KR102294093B1 - Burnup adaptation method and apparatus - Google Patents

Abstract

(상기 I_Z는 축 노드 지수(axial node index), 상기 M_B와 M_Z는 핵연료 집합체 연소도 조정 인자, 상기 BU_old는 수정 전의 연소도, 상기 BU_new는 새롭게 수정된 연소도, 상기 Shape는 축방향 연소도 분포(axial BU distribution)를 조정하는 형상 함수)A burnup adjustment apparatus according to an embodiment of the present invention includes a storage unit for storing data actually measured in a nuclear fuel assembly, an adjustment unit for adjusting the burnup of the nuclear fuel assembly, and an output distribution of the nuclear fuel assembly with the adjusted burnup. Including a measuring unit that calculates, wherein the adjusting unit adjusts the burnout by using the following equation (1).
Formula (1)

(The I _Z is the axial node index, the M _B and M _Z are the nuclear fuel assembly burn-up adjustment factors, the BU _old is the burn-up before modification, the BU _new is the newly modified burn-up, and the Shape is shape function that adjusts the axial BU distribution)

Description

BURNUP ADAPTATION METHOD AND APPARATUS

The present invention relates to a method and an apparatus for adjusting the degree of combustion by correcting an error for an unpredictable phenomenon related to combustion.

Physical phenomena in the reactor can be simulated and calculated through the core design code. In general, the STREAM/RAST-K code system is used. Here, the STREAM code is the neutron transport analysis code, and the RAST-K code is the neutron diffusion analysis code. However, during actual operation of a nuclear reactor, operating conditions are changed due to various unknown phenomena, and it is difficult to quantify all these phenomena through code calculation. Due to such an unpredictable phenomenon, the simulated calculation has a difference from the actual measured value. Therefore, in order to accurately predict a physical phenomenon, the difference must be corrected.

Korea Registration Gazette, No. 10-1002981 (Registered on Dec. 15, 2010)

SUMMARY OF THE INVENTION An object of the present invention is to provide a method and apparatus for adjusting the degree of combustion by correcting an error for an unpredictable phenomenon related to combustion.

However, the problems to be solved of the present invention are not limited to those mentioned above, and other problems to be solved that are not mentioned can be clearly understood by those of ordinary skill in the art to which the present invention belongs from the following description. will be.

The apparatus for adjusting the location burnout according to an embodiment of the present invention includes a storage unit for storing data actually measured in a nuclear fuel assembly, an adjustment unit for adjusting the burnup of the nuclear fuel assembly, and the adjusted combustion degree of the nuclear fuel assembly. A burn-up adjustment device comprising a measuring unit for calculating an output distribution, wherein the adjusting unit adjusts the burn-up by using Equation (1) below.

Formula (1)

(The I _Z is the axial node index, the M _B and M _Z are the nuclear fuel assembly burn-up adjustment factors, the BU _old is the burn-up before adjustment, the BU _new is the newly adjusted burn-up, and the Shape is shape function that adjusts the axial BU distribution)

In addition, the measurement unit may obtain the number density of nuclides of the nuclear fuel assembly by applying the adjusted burnup to the following equation (2).

Equation (2)

(The ND _new is the number density of the newly modified nuclide, the ND _old is the number density of the nuclide before fertilization, the ND _{Table, old} is a value obtained from the nuclear cross-section information using the burnup before adjustment, and the ND _{Table, new} is the adjusted Values obtained from nuclear cross-section information using burnup)

The method for adjusting the location burnout according to an embodiment of the present invention includes the steps of adjusting the burnup, correcting the number density of nuclides with the adjusted burnup, and power distribution of a nuclear fuel assembly with the modified number density of the nuclides Including the step of correcting, the step of adjusting the burn-up is to apply the following equation (1).

Formula (1)

(The I _Z is the axial node index, the M _B and M _Z are the nuclear fuel assembly burn-up adjustment factors, the BU _old is the burn-up before adjustment, the BU _new is the newly adjusted burn-up, and the Shape is shape function that adjusts the axial BU distribution)

In addition, in the step of correcting the number density of the nuclide, the following formula (2) may be applied.

