How to perform a STAR / ARWV match

Abstract

A method for transitioning a nuclear reactor during initial cycle startup to a power generating state is disclosed. The method includes placing the reactor in a zero power state, omitting a low power physical test (LPPT) for the current cycle of the reactor based on a predetermined set of criteria, and transitioning the reactor to the power generating state without conducting the LPPT based on a cross-check. The cross-checking includes predicting a first set of values ​​for elements of the LPPT using a first design code, developing empirical equations for the elements of the LPPT using data from past cycles of the reactor, predicting a second set of values ​​for the elements of the LPPT using the empirical equations, and cross-checking the first values ​​against the second values.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims the benefit of and priority under 35 U.S.C. § 120 to U.S. patent application Ser. No. 17 / 930,909, filed Sep. 9, 2022, and entitled "METHOD FOR PERFORMING STAR / ARWV RECONCILIATION," the contents of which are incorporated herein by reference in their entirety.

[0002] The present invention relates generally to a method for reducing the start-up testing time required before a nuclear reactor is placed into power generation during initial cycle start-up. [Brief explanation of the drawings]

[0003] The various features of the embodiments described herein, together with their advantages, will be understood from the following description read in conjunction with the accompanying drawings, in which:

[0004] [Figure 1] 1 illustrates a method for transitioning a nuclear reactor to power generation during initial cycle start-up, according to at least one aspect of the present disclosure.

[0005] Corresponding reference characters indicate corresponding parts in the several drawings. The examples described herein illustrate aspects of various embodiments of the invention, and such examples are not to be construed as limiting the scope of the invention in any way. DETAILED DESCRIPTION OF THE INVENTION

[0006] Various specific details are described to provide a thorough understanding of the overall structure, function, manufacture, and use of the embodiments described herein and illustrated in the accompanying drawings. Well-known operations, components, and elements are not described in detail so as not to obscure the embodiments described in the specification. Readers of this specification should understand that the embodiments described and illustrated herein are non-limiting examples, and therefore, the specific structural and functional details disclosed herein will be understood to be representative and exemplary. Variations and modifications may be made without departing from the scope of the claims.

[0007] When nuclear power plants are brought back to power generation, certain tests, such as low-power physical tests (LPPT), must be performed. These tests are conducted under non-standard plant operating conditions, increasing the risk of plant problems and erroneous test results. In 2019, the Pressurized Water Reactor Group ("PWROG") launched an industry-wide initiative to reduce start-up test times to support a faster return to power generation.

[0008] The CE-NSSS plant achieved this initiative in 2005 through the NRC-approved Startup Test Activity Reduction (STAR) program, which allows for the elimination of LPPT measurements of control rod worth and high-temperature zero-power (HZP) moderator temperature coefficient (MTC). The STAR method requires that the STAR applicability requirements be determined for each cycle to ensure that the cycle meets all requirements for the elimination of these LPPT tests. The STAR applicability requirements are set forth in Table 3-4 of WCAP-16011-PA, "Startup Test Activity Reduction Program," February 2005, the contents of which are incorporated herein by reference in their entirety.

[0009] While each operator has developed their own justification for eliminating control rod worth, only Westinghouse's Alternative Control Rod Worth Verification (ARWV) method, which is based closely on the NRC-approved STAR method, is fully compliant with current W-NSSS safety analysis methodology.

[0010] Both the current STAR and ARWV methods require the use of a second qualification method using an independent surrogate approach based on plant measurements to predict HZP control rod worth and (in the case of STAR) MTC, which are then compared (checked) against design code predictions. Checking design code predictions against independent surrogate predictions provides a good (possibly better) alternative to verification by actual measurements.

[0011] The current approach to do this is to use predictions from a second design-qualified neutron optical code. This approach requires maintaining a second code for all units and cycles. However, maintaining this second code requires a lot of man-hours and associated undesirable costs. This aspect is a major obstacle to adopting the ARWV method to eliminate control rod worth tests in W-NSSS plants. Furthermore, it has led to dissatisfaction in CE-NSSS plants that use STAR.

[0012] As an example, Westinghouse's ANC design code predictions are currently compared to predictions using an independent NRC-approved alternative design code because both predictions are based on plant measurements. However, this approach requires that the alternative design code be maintained and updated every cycle, possibly solely for use in STAR matching.

[0013] Therefore, to justify the elimination of LPPT during plant start-up, it is necessary to develop accessible, independent surrogate forecasts that can be checked against cycle-by-cycle forecasts.

[0014] STAR Topical allows for alternative means of reconciliation, including extrapolating current cycle conditions from past measurements. STAR Topical requires consideration of changes in power distribution, core mean enrichment, burnable absorber quantity and type, reactor coolant system (RCS) boron concentration, and moderator temperature to estimate Control Element Assembly (CEA) worth. Estimating MTC requires consideration of changes in RCS boron concentration, burnable absorber quantity and type, moderator temperature, core leakage, and core mean enrichment. STAR Topical restricts the use of estimation methods for reconciliation to cycles that are within core design application requirement #3 in WCAP-16011-PA Table 3-4, have characteristics relative to the measurement cycle that are within ±2% of the water-to-fuel metal ratio, the same fuel pin pitch, and the same fuel management style (i.e., low leakage).

