METHOD AND APPARATUS FOR MEASURING POWER DISTRIBUTION IN A REACTOR CORE

Abstract

Method and apparatus for measuring a power distribution in a reactor core. This method measures a power distribution in a reactor core according to a neutron transport equation representing the relationship between the power densities of a plurality of fuel elements in a pressure vessel of a nuclear reactor, the output signals from neutron detectors at locations of the plurality of neutron detectors inside and outside the pressure vessel, and a detector sensitivity relative to the positions of the fuel elements and the neutron detectors. The power distribution of the nuclear reactor core is calculated from the product of the matrix of output signals from the neutron detectors and the pseudo-inverse matrix relative to the detector sensitivity.Measuring the internal power distribution of nuclear reactors with limited spaces for neutron detector insertion, such as high-temperature gas reactors and fast reactors, is now possible. [Selection drawing] FIG. 3.

Description

Title of the invention: METHOD AND APPARATUS FOR MEASURING A POWER DISTRIBUTION IN A REACTOR CORE Technical field

[0001] The present invention relates to a method and apparatus for measuring a power distribution in a reactor core by inverse solution using signals from neutron detectors. Basic technology

[0002] In current light water reactors, the environment inside the reactor is at a temperature of about 300 to 400 °C. Therefore, neutron detectors are loaded directly near the reactor fuel assembly, the power distribution is measured and the fuel combustion in the reactor is controlled according to the measured power distribution (patent document 1). On the other hand, since the temperature inside a high temperature gas-cooled reactor (HTGR) reaches up to about 1000 °C and that in a fast reactor reaches about 600 °C, no attempt has been made to measure the power distribution in the reactor core.

[0003] [Patent Document 1] Patent No. 5,954,902 Summary of the invention Problems that the invention aims to solve

[0004] In recent years, efforts have been made to develop high-temperature resistant neutron detectors, such as ceramic detectors, but inserting the detectors into the reactor coolant outlet area in a gas-cooled high-temperature reactor is not practical, and the insertion location in the reactor core is limited. Moreover, from the point of view of the internals of a reactor, in gas-cooled high-temperature reactors and fast reactors it seems realistic to insert the detector within the reactor using control rod guide tubes. Placing a detector directly near each fuel body is not practical.

[0005] As described above, the present invention makes it possible to measure the internal power distribution of reactors such as gas-cooled high-temperature reactors and fast reactors, where neutrons have a long range and detectors cannot be inserted into the reactor core, or if they can be inserted, their insertion location is limited.

[0006] A main objective of the present invention is to make possible the measurement of the internal power distribution of nuclear reactors such as high-temperature gas reactors and fast reactors, in which the locations where neutron detectors are inserted are limited. However, it goes without saying that this method can also be applied to light-water reactors such as boiling water reactors and pressurized water reactors, in which the neutron detector can be inserted relatively freely. Ways to solve the problem

[0007] A method for measuring power distribution according to a first aspect of the present invention is as follows. A method of measuring a power distribution in a reactor core, according to a neutron transport equation representing the relationship between power densities of a plurality of fuel elements in a pressure vessel of a nuclear reactor, output signals from neutron detectors at locations of the plurality of neutron detectors inside and outside the pressure vessel, and a detector sensitivity relative to the positions of the fuel elements and the neutron detectors, characterized in that the power distribution of the nuclear reactor core is calculated from the product of the matrix of the output signals of the neutron detectors and the pseudoinverse matrix relating to the detector sensitivity.

[0008] More specifically, the method for measuring a power distribution in a reactor core according to the present invention, according to a neutron transport equation representing the relationship between a power density pi of n fuel elements i inside the pressure vessel, a neutron detector signal Rj at m detector positions j inside and outside the pressure vessel, and a detector sensitivity wj,i relative to a fuel element i) and a detector position], comprises the following steps: (1) obtaining the signal from the neutron detector from the following equation:

[0009] [Math.l] (2) the representation of the neutron detector signal Rj, the power density pi and the detector sensitivity wj,i in a matrix representation of the following equation,

[0010] [Math.2] R = WP (3) the calculation of a pseudo-inverse matrix W+ of the matrix representation of the detector sensitivity wj,i using the matrix representation of the following equation,

[0011] [Math.3] (4) calculating the matrix representation of the power density pi using the following equation which represents the matrix representation of the neutron detector signal Rj and the pseudo-inverse matrix W+.

