion positions while stabilizing the loop system for at least two adjacent determined insertion positions and while satisfying the digital conditions corresponding to all operational constraints (see fig. 8).
For example, the gain matrix K is determined by an optimization algorithmpAnd KiTo stabilize the loop system for said determined insertion position, andthe loop system is stabilized for four determined insertion locations adjacent to the insertion location on each side of the determined insertion location.
In practice, interpolation of LTI modulators synthesized at different operating points may pose certain difficulties, particularly when the synthesis of two modulators with two adjacent operating points does not provide modulators that are sufficiently close to each other. In this case, a regulator that interpolates between these two operating points does not necessarily constitute a viable solution, since it may cause instability, or it causes too abrupt transients when the coefficients change.
To address this problem, the determination of the gain at a given operating point includes a per-region multi-model approach as described above. The resulting regulator will check the constraints and will be optimal for all models in question.
In addition, the controller optimized at one operating point is used to initiate optimization at an adjacent operating point.
Finally, the variation of the coefficients of the adjuster matrix is constrained so as to keep its coefficients sufficiently close to those of the original adjuster (i.e., the adjacent adjuster).
For a scenario corresponding to a power ramp from 100% PN to 60% PN at 5% PN/min, the regulator 33 alone makes it possible to obtain the following performance:
|ΔAOmax|＝5.06％AO～5％AO；
these properties are true for Tm and Pbank, but are at the authorized limits for AO.
The supervisor 31 will now be described.
The model for the supervisor is the non-linear model described above. The benefits of this model are:
the effect of xenon was modeled.
The actual delay of boron is modeled.
More accurate than a linearized model.
The model equations are given above. We then define the model used by the supervisor as follows:
yS＝GS(xS,US)
wherein x isSIs state, USIs a signal of a reference command calculated by a supervisor, ySIs an output, FSAnd GSIs a function that defines state development and output as a function of input and state. Using the same notation as before, we get:
yS＝(TcTmAO PKPbank)T
and is
US＝(VPbankVHbankUQ)T
Wherein, VPbank、VHbankAnd UQIs a reference command for each actuator calculated by the supervisor.
Unlike the linearized model, which uses the laguerre approximation to represent neutron poison delays, this time the model is considered as follows:
wherein, UQDenotes neutron poison control, and hboreIndicating neutron poison delay. For example, the delay may be 300 seconds.
Typically, the following parameters are selected for the supervisor settings:
sampling: t isS100 (second)
Predicting a time domain: n is a radical ofp＝10
Command time domain: n is a radical ofc＝9
We composed of
the basis of the function for the command is the basis of a piecewise constant function. This means that the command will be constant over the sampling period and discontinuous from one sampling step to the next.
At each sampling step, the supervisor optimizes NcValue, define the command on each channel (Pbank, Hbank, and boron flow). We will want to
thus, at each sampling step, we will get:
thus, a matrixCorresponds to an optimization decision variable. Finally, at each sampling step j, the first annotated calculation command is then appliedThen, a control signal, denoted as U, is applied to the processSContinuously evolving according to the following relation:
the objective function in the discussion for the supervisor is based on the performance objectives defined above. The goal of the supervisor would be to calculate the reference commands for Pbank, Hbank, and neutron poison actuators, which minimizes the deviation of the parameters to be examined from their respective references.
The parameters to be checked are the same as the regulator 33:
annotated as TmThe average temperature of (2).
Expressed as the axial power distribution of AO.
Is denoted as PbankOf the first Pbank subset.