[0015] The STAR verification method must meet many requirements. The method must be capable of predicting the HZP total control rod worth (TRW), total control bank worth (RBW), and MTC at the beginning of cycle (BOC) of the current reactor cycle. Furthermore, since the rationale for using analytical predictions instead of measurements to verify the safety analysis uncertainties of the design code is that the verification method is as accurate as the design code, the method must have plant-based uncertainties similar to the design code values. In one aspect, the method must consider the factors listed in item 4 of Table 3-4 of WCAP-16011-PA. In one aspect, the method must not rely on measurements at each cycle or calculated data from the design code that has not been independently verified by an independent qualified method. It is recommended that verification be performed using an alternative method well before startup in case the verification does not meet the criteria and HZP control rod worth and / or MTC measurements are required.

[0016] Therefore, the surrogate matching approach provided by this disclosure provides cycle-specific TRW, total RBW, and MTC predictions for HZP BOC conditions according to empirical equations based on a combination of calculated and measured data from past reactor cycles. In various embodiments, all parameters in the equations are based on results from rodless cycle-specific design codes. This is an acceptable approach because the rodless model is validated by measurements during power-up start-up testing on a cycle-by-cycle basis.

[0017] In various embodiments, the method provided herein is in the form of three specific empirical equations for TRW, total RBW, and MTC, with coefficients determined on a plant-specific basis. All terms in these equations are based on parameters calculated by a rodless design model under nominal conditions. In various embodiments, uncertainties determined on a plant-specific basis are also included. [Example]

[0018] Westinghouse validated the method using data from a plant cycle in which LPPT measurements of control rod worth and MTC were performed (17 cycles) and from a subsequent cycle (post-STAR) in which no measurements were performed (6 cycles).

[0019] The measured data, associated core states, and rodless flux distribution data were analyzed (using insights gained from fundamental reactor physics) to determine the key parameters affecting MTC and rod worth, and to obtain empirical correlations that allow implementation of estimation methods for STAR verification. The applied parameters were selected based on theoretical considerations and requirements specified in the STAR topical. Regression fitting was performed on 17 measurement cycles to obtain reasonable fits for TRW, RBW, and MTC. This fit was applied to all 17 measurement cycles and 6 non-measurement cycles to determine the uncertainties associated with the regression fits.

[0020] Based on the identified key decision parameters, the present disclosure also demonstrates that the dependency between TRW and MTC can be modeled using a neural network approach. The neural network approach provided comparable but slightly larger uncertainties. In one aspect, cycle-specific evaluation of the neural network approach requires the development and maintenance of software routines (e.g., Excel macros) to evaluate the neural network to obtain cycle-specific values. In one aspect, the neural network approach is in the form of a three-layer neural network represented by a specific set of interconnected node weights. HZP MTC

[0021] Developing an estimation method for HZP MTC is relatively straightforward because there are few global core-related parameters that significantly affect MTC. The first parameter is the core soluble boron concentration, on which MTC is highly dependent. This is because a decrease in moderator density also decreases the soluble absorber concentration throughout the core.

[0022] The second parameter, on which MTC depends at least in part, is core neutron leakage. This is because a decrease in moderator density increases the mean free path of neutrons, making the core more permeable to neutrons, and thus increasing core neutron leakage. In a high-leakage core, where neutron leakage has a significant effect on core reactivity, a change in moderator density results in a larger negative MTC. In a low-leakage core, where neutron leakage has a smaller effect on core reactivity, a change in moderator density has less effect on MTC.

[0023] The third parameter, on which the MTC depends at least in part, is the fast flux / heat flux ratio of the core. Cores with a higher fast flux / heat flux ratio have a more negative MTC because more fast neutrons are slowed down to thermal energy to initiate U-235 fission. The fast flux / heat flux ratio depends primarily on the average enrichment and burnup of the core.

[0024] The fourth parameter is moderator temperature, on which the MTC depends at least in part because moderator density varies with temperature. However, in some embodiments, the reference is made at the HZP temperature (565°F), so moderator temperature may not be included in the empirical formula.

