JP2005283439A - Evaluation method for relief safety valve capacity, and evaluation program for releif safety valve capacity - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an evaluation method for relief safety valve capacity and an evaluation program for relief safety valve capacity, capable of designing the proper number and capacity of relief safety valves while setting a safety margin small by further accurately executing dynamic characteristic analysis of a reactor in a nuclear power plant. <P>SOLUTION: This evaluation method for relief safety valve capacity comprises steps S8, S9, S10, S10, S11 and S12 of perturbing an analytic parameter to be inputted to an analysis code for executing the dynamic characteristic analysis of the reactor to determine the distribution of pressure peak value of the reactor; and steps S14 and S15 for determining the statistic upper limit value of the distribution of pressure peak value of the reactor. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a relief safety valve capacity evaluation method and a relief safety valve capacity evaluation program when designing the capacity of a relief safety valve used in a nuclear reactor in a nuclear power plant such as a boiling water nuclear power plant.

  Equipment such as boiling water nuclear power plants is provided with a safety relief valve that allows steam to escape in order to avoid an increase in reactor pressure if a transient change or accident occurs due to some abnormality and the reactor pressure increases. .

  This relief safety valve is connected to a suppression pool in which water for cooling the steam is stored via an exhaust pipe. The relief safety valve is configured to be opened when the pressure of the main steam pipe or the pressure of the reactor system exceeds a preset value.

  When the pressure in the reactor system or main steam system rises, the relief safety valve opens and the steam is released under the surface of the suppression pool through the exhaust pipe, and the reactor in the reactor system is opened and closed by opening and closing the relief safety valve. The increase in pressure is suppressed so that the pressure does not exceed the specified value.

  For this reason, the relief valve used in boiling water nuclear power plants has the necessary number of valves and valve capacity based on the required design criteria so that the increase in reactor pressure of the boiling water nuclear power plant is reliably suppressed. Designed to be

  Therefore, in order to determine the number or capacity of the relief valve required for boiling water nuclear power plants, dynamic characteristic analysis has been simulated by an analysis code for dynamic characteristics analysis of boiling water nuclear power plants. The peak value of the furnace pressure is obtained. Then, even if the reactor pressure of the boiling water nuclear power plant reaches a peak value, the number of valves or the capacity relief valve required to suppress the increase in the reactor pressure is provided in the boiling water nuclear power plant.

  As an analysis code for analyzing dynamic characteristics of a boiling water nuclear power plant used in the past, there is one that solves a dynamic characteristic equation representing the entire system of the boiling water nuclear power plant in the time domain. This analysis code approximates the core of the nuclear reactor as a single point, divides the core and vessel into a plurality of simplified regions, and calculates the average mass and energy balance of the entire two-phase flow.

  Based on the design data of the components of the boiling water nuclear power plant, the data to be input to the analysis code for dynamic characteristic analysis is set, and the input data thus set is input to the analysis code to enter the boiling water nuclear power generation The dynamic characteristic analysis of the place is simulated.

  Here, a safety margin is set in the analysis result in consideration of an error, that is, an uncertainty in the result of the dynamic characteristic analysis of the boiling water nuclear power plant by the analysis code. In other words, the analysis parameters such as reactor power, scram velocity, scram reactivity, void reactivity coefficient, relief valve setting pressure, etc. that are input to the analysis code are conservatively added so that the conditions are sufficiently severe. Is used.

  Then, as a result of executing transient analysis by inputting analysis parameters with conservative addition to the analysis code, the number and capacity of safety valves are released depending on whether or not the obtained peak value of the reactor pressure satisfies the design criteria. The design is evaluated.

  Note that there is no document such as a documented publication regarding the conventional relief valve capacity evaluation method.

  The conventional relief safety valve capacity evaluation method is a method of inputting and analyzing data that has been added to the analysis code so that the conditions are sufficiently strict, so the analysis conditions become strict and the number and capacity of the required relief valve are required. Tends to be excessive.

  However, in the design of boiling water nuclear power plants and reactors in recent years, rational design that is economical while maintaining sufficient safety is required. In particular, when designing a new nuclear power plant, if the safety and maintainability of the nuclear power plant are designed to be larger than necessary, a large number and capacity of relief valves are required. For this reason, there is a risk that the construction cost of the nuclear power plant becomes high.

  Similarly, when changing the design of the nuclear power plant basic specifications such as reactor power, it may be necessary to add a relief valve and excessive safety and maintainability lead to high costs.

  Therefore, instead of the conservative conventional relief safety valve capacity evaluation method for setting a large safety margin, it is necessary to develop an analysis method for designing an appropriate number and capacity of relief safety valves.

  The present invention has been made in order to cope with such a conventional situation, and sets the safety margin to a small value by executing the dynamic characteristic analysis of the nuclear reactor in the nuclear power plant with higher accuracy, and the number of appropriate relief safety valves. It is another object of the present invention to provide a relief safety valve capacity evaluation method and a relief safety valve capacity evaluation program capable of designing the capacity.

  In order to achieve the above-mentioned object, the relief safety valve capacity evaluation method according to the present invention perturbs an analysis parameter input to an analysis code for executing a dynamic characteristic analysis of a nuclear reactor as described in claim 1. And determining the distribution of the peak value of the reactor pressure and determining the statistical upper limit value of the distribution of the peak value of the reactor pressure.

  Moreover, in order to achieve the above-mentioned object, the relief safety valve capacity evaluation program according to the present invention is inputted to an analysis code for executing a dynamic characteristic analysis of a nuclear reactor as described in claim 8. And functioning as a statistical upper limit calculating unit for obtaining a statistical upper limit value of the distribution of the peak value of the reactor pressure and a statistical upper limit value of the distribution of the peak value of the reactor pressure. It is what.

  In the relief safety valve capacity evaluation method and the relief safety valve capacity evaluation program according to the present invention, the safety margin is set small by executing the dynamic characteristics analysis of the nuclear reactor at the nuclear power plant more accurately, and the number of the appropriate safety valve And capacity can be designed.

  Embodiments of a relief safety valve capacity evaluation method and a relief safety valve capacity evaluation program according to the present invention will be described with reference to the accompanying drawings.

  FIG. 1 is a configuration diagram showing a first embodiment of a relief safety valve capacity evaluation system constructed using a relief safety valve capacity evaluation program according to the present invention.

  The relief safety valve capacity evaluation system 1 causes the computer to read the relief safety valve capacity evaluation program, and optimizes the plant optimum evaluation means 2, individual sensitivity analysis means 3, experiment design sampling means 4, transfer function creation means 5, Monte Carlo calculation means 6, regular It functions as sex determination means 7 and statistical upper limit calculation means 8.

  The relief safety valve capacity evaluation system 1 is applied, for example, when designing the number or capacity of relief valves provided in a nuclear power plant nuclear reactor such as a boiling water nuclear power plant.

  FIG. 2 is a schematic configuration diagram of a boiling water nuclear power plant 10 that is an example of an application target of the relief safety valve capacity evaluation system 1 shown in FIG. 1.

  The boiling water nuclear power plant 10 includes a nuclear reactor system 11, a main steam system 12, a recirculation system 13, and a control system (not shown). The reactor system 11 and the recirculation system 13 are provided inside the reactor containment vessel 14.

  The nuclear reactor system 11 includes a nuclear reactor 15, and is connected to a main steam system 12, a recirculation system 13, and a control system (not shown). The control system is configured to control the operation of the reactor 15 of the reactor system 11.

  The recirculation system 13 includes a circulation path 16 and a recirculation pump 17. The circulation path 16 is provided via the reactor system 11, and the recirculation pump 17 is provided on the circulation path 16. The reactor system 11 is cooled by circulating a required amount of coolant through the circulation path 16 by the recirculation pump 17.