From Tm,ref、AOrefAnd Pbank,refReference is given to these parameters. We then fit TmAO and PbankAre set to deviations from the respective reference of the parameter to be checked such that:
Tm＝Tm-Tm,ref
AO＝AO-AOref
Pbank＝Pbank-Pbank,ref
the objective function is constructed as follows:
J＝JU+JZ
we define here
To simplify writing, we mean
Criterion J for controlZThen defined as follows:
and the criteria are defined as follows:
wherein the content of the first and second substances,and KQIs a weight, andandis a filtered command input. The latter is filtered in order to penalize high frequencies. We then define a high-pass filter on the command and the filtered signal is:
wherein the content of the first and second substances,
criterion defined by the above equation for conversion in discrete fields (whereA matrix of commands as defined above) is expressed in the following form:
in addition, we will use
the constraints imposed on the supervisor by the command problem are caused by requirements set out in the specifications regarding the requirements for the commands. The benefit of the supervisor 31 compared to the regulator 33 is its ability to explicitly consider regular time constraints, whether these constraints are related to inputs or state variables: here the position constraint and the maximum velocity of the set of beams and the maximum flow rate of dilution/boronation.
Then, we formulate the following constraints inferred from the specification:
the predictive control algorithm used in the present invention is as follows.
The model used to compute the output of the model from the commands (decision variables) is a nonlinear model. Given the constraints and the previously defined objective function, a nonlinear under-constraint optimization algorithm is required to solve this problem. For example, an algorithm is optimized under the constraint of non-linearity based on the interior point method, and as implemented by the matrix laboratory's function fmincont.
The supervisor algorithm is presented in the form of a schematic diagram in fig. 9. The figure gives an illustration of the different functions implemented and the flow of information they exchange at each sampling step.
At each sampling step, the supervisor receives the measurement Y from the system, to be checkedReference Z of the outputrefAnd the turbine power curve D usedU... during this sampling step:
-the supervisor updating the value of the initial state vector of the system at step k, this vector being represented as(assuming the complete state is reconstructed here),
-from the input data, the supervisor calculates the sequence of optimal commands by means of the function fmincon
Supervisor from tjTo tj+TSFirst element of command sequence to be calculated within a sampling periodThe method is applied to the actual system,
supervisor memory command sequenceTo initialize the optimization at the next sampling step,
-and finally, the supervisor memorizes the neutron poison commands applied (in step j) and updates the delayed neutron poison commands
For scenarios corresponding to a power ramp from 100% PN to 60% PN at 5% PN/min, the supervisor 31 alone makes it possible to obtain the following performance:
|ΔAOmax|＝4.62％AO<5％AO；
these properties are true for Tm and Pbank, but are at the authorized limits for AO.
Fig. 11 illustrates the performance obtained by the supervisor in the case of frequency adjustment, where the nominal power follows the curve illustrated in fig. 10.
We can see in fig. 11 that the supervisor alone cannot counteract the power variations due to frequency adjustment. The temperature exceeds the upper and lower limits defined by the specification.
Simulation results of the method of the present invention, which implements a hierarchical control including a supervisor and multi-target regulators with sequential gains, which will be referred to as SMORC for the supervised multi-target regulators of the core, will be described below.
The SMORC was simulated on the non-linear model of the reactor described above. To meet actuator demand requirements, saturation will be introduced to the requirements according to the maximum demand defined in the specification.
The behavior of SMORC was first tested on transient loads from 100% PN to 60% PN at 5% PN/min, and then the load was ramped up from 60% PN to 100% PN at the same speed. Second, the behavior was tested for a power step of 10% PN. Finally, the behavior is tested in the case of frequency adjustments superimposed on the transient load.
SMORC simulation curves for 100-60-100% PN power ramps at 5% PN/min are shown in FIGS. 12-19.
In this ramp scenario, SMORC provides the correct results for the control criteria. It can be seen that all outputs to be regulated remain in the authorized domain defined by the LCO, i.e., no outputs exceed their associated maximum and minimum limits.
We first note that the difference in mean temperature, AO and Pbank positions are 0.19 ℃, 2.9% AO and 6.7PE, respectively, or 12%, 58% and 22% of the maximum authorized deviation of these variables, respectively. We note that the difference in average temperature (in%) is lower than other variables due to prioritization of average temperature compared to other outputs, particularly due to frequency weighting
In addition, xenon is fully compensated for, even by variations in boron as expected by the regulator. It should also be noted that the velocity of the actuator saturates during the simulation. Therefore, they cannot exceed the physical limits of the actual actuator.