[0012] [Math.4]

[0013] An apparatus according to a second aspect of the present invention has the following configuration.

[0014] An apparatus for measuring a power distribution of a reactor core, according to a neutron transport equation representing the relationship between power densities of a plurality of fuel elements in a pressure vessel of a reactor, neutron detector signals at a plurality of detector positions inside and outside the pressure vessel and a detector sensitivity relative to the position of the fuel element and the detector, which comprises: a computer for inputting signals from neutron detectors and performing a predetermined calculation according to a computer program; and a memory device for storing the computer program that enables the computer to calculate the power distribution of the reactor core by inverse analysis of the detector sensitivity.

[0015] More specifically, the apparatus for measuring a power distribution in a reactor, according to a neutron transport equation representing the relationship between a power density pi of the n multiple fuel elements i in the pressure vessel, neutron detector signals Rj at m multiple detector positions j inside and outside the pressure vessel, and a detector sensitivity wj,i relative to the fuel elements i and the detector positions j, wherein the above-mentioned program executes the following steps: (1) obtaining the neutron detector signal from the following equation:

[0016] [Math.5] (2) the representation of the neutron detector signal Rj, the power density pi and the detector sensitivity wj,i in a matrix representation of the following equation,

[0017] [Math.6] R = WP (3) the calculation of the pseudo-inverse matrix W+ of the matrix representation of the detector sensitivity wj,i by the matrix representation of the following equation,

[0018] [Math.7] (4) calculating the matrix representation of the power density pi using the following equation which represents the matrix representation of the neutron detector signal Rj and the pseudo-inverse matrix W+.

[0019] [Math.8] P = R Effects of the invention

[0020] The present invention produces the following effects. (1) For a small core with long neutron range, the power distribution in the core can be measured using detector signals from only the external detectors. (2) If the detector can be inserted into the reactor and the insertion location is limited, the internal power distribution of the entire core can be measured from the detector signals at the limited location in the reactor.

[0021] As described above, even in a short-neutron-range light water reactor, by applying the present invention it is possible to measure the power distribution in the reactor, and the resolution of the power distribution measurement can be improved more than before. Brief description of the figures

[0022] [Fig.l] [Fig.l] is an explanatory diagram of the detection sensitivity of external detectors in light water reactors.

[0023] [Fig.2] Figure 2A is an explanatory diagram of the detection sensitivity of a external detector in a gas-cooled high-temperature reactor, and Figure 2B is an explanatory diagram of the detection sensitivity of an internal detector.

[0024] [Fig.3] [Fig.3] is a flowchart schematically showing a method of measurement of the power distribution in the reactor according to the present invention.

[0025] [Fig.4] [Fig.4] is a schematic explanatory diagram illustrating the relationship of position between an external detector used to measure the power distribution in the core according to the present invention and the reactor core;

[0026] [Fig.5] [Fig.5] is a diagram showing an example of training a external detector in a gas-cooled high-temperature reactor.

[0027] [Fig.6] [Fig.6] is a diagram showing an example of training a internal detector in a gas-cooled high-temperature reactor. Method of carrying out the invention

[0028] As shown in [Fig.l], the detection sensitivity of the external detectors for Each fuel assembly in a light water reactor is limited to the fuel assemblies located on the outer periphery of the core. Therefore, it is in principle impossible to directly measure the power distribution at locations internal to the center of the reactor using external instrumentation. In pressurized water reactors (PWRs), as disclosed, for example, in patent No. 5954902, to monitor the axial power deviation of the power distribution up and down the core in the axial direction (axial shift) in order to control the Xe oscillation, the axial shift is evaluated by the external instrumentation. Although the purpose is to evaluate the power distribution, it is actually a problem of determining the absolute value of the assumed power distribution from the measured values ​​of the periphery.Since the power distribution itself at the center of the core is assumed, it is not possible to obtain a detailed power distribution used for combustion control, which is the subject of the present invention.

[0029] Indeed, light water has excellent performance as a moderator in light water reactors, so that the neutrons generated by nuclear fission collide with the hydrogen contained in the light water and instantly transform into thermal neutrons, which are easily absorbed by the nuclear fuel materials. As a result, the range is very short and, as shown in [Fig.l], the neutrons generated in the center of the core hardly escape from the reactor.