  On the other hand, the main steam system 12 includes a turbine 18 and a condenser 19, and is connected to the reactor system 11 by a main steam pipe 20. High-temperature and high-pressure main steam generated in the reactor system 11 is guided to the upstream main steam pipe 20 connected to the reactor system 11. Further, the main steam pipe 20 on the upstream side is branched and one is led to the turbine 18 and the other is led to the condenser 19. From the condenser 19, a downstream main steam pipe 20 led to the nuclear reactor system 11 is provided.

  The turbine 18 of the main steam system 12 is provided with a generator 21. In the nuclear reactor system 11, the turbine 18 is rotated by the generated main steam, and electric power is generated in the generator 21 by the rotation of the turbine 18. The main steam that has passed through the turbine 18 is reduced in temperature and pressure in the condenser 19 and is again led to the reactor system 11 to be heated.

  The main steam pipe 20 on the upstream side of the main steam system 12 is provided with a main steam isolation valve 22, a turbine main steam stop valve 23, a turbine main steam control valve 24, and a turbine bypass valve 25. The main steam isolation valve 22 is provided in the vicinity of the reactor system 11 of the main steam pipe 20. The turbine main steam stop valve 23 and the turbine main steam control valve 24 are provided on the turbine 18 side of the branched main steam pipe 20, while the main steam pipe 20 on the condenser 19 side is provided with a turbine bypass valve 25. .

  Further, a relief safety valve 26 is provided between the main steam isolation valve 22 of the main steam pipe 20 and the reactor system 11. The exhaust pipe 27 branched from the main steam pipe 20 by the relief safety valve 26 is guided to the suppression pool 28. The suppression pool 28 stores water for cooling the steam.

  Here, the reactor pressure in the reactor system 11, which is an example of the equipment pressure, is controlled based on the detected value of the reactor dome pressure or the turbine inlet pressure. When the reactor pressure rises abnormally, in order to mitigate the rise in the reactor pressure, the reactor 15 is controlled so that the output of the reactor 15 is reduced by an emergency stop, that is, a reactor scram. The Thus, the reactor scram facility is configured to operate when the reactor pressure exceeds a preset value.

  Further, in the main steam system 12, when the pressure of the main steam pipe 20 increases and the turbine main steam stop valve 23 is closed due to a turbine trip or when the turbine main steam control valve 24 is closed due to load interruption, the turbine bypass By opening the valve 25 and allowing the main steam to escape to the condenser 19, the pressure of the main steam pipe 20 or the reactor pressure in the reactor system 11 is reduced.

  Further, when the pressure in the reactor system 11 or the main steam system 12 rises, the relief safety valve 26 is opened and the steam is released under the surface of the suppression pool 28 through the exhaust pipe 27. The relief safety valve 26 is configured to be opened when the pressure of the main steam pipe 20 or the pressure of the reactor system 11 exceeds a preset value. And by the opening and closing of the relief safety valve 26, the pressure rise is suppressed so that the reactor pressure in the reactor system 11 does not exceed the specified value.

  For this reason, the relief valve 26 used in the boiling water nuclear power plant 10 increases the reactor pressure even when a transient change or an accident occurs in the boiling water nuclear power plant 10 due to some abnormality. In order to reliably suppress the valve, the valve is designed to have the required number of valves and valve capacity based on the required design criteria.

  FIG. 3 is a structural diagram of the relief safety valve 26 shown in FIG.

  The relief safety valve 26 includes an actuator 30 and a valve body 31. The valve body 31 includes a body 32, a spring 33, a valve rod 35 provided with a valve body 34 at the end, and a valve seat 36. The valve body 34 and the valve seat 36 are provided inside the body 32. The spring 33 is provided outside the body 32, and the side of the valve rod 35 where the valve body 34 is not provided penetrates the body 32 and is connected to the spring 33.

  In addition, the body 32 of the valve body 31 is provided with an inlet 37 and an outlet 38. A steam Y flow path 39 from the inlet 37 to the outlet 38 is formed inside the body 32, and the valve body 34 is driven to the valve seat 36 side together with the valve rod 35 by the action of the spring 33. As a result, the steam Y flow path 39 is blocked. When the spring 33 is compressed by the valve inlet pressure applied to the valve body 34, a gap is generated between the valve body 34 and the valve seat 36, and the steam Y can pass therethrough.

  Furthermore, the valve body 34 is forcibly separated from the valve seat 36 together with the valve rod 35 to allow the steam Y to pass through by controlling the actuator 30 by giving an external signal to the actuator 30 as necessary. The actuator 30 is configured to be actuated by a remote operation switch or a pressure switch signal based on a measured value of a steam Y pressure sensor (not shown).

  That is, the relief safety valve 26 functions as a safety valve by the operation of the spring 33, and assists if the pressure of the steam Y inside the body 32 reaches a predetermined set pressure even when the pressure of the steam Y required for the operation of the spring 33 is equal to or less. It has a relief valve function capable of forcibly opening the valve by the actuator 30 which is an actuating device.

  When designing the number and the valve capacity of the relief valves 26 or the set pressure required for operating the spring 33, even if an event that causes a severe rise in the reactor pressure occurs, the designed relief is used. It is analyzed and evaluated whether or not the rise in the reactor pressure can be appropriately suppressed by the number and the valve capacity of the safety valve 26 and the set pressure for blowing out the steam Y.

  Examples of events in which the increase in the reactor pressure becomes severe include events called “generator load shut-off / turbine bypass valve malfunction” and “main steam isolation valve misclose”.

  “Generator load cut-off / turbine bypass valve non-operation” is a signal from an output load imbalance detection circuit (not shown) due to a load cut-off of the generator 21 caused by a power system fault or the like during the output operation of the reactor 15. This is an event in which the reactor pressure rises due to the rapid closing of the turbine main steam control valve 24.

  When the “generator load shut-off / turbine bypass valve inactive” state is reached, the reactor 15 is scrammed to lower the reactor pressure, and when the reactor pressure reaches the set pressure of the relief valve 26, the relief valve 26 is activated. Then, the valve body 34 is released by moving away from the valve seat 36.

  “Accidental shut-off of main steam isolation valve” is an event in which the main steam isolation valve 22 closes due to an error signal such as a low reactor water level or a malfunction during the output operation of the reactor 15 and the reactor pressure rises. .

  Even in the “main steam isolation valve erroneously closed” state, when the reactor pressure is released and reaches the set pressure of the safety valve 26, the relief valve 26 is activated and the valve element 34 is moved to prevent the reactor pressure from rising. It is opened by leaving the seat 36.

  For this reason, the design criteria for the number and valve capacity of the relief safety valve 26 and the set pressure when the steam Y is allowed to escape are, for example, “generator load shut-off / turbine bypass valve non-operation” and “main steam isolation valve erroneous closure”. Of the two conditions, the boiling water nuclear power plant 10 has been analyzed for dynamic events for severer reactor pressure rise events so that the reactor pressure can be safely reduced no matter which reactor pressure increases. It is determined.

  In order to analyze the dynamic characteristics of the boiling water nuclear power plant 10, the reactor system 11 including the shape data of the fuel, the core and the reactor internal structure, the main steam system 12 including the main valve characteristics, the recirculation pump 17 It is necessary to calculate with the analysis code using the set values of components such as the recirculation system 13 including the characteristics and the main control system for controlling the operation of the nuclear power plant as analysis parameters. For this reason, analysis parameters to be input to the analysis code for dynamic characteristic analysis are set based on design data of components such as the reactor system 11, the main steam system 12, the recirculation system 13, and the control system.