Let us now compare the results of SMORC with the results of the supervisor alone. We note that on the same scenario, all deviations of the output to be adjusted by the supervisor alone are higher than in the SMORC case; particularly because SMORC benefits from fine control, as opposed to a supervisor alone. We can therefore see here the benefits of the proposed hierarchical architecture.
Therefore, in view of the foregoing elements, we can say that SMORC exhibits good performance in this scenario.
Simulated curves for 100-90% PN power steps are shown in fig. 20-26.
The difference between the average temperature, AO and Pbank position was 1.0 deg.C, 5.09% AO and 19PE, respectively.
The conclusions of these simulation results are similar to those of the previous section, namely:
the outputs to be regulated are all maintained within the authorized operating range in question. The overshoot of the AO is very low and within a short period of time, which is to a large extent tolerable.
The static error is zero.
Actuator speed and flow saturation, thus satisfying the associated requirements.
Boron compensates well for the change in xenon concentration.
The apparent behavior of SMORC is to insert Hbank during load changes to assist average temperature control, then pull out to provide AO control.
However, we note that in this scenario, the AO is closer to the authorized limit than in the case of a load ramp. This is illustrated by the scenario studied here that is considered to be the maximum size customization in the question in question.
Finally, SMORC provides good results according to specifications, taking into account the previous elements.
SMORC simulation curves for 100-70% PN ramp at 5% PN/min with frequency adjustment are shown in FIGS. 27-33.
We note the difference in mean temperature, AO and Pbank positions as 0.47 deg.C, 3.3% AO and 10.1PE, respectively.
The conclusions of these simulation results are similar to those of the previous section.
The specification and adjustment method for the second control mode will now be described.
Only the points at which these specifications and this adjustment method differ from those of the first embodiment will be described in detail below.
The specification does not include a criterion for positional deviation of the first set of groups.
Each linear regulator of the sequential gain control algorithm is determined, again for a particular operating point of the nuclear reactor. On the other hand, each operating point is characterized by, and typically only by, the power required by the turbine.
The commands are only the velocity of the first set (group R) and the injection rate of the neutron poison or diluent fluid.
The controlled operating parameters include only the average core temperature and the axial power imbalance.
In addition to the content indicated for the first control mode, the output may also include the power required by the turbine.
The specification and the adjustment method for the third control mode will now be described.
Only the points at which these specifications and this adjustment method differ from those of the first embodiment will be described in detail below.
The specification does not include a criterion for positional deviation of the first set of groups.
The command is only the velocity of the first set, and the injection rate of the neutron poison or diluent fluid.
The controlled operating parameters include only the average core temperature and the axial power imbalance.
In addition to the content indicated for the first control mode, the output may also include the power required by the turbine.
According to an alternative embodiment applicable to the three control modes, the sequencing of the regulators is carried out by taking into account other parameters, such as for example the rate of combustion (burn-up) or the cycle. In other words, the gain matrix KpAnd KiIs varied in accordance with these parameters. To this end, we always do in the same way by building a linear model around the predetermined operating point and by interpolating the gains. However, the operating point is no longer characterized by a single parameter, but by three parameters that vary. These parameters may be, for example, Pbank position, burn (burn-up) rate, and cycle.
According to a second aspect, the invention relates to the nuclear reactor 1 described above. The nuclear reactor includes: a core 5 and a regulating assembly 25 for regulating the operating parameters of the core, including at least the average temperature of the core and the axial power imbalance.
The nuclear reactor 1 further comprises:
means 27 for acquiring at least one input DU、DPThe current value of (a);
means 29 for obtaining the current value Y of the output vector, the output comprising at least the operating parameters;
the adjustment assembly 25 includes:
a module 35 for using at least one input signal DU、DPForming a reference value Y of the vector of outputsref；
A supervisor 31 programmed to use at least one input DU、DPAnd a current value Y of the output vector, forming a control value vector U of the nuclear reactor by implementing a predictive control algorithmS；
A regulator 33 programmed to use a current value Y of the outputted vector and a reference value Y of the outputted vectorrefForming a correction value vector u of nuclear reactor commands by implementing a sequential gain control algorithmk；
A module 37 for using a vector U of command values generated by the supervisor 31SAnd a commanded correction value vector u generated by regulator 33kForming a correction value vector U of the nuclear reactor command; and
a module 39 for adjusting an operating parameter of the nuclear reactor by controlling the actuator using the vector U of corrected values of control.
