GB2615387A - Method and apparatus for measuring a power distribution in a reactor core - Google Patents

Abstract

A method of measuring a power distribution in a reactor core is based on a neutron transport equation representing the relationship between power densities of a plurality of fuel elements within a pressure vessel of the nuclear reactor, output signals from neutron detectors at a plurality of locations, and detector sensitivity with respect to the positions of the fuel elements and the neutron detectors. A detector sensitivity matrix represents the sensitivities of each neutron detector location to the power density at each fuel element position. The power distribution is calculated from the product of the matrix the output signals of the neutron detectors and the pseudo-inverse of the detector sensitivity matrix. The neutron detectors may be positioned inside or outside the reactor pressure vessel. The measured power distribution may be considered valid when the rank of the pseudo-inverse matrix is greater than or equal to 0.8n, where n is the number of fuel elements.

Description

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.

[Background technology]

[0002] In current light water reactors, the environment inside the reactor is around 300-400°C. Therefore, neutron detectors are directly loaded near the fuel assembly of the reactor, the power distribution is measured, and the burnup of the fuel in the reactor is controlled based on the measured power distribution (Patent Document 1). On the other hand, since the temperature inside the high temperature gas-cooled reactor (HTGR) reaches up to about 1000°C and that in the 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 to be solved by the invention] [0004] In recent years, development of high temperature resistant neutron detectors, such as ceramic detectors, has been pursued, but it is not practical to insert the detectors into the reactor coolant outlet area in a high temperature gas-cooled reactor, and the insertion location into the reactor core is limited. Also, from the viewpoint of the reactor internals, it seems realistic to insert the detector into the reactor both in high temperature gas-cooled reactors and in fast reactors, by using control rod guide tubes. Placing a detector directly near each fuel body is impractical.

[0005] As described above, the present invention enables measurement of in-core power distribution for reactors such as high temperature gas-cooled 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, the location of insertion is limited.

[0006] A main object of the present invention is to make it possible to measure the in-core power distribution of nuclear reactors such as high temperature gas reactors and fast reactors, in which the places where neutron detectors are inserted are limited. However, as a matter of course, it goes without saying that this method can also be applied as it is to light water reactors such as boiling water reactors and pressurized water reactors, in which the neutron detector can be inserted relatively freely.

[Means for solving the problem] [0007] A power distribution measuring method according to a first aspect of the present invention is as follows.

A method of measuring a power distribution in a reactor core, based on a neutron transport equation representing the relationship between power densities of a plurality of fuel elements within 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 detector sensitivity with respect 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 from the neutron detectors and the pseudo-inverse matrix relating to the detector sensitivity.

[0008] More specifically, the method of measuring a power distribution in a reactor core according to the present invention, based on a neutron transport equation representing the relationship between power density pi of n fuel elements i inside the pressure vessel, neutron detector signal Rj at m detector positions j inside and outside the pressure vessel, and detector sensitivity wj,i with respect to fuel element (i) and detector position j, which comprises the steps of: [0009] (1) obtaining the neutron detector signal from the following equation, Rj = Eit=1. wi,iPi [0010] (2) representing neutron detector signal Rj, power density pi, and detector sensitivity wj,i in a matrix representation of the following equation, = wP [0011] (3) calculating a pseudo-inverse matrix W+ of the matrix representation of detector sensitivity wj,i by using the matrix representation of the following equation, vv+ (wTw)_lwT [0012] (4) calculating the matrix representation of the power density pi by using the following equation which represents the matrix representation of the neutron detector signal Rj and the pseudo inverse matrix W. [0013] An apparatus according to a second aspect of the present invention has the following configuration.

The apparatus for measuring a power distribution of a reactor core, based on a neutron transport equation representing the relationship between power densities of a plurality of fuel elements in a reactor pressure vessel, neutron detector signals at a plurality of detector positions inside and outside the pressure vessel, and detector sensitivity with respect to the position of the fuel element and the detector, which comprises: a computer for inputting neutron detector signals and performing a predetermined computation based on a computer program; and a memory device for storing the computer program which allows the computer to calculate the power distribution of the reactor core by inverse analysis of the detector sensitivity.