  The plant optimum evaluation means 2 of the relief safety valve capacity evaluation system 1 is constructed by reading a plant optimum evaluation code, which is an example of an analysis code, into a computer and uses the set values of the components in the boiling water nuclear power plant 10 as analysis parameters. It has a function as means for executing an analysis code for analyzing dynamic characteristics. That is, the plant optimum evaluation means 2 has a function of simulating the dynamic characteristic analysis of the boiling water nuclear power plant 10 by inputting the set analysis parameters.

  In the plant optimal evaluation code constituting the plant optimal evaluation means 2, the nuclear thermal hydraulic system of the core is a three-dimensional model, and the core and vessel are divided into a number of nodes. In the plant optimum evaluation code, transient changes in the reactor 15 are realistically analyzed by calculating combinations of mass, energy, and momentum conservation formulas for each phase of the two-phase fluid at each divided node. The

  For example, (1) JA Borkowski, et. Al., TRAC-BF1 / MOD1: An Advanced Best Estimate Program for BWR Accident Analysis, NUREG / CR-4356, Idaho National Engineering Laboratory, August 1992 ( 2) DD Taylor et. Al., TRAC-BD1 / MOD1: An Advanced Best Estimate Computer Program for Boiling Water Reactor Transient Analysis, Volume 1: Model Description, NUREG / CR-3633, EGG-2294, April 1984, (3) RJ Pryor et. Al., TRAC-PIA, An Advanced Best Estimate Computer Program for PWR LOCA Analysis, Los Alamos Scientific Laboratory, NUREG / CRA-0665, May 1979, (4) S. Kawamura et. Al., Best Estimate Methods for Licensing Analysis, International Meeting on “Best-Estimate” Methods in Nuclear Installation Safety Analysis, Washington DC, November, 2000, etc.

  The peak value of the reactor pressure is obtained from the analysis result obtained by inputting the analysis parameter to the plant optimum evaluation code, and the number of relief valves 26 and the valve of the relief safety valve 26 are obtained based on the peak value of the reactor pressure. The design value of the relief valve 26 such as the capacity and the set pressure for the steam Y to blow out can be set.

  Here, in consideration of the analysis error of the dynamic characteristic analysis by the plant optimum evaluation code, that is, the error of the peak value of the reactor pressure, a safety margin is provided in the design value of these relief valves 26. That is, in addition to the design value of the relief safety valve 26 required by the analysis result of the plant optimum evaluation code, the capacity of the relief safety valve 26 is further added as a safety margin.

  This safety margin is set by quantifying the uncertainty of the analysis result of the plant optimum evaluation code. The uncertainty of the analysis result of the plant optimum evaluation code can be mathematically obtained by using a statistical method from the uncertainty of the analysis parameter input to the plant optimum evaluation code.

  The cause of the uncertainty of the analysis parameters used for the dynamic characteristic analysis of the plant optimum evaluation code is the error between the element model used for the plant optimum evaluation code and the set value of the actual device, and the error between the analysis parameter and the design value. Etc. That is, even during steady operation of the plant, the set values such as the pressure and output of the equipment cannot be controlled completely constant due to factors such as instrument errors, and thus vary to some extent with time. And the uncertainty in an analysis parameter arises by the dispersion | variation in the setting value of such an apparatus.

  Therefore, the relief safety valve capacity evaluation system 1 obtains the statistical distribution of the peak value of the reactor pressure when each analysis parameter is changed by the experimental design method, and the statistical distribution of the obtained peak value of the reactor pressure. The statistical method of deriving a transfer function that shows the relationship between each analysis parameter and the peak value of the reactor pressure from the calculation results in the uncertainty of the analysis result of the plant optimum evaluation code, that is, the variation in the peak value of the reactor pressure. Desired.

  That is, the relief safety valve capacity evaluation system 1 treats the uncertainties of all analysis parameters that affect the analysis results of the plant optimum evaluation code as random variables, and uses a statistical method based on the uncertainties (variations) of individual analysis parameters. Transient change analysis is performed by creating a large number of cases of combinations of analysis parameters changed by. Then, a statistical quantity such as a standard deviation or an average value is obtained from the statistical distribution of the transient change analysis result, whereby the uncertainty of the analysis result of the plant optimum evaluation code is quantified and a safety margin is set.

  In other words, in the relief safety valve capacity evaluation system 1, the statistical upper limit value of the peak value of the reactor pressure is obtained from the variation in the analysis result of the plant optimum evaluation code when each analysis parameter is used, and this statistical upper limit value is obtained. Safety margin is evaluated based on this. Here, the statistical upper limit value is the strictest value among values that can occur with a certain degree of reliability within a certain probability.

  By the way, there are a relatively large number of analysis parameters that affect the peak value of the reactor pressure, and the calculation of the peak value of the reactor pressure using all the analysis parameters becomes complicated. For this reason, it is effective to analyze the statistical upper limit value of the peak value of the reactor pressure more simply by using only the analysis parameter dominant to the fluctuation of the peak value of the reactor pressure.

  Therefore, as a result of the transient change analysis performed by changing the analysis parameter and executing the plant optimum evaluation code with sufficiently high sensitivity to the peak value of the reactor pressure, the reactor pressure that is the transient change analysis result It is necessary to extract an analysis parameter such that the magnitude of the change in the peak value is constant. In this way, by narrowing down the analysis parameters to those having sufficiently high sensitivity, it is possible to obtain an efficient and accurate result even in a limited computer environment.

  Here, in reality, each analysis parameter varies depending on each other. Therefore, assuming that one analysis parameter does not depend on other analysis parameters, the uncertainty of each analysis parameter with respect to the peak value of the reactor pressure By performing sensitivity analysis, analysis parameters to be included in the analysis of the statistical upper limit value can be extracted more easily.

  The individual sensitivity analysis means 3, the experimental design sampling means 4, the transfer function creation means 5, the Monte Carlo calculation means 6, the normality determination means 7, and the statistical upper limit value calculation means 8 of the relief safety valve capacity evaluation system 1 include the methods described above. Provides various functions for determining the statistical upper limit of the peak value of the reactor pressure.

  That is, the individual sensitivity analysis means 3 assumes that each analysis parameter does not depend on each other, perturbs each analysis parameter individually, gives it to the plant optimum evaluation means 2, and executes dynamic characteristic analysis for each analysis parameter. A function that performs sensitivity analysis for the peak value of reactor pressure (hereinafter referred to as "individual sensitivity analysis") and extracts analysis parameters with relatively high sensitivity based on the results of individual sensitivity analysis and defines them as uncertainty parameters It has a function.

  The experimental design sampling means 4 has a function to set a plurality of analysis cases of combinations in which the uncertainty parameters defined by the individual sensitivity analysis means 3 are simultaneously changed according to the respective perturbation conditions by performing sampling by the experimental design. By giving the set analysis case to the plant optimum evaluation means 2 and executing the dynamic characteristic analysis, sensitivity analysis of each uncertainty parameter with respect to the peak value of the reactor pressure when each uncertainty parameter is changed simultaneously (hereinafter, "Simultaneous change sensitivity analysis").

  As a result, a simultaneous change distribution which is the distribution of the peak value of the reactor pressure when the uncertainty parameters are simultaneously changed by the experimental design sampling means 4 is obtained. For this reason, a quantitative relationship between the uncertainty parameter and the peak value of the reactor pressure can be obtained.

  The experimental design sampling means 4 has a function of providing the transfer function creating means 5 with the simultaneous change distribution of the peak value of the reactor pressure.