Equation (2)

(The ND _new is the number density of the newly modified nuclide, the ND _old is the number density of the nuclide before fertilization, the ND _{Table, old} is a value obtained from the nuclear cross-section information using the burnup before adjustment, and the ND _{Table, new} is the adjusted Values obtained from nuclear cross-section information using burnup)

In addition, the variables M _B and M _Z may be values such that G(x) is minimized in Equation (3) below.

Equation (3)

(The RMSE is the root mean square error of the difference between the calculated two-dimensional radial power distribution and the measured two-dimensional radial power distribution, the ASI is the axial output deviation, and the ASI _ref is the Axial output deviation obtained through the measured value, where x is a matrix satisfying Equation (4) below)

Equation (4)

In addition, a value that minimizes G(x) can be obtained by the following formula (5).

Equation (5)

Also, x can be updated from the following equation (6).

Equation (6)

(The x ⁽⁰⁾ is the initial guess, the γ ₀ is the learning rate, and the J _G is the Jacobian matrix)

_{In addition, the J G} is obtained through Equation (7) below, and the J _G may be updated whenever the x is obtained.

Equation (7)

(The above x ⁽⁰⁾ , x ^(-1) and x ^(-2) are different values)

The combustion degree adjustment method and apparatus according to an embodiment of the present invention can more accurately simulate combustion-related physical phenomena.

1 is a block diagram of a burnup control apparatus according to an embodiment of the present invention.
2 is a flowchart of a burn-up adjustment method according to an embodiment of the present invention.
3 is a diagram illustrating a shape function.
4 is a graph in which RMSE and ASI are calculated to obtain G(x).
5 is a graph simulating the power distribution of a nuclear reactor.

Advantages and features of the present invention and methods of achieving them will become apparent with reference to the embodiments described below in detail in conjunction with the accompanying drawings. However, the present invention is not limited to the embodiments disclosed below, but may be implemented in various different forms, and only these embodiments allow the disclosure of the present invention to be complete, and common knowledge in the art to which the present invention pertains It is provided to fully inform those who have the scope of the invention, and the present invention is only defined by the scope of the claims.

In describing the embodiments of the present invention, if it is determined that a detailed description of a well-known function or configuration may unnecessarily obscure the gist of the present invention, the detailed description thereof will be omitted. In addition, the terms to be described later are terms defined in consideration of functions in an embodiment of the present invention, which may vary according to intentions or customs of users and operators. Therefore, the definition should be made based on the content throughout this specification.

1 is a block diagram of a burn-up adjustment apparatus 100 according to an embodiment of the present invention, FIG. 2 is a flowchart of a burn-up adjustment method according to an embodiment of the present invention, and FIG. 3 shows a shape function It is a diagram, and FIG. 4 is a graph obtained by calculating RMSE and ASI to obtain G(x), and FIG. 5 is a graph simulating the power distribution of a nuclear reactor.

A nuclear reactor is operated while having an operating cycle, and it is necessary to predict what kind of power distribution it will have in the next operating cycle through the reactor data of the previous cycle and prepare for the operation of the reactor. Accordingly, the burnup adjustment device 100 should perform a simulation so that the simulated result by adjusting the burnup of the fuel assemblies of the nuclear reactor is similar to the actual measured value.

The combustion control apparatus 100 includes a storage unit 110 , an adjustment unit 120 , and a measurement unit 130 . The storage unit 110 stores data actually measured in the nuclear fuel assembly of the nuclear reactor. Measured data is saved every time a nuclear reactor is operated, and the stored data can be utilized when simulating the power distribution of a nuclear reactor.

The adjusting unit 120 adjusts the degree of combustion of the nuclear fuel assembly. Accurate prediction is possible when simulating the operation of a nuclear reactor by adjusting the burnout. The data of the storage unit 110 is used when adjusting the burn rate.

The measurement unit 120 performs a simulation of the actual operation of the nuclear reactor. It is possible to predict how the nuclear reactor will operate by calculating the power distribution of the nuclear fuel assembly by using the burnup adjusted by the adjusting unit 120 .

A detailed operation of the combustion control device 100 will be described in detail below.

Referring to FIG. 2 , the burnup adjustment method for calculating the power distribution of a nuclear fuel assembly includes the steps of adjusting the burnout ( S100 ), correcting the number density of nuclides with the adjusted burnup ( S110 ), and the number density of the modified nuclides. A step (S120) of correcting the output distribution of the nuclear fuel assembly is performed.