[0014] More specifically, the apparatus for measuring a power distribution in a reactor, based on a neutron transport equation representing the relationship between 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 detector sensitivity wj,i with respect to the fuel elements i and the detector positions j, wherein the above-mentioned program executes the following steps of: [0015] (1) obtaining the neutron detector signal from the following equation, Rj = EPLi wi,tPi [0016] (2) representing neutron detector signal Rj, power density pi, and detector sensitivity wj,i in a matrix representation of the following equation, = wP [0017] (3) calculating pseudo-inverse matrix 1AP-of the matrix representation of the detector sensitivity wj,i by the matrix representation of the following equation, \AT+ (wr \A) -lwr [0018] (4) calculating the matrix representation of the power density pi by using the following equation which represents the matrix representation of the neutron detector signal Rj and the pseudo inverse matrix W. P = w-Fri [Effects of the invention] [0019] The present invention achieves the following effects.

(1) For a small core with a long range of neutrons, it is possible to measure the in-core power distribution using detector signals from only the ex-core detectors.

(2) If the detector can be inserted into the reactor and the insertion location is limited, it is possible to measure the in-core power distribution of the entire core from the detector signals at the limited location in the reactor [0020] As described above, even in a light water reactor with a short range of neutrons, 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 drawings] [0021]

FIG. 1 is an explanatory diagram of the detection sensitivity of ex-core detectors in light water reactors.

FIG. 2A is an explanatory diagram of the detection sensitivity of the ex-core detector in the high temperature gas-cooled reactor, and FIG. 2B is an explanatory diagram of the detection sensitivity of the in-core detector.

FIG. 3 is a flow chart schematically showing a method for measuring the power distribution in the reactor according to the present invention.

FIG. 4 is a schematic explanatory diagram showing the positional relationship between an ex-core detector used for measuring the in-core power distribution according to the present invention and the reactor core; FIG. 5 is a diagram showing an example of driving an ex-core detector in a high temperature gas-cooled reactor.

FIG. 6 is a diagram showing an example of driving an in-core detector in a high temperature gas-cooled reactor.

[Mode for carrying out the invention]

[0022] As shown in FIG. 1, the detection sensitivity of the ex-core detectors for each fuel assembly in a light water reactor is limited to the fuel assemblies on the outer periphery of the core. Therefore, it is impossible in principal to directly measure the power distribution at in-core locations in the center of the reactor using ex-core instrumentation. In pressurized water reactors (PWRs), as disclosed, for example, in Patent No. 5954902, To monitor the axial power deviation of the power distribution to the top and bottom of the core in the axial direction (axial offset) to control the Xe oscillation, the axial offset is evaluated by the ex-core instrumentation. Although this is intended 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 burnup control, which is the object of the present invention.

[0023] This is because light water has excellent performance as a moderator in light water reactors, so neutrons generated by nuclear fission collide with hydrogen contained in light water and instantly change into thermal neutrons, which are easily absorbed by nuclear fuel materials. As a result, the range is very short and, as shown in FIG. 1, neutrons generated in the center of the core hardly leak out of the reactor.

[0024] On the other hand, FIG. 2 shows the detector sensitivity when assuming the layout of the ex-core detectors 1 and in-core detectors 2 as assumed in this invention, for the system of the engineering test reactor HTTR 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. Assuming this characteristic, 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.

R(r d) = f w(rd,r)S(r)dr3 (1) [0025] w(r,rd) is the detector sensitivity for neutrons generated at reactor core position r to be detected at 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.

L(r) = 5(r) (2) [0026] L is the neutron loss operator, which expresses the neutron loss due to neutron transport, scattering and absorption. As a result, the detector response of the obtained neutron flux (1)(r) becomes the detector signal.

R(rd, r) = Edd)(r) (3) [0027] Ed 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 in-core position r.

[0028] Here, if neutron source S(r) is assumed to be a unit fission source from only in-core position n, 5(r)= XV) -ri) 47r where x is the fission spectrum [0029] Since this reaction rate is itself the detector sensitivity, w(rd, r) = R(rd,r) (5) core (4) [0030] On the other hand, for convenience, since the power distribution is evaluated for a fuel element with a specific breadth, the detector sensitivity should also be defined for the fuel element, defined as: w1 = w(rd,r)dr3 (6) [0031] This is the sensitivity when detecting neutrons at detector position j for neutrons generated from fuel element i.