[0030] On the other hand, [Fig. 2] shows the detector sensitivity assuming the arrangement of the external detectors 1 and the internal detectors 2 as assumed in the present invention, for the HTTR engineering test reactor system of the high-temperature gas-cooled reactor. It can be seen that the detector sensitivity is distributed over a wider range than that of the light water reactor. With this characteristic being assumed, we present a technique for inverse analysis of the detector signal and reconstruction of the power distribution. The measurement principle is as follows. As shown in [Fig. 2], the neutron sensitivity from the detector position to the nuclear fuel region is evaluated in advance by neutron transport calculations.

[0031] [Math.9] r)S(r)dr3 (ij

[0032] w(r,rd) is the detector sensitivity for neutrons generated at a reactor core position r to be detected at a detector position rd, and S(r) is the fission neutron source. On the other hand, in order to evaluate the detector sensitivity, it is necessary to solve the following neutron transport equation.

[0033] [Math. 10] L <j)(r)=S(r) (2)

[0034] L is the neutron loss operator, which expresses the loss of neutrons due to neutron transport, scattering, and absorption. Consequently, the detector response of the obtained neutron flux (])(r) becomes the detector signal.

[0035] [Math. 11] R(r* r) = ^(r) (3)

[0036] Sd indicates the cross section of the neutron reaction in the detector. R(rd,r) is the detector signal at detector position rd due to neutrons generated at internal position r.

[0037] If we assume here that the neutron source S(r) is a unitary fission source from the internal position p alone,

[0038] [Math. 12] S(r) = (4j

[0039] where x is the fission spectrum

[0040] Since this reaction speed itself constitutes the detector sensitivity,

[0041] [Math. 13] w(w)=R(rj,r) (5)

[0042] On the other hand, for convenience, since the power distribution is evaluated for a fuel element of a specific width, the detector sensitivity must also be defined for the fuel element, defined as follows:

[0043] [Math. 14] (6)

[0044] This is the sensitivity when detecting neutrons at the detector position] for neutrons generated by the fuel element i.

[0045] On the other hand, to obtain the detector sensitivity, it is necessary to perform a neutron transport calculation using equation (2) for the number of fuel elements, in which neutron sources distributed only in a specific region of the fuel element i, which is expressed in equation (4), are used. Since this increases the calculation time and may introduce errors due to the large number of numerical processes, the following solution method for the adjoint neutron transport equation is generally used.

[0046] [Math. 15] lW, / .(7)

[0047] In this equation, lt is the adjoint neutron loss operator, and / rj is the adjoint neutron flux. Accordingly, the detector sensitivity in equation (5) can be expressed as follows.

[0048] [Math. 16] ^(¾ r) =.1(1)7¾ r, E)x(r, E}dE (8)

[0049] In this calculation method, the detector sensitivity for each fuel element can only be evaluated by solving the adjoint neutron transport equation (7) once and performing the work of tabulating equations (6) and (8).

[0050] Here, the detector signal Rj at detector position j can be expressed by the sensitivity wj,i at detector position j for fuel element i and the power density pi for fuel element i as follows. To clarify the physical picture, the fission neutron source is replaced by the power density, which is proportional to the fission neutron source.

[0051] [Math. 17] Ln

[0052] Obtaining detector signals at multiple detector positions j produces multiple equations which, in matrix representation, can be expressed as:

[0053] [Math. 18] R = WP (10)

[0054] If n is the number of fuel elements and m is the number of detector positions, the detector sensitivity is a matrix of m rows and n columns. If the number of fuel elements and the number of detector positions are the same, n = m, and if the row vectors of the detector sensitivities are linearly independent, the detector sensitivity matrix W is a regular matrix of n rows and n columns, and the inverse matrix is ​​said to have

[0055] [Math. 19] P=W a R (11)

[0056] In this case, the power density vector p can be obtained directly from equation (11) as an exact solution. This is synonymous with the theorem that a number of equations equal to the number of variables is required as a condition for obtaining the solution of simultaneous linear equations. However, in reality, the linear independence of the detection efficiency of n arbitrarily measured measuring points is not guaranteed. Even if n measuring points are defined, it is quite possible that m as a linearly independent measuring point becomes m <n.

[0057] On the other hand, finding the least squares solution gives a general expression which includes this exact solution.