  Based on the simultaneous change distribution of the peak value of the reactor pressure obtained as a result of the simultaneous change sensitivity analysis by the experimental design sampling means 4, the transfer function creating means 5 is based on the uncertainty parameter and the increase amount of the peak value of the reactor pressure. Has a function of formulating a transfer function for the above by fitting such as least square fitting.

  The Monte Carlo calculation means 6 has a function of obtaining the distribution of the peak value of the reactor pressure by the Monte Carlo calculation of the transfer function derived by the transfer function creating means 5.

  With the above configuration, the experimental design sampling means 4, the transfer function creating means 5, and the Monte Carlo calculation means 6 function as means for obtaining the distribution of the peak values of the reactor pressure.

  The normality determination means 7 has a function of testing whether or not the distribution of the peak value of the reactor pressure obtained by the Monte Carlo calculation means 6 can be regarded as a normal distribution, that is, the normality.

  The statistical upper limit calculation means 8 has a function of obtaining the statistical upper limit value of the reactor pressure peak value based on the distribution of the peak value of the reactor pressure obtained by the Monte Carlo calculation means 6. At this time, if the statistical upper limit calculation means 8 determines that the distribution of the peak value of the reactor pressure is normal by the normality determination means 7, the peak value of the reactor pressure is estimated by the interval estimation. If it is determined that the normality is not recognized, the statistical upper limit of the peak value of the reactor pressure is obtained by order statistics.

  Next, the operation of the relief safety valve capacity evaluation system 1 will be described.

  FIG. 4 is a flowchart showing a flow when calculating the statistical upper limit value of the peak value of the reactor pressure by the method of calculating the transfer function obtained by the experimental design method by the relief safety valve capacity evaluation system 1 shown in FIG. Indicates. Moreover, the code | symbol which attached | subjected the number to S in the figure shows each step of a flowchart.

  First, in step S1, the individual sensitivity analysis means 3 analyzes plant data D1 in the base case of the boiling water nuclear power plant 10, for example, plant data D1 such as nominal design values of components and parts under basic base conditions. The parameters are given to the plant optimum evaluation means 2 to execute the dynamic characteristic analysis. As a result, the plant optimum evaluation means 2 obtains a nominal value of the peak value of the reactor pressure by executing the plant optimum evaluation code using the base case analysis parameters, and the individual sensitivity analysis means 3 obtains the plant optimum evaluation means 2. Receives the nominal value of the reactor pressure peak.

  Here, there are uncertainties in the analysis parameters of the plant optimum evaluation code, and there are also uncertainties in the peak value of the reactor pressure as the analysis result. For this reason, it is necessary to mathematically obtain the uncertainty of the peak value of the reactor pressure mathematically from the uncertainty of the analysis parameters, but since there are so many analysis parameters, all the analysis parameters If it is used to find the uncertainty of the peak value of the reactor pressure, the calculation becomes complicated.

  Therefore, an individual sensitivity analysis is performed assuming that each analysis parameter for the peak value of the reactor pressure does not depend on each other, and an analysis parameter with high sensitivity is extracted.

  First, in step S 2, an analysis parameter distribution, which is an input parameter when performing individual sensitivity analysis of analysis parameters, is input by an input unit (not shown) and given to the individual sensitivity analysis unit 3. As the distribution of the analysis parameters, distribution data such as manufacturing tolerances of components and parts in the boiling water nuclear power plant 10 and variations in verification test data can be used.

  Next, in step S3, the individual sensitivity analysis means 3 creates an analysis parameter changed from the nominal value of the analysis parameter based on the distribution of the analysis parameter as input data for the individual sensitivity analysis. The method of obtaining the input data for the individual sensitivity analysis differs between a method that assumes that the analysis parameter has a uniform distribution and a method that assumes that the analysis parameter has a normal distribution.

  When the analysis parameter is an analysis parameter such as an output value that can be directly measured by instruments, a uniform distribution can be assumed. In this case, the upper and lower limit values of the analysis parameter can be used as input data for the individual sensitivity analysis. As the upper and lower limit values of the analysis parameters, for example, the instrument errors of the instruments described in the set value rationale for each plant can be used.

  Further, when the analysis parameter is an analysis parameter that cannot be directly controlled mechanically, it can be assumed to be a normal distribution. In this case, input data for individual sensitivity analysis can be obtained from the standard deviation.

  At this time, the standard deviation of the analysis parameter can be obtained from experimental data obtained by various tests such as a plant start-up test and a small scale test. For example, when the analysis parameter is heat flux, the test is repeatedly performed by changing conditions such as pressure, flow rate, and temperature. Then, by comparing the experimental data obtained by the test with the analysis result by the dynamic characteristic analysis code simulating the same conditions as the test, the distribution of the difference between the experimental value and the analytical value is obtained, Uncertainty of analysis parameters including errors can be obtained.

  Here, since the difference between the experimental value of the analysis parameter and the analysis value is statistically distributed, the standard deviation, which is an index of the distribution, can be obtained by a general definition equation represented by Equation (1).

  Assuming that the analysis parameters are assumed to be normally distributed, the details of the test for determining the uncertainty of the analysis parameters are described in Boyak et al., “Quantifying Reactor Safety Margins: Application of Code Scaling, Applicability, and Uncertainty Evaluation Methodology. to a Large-Break, Loss-of-Coolant Accident, ”NUREG / CR-5249, (1989).

  Next, in step S4, the individual sensitivity analysis unit 3 gives the created input data of the individual sensitivity analysis as an analysis parameter to the plant optimum evaluation unit 2 to perform dynamic characteristic analysis. That is, the individual sensitivity analysis means 3 performs the individual sensitivity analysis on the peak value of the reactor pressure of the analysis parameter uncertainty by perturbing the analysis parameter having uncertainty and executing the dynamic characteristic analysis by the plant optimum evaluation code. To do.

  As a result, the plant optimum evaluation means 2 obtains the peak value of the reactor pressure according to the perturbation conditions such as the standard deviation and upper and lower limit values of the analysis parameters, and the individual sensitivity analysis means 3 receives the dynamic characteristic analysis from the plant optimum evaluation means 2. The peak value of the resulting reactor pressure is received.

  Next, in step S5, the individual sensitivity analysis means 3 changes the peak value of the reactor pressure due to the perturbation of the analysis parameter, that is, the peak value of the reactor pressure obtained by perturbing the analysis parameter and the reactor pressure in the base case. A difference between the peak value and the nominal value is obtained, and it is determined whether or not the obtained difference is larger than a predetermined reference value.

  When the individual sensitivity analysis unit 3 determines that the difference between the peak value of the reactor pressure obtained by perturbing the analysis parameter and the nominal value of the peak value of the reactor pressure is larger than the reference value, In step S6, the analysis parameter is defined as an uncertainty parameter. On the other hand, if it is not determined that the analysis parameter is larger than the reference value, the analysis parameter is not defined as an uncertainty parameter.

  Next, in step S7, another analysis parameter i is selected, and in step S2 to step S6 again for the analysis parameter i, if the amount of change in the peak value of the reactor pressure due to perturbation is large, it is defined as an uncertainty parameter. The Further, similar processing is performed for each analysis parameter.

  As a result, the sensitivity of each analysis parameter to the peak value of the reactor pressure is obtained, and an analysis parameter with high sensitivity is extracted and defined as an uncertainty parameter.

  FIG. 5 is a diagram showing an example of the individual sensitivity analysis result for the peak value of the reactor pressure as the analysis parameter obtained by the individual sensitivity analysis means 3 shown in FIG.