[0032] On the other hand, to obtain the detector sensitivity, it is necessary to perform the neutron transport calculation using Equation (2) for the number of fuel elements, in which neutron sources distributed only in a specific region of fuel element i, which is expressed in Equation (4), is used. Because this increases the calculation time and may introduce errors due to the large number of numerical processes, in general, the following solution method for the adjoint neutron transport equation is used.

Lt (rd, r) = EdS(r -rd) (7) [0033] Where, Lt is the adjoint neutron loss operator, and Ot(r) is adjoint neutron flux. As a result, the detector sensitivity in equation (5) can be expressed as follows.

w(rd,r) = Itt(rd,r, E)x(r, E) dE (8) [0034] In this calculation method, the detector sensitivity for each fuel element can be evaluated only by solving the adjoint neutron transport equation (7) once, and by performing the tabulation work of Equations (6) and (8).

[0035] Here, the detector signal Rj at detector position j can be expressed by sensitivity wj,i at detector position j for fuel element i and power density pi for fuel element i as follows. To clarify the physical image, the fission neutron source is replaced by the power density, which is proportional to the fission neutron source.

wi,iPi (9) =1 [0036] Obtaining detector signals at multiple detector positions j yields multiple equations, which in matrix representation can be expressed as = wP (10) [0037] 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 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 known to have P =w-1fi (11) [0038] In this case, the power density vector P can be obtained directly from Eq. (11) as an exact solution. This is synonymous with the theorem that the 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 measurement points measured arbitrarily is not guaranteed. Even if n measurement points are set, it is quite possible that m as a linearly independent measurement point becomes m<n.

[0039] On the other hand, finding the least-squares solution gives a general expression that includes this exact solution. (12)

[0040] The condition for minimizing the squared error J defined by Eq. (12) is the solution of VJ = 0 (13) [0041] This solution is obtained as P =w+P (14) [0042] vv+ (wTw)lwT (15) [0043] The steps up to this point are briefly illustrated in FIG. 3. Where W+ is called the pseudo-inverse matrix. As described above, W is an m-by-n matrix, which does not have an inverse unless n=m and the row vectors of the detector sensitivities are linearly independent. If this condition is met, W± = W-1 (16) [0044] By the same calculation, an exact solution similar to that of Eq. (11) can be obtained. On the other hand, when r4m, the solution obtained by Eq. (14) is said to be a least squares solution but not unique, that is, it is not guaranteed to be a true value.

[0045] Here, when m<n, that is, when the number of equations is insufficient for the number of variables (in this case, the number of measurement points is insufficient), the solution as simultaneous linear equations cannot be determined. Although it is possible to determine the solution as an approximate solution that minimizes the squared error shown in Eq. (13), as will be confirmed in later numerical experiments, an error occurs in the predicted power distribution due to the lack of measurement points.

[0046] Conversely, if m>n, i.e., if there are more equations than the number of variables (here, the number of measurement points), then again it is a least-squares solution and 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 are set. This is self-evident from the following point of view. This is because if the number of equations is large, the exact solution can be obtained using Eq. (16) by ignoring the number of equations.

[0047] For example, if the detector sensitivities at m measurement points are linearly independent, the measurement points (equations) are divided into n groups and m-n groups.

[0048] Initially, the exact solution of the power distribution is obtained from Eqs. (14) and (16) for the n groups. Naturally, the detector signals of the remaining m-n groups satisfy the conditions of Eq. (9). In other words, the detector signals corresponding to the detector positions of the m-n groups obtained from the exact power distribution (actual power distribution) and the calculation of Eq. (9) match the detector signals of the m-n groups. even if the exact power distribution is obtained from Eqs. (14) and (16) for the n groups.

In other words, in order to correctly calculate the power distribution, it is sufficient if rnn.