[0058] [Math.20] j^||w-æ|| 2 (12)

[0059] The condition for minimizing the squared error J defined by equation (12) is the solution of

[0060] [Math.21] VJ = 0 (13)

[0061] This solution is obtained in the form

[0062] [Math.22] p^W^R (14)

[0063] [Math.23] w+= (w^w^w 7 ” (15)

[0064] The steps up to this point are briefly illustrated in [Fig.3] where W+ is called a pseudo-inverse matrix. As described above, W is an mxn matrix, which has no inverse unless n = m and the row vectors of the detector sensitivities are linearly independent. If this condition is satisfied,

[0065] [Math.24] W + =W ! (16)

[0066] By the same calculation, an exact solution similar to that of equation (11) can be obtained. On the other hand, when n^m, the solution obtained by equation (14) is said to be a least squares solution but is not unique, i.e., it is not guaranteed to be a true value.

[0067] Here, when m <n, autrement dit, lorsque le nombre d’équations est insuffisant pour le nombre de variables (dans ce cas, le nombre de points de mesure est insuffisant), la solution en tant qu’équations linéaires simultanées ne peut pas être déterminée. Bien qu’il soit possible de déterminer la solution comme une solution approximative qui minimise l’erreur au carré indiquée à l’équation (13), comme cela sera confirmé dans des expériences numériques ultérieures, une erreur se produit dans la distribution de puissance prévue en raison de l’absence de points de mesure.

[0068] Conversely, if m>n, i.e. if there are more equations than the number of variables (here, the number of measurement points), then again this is a least-squares solution which is considered non-unique. However, as will be confirmed in later numerical experiments, in this problem exact solutions are obtained even when an excessive number of measurement points is defined. This is self-evident from the following point of view. Indeed, if the number of equations is large, the exact solution can be obtained using equation (16) by ignoring the number of equations.

[0069] For example, if the sensitivities of detectors at m measuring points are linearly independent, the measuring points (equations) are divided into n groups and mn groups.

[0070] Initially, the exact solution of the power distribution is obtained from equations (14) and (16) for the n groups. Naturally, the detector signals of the remaining mn groups satisfy the conditions of equation (9). In other words, the detector signals corresponding to the detector positions of the mn groups obtained from the exact power distribution (actual power distribution) and the calculation of equation (9) correspond to the detector signals of the mn groups, even if the exact power distribution is obtained from equations. (14) and (16) for the n groups.

[0071] In other words, to correctly calculate the power distribution, it is sufficient that m^n.

[0072] Furthermore, if an error is introduced into the measurement,

[0073] [Math.25] (n)

[0074] If the error has a uniform distribution such as electrical noise, taking into account the properties of the least squares method, the more measurement points there are, the more the influence of uncertainty such as noise is likely to be eliminated. This tendency can also be confirmed by the fact that the more measurement points there are, the more the errors considered as numerical errors are reduced in the numerical experiments that will be carried out later. If we consider noise explicitly, we can say that the greater the number of measurement points, the better.

[0075] In the present invention, many measurement points can be ensured by moving the detector, as described in detail below. However, due to constraints such as the structure of the installed nuclear reactor and the integrity of materials, such as the high-temperature and high-dose environment, there are cases where sufficient measurement points cannot be ensured, or the resolution of the power distribution to be evaluated is expressed in units of fuel rods. For these reasons, it is quite conceivable that the number of measurement points is insufficient for the number of fuel elements that have a power distribution. In this case, the validity of the measurement results is ensured by the following method.Conveniently, the power distribution can be determined using equation (14) by calculating the pseudo-inverse matrix shown in equation (15) independently of the magnitude relationship between the number of measuring points m and the number of fuel elements n. The question of whether the number of points of . Whether the pseudoinverse matrix is ​​sufficient or not can be determined by checking the rank of this pseudoinverse matrix. The rank of a matrix indicates the number of linearly independent rows in each row of the matrix. The pseudoinverse has n rows and n columns, with a maximum rank of n.

[0076] As the number of measurement points increases, the rank increases and reaches saturation at the maximum value of n. Numerical experiments associated with the present invention have confirmed that an exact solution can be obtained when the rank takes the maximum value of n. On the other hand, if the rank is less than n, an error occurs in the predicted power density. According to the present invention, in numerical experiments to be described later, from the results shown in Table 2, it has been found that the output density distribution can be reproduced with sufficiently acceptable accuracy when a pseudoinverse matrix with a rank of 0.8n or more is obtained.