  In FIG. 5, the vertical axis indicates the ID of the analysis parameter, and the horizontal axis indicates the amount of change in the peak value of the reactor pressure when each analysis parameter is changed based on the perturbation condition, that is, the peak value of the reactor pressure. The difference from the nominal value is shown.

  As shown in FIG. 5, the analysis parameters to be subjected to sensitivity analysis are, for example, from parameter A to parameter X. Comparing the sensitivity of each analysis parameter to the peak value of the reactor pressure, that is, the amount of change in the peak value of the reactor pressure, the parameter S and the parameter X are relatively high in sensitivity, and the parameter M and the parameter O are relatively insensitive. I understand.

  That is, the individual sensitivity analysis means 3 evaluates the sensitivity of the analysis parameter based on the magnitude of the change amount of the peak value of the reactor pressure from the base case when the analysis parameter is changed by perturbation, and the sensitivity is relatively high. High analysis parameters are extracted and defined as uncertainty parameters. Therefore, the distribution of the peak value of the reactor pressure can be obtained by a statistical method by treating the uncertainty parameter as a random variable.

  Here, when the distribution of the peak value of the reactor pressure is obtained by a statistical method, it is effective to perform the simultaneous change sensitivity analysis of the uncertainty parameter by using the experimental design method for simplifying the calculation. Therefore, the individual sensitivity analysis means 3 gives the defined uncertainty parameter to the experimental design sampling means 4.

  In step S8, the experiment design method sampling means 4 simultaneously performs the analysis cases of the combinations in which the uncertainty parameters defined by the individual sensitivity analysis means 3 are simultaneously changed according to the respective perturbation conditions by performing sampling by the experiment design method. Multiple input parameters are used for change sensitivity analysis.

  FIG. 6 is a diagram showing an example of an analysis case set in sampling by the experimental design method by the relief safety valve capacity evaluation system 1 shown in FIG.

  As shown in FIG. 6, a plurality of analysis cases (case 1, case 2,...) Are assigned by assigning −1 and +1 to each uncertainty parameter (parameter 1, parameter 2,...). ) Is created. The input parameter for the simultaneous change sensitivity analysis can be set by perturbing the analysis parameter assigned +1 to the positive side while perturbing the analysis parameter assigned −1 to the negative side.

  Here, when it is assumed that the uncertainty parameter has a uniform distribution and the probability is 100%, the same upper and lower limit values as in the individual sensitivity analysis can be used as the perturbation conditions for the simultaneous change sensitivity analysis as they are. . That is, the upper limit value is used as an input parameter for the simultaneous change sensitivity analysis for the analysis parameter to which +1 is assigned, and the lower limit value is used for the analysis parameter to which -1 is assigned.

  On the other hand, when the uncertainty parameter is assumed to be a normal distribution, values such that the probability that the uncertainty parameter exceeds a certain value is within the target value can be used as the upper limit value and the lower limit value. That is, an appropriate perturbation condition can be estimated so that the distribution of the dynamic characteristic analysis result falls within an appropriate probability range.

  The method for estimating the appropriate perturbation conditions so that the distribution of the dynamic characteristic analysis results falls within the appropriate probability range is described in general probability statistics textbooks such as “Probability and Statistics Junkichi Satsuma Iwanami Shoten”. Yes. That is, the perturbation condition can be obtained from a standard deviation and a numerical table of normal distribution.

  In the normal distribution, when the standard deviation is σ and the probability outside a certain value μ ± zσ is α, the probability α for the z value can be obtained from the numerical table of the normal distribution. For example, when the z value is 1.65, the probability α is 0.0495 according to the numerical table of the normal distribution, so the probability outside of μ ± 1.65σ is about 5%. Therefore, the range covering the one-sided probability of 95% (α≈0.05) is μ + 1.65σ.

  Here, the one-sided probability of 95%, which is the probability range, corresponds to a two-sided probability of 90%, but the probability range is set as one-sided because the dynamic characteristic analysis result is the distribution of the peak value of reactor pressure and only the upper limit value is examined. did.

  In addition, since the peak value of reactor pressure, which is the result of simultaneous change sensitivity analysis, is obtained by perturbation of multiple uncertainty parameters, the probability of the peak value of reactor pressure does not exactly match the probability of the uncertainty parameter. . Therefore, for example, by using a normal distribution number table, it is possible to estimate what percentage of the probability of the peak value of the reactor pressure corresponds to the probability.

  For example, if the simultaneous change distribution of the peak value of the reactor pressure is to be 95% one-sided probability (90% two-sided probability, corresponding to approximately μ + 1.65σ), the uncertainty parameter assumed to be a normal distribution is χ ± 2σ (χ Is in the range of the normal distribution from the numerical table of the normal distribution with a two-sided probability of 97.7% (one-sided probability of 98.8%), so if the perturbation condition of the uncertainty parameter is χ ± 2σ, the reactor It can be estimated that the peak value of the pressure will be at least within the range of 95% probability on one side. For this reason, when the simultaneous change distribution of the peak value of the reactor pressure is to be 95% one-sided probability (two-sided probability 90%), χ ± 2σ is considered to be an appropriate perturbation condition for the uncertainty parameter.

  Next, in step S9, the experimental design sampling means 4 gives the analysis case set as the combination of the uncertainty parameters according to the perturbation condition to the plant optimum evaluation means 2 to execute the dynamic characteristic analysis by the plant optimum evaluation code. Thus, the simultaneous change sensitivity analysis of each analysis parameter is executed.

  Next, in step S10, another analysis case n is given to the plant optimum evaluation means 2, and in step S9, the simultaneous change sensitivity analysis for the analysis case n is executed again. Then, the simultaneous change sensitivity analysis is repeatedly performed for each analysis case n (1 ≦ n ≦ the total number of analysis cases), and the simultaneous change distribution which is the distribution of the peak value of the reactor pressure when the uncertainty parameters are changed simultaneously. Is obtained.

  Then, the experimental design sampling means 4 provides the transfer function creation means 5 with the simultaneous change distribution of the peak value of the reactor pressure.

Next, in step S11, the transfer function creating means 5 is based on the simultaneous change distribution of the peak value of the reactor pressure received from the experimental design sampling means 4, and the amount of increase in the uncertainty parameter and the peak value of the reactor pressure. A transfer function showing a quantitative relationship with is derived. As a method of deriving the transfer function, for example, there is a method of formulating the transfer function as a quadratic expression by obtaining a fitting coefficient by least square fitting as shown in Expression (2).

However,
Y: Amount of increase in peak value of reactor pressure f: Transfer function X ₁ , X ₂ ,..., X _N : Uncertainty parameter N: Number of uncertainty parameters (pieces)
c ₀ , c _i , c _ij : fitting coefficients

  That is, in Equation (2), the fitting coefficient is obtained by fitting from the simultaneous change distribution of the peak value of the reactor pressure.

  FIG. 7 is a diagram in which an example of a transfer function obtained by least square fitting by the relief safety valve capacity evaluation system 1 shown in FIG. 1 is plotted.

FIG. 7 is a diagram in which two uncertainty parameters X ₁ and X ₂ are plotted three-dimensionally as parameters in the transfer function Y = f (X ₁ , X ₂ ,..., X _N ). When plotting two uncertainty parameters as parameters as shown in FIG. 7, the peak value Y of the reactor pressure is expressed by a curved surface.

  The transfer function creation means 5 gives the transfer function derived in this way to the Monte Carlo calculation means 6.

  Next, in step S12, the Monte Carlo calculation means 6 creates a random number and performs a Monte Carlo calculation of the transfer function. A known method can be used as a method for generating random numbers in the Monte Carlo calculation.