[0049] In addition, if some error is mixed in the measurement, RJ = Ej (17) i=1 [0050] If the error has a uniform distribution such as electrical noise, considering the properties of the least-squares method, the more measurement points, the more likely it is to eliminate the influence of uncertainty such as noise. This tendency can also be confirmed from the fact that the more measurement points there are, the more the errors that are thought to be numerical errors are reduced in the numerical experiments that will be carried out later. When considering noise explicitly, it can be said that the larger the number of measurement points, the better.

[0051] In the present invention, many measurement points can be secured by moving the detector, as described in detail below. However, due to constraints such as the structure of the installed nuclear reactor and material integrity such as high temperature and high dose environment, there are cases where sufficient measurement points cannot be secured, or the resolution of the power distribution to be evaluated is 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 that case, the validity of the measurement results shall be guaranteed by the following method. Conveniently, the power distribution can be determined by using the equation (14) by calculating the pseudo inverse matrix shown in the equation (15) regardless of the magnitude relationship between the number of measurement points m and the number of fuel elements n. Whether or not the number of measurement points is sufficient can be determined by checking the rank of this pseudo-inverse matrix. The rank of a matrix indicates the number of linearly independent rows in each row of the matrix. The pseudo-inverse has n rows and n columns, with a maximum rank of n.

[0052] As the number of measurement points increases, the rank increases and becomes saturated 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 was found that the output density distribution can be reproduced with sufficiently acceptable accuracy when a pseudo-inverse matrix with a rank of 0.8n or more is obtained.

[0053] Therefore, the number of measurement 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 desired to further divide the inside of the fuel assembly for burnup control, the number of fuel elements is further increased. Taking the HTTR, which is a high temperature engineering test reactor and research reactor, as an example, it consists of 150 hexagonal prism-shaped fuel blocks with an opposing face distance of 36 cm and a height of 58 cm. Even if 150 detector signals are measured at the minimum, it is not realistic to measure with individual detectors, and it is necessary to move a single detector or multiple detectors to measure detector signals.

[0054] Therefore, in this method, it is assumed that detector signals are measured by assuming ex-core instrumentation, in-core instrumentation, and, if necessary, a combination of both.

[0055] When the power distribution is measured using only the ex-core detector, leaked neutrons from inside of the core are detected from 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 motions with only one detector This method is a drive method also used in general X-ray CT. However, from the viewpoint of manufacturability and maintainability, it is simpler to arrange a plurality of detectors on the outer circumference of the pressure vessel and vertically drive each detector. This makes it possible to measure from an almost infinite number of measurement points.

[0056] When adopting for in-core instrumentation, it should be noted that in the case of high temperature gas-cooled reactors, the environment inside the reactor is extremely high, and in the case of fast reactors, radiation damage to detectors is conspicuous. 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 room for the control rod guide tubes, and it is possible to change the design to drive the detector.

[0057] FIG. 6 shows an example of a high temperature gas reactor. Assume the insertion of the detector from the standpipe 20 that houses the control rods. When not in use, the detector is retracted and stored within the standpipe 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, insert continuously to secure the number of measurement points. In the case of HTTR, 30 fuel bodies are arranged in the radial direction, while there are 16 control rod guide blocks. When evaluating the power distribution for each fuel block, if two measurement points are set in the height direction within the fuel block height of 58 cm, and every 29 cm, the same number of measurement points as the fuel block can be secured. When avoiding high temperature regions as shown in FIG. 4, the number of measurement points is reduced, so it is expected that the accuracy of power distribution evaluation will be reduced. If the measurement accuracy is unacceptable, it is possible to avoid a decrease in accuracy by taking countermeasures such as increasing the number of in-core detectors by changing the design.

[0058] Also, the more the number of measurement points is increased, the higher the resolution of the power distribution to be measured. Therefore, by using both the ex-core detector and the in-core detector, it becomes possible to measure the power distribution with higher accuracy.

[0059] In the process of conceiving the present invention, a core with a long neutron range, which is different from light water reactors, was assumed. In the in-core 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 Considering that we are measuring leakage neutrons, we can directly determine the power distribution for each assembly by performing inverse analysis using the pre-evaluated detector sensitivity distribution for the core with long neutron range.