[0077] Therefore, the number of measuring points should be equal to or greater than the number of fuel elements. The number of fuel elements depends not only on the number of fuel assemblies, but also on the required resolution. If it is desirable to further divide the interior of the fuel assembly for combustion control, the number of fuel elements is further increased. Taking the HTTR, which is a high-temperature engineering test reactor and a research reactor, as an example, it consists of 150 hexagonal prism-shaped fuel blocks with a distance between opposite faces of 36 cm and a height of 58 cm. Even if at least 150 detector signals are measured, a measurement with individual detectors is not realistic, and it is necessary to move only one or more detectors to measure the detector signals.

[0078] Therefore, in the present method, it is assumed that the detector signals are measured using external instrumentation, internal instrumentation and, if necessary, a combination of the two.

[0079] When the power distribution is measured using only the external detector, neutrons escaping from inside the core are detected outside the pressure vessel, as shown in [Fig. 4]. Then, to obtain detector signals of different heights, the detector is driven along the spiral track 10 as shown in [Fig. 5]. With this method, it is possible to measure a series of movements with a single detector. This method is a control method also generally used in X-ray computed tomography. However, from the point of view of manufacturability and maintainability, it is simpler to arrange a plurality of detectors on the outer circumference of the pressure vessel and to drive each detector vertically. This allows measurements to be made at from an almost infinite number of measurement points.

[0080] If internal instrumentation is chosen, it should be noted that in the case of gas-cooled high-temperature reactors, the temperature of the environment inside the reactor is extremely high, and in the case of fast reactors, radiation damage to the detectors is visible. Instead of placing them in the core, it is practical to use control rod guide tubes, insert them when in use, and store them outside the reactor when not in use. Since the control rod guide tubes exist independently of the fuel in both the HTGR and the fast reactor, there is space for the control rod guide tubes, and it is possible to modify the design to drive the detector.

[0081] [Fig. 6] shows an example of a high-temperature gas reactor. Assume the insertion of the detector from the riser 20 which houses the control rods. When not in use, the detector is retracted and stored in the riser 20. It can be stored at a temperature of about 300°C by a cooling flow and can be protected from radiation damage. When in use, it is inserted continuously to ensure the number of measuring points. In the case of the HTTR, 30 fuel bodies are arranged in the radial direction, for 16 control rod guide blocks. When evaluating the power distribution for each fuel block, if two measuring points are established in the height direction below the fuel block height of 58 cm, and every 29 cm, the same number of measuring points as the fuel block can be ensured.By avoiding high temperature regions as shown in [Fig.4], the number of measurement points is reduced, so reduced accuracy of the power distribution evaluation will be expected. If the measurement accuracy is unacceptable, a decrease in accuracy can be avoided by taking countermeasures through design modification such as increasing the number of internal detectors.

[0082] In addition, the more the number of measuring points is increased, the higher the resolution of the power distribution to be measured. Therefore, by using both the external detector and the internal detector, the power distribution can now be measured with greater precision.

[0083] In the design process of the present invention, a long-range neutron core, different from light water reactors, was assumed. In the internal instrumentation of light water reactors, the power distribution that can be predicted from the measured neutrons is treated as representing the average power of the fuel assembly around the detector. Since we measure the leakage neutrons, we can directly determine the power distribution for each assembly by performing an inverse analysis using the pre-estimated detector sensitivity distribution for the long-range neutron core. Industrial applicability

[0084] Utilities operating current light water reactors directly monitor combustion and manage fuel in the reactor by directly measuring power distribution using internal instrumentation. In contrast, for HTGRs and fast reactors, no internal instrumentation has been developed due to the high-temperature environment, and no technology for directly measuring internal power distribution has been developed. The present invention makes it possible for the first time to measure the internal power distribution of these two advanced reactors, enabling the same internal fuel management as in light water reactors, and significantly improving economics and safety.

[0085] In a small core system, if sufficient detector sensitivity can be ensured up to the combustible bodies in the center of the core, it is possible to measure the power distribution using only external instrumentation. By driving the external detectors, it is possible to reduce the number of detectors required to obtain the necessary measurement points and eliminate the work of correcting the detection efficiency due to the construction of a plurality of detectors.