The nuclear reactor 1 generally comprises:
-a tank 3;
a core 5 comprising a plurality of nuclear fuel assemblies, placed in the tank 3;
bundles 7 for controlling the reactivity of the core 5 and mechanisms 9, these mechanisms 9 being configured to move each bundle 7 in the direction of insertion into the core 5 or in the direction of extraction from the core 5;
a primary circuit 10 for cooling the core 5, in which a primary coolant circulates, comprising a
an injection circuit 15 configured to selectively inject a neutron poison or a diluent fluid without a neutron poison into the primary heat transfer fluid.
The neutron poison is typically boron. The diluent fluid is typically water.
In this case, controlling advantageously comprises controlling at least one rate of movement of the beam and at least one rate of injection of the neutron poison or dilution fluid.
Typically, the control component 25 is configured to move the beams 7 in groups. The beams of the same group move together and are always all in the same insertion position.
Advantageously, the groups are divided into one or more sets. The distribution of the groups and their use depends on the control mode of the nuclear reactor.
In some control modes, several groups are grouped in a first group.
In this case, the groups of the first set are typically moved sequentially. This means that they are inserted one after the other with a predetermined overlap, as follows. Alternatively, the overlap may be variable.
According to an alternative embodiment, all groups of the first set move together. This is understood to mean that they are always all in the same insertion position and move together.
In other control modes, the first set has only one group.
In some control modes, other groups are grouped in a second group.
In this case, the groups of the second subset typically move together.
In other control modes, all groups are aggregated in a first set and there is no second set.
Several examples of control modes, inspired by modes T, G and A, respectively, will be described in detail below.
In a control mode particularly suitable for EPR (european pressurized reactor) inspired by the T mode, the groups are divided into two sets:
-a first set, called Pbank;
a second set, called Hbank.
The first set is particularly suitable for controlling the average temperature Tm. The second set Hbank is generally particularly suitable for controlling the axial offset AO.
The groups of the first Pbank set move sequentially. The groups of the second Hbank set move together.
In a second control mode inspired by G-mode, the groups are divided into two sets:
the first set comprises the R groups formed by the black beams (i.e. the very absorbing ones);
the second set of PCGs, called the set for power compensation, consists of groups G1 and G2(G for the grey beam) and groups N1 and N2(N for the black beam). The absorption of the gray beam is relatively lower than that of the black beam.
The groups of the second subset are inserted sequentially. Advantageously, they are inserted according to the electric power requested by the turbine.
In this second control mode, AO is advantageously controlled primarily by injection of neutron poison or diluent fluid.
In a third control mode inspired by mode a, the functional groups are all grouped together in a first set, here denoted by the acronym DCBA.
This is typically composed of four sets A, B, C and D, which are inserted in sequence like Pbank.
The first set is particularly suitable for controlling the average temperature Tm.
In this third control mode, AO is advantageously controlled primarily by injection of neutron poison or diluent fluid.
In some control modes (e.g., the first control mode), the at least one rate of movement of the control beam typically includes a rate of movement of a group of the first Pbank set and a rate of movement of a group of the second Pbank set. These velocities are noted as vP, respectivelybankAnd vHbank。
In other control modes (e.g., the second and third control modes), at least one rate of movement of the control beams generally corresponds to a rate of movement of the groups of the first set.
The adjustment assembly 25 is configured to implement the adjustment method already described above.
In particular, the supervisor 31 and the regulator 33 are as described above with respect to the regulating method.
Modules 35 and 37 are also described above.
The means 25, 27 are as described above.
The operating parameter adjustment module 39 is configured to send commands to actuators, which are the mechanisms 9 for moving the beam 7 and the implantation loop 15.
Preferably, the management of the groups, in particular the distribution of the groups in the first and second sets Pbank and Hbank, and the movement of the first and second sets is performed as described above.
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