The step of adjusting the burnout (S100) is performed by the adjusting unit 120 and can be obtained by applying [Equation 1].

In [Equation 1], IZ is an axial node index, M _B and M _Z are nuclear fuel assembly burn-up adjustment factors, BU _old is the burnup before adjustment, BU _new is the newly adjusted burnup, the Shape is a shape function that adjusts the axial burnup distribution. The shape function is fixed to a sinusoidal shape as shown in FIG. 1 and controls the axial combustion control.

The adjusted burn-up can be obtained by using the burn-up before adjustment, the variables M _B and M _{Z , and the shape function.}

Then, the number density of the nuclides can be modified through the adjusted burn-up (BU _{new ).} Correcting the number density of nuclides (S110) is performed by the measurement unit 120 and can be obtained by applying [Equation 2].

In [Equation 2], ND _new is the number density of newly modified nuclides, ND _old is the number density of nuclides before fertilization, ND _Table,old is the value obtained from the nuclear cross-section information using the burnup before adjustment, ND _Table,new is Values obtained from nuclear cross-section information using the adjusted burn-up.

The number density ND _{new of the modified nuclide can be obtained by using the number density ND old} of the nuclide before fertilization, and the number density cross-sectional area table of the nuclide using the burn-up before adjustment and the adjusted burn-up. By adjusting the burnout, the number density of the nuclides can be modified accordingly.

Here, the nuclear cross-section information is generally used by interpolation with respect to variables such as burnup and nuclear fuel temperature in a three-dimensional whole-core analysis, and can be obtained through a two-dimensional nuclear fuel assembly analysis. Specifically, the nuclear cross-section information calculated through the two-dimensional nuclear fuel assembly analysis can be functionalized with respect to various variables such as burn-up (BU), nuclear fuel temperature, and coolant temperature. Variables M _B and M _Z can be obtained through [Equation 3].

[Equation 3] is a matrix, and RMSE is the root mean square error of the difference between the calculated two-dimensional radial power distribution and the measured two-dimensional radial power distribution (specifically, the fuel assembly burnup adjustment factor) Relative error between the simulated aggregate output and experimental values using the burnup adjusted by M _B , M _{Z ), ASI is the axial shape index, and ASI ref} is the axis obtained from the measured values of the nuclear fuel assembly. It is the direction shape exponent. _{ASI ref} may be obtained through the reactor measurement data stored in the storage unit 110 . Variables M _B and M _Z may be set to a value at which G(x) of [Equation 3] is the minimum. The meaning that G(x) becomes the minimum means that the value most similar to the actual measured value is to be found and selected.

x of G(x) is the same as [Equation 4].

x is a matrix of _{variables M B} and M _{Z .}

RMSE(x) and ASI(x) can be implemented as a graph as shown in FIG. 4 , and through this, variables M _B and M _Z that minimize G(x) can be obtained.

[Equation 5] can be used to obtain a value that minimizes G(x).

The value at which the F(x) function minimizes is the value at which G(x) becomes the minimum. RMSE(x) is 0 or minimum, ASI _ref - ASI(x) is 0 or minimum is a value at which F(x) is minimum, and eventually G(x) is a minimum value.

Meanwhile, in order to obtain F(x), an initial guess value of x is required, and the value of x that changes after the initial guess value must be continuously applied to [Equation 5]. [Equation 6] is used to update the initial value of x and x.

In [Equation 6], x ⁽⁰⁾ is an initial guess value, x ⁽¹⁾ is the next value of x ⁽⁰⁾ _{, γ 0} is a learning rate, and J _G is a Jacobian matrix.

The Jacobian matrix of [Equation 6] can be obtained through [Equation 7].

^{x (0)} , x ^(-1), and x ^(-2) in [Equation 7] are different values, and the Jacobian matrix J _G changes whenever the value of x is updated.

As the value of x is updated, G(x) of [Equation 3] can be expressed as a graph as shown in FIG. 4, and x that satisfies the minimum value of G(x) is finally selected to become the corrected burnup BU _new .

The power distribution of the nuclear fuel assembly is corrected by using the number density of the modified nuclides. Correcting the output distribution of the nuclear fuel assembly ( S120 ) is performed by the measurement unit 130 .

5 shows a comparison between the simulated result (BU Adaptation) and the actual measured data (Measured). "BU Adaptation" was obtained using the adjusted burnup (BU Adaptation), and it can be seen that the calculated ASI is quite similar to the actual measured data (Measured).