[0086] In a core where the internal instrumentation can be installed, it is possible to measure the power distribution in a wide range for the limited insertion position in the core. Even if the loading location is limited due to structural problems, temperature or irradiation environment, etc., it is possible to measure the power distribution. With regard to the internal instrumentation, by making the internal detector movable, it is possible not only to increase the number of measurement points, but also to avoid deterioration when the detector is not in use. In high-temperature gas-cooled reactors and fast reactors, the control rod guide tubes are independent of the fuel assemblies, and there is ample space for placing the driven detectors.

[0087] The performance of the present invention was applied to the high temperature engineering test reactor (HTTR) system and confirmed by simulation. With regard to external instrumentation, the power distribution of 150 fuel blocks was measured at a total of 180 points, 36 points on the circumference of the pressure vessel and 5 points on the height, and the results are shown in Table 1.

[0088] [Table 1]

[0089] Power distribution measurement error in HTTR system Table 1 Power distribution measurement error with an external detector Parameters Values ​​Values ​​Whole core error Mean error (%) 1.2x 10'® 3.2 x 10'11 Standard deviation (%) 1.8x 10'® 3.8 x 10'11 Maximum local error Error (%) 1.1 x 10'8 2.4 x 10'10 Column 1D1 1C1 Layer 4 5 Inverse matrix rank 150 150

[0090] The average measurement error of all fuel blocks was 1.2 x 109%, and the block with the maximum error had a negligible error of 1.1 x 108%. The internal instrumentation was evaluated by measuring 320 points, 16 detectors, and 20 height positions. Table 1 shows the results. The average measurement error of all fuel blocks is 3.2 x 10 11%, and the block with the maximum error is about 2.4 x 10 10%, which can be considered an exact solution. Table 2 shows the results when a partial insertion was performed to avoid inserting the detector in the lower part of the core where the temperature becomes high.

[0091] [Table 2]

[0092] Power distribution measurement error when internal detector is partially inserted into HTTR system Table 2 Power distribution measurement error with partially inserted internal detector Parameters 90% 80% 50% 45% 40% Whole core error Mean error (%) 3.7 x 10'11 4.7 x 10'11 1.8 x 10'7 0.28 1.1 Standard deviation (%) 4.9 x 10'11 5.3 x 10'11 4.4 x 10'7 0.65 1.8 Maximum local error Error (%) 3 .7x10"10 4 0x 10-10 2.5 x 10'6 5.0 6.5 Column 1A1 1A1 1C1 3D1 3B3 Layer 5 5 5 5 5 Inverse matrix rank 150 150 150 144 128

[0093] The positions of the measuring points are fixed, and the measuring points located below the core are excluded from the 20 points in the height direction by partial insertion. Even in the case of 50% insertion, the table shows a good match that can be considered an exact solution. At 45% and 40% partial insertion, the average core errors are 0.28% and 1.1%, and the maximum local errors are 5.0% and 6.5%. As is clear from the inverse matrix rank reduction, this error is due to the absence of measuring points rather than the partial insertion position. Improvement is possible by eliminating errors even in partial insertion by moving the measuring points closer together. In this way, the power distribution of the entire core can be measured by inserting about half of the detectors into the reactor, and it is possible to avoid inserting detectors in the high-temperature regions.With a partial insertion of 50%, one can anticipate a drop in the ambient temperature of the detector by approximately 200 °C and a considerable reduction in the load on the detector in terms of the thermal resistance of the detector.

[0094] The applicability of the power distribution measurement method using external instrumentation is determined by the relationship between neutron range and core size. Table 3 shows the average flight path from a source to neutron absorption as the neutron pot for each reactor type.