  Random numbers according to the uniform distribution can be created by a known appropriate algorithm. As a method for generating random numbers with uniform distribution, for example, a linear congruential method can be cited. That is, random numbers with a uniform distribution can be created using the equations (3-1) and (3-2).

[Equation 3]
z _{i + 1} = ax _i + b (mod m) (3-1)
η = (β−α) ξ + α (3-2)

That is sequence x _i a random integer creation of 0 ≦ xi] <m by the equation (3-1), uniformly distributed 0 ≦ ξ <1 range by dividing the sequence x _i of the integers m A random number ξ is obtained. Furthermore, the random number η uniformly distributed in the range of α ≦ η <β is obtained by performing variable transformation on the random number ξ obtained in the equation (3-1) by the equation (3-2).

  When creating a random number according to the normal distribution, first, a standard normal random number according to the standard normal distribution is generated. Here, the standard normal random number is a random number normally distributed with an average of zero and a variance of one. There are various methods for generating a standard normal random number, and a frequently used method is the Box-Muller method. In the Box-Muller method, first, random numbers ξ1, ξ2 (0 ≦ ξ1, ξ2 <1) according to two uniform distributions are created, and using these, two equations are obtained by equations (4-1) and (4-2). Standard normal random numbers X1 and X2 are generated.

[Equation 4]
X1 = (− 2 logξ1) ^(1/2) sin (2πξ2) (4-1)
X2 = (− 2 logξ1) ^(1/2) cos (2πξ2) (4-2)

  Furthermore, by performing variable conversion of the standard normal random numbers X1 and X2 using the equations (5-1) and (5-2), it is possible to create a random number η that is normally distributed with an average μ and a standard deviation σ.

[Equation 5]
η = σX1 + μ (5-1)
η = σX2 + μ (5-2)

  Then, the distribution of the peak value of the reactor pressure can be obtained by performing the Monte Carlo calculation of the transfer function using such random numbers.

  FIG. 8 shows the distribution of the peak value of the reactor pressure obtained by Monte Carlo calculation of the transfer function for the increase amount of the uncertainty parameter and the peak value of the reactor pressure by the relief safety valve capacity evaluation system 1 shown in FIG. It is a figure which shows an example of a figure.

  In FIG. 8, the horizontal axis indicates the peak value of the reactor pressure, and the vertical axis indicates the frequency of the peak value of the reactor pressure. As shown in FIG. 8, the distribution of the peak value of the reactor pressure can be obtained.

  Then, the Monte Carlo calculation means 6 gives the distribution of the peak value of the reactor pressure to the normality determination means 7.

  Next, in step S13, the normality determining means 7 determines whether or not normality is recognized in the distribution of the peak value of the reactor pressure, that is, whether or not it can be regarded as a normal distribution. When the normality is recognized in the distribution of the peak value of the reactor pressure, the probability distribution of the peak value of the reactor pressure is given to the statistical upper limit calculating means 8 together with the information that the normality is recognized. When the normality is not recognized, the distribution of the peak value of the reactor pressure is given to the statistical upper limit calculating means 8 together with the information that the normality is not recognized.

  If normality is recognized in the distribution of the peak value of the reactor pressure, in step S14, the statistical upper limit calculating means 8 determines the peak of the reactor pressure by estimating the section from the distribution of the peak value of the reactor pressure. Find the statistical upper limit of the value.

  The probability p% when calculating the statistical upper limit is the extent to which the upper limit of the uncertainty parameter probability is defined when defining the upper and lower limits of the uncertainty parameter variation in the simultaneous change sensitivity analysis based on the experimental design method. It can be determined by using values that are covered up to.

  In addition, the distribution of the peak value of the reactor pressure was obtained by setting a small number of analysis cases using the plant optimum evaluation code according to the experimental design method, and this is a sample randomly sampled from the actual population. Can think. In other words, the statistical upper limit of the peak value of the reactor pressure has a statistical distribution because it is a value obtained by performing a transient change analysis in a case where a sample is randomly selected from the population.

  In addition, when the number of trials of Monte Carlo calculation is sufficiently large, the distribution of the peak value of the reactor pressure is often recognized as being compatible with the normal distribution. Therefore, when normality is recognized in the distribution of the peak value of the reactor pressure, the most severe value with the probability p% is obtained with a certain reliability q% using interval estimation, and this value is statistically calculated. Evaluation can be performed as an upper limit. That is, a statistical upper limit value at a certain reliability can be obtained from a numerical table of normal distribution and statistical values such as standard deviation and average value. For example, in the case of the statistical upper limit value of 95% reliability, Pmax = μ + 1.96σ.

  On the other hand, when normality is not recognized in the distribution of the peak value of the reactor pressure, in step S15, the statistical upper limit calculating means 8 determines the reactor pressure by the order statistics from the distribution of the peak value of the reactor pressure. Find the statistical upper limit of the peak value.

  A method based on order statistics will be described. The probability that a random sampled statistic X belongs to a distribution region within 100 α% points of a population according to an arbitrary distribution (distribution free) is represented by α, and the probability exceeding 100 α% is represented by 1-α. Therefore, when the number of samples is N, the probability P that r samples are within 100 α% points and N−r samples exceed 100 α% is expressed by Expression (6).

[Equation 6]
P = α ^r (1−α) ^N−r (6)
Here, since the number of combinations when selecting r samples from N samples is _N C _{r, r} samples out of the number N of samples, in other words, the r-th largest sample is at least 100α. The probability Pr belonging to the distribution region within the% probability point is expressed by Equation (7) and follows a binomial distribution.

Therefore, if the reliability is β, the probability Pr only needs to be equal to or higher than the reliability β, and therefore the inequality of Expression (8) is established.

Here, in equation (8), when r = N, r = N-1, and r = N-2, equations (9-1), (9-2), and (9-3) are derived, respectively. .

  Further, in the formulas (9-1), (9-2), and (9-3), for example, in the case of 95% probability and 95% reliability, α = β = 0.95. At this time, the maximum Ns that satisfy the expressions (9-1), (9-2), and (9-3) are 59, 93, and 124, respectively. These results show that r is the rank of the magnitude of the statistic, and in the case of 95% probability and 95% reliability, the upper limit is r = N when 59 ≦ N ≦ 92, and r = 93 when 93 ≦ N ≦ 123. It means N-1.

  That is, when the number of reactor pressure peak values (number of analysis cases of simultaneous change sensitivity analysis), which is the number of samples, is 59 to 92, the probability that all the reactor pressure peak values are at least 95% 95 In order to satisfy the% reliability, the peak value of the largest reactor pressure can be set as the statistical upper limit value. Also, when the number of peak values of reactor pressure is 93 to 123, the peak values of all reactor pressures except for one data satisfy at least 95% probability and 95% reliability. A large value can be used as the statistical upper limit value.

  For this reason, for example, in the case where the number of analysis cases of the simultaneous change sensitivity analysis is 100, if normality is not recognized in the distribution of the peak value of the reactor pressure, the peak value of the second largest reactor pressure is It can be a statistical upper limit.

  Further, in step S16, the statistical upper limit value of the peak value of the reactor pressure obtained in this way is given to an output device (not shown) by the statistical upper limit value calculation means 8 and outputted.

  Here, since the design values such as the number and capacity of the relief safety valves 26 are also one of the analysis parameters of the plant optimum evaluation code, the design values of the relief safety valves 26 are changed, and the design values of the relief safety valves 26 are the same. The transfer function is derived by the above procedure, and the distribution of the peak value of the reactor pressure is obtained.