On the other hand, the idea of the present invention may be implemented in the form of a computer program stored in a computer-readable recording medium, or stored in a computer-readable recording medium storing the computer program.

The above description is merely illustrative of the technical idea of the present invention, and various modifications and variations will be possible without departing from the essential quality of the present invention by those skilled in the art to which the present invention pertains. Therefore, the embodiments disclosed in the present invention are not intended to limit the technical spirit of the present invention, but to explain, and the scope of the technical spirit of the present invention is not limited by these embodiments. The protection scope of the present invention should be interpreted by the following claims, and all technical ideas within the scope equivalent thereto should be interpreted as being included in the scope of the present invention.

100: combustion control device
110: storage unit
120: adjustment unit
130: measurement unit

Claims (10)

a storage unit configured to store data actually measured in the nuclear fuel assembly;
an adjustment unit for adjusting the burn-up of the nuclear fuel assembly; and
Comprising a measuring unit for calculating the output distribution of the nuclear fuel assembly with the adjusted burnup,
The burner adjusting unit adjusts the burnup by using the following formula (1).
Formula (1)

(The I _Z is the axial node index, the M _B and M _Z are the nuclear fuel assembly burn-up adjustment factors, the BU _old is the burn-up before modification, the BU _new is the newly modified burn-up, and the Shape is shape function that adjusts the axial BU distribution) The method of claim 1,
The measuring unit applies the adjusted burnup to the following equation (2) to obtain a number density of nuclides of the nuclear fuel assembly.
Equation (2)

(The ND _new is the number density of the newly modified nuclides, the ND _old is the number density of the nuclides before fertilization, the ND _{Table, old} is the value obtained from the nuclear cross-section information using the burnup before adjustment, ND _{Table, new} is the adjusted combustion Values obtained from nuclear cross-section information using diagrams) A method for calculating the burn-up of a nuclear fuel assembly, the method comprising:
adjusting the burnout;
modifying the number density of nuclides with the adjusted burnout; and
modifying the power distribution of the nuclear fuel assembly with the number density of the modified nuclides;
The step of adjusting the burnup is to apply the following formula (1)
How to adjust burnout.
Formula (1)

(The I _Z is the axial node index, the M _B and M _Z are the nuclear fuel assembly burn-up adjustment factors, the BU _old is the burn-up before adjustment, the BU _new is the newly adjusted burn-up, and the Shape is shape function that adjusts the axial BU distribution) 4. The method of claim 3,
The step of correcting the number density of the nuclide is to apply the following formula (2)
How to adjust burnout.
Equation (2)

(The ND _new is the number density of the newly modified nuclides, the ND _old is the number density of the nuclides before fertilization, the ND _{Table, old} is the value obtained from the nuclear cross-section information using the burnup before adjustment, ND _{Table, new} is the adjusted combustion Values obtained from nuclear cross-section information using diagrams) 4. The method of claim 3,
The variables M _B and M _Z are values that minimize G(x) in Equation (3) below.
How to adjust burnout.
Equation (3)

(The RMSE is the root mean square error of the difference between the calculated two-dimensional radial power distribution and the measured two-dimensional radial power distribution, the ASI is the axial shape index, and the ASI _ref is the Axial shape index obtained through the measured value, where x is a matrix satisfying the following equation (4))
Equation (4)

6. The method of claim 5,
To obtain a value that minimizes G(x) by the following formula (5)
How to adjust burnout.
Equation (5)

(The F(x) is a function for obtaining the value such that the G(x) is a minimum) 7. The method of claim 6,
where x is updated from the following equation (6)
How to adjust burnout.
Equation (6)

(The x ⁽⁰⁾ is the initial guess, the γ ₀ is the learning rate, and the J _G is the Jacobian matrix) 8. The method of claim 7,
_{The J G} is obtained through the following equation (7), and the J _G is updated every time the x is obtained.
How to adjust burnout.
Equation (7)

(The above x ⁽⁰⁾ , x ^(-1) and x ^(-2) are different values) A computer program stored in a computer readable recording medium programmed to perform including each step included in any one of claims 3 to 8. A computer-readable recording medium storing a computer program programmed to perform including each step included in any one of claims 3 to 8.

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