[Industrial applicability]

[0060] Electric power companies that operate current light water reactors directly monitor the burnup and manage fuel in the reactor by directly measuring the power distribution using in-core instrumentation. On the other hand, for HTGRs and fast reactors, no in-core instrumentation has been developed due to the high temperature environment, and direct in-core power distribution measurement technology has not been developed. The present invention makes it possible for the first time to measure the in-core power distribution of both advanced reactors, enabling the same in-core fuel management as in light water reactors, and significantly improving economy and safety.

[0061] In a small core system, if sufficient detector sensitivity can be secured up to the fuel bodies in the center of the core, it is possible to measure the power distribution using only external instrumentation. By driving the ex-core detectors, the number of detectors required for obtaining the necessary measurement points can be reduced, and the labor of correcting the detection efficiency due to the construction of a plurality of detectors can be avoided.

[0062] In the core where the in-core 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 problems, etc., it is possible to measure the power distribution. As for the in-core instrumentation, by making the in-core detector movable, it is possible not only to become possible to increase the number of measurement points but also to avoid deterioration when the detector is not used. In high temperature gas-cooled reactors and fast reactors, the control rod guide tubes are independent from the fuel assemblies, and there is plenty of room for locating driven detectors.

[0063] The performance of the present invention was applied to the High Temperature engineering Test Reactor (HTTR) system and confirmed by simulation. As for the ex-core 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.

Table 1 Error in power distribution measurement in the HTTR system Table 1 En ch,te.dor power distribam Values A, 2.4 a 1 0 Cola-Qat Layer inversv tam.da 150 [0064] The average measurement error of all fuel blocks was 1.2x10-9 %, and the block showing the maximum error showed a negligible error of 1.1x10-8 %. The in-core 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 3.2x10-11 %, and the block showing the maximum error is about 2.4x10-1° %, which can be said to be an exact solution. Table 2 shows the results when partial insertion was performed in order to avoid insertion of the detector into the lower part of the core where the temperature becomes high. Items

IC

Table 2 Error in power distribution measurement when the in-core detector is partially inserted in the HTTR system Table 2 Error of hi-cote deomor power distribution rnamrement with -ertion items 90% 80% 5034 45% 40% Wholo tare error Avetaged -tor (N) 3.7x104 7:0(03 0.28 FRandinxi deviation (%) aximur.i 4,910' 5.341041 4 4 0.65.8 Error Pito 3 7x Id" 4 0,10'1° 2.5i0'° 5 0 Column 1A1 3D R: 1 0 C inverse, matrix: 150 150 150 144 328 [0065] The positions of the measurement points are fixed, and the measurement points below the core are excluded from the 20 points in the height direction by partial insertion. Even in the case of 50% insertion, it shows a good match that can be said to be an exact solution. At 45% and 40% partial insertion, core average errors are 0.28% and 1.1%, and maximum local errors are 5.0% and 6.5%. As is clear from the reduction in the rank of the inverse matrix, this error is due to the lack of measurement points rather than the position of partial insertion. There is room for improvement in eliminating errors even in partial insertion by placing the measurement 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 into high temperature regions. With 50% partial insertion, the environmental temperature of the detector can be expected to drop by about 200°C, and the load on the detector can be greatly reduced in terms of heat resistance of the detector.

[0066] The applicability of the power distribution measurement method using ex-core instrumentation is determined by the relationship between the range of neutrons and the size of the core. Table 3 shows the average flight path from a source to absorption of neutrons as the range of neutrons for each reactor type.

Table 3 Diffusion length of each reactor type Tthl.DiffuionIen.gth of 04 tyne pcjw.:.tiQrs [0067] 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 that, and the fast reactor is about 6 times that. 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 40cm60cm 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 detector sensitivity distribution 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 length of the core. In the high-power core, from the viewpoint of safety in the event of a decompression accident, since it takes the shape of an annular core without arranging fuel in the center of the core, it is applicable not only to a HTTR with a core output of 30 MW, but also to a 50 MW, 165 MW, and 600 MW commercial reactor 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 design of fast reactor SMR, 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.