[0095] [Table 3]

[0096] Diffusion length of each reactor type Table 3 Diffusion length of each reactor type LWR HTGR FR Diffusion length (cm) 7 27 40

[0097] The diffusion lengths were evaluated and compared to the fuel section. While the light water reactor is about 7 cm, the high temperature gas reactor is about 4 times larger, and the fast reactor is about 6 times larger. It is possible to estimate the power distribution of the fuel assembly over a wide range from the measured neutron information. The detector sensitivity of light water reactors is about 40 cm to 60 cm, as shown in [Fig. 1]. Even the design of NuScale Power, LLC, which is being developed as a small nuclear reactor (SMR), has a core radius of about 120 cm, so it cannot be applied to light water reactors. For the HTGR, a wide distribution of detector sensitivity is obtained as shown in [Fig. 2].Assuming that the effective core radius of the HTTR, which is about 130 cm, can be observed from the outer circumference of the core, the higher power of the HTGR will increase the power density and increase the core length. In the high-power core, from the point of view of safety in case of decompression sickness, since it takes the form of an annular core without arranging the fuel in the center of the core, it is applicable not only to an HTTR with a core power of a commercial reactor of 30 MW, but also 165 MW, and 600 MW designed by the Japan Atomic Energy Agency. For fast reactors, a wider range of detector sensitivities can be expected due to the longer diffusion lengths.Since the PRISM (Power Reactor Innovative Small Module) reactor, which is a typical PRM fast reactor design, has a core radius of about 130 cm, it is fully applicable. On the other hand, for a large fast reactor with a core radius of about 300 cm, it is difficult to apply only external detectors.

[0098] The method using internal instrumentation can be applied not only to high-temperature gas-cooled reactors and fast reactors, but also to the processing of current internal instrumentation data in current light-water reactors. By applying the inverse core analysis method, it is possible to improve the resolution of the power distribution in the core. While the The current method is an integral approach in which the measured value of the internal instrumentation is the average value of the power of the peripheral fuel assembly, the present analysis is a differential approach in which measurement signals are assigned to each region and reconstructed.

[0099] In the above explanation, a pseudo-inverse matrix is ​​used to show the essential mathematical structure, and the rank of the pseudo-inverse matrix is ​​used as an index to measure the independent linear component. However, there are also approaches such as numerical solutions that do not use inverse matrices and maximum likelihood methods that replace the least squares method. There are multiple implementations of inverse methods.

Claims

Claims

1. A method of measuring a power distribution in a reactor core, according to a neutron transport equation representing the relationship between power densities of a plurality of fuel elements in a pressure vessel of a nuclear reactor, output signals from neutron detectors located at locations of the plurality of neutron detectors inside and outside the pressure vessel, and detector sensitivity relative to the positions of the fuel elements and the neutron detectors, characterized in that the power distribution of the nuclear reactor core is calculated from the product of the matrix of output signals from the neutron detectors and the pseudo-inverse matrix relative to the detector sensitivity.

2. A method for measuring a power distribution in a reactor core according to claim 1, wherein said output signals of the neutron detectors are calculated by the following equation, and [Math. 26] wp said pseudo-inverse matrix relating to the detector sensitivity is calculated using the matrix representation of the following equation, [Math. 27] W+ _ \vr°ù P* reRepresents the power density of n fuel elements i inside the pressure vessel, Rj represents neutron detector signals at m detector positions inside and outside the pressure vessel, wj,i represents a detector sensitivity relative to a fuel element i and a detector position], and W+ represents the pseudo-inverse matrix relating to the detector sensitivity.

3. A method of measuring a power distribution in a reactor core according to claim 1, wherein said power distribution is obtained according to a neutron transport equation representing the relationship between a power density pi of n fuel elements i inside the vessel under pressure, a neutron detector signal Rj at m detector positions j inside and outside the pressure vessel, and a detector sensitivity wj,i relative to a fuel element i and a detector position j, which comprises the following steps: obtaining the neutron detector signal from the following equation, [Math. 28] fi. _ V” w. « representing a neutron detector signal Rj, a power density pi and a detector sensitivity wj,i in a matrix representation of the following equation, [Math. 29] R = W? calculating a pseudo-inverse matrix W+ of the matrix representation of the detector sensitivity wj,i using the matrix representation of the following equation, [Math.30] W+ _ ca^cu^ of the matrix representation of the power density pi using the following equation which represents the matrix representation of the neutron detector signal Rj and the pseudo-inverse matrix W+. [Math. 31] P = R.

4. A method of measuring a power distribution in a reactor core according to claim 1 or 2, wherein the neutron detector signals are acquired by driving neutron detectors positioned at multiple locations inside and outside the pressure vessel.

5. A method for measuring a power distribution in a reactor core according to any one of claims 1 to 3, wherein the measured value is output as a valid measurement result when the rank of the pseudo-inverse matrix is ​​equal to or greater than 0.8n (n is the number of the plurality of fuel elements).

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