  Then, for each design value of the relief safety valve 26, a statistical upper limit value of the peak value of the reactor pressure is obtained from the distribution of the peak value of the reactor pressure, for example, when the 95% probability is 95% reliability. Even if the statistical upper limit value of the peak value is reached, each design value of the relief valve 26 is evaluated depending on whether or not an excessive increase in the reactor pressure can be sufficiently avoided by each design value of the relief valve 26.

  In other words, according to the relief safety valve capacity evaluation system 1, the appropriate safety margin in the number and capacity of the relief safety valve 26 can be obtained from the statistical upper limit value of the peak value of the reactor pressure obtained by the statistical method. . According to the relief safety valve capacity evaluation system 1, the safety margin is set small by executing the dynamic characteristic analysis of the facility such as the nuclear power plant with higher accuracy than before, and the valve number and capacity of the relief safety valve 26 are more appropriate. Can be designed.

  FIG. 9 shows the statistical upper limit of the peak value of the reactor pressure obtained using the statistical method by the relief safety valve capacity evaluation system 1 shown in FIG. 1 and the reactor pressure obtained by the conventional relief safety valve capacity evaluation method. It is the figure which compared an example of the peak value.

  In FIG. 9, the horizontal axis indicates the number of relief safety valves 26, and the vertical axis indicates the peak value of the reactor pressure. Further, the solid line in FIG. 9 is data A indicating the statistical upper limit value of the peak value of the reactor pressure obtained by the statistical method using the relief safety valve capacity evaluation system 1, and the dotted line is the conventional relief safety valve capacity. It is the data B which shows the peak value of the reactor pressure obtained by the evaluation method.

  Further, the alternate long and short dash line in FIG. 9 indicates the criterion C for determining the peak value of the reactor pressure that is the capacity of the relief valve 26 required for the boiling water nuclear power plant 10. The criterion C for determining the peak value of the reactor pressure in the boiling water nuclear power plant 10 is set to 1.1 times the maximum operating pressure of the boiling water nuclear power plant 10, for example.

  According to the data B indicating the peak value of the reactor pressure obtained by the conventional relief safety valve capacity evaluation method of FIG. 9, the peak value of the reactor pressure is already the relief valve in the number of the relief valves 26 serving as a base. It can be seen that when the number of valves 26 is decreased, the data B of the peak value of the reactor pressure increases and exceeds the judgment standard C of the peak value of the reactor pressure.

  On the other hand, according to the data A indicating the statistical upper limit value of the peak value of the reactor pressure obtained by the statistical method by the relief safety valve capacity evaluation system 1 of FIG. 9, the statistical upper limit of the peak value of the reactor pressure is obtained. It can be seen that the value is sufficiently smaller than the criterion C for the peak value of the reactor pressure in the number of relief relief valves 26 serving as a base.

  Further, according to the data A indicating the statistical upper limit value of the peak value of the reactor pressure obtained by the relief safety valve capacity evaluation system 1, the statistical upper limit of the peak value of the reactor pressure is gradually increased as the number of the relief safety valves 26 is decreased. The statistical upper limit of the peak value of the reactor pressure when the value increases and the number of the relief safety valve 26 is four times less than the number of the relief relief valve 26 as a base is a criterion for determining the peak value of the reactor pressure It can be seen that the value of C roughly matches. Therefore, if the number or capacity of the relief safety valve 26 is evaluated using the relief safety valve capacity evaluation system 1, it can be understood that the number of the relief safety valve 26 can be smaller than the number of the relief safety valve 26 as a base.

  That is, if the relief safety valve capacity evaluation system 1 is used, the peak value of the reactor pressure in the boiling water nuclear power plant 10 can be analyzed more accurately, so that an excessive safety margin is avoided and a more appropriate and less relief valve 26 is provided. It is possible to design the number of valves or the capacity.

  FIG. 10 is a block diagram showing a second embodiment of the relief safety valve capacity evaluation system according to the present invention.

  The relief safety valve capacity evaluation system 1A shown in FIG. 10 replaces the experiment design sampling means 4, the transfer function creation means 5 and the Monte Carlo calculation means 6 with the Monte Carlo sampling means 40, and the relief safety valve capacity evaluation shown in FIG. Different from the system. Other configurations and operations are substantially the same as those of the relief safety valve capacity evaluation system shown in FIG.

  The relief safety valve capacity evaluation system 1A has a function of obtaining the distribution of the peak value of the reactor pressure by executing the simultaneous change sensitivity analysis by the Monte Carlo sampling means 40 using the uncertainty parameter defined by the individual sensitivity analysis means 3. Have. That is, the Monte Carlo sampling means 40 randomly sets a combination of perturbation conditions of uncertainty parameters as a plurality of analysis cases, and gives the set analysis cases to the plant optimum evaluation means 2 to perform dynamic characteristic analysis. It has a function to perform simultaneous change sensitivity analysis of each uncertainty parameter with respect to the peak value of the furnace pressure.

  That is, the Monte Carlo sampling means 40 functions as a means for obtaining the distribution of the peak value of the reactor pressure.

  Then, the normality determining means 7 is adapted to test the normality with respect to the distribution of the peak value of the reactor pressure obtained by the Monte Carlo sampling means 40.

  Next, the operation of the relief valve capacity evaluation system 1A will be described.

  FIG. 11 is a flowchart showing a flow when the statistical upper limit value of the peak value of the reactor pressure is calculated by the direct Monte Carlo method by the relief safety valve capacity evaluation system 1A shown in FIG. Moreover, the code | symbol which attached | subjected the number to S in the figure shows each step of a flowchart, attaches | subjects the same code | symbol about the step equivalent to FIG. 4, and abbreviate | omits description.

  First, similarly to the flowchart shown in FIG. 4, an uncertainty parameter is defined in steps S1 to S7.

  Next, in step S20, the Monte Carlo sampling means 40 generates random numbers based on the statistical distribution of each uncertainty parameter by Monte Carlo sampling, that is, the Monte Carlo method, and randomly perturbs in the simultaneous change sensitivity analysis of the uncertainty parameters. Multiple combinations of conditions are set as analysis cases.

  Next, in step S21, the Monte Carlo sampling unit 40 gives the set analysis case to the plant optimum evaluation unit 2 to perform dynamic characteristic analysis, thereby simultaneously changing the sensitivity of each uncertainty parameter to the peak value of the reactor pressure. Perform analysis.

  Next, in step S22, another analysis case n is given to the plant optimum evaluation means 2, and in step S21, the simultaneous change sensitivity analysis for the analysis case n is executed again. Then, the simultaneous change sensitivity analysis is repeatedly performed for each analysis case n (1 ≦ n ≦ the total number of analysis cases), and the distribution of the peak value of the reactor pressure when the uncertainty parameters are simultaneously perturbed and changed is obtained. It is done.

  Then, the Monte Carlo sampling unit 40 gives the distribution of the peak value of the reactor pressure to the normality determining unit 7, and the normality of the distribution of the peak value of the reactor pressure in steps S13 to S16 as in the flowchart of FIG. Then, the statistical upper limit value of the peak value of the reactor pressure is obtained and output based on the interval estimation or order statistics depending on the presence or absence of normality.

  When the simultaneous change distribution of the peak value of the reactor pressure does not become a probability distribution type, a non-parametric method is applied, and a statistical upper limit value of the peak value of the reactor pressure is obtained based on order statistics.

  FIG. 12 is a diagram showing an example of the distribution of the peak value of the reactor pressure and the statistical upper limit value in each analysis case obtained by using the direct Monte Carlo method by the relief safety valve capacity evaluation system 1A shown in FIG.