[0068] The method using in-core instrumentation can be applied not only to high temperature gas-cooled reactors and fast reactors, but also to data processing of current in-core instrumentation in current light water reactors. By applying the core inverse analysis method, it is possible to improve the resolution of the in-core power distribution. While the current method is an integral approach in which the measured value of the in-core instrumentation is the average value of the peripheral fuel assembly power, the present analysis is the differential approach in which measurement signals are assigned to each region and reconstructed. [0069] 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 for measuring the linear independent 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 (9)

1. WHAT IS CLAIMED IS: 1. A method of measuring a power distribution in a reactor core, based on a neutron transport equation representing the relationship between power densities of a plurality of fuel elements within 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 detector sensitivity with respect 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 from the neutron detectors and the pseudo-inverse matrix relating to the detector sensitivity.
2. 2. The method of measuring a power distribution in a reactor core according to claim 1, wherein said output signals from the neutron detectors are calculated by the following equation, and Rj = ErLiwi said pseudo-inverse matrix relating to the detector sensitivity is calculated by using the matrix representation of the following equation, W+ = (wTw)_iwr where, pi represents power density of n fuel elements i inside the pressure vessel, Rj represents neutron detector signals at m detector positions j inside and outside the pressure vessel, wj,i represents detector sensitivity with respect to fuel element i and detector position j, and W+ represents the pseudo-inverse matrix relating to the detector sensitivity
3. 3. The method of measuring a power distribution in a reactor core according to claim 1, wherein said power distribution is obtained based on a neutron transport equation representing the relationship between power density pi of n fuel elements i inside the pressure vessel, neutron detector signal Rj at m detector positions j inside and outside the pressure vessel, and detector sensitivity wj,i with respect to fuel element i and detector position j, which comprises the steps of: obtaining the neutron detector signal from the following equation, = E7=1. wi,iPi representing neutron detector signal Rj, power density pi, and detector sensitivity wj,i in a matrix representation of the following equation, = wP calculating a pseudo-inverse matrix W+ of the matrix representation of detector sensitivity wj,i by using the matrix representation of the following equation, w+ (wT1A)-1wT calculating the matrix representation of the power density pi by using the following equation which represents the matrix representation of the neutron detector signal Rj and the pseudo inverse matrix W. P = w±n
4. 4. The 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. 5. The method of measuring a power distribution in a reactor core according to any 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 0.8n (n is the number of the plurality of fuel elements) or more.
6. 6. An apparatus for measuring a power distribution of a reactor core, based on a neutron transport equation representing the relationship between power densities of a plurality of fuel elements in a reactor pressure vessel, neutron detector signals at a plurality of detector positions inside and outside the pressure vessel, and detector sensitivity with respect to the position of the fuel element and the detector, which comprises: a computer for inputting neutron detector signals and performing a predetermined computation based on a computer program and a memory device for storing the computer program which allows the computer to calculate the power distribution of the reactor core by inverse analysis of the detector sensitivity, and an arithmetic unit that inputs signals from said detectors and performs predetermined calculations based on said program.
7. 7. The apparatus for measuring a power distribution in a reactor core according to claim 6, wherein the power distribution is calculated based on a neutron transport equation representing the relationship between 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 detector sensitivity wj,i with respect to the fuel elements i and the detector positions j, and wherein the above-mentioned program executes the following steps of: obtaining the neutron detector signal from the following equation, -Et=1 WittPt representing neutron detector signal Rj, power density pi, and detector sensitivity wj,i in a matrix representation of the following equation, fi = wP calculating pseudo-inverse matrix W+ of the matrix representation of the detector sensitivity wj,i by the matrix representation of the following equation, W+ (wT \ -1wT calculating the matrix representation of the power density pi by using the following equation which represents the matrix representation of the neutron detector signal Rj and the pseudo inverse matrix W.
8. 8. The apparatus for measuring a power distribution in a reactor core according to claim 6 or 7, wherein the neutron detector signals are acquired by driving neutron detectors positioned at multiple locations inside and outside the pressure vessel.
9. 9. The apparatus for measuring a power distribution in a reactor core according to any of claims 6 to 8, wherein the measured value is output as a valid measurement result when the rank of the pseudo-inverse matrix is 0.8n (n is the number of the plurality of fuel elements) or more.