  In FIG. 12, the horizontal axis indicates the analysis case, and the vertical axis indicates the peak value of the reactor pressure. Further, the circles in FIG. 12 indicate the peak values of the reactor pressure obtained by executing the dynamic characteristic analysis in each analysis case. Further, the solid line in FIG. 12 indicates the average value D of the peak value of the reactor pressure, and the dotted line indicates the nominal value E of the peak value of the reactor pressure.

  As shown in FIG. 12, the peak value of the reactor pressure in each analysis case is a random value in both the plus region and the minus region, with the average value D or the nominal value E of the reactor pressure peak value being approximately the center. In this case, the distribution of the peak value of the reactor pressure is not normal, and the nonparametric method is used.

  Therefore, based on the order statistics, for example, when the number of analysis cases is 100 and the 95% probability is 95% reliability, in Equation (8), N = 100 and α = β = 0.95. The peak value of the reactor pressure is very large as the statistical upper limit value.

  In FIG. 12, the second largest reactor pressure peak value is the reactor pressure peak value G indicated by the circle surrounded by the curve F. Therefore, the reactor pressure peak indicated by the circle surrounded by the curve F is shown in FIG. The value G can be the statistical upper limit of the reactor pressure.

  When the 95% probability is 95% reliability, the statistical upper limit G of the peak value of the reactor pressure obtained by the direct Monte Carlo method by the relief safety valve capacity evaluation system 1A is the relief safety valve capacity evaluation system shown in FIG. According to 1, the peak value of the reactor pressure obtained by the method of calculating the transfer function obtained by the experimental design method becomes substantially the same value.

  The relief valve capacity evaluation system 1A as described above obtains the statistical upper limit value of the peak value of the reactor pressure using the analysis case of the uncertainty parameter set at random by Monte Carlo sampling.

  For this reason, according to the relief safety valve capacity evaluation system 1A, since the statistical upper limit value of the peak value of the reactor pressure can be obtained with higher accuracy, the same effect as the relief safety valve capacity evaluation system 1 shown in FIG. 1 is obtained. be able to.

The block diagram which shows 1st Embodiment of the relief safety valve capacity | capacitance evaluation system which concerns on this invention. The schematic block diagram of the boiling water nuclear power plant which is an example of the application object of the relief safety valve capacity evaluation system shown in FIG. FIG. 3 is a structural diagram of the relief safety valve shown in FIG. 2. The flowchart which shows the flow at the time of calculating the statistical upper limit of the peak value of a reactor pressure by the method of calculating the transfer function obtained by the design of experiment by the relief safety valve capacity evaluation system shown in FIG. The figure showing an example of the individual sensitivity analysis result with respect to the peak value of the reactor pressure of the analysis parameter obtained by the individual sensitivity analysis means shown in FIG. The figure which shows the example of the analysis case set in the sampling by an experiment design method by the relief safety valve capacity evaluation system shown in FIG. The figure which plotted an example of the transfer function calculated | required by least square fitting by the relief safety valve capacity | capacitance evaluation system shown in FIG. The figure which shows an example of the probability distribution figure of the peak value of the reactor pressure obtained by carrying out the Monte Carlo calculation of the transfer function about the increase amount of the analysis parameter and the peak value of the reactor pressure by the Monte Carlo calculation means shown in FIG. The statistical upper limit value of the reactor pressure peak value obtained by the statistical method by the relief safety valve capacity evaluation system 1 shown in FIG. 1 and the peak value of the reactor pressure obtained by the conventional relief safety valve capacity evaluation method. The figure which compared an example. The block diagram which shows 2nd Embodiment of the relief safety valve capacity | capacitance evaluation system which concerns on this invention. The flowchart which shows the flow at the time of calculating the statistical upper limit of the peak value of a reactor pressure by the direct Monte Carlo method by the relief safety valve capacity evaluation system shown in FIG. The figure which shows an example of distribution of the peak value of a reactor pressure, and a statistical upper limit in each analysis case obtained using the direct Monte Carlo method by the relief safety valve capacity evaluation system shown in FIG.

Explanation of symbols

1,1A Relief Safety Valve Capacity Evaluation System 2 Plant Optimal Evaluation Unit 3 Individual Sensitivity Analysis Unit 4 Experimental Design Sampling Unit 5 Transfer Function Creation Unit 6 Monte Carlo Calculation Unit 7 Normality Judgment Unit 8 Statistical Upper Limit Calculation Unit 10 Boiling Water Nuclear Power plant 11 Reactor system 12 Main steam system 13 Recirculation system 14 Reactor containment vessel 15 Reactor 16 Circulation path 17 Recirculation pump 18 Turbine 19 Condenser 20 Main steam pipe 21 Generator 22 Main steam isolation valve 23 Turbine main Steam stop valve 24 Turbine main steam control valve 25 Turbine bypass valve 26 Relief safety valve 27 Exhaust pipe 28 Suppression pool 30 Actuator 31 Valve body 32 Body 33 Spring 34 Valve body 35 Valve rod 36 Valve seat 37 Inlet 38 Outlet 39 Flow path 40 Monte Carlo sampling Mean A Atom obtained using statistical methods Data indicating the peak value of pressure B Data indicating the peak value of reactor pressure obtained by the conventional relief valve capacity evaluation method C Criteria for determining the peak value of reactor pressure D Average value of the peak value of reactor pressure E Atom Nominal value F of peak value of reactor pressure Curve G Second peak value of reactor pressure Y Steam

Claims (8)

Perturbing the analysis parameters input to the analysis code for executing the dynamic characteristics analysis of the reactor to obtain the distribution of the peak value of the reactor pressure, and statistics of the distribution of the peak value of the reactor pressure A relief valve capacity evaluation method comprising: a step of obtaining a dynamic upper limit value. Sampling by experimental design to set a combination of simultaneous changes in the perturbation conditions of the analysis parameters and setting them as multiple analysis cases, and performing a Monte Carlo calculation of the transfer function obtained from the dynamic characteristic analysis results using the set analysis cases 2. The relief valve capacity evaluation method according to claim 1, wherein the distribution of the peak value of the pressure of the nuclear reactor is obtained by this. The combination of simultaneously changing the perturbation conditions of the analysis parameters is set as a plurality of random analysis cases by performing sampling by the Monte Carlo method, and the dynamic pressure analysis is performed using the set analysis cases, whereby the pressure of the reactor 2. The relief valve capacity evaluation method according to claim 1, wherein a distribution of peak values of the relief valve is obtained. The analysis parameter used for obtaining the distribution of the peak value of the reactor pressure is an uncertainty parameter whose individual sensitivity to the peak value of the reactor pressure exceeds a certain reference value. The relief valve capacity evaluation method according to 1, wherein 2. The statistical upper limit value of the peak value of the reactor pressure is obtained based on the interval estimation when normality is found in the distribution of the peak value of the reactor pressure. Relief safety valve capacity evaluation method. The statistical upper limit value of the peak value of the reactor pressure is obtained based on order statistics when normality is not recognized in the distribution of the peak value of the reactor pressure. Evaluation method for safety valve relief. The analysis code is a three-dimensional model of the nuclear thermal hydraulic system of the core of the reactor, and the core and vessel are divided into a number of nodes, and each phase of the two-phase fluid at each divided node is 2. The relief safety valve capacity evaluation method according to claim 1, wherein a plant optimum evaluation code for analyzing a transient change of a nuclear reactor is calculated by combining a conservation formula of mass, energy, and momentum. Means for obtaining a distribution of the peak value of the reactor pressure by perturbing an analysis parameter input to an analysis code for executing a dynamic characteristic analysis of the reactor, and a distribution of the peak value of the reactor pressure A relief valve capacity evaluation program for allowing relief to function as a statistical upper limit calculation means for obtaining a statistical upper limit of

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