[0025] Based on these considerations, a preliminary analysis of 17 measurement cycles showed that the MTC for an all-control-rods-out ("ARO") BOC HZP of 565°F can be reasonably expressed by the following empirical formula:

number

number

[0026] As an example, the following uncertainties based on actual plant measurements demonstrate the accuracy of MTC predictions using this approach: Bias: 0.084 StdDev: 0.271 pcm / °F kσ:0.631 UTL: 0.761 pcm / °F Total CEA value

[0027] Unlike MTCs, CEAs are strong, discrete absorbers located at specific locations in the core, so the CEA worth is affected by both global and local parameters. Therefore, the CEA worth is significantly affected by the flux and reactivity distribution throughout the core. In this case, the core neutron perturbation method can be used instead of detailed core flux calculations to estimate the CEA reactivity worth. The reactivity worth (ρ) of a change in local absorption δΣa is given by neutron perturbation theory as follows:

number

[0028] Unfortunately, Westinghouse does not have a core design code that can solve the three-dimensional adjoint multigroup diffusion equations. However, noting that the one-group diffusion equations are self-adjoint, the equivalent one-group perturbation equations can be written as follows:

number

[0029] It should be noted that if all inserted CEA fingers are of the same design, the average control rod group cross-sectional area of ​​the assembly can be approximated as:

number

[0030] Therefore, the control rod worth is approximately proportional to:

number

[0031] While the above equation reasonably captures the effect of flux distribution on the total CEA worth, it does not capture the effect of changes in the neutron spectrum and neutron mean free path, which significantly affect the CEA worth. These effects can be reasonably captured by including the thermal / fast neutron flux ratio, moderator temperature, and soluble boron concentration in the correlation. In some embodiments, moderator temperature may not be considered in the HZP situation because it does not change from cycle to cycle.

[0032] Note that the above perturbation approach assumes that incremental changes in absorption do not significantly change the unperturbed flux distribution in the core. This is approximately true for total control rod worth, since nearly all assemblies contain CEAs, and the overall core flux distribution with control rods inserted does not change significantly when all CEAs are inserted. However, in some embodiments, this is certainly not the case when only a few CEAs are inserted, significantly redistributing the core flux distribution.

[0033] In some aspects, the total control rod worth is dependent on the moderator density because it affects the neutron mean free path, i.e., the number of neutrons actually absorbed by the control rod. However, in various embodiments, the moderator density may not be included in the equation because the check is performed at the HZP temperature (565°F).

[0034] Based on these considerations, a regression analysis of 17 measurement cycles revealed that the TRW of a CEA with an Ag-In-Cd tip at a BOC HZP of 565°F can be reasonably expressed by the following empirical equation:

number

[0035] As an example, the following uncertainties based on actual plant measurements demonstrate the accuracy of predicting total control rod worth using this approach: Bias:-0.01% StdDev: 0.75% kσ: 1.75% LTL:-1.76% Total Control CEA Value

[0036] As noted above, in some aspects, the assumption of no significant change in the unperturbed flux distribution does not hold when only a few CEAs are inserted and the insertion of the CEAs significantly redistributes the core flux distribution. Thus, in various embodiments, the control bank worth correlation includes an additional term related to the redistribution of core flux when sparsely distributed CEAs are inserted. In some embodiments, by analyzing the data and insights from fundamental reactor physics, it has been determined that the appropriate correction terms are the higher-order perturbation terms (which have the effect of reducing control rod worth by reducing flux in the control rod assemblies), the core mean travel distance, and the k∞ ratio of rodless assemblies to rod-loaded assemblies, which have a significant impact on the flux redistribution.

[0037] The correlation for Control Bank Worth (RBW) for Ag-In-Cd tipped CEA at BOC HZP 565°F based on data from 17 measurement cycles is as follows:

number

number

number

[0038] Note that control rod worth also depends on moderator density. In various embodiments, moderator density may not be included in the equation because the check is performed at the HZP temperature (565°F).

[0039] As an example, the following uncertainties based on actual plant measurements demonstrate the accuracy of control rod worth predictions using this approach: Bias:-0.02% StdDev: 1.60% kσ:3.61% LTL:-3.64% STAR Matching Criteria

[0040] WCAP-16011-PA requires that the criterion for reconciliation "shall not be greater than the corresponding uncertainties established for the benchmark CEA values ​​and isothermal temperature coefficients (ITCs)." This reconciliation may be performed by determining whether the differences in parameter predictions between the two cores match the corresponding differences using different core design methods, provided that both methods are evaluated in accordance with Core Design Applicability Requirement #3.

[0041] Note that this match actually compares the difference in control rod worth changes (ΔTRW, ΔRBW) and MTC changes (ΔMTC) between the current cycle and the previous reference measurement cycle calculated by the two methods. By comparing the cycle-to-cycle differences rather than directly comparing the control rod worth and MTC predictions for the current cycle design with the differences predicted by the match method, the comparison eliminates the systematic bias inherent in the methods, leaving only the variance that affects the match comparison. Bias has been found to vary more than variance across plants and fuel types. In some aspects, the reference cycle selected should be one with a small measured-to-predicted (MP) difference. In various embodiments, the same reference cycle is selected for both methods.

[0042] The matching criterion is based on the two-sided 95 / 95 uncertainty associated with the difference between two independent estimates of the TRW and MTC differences between the current and reference cycles. Since STAR matching is performed on the Δ difference, the appropriate matching variance (hereafter referred to as σ 2 Recon") is twice the sum of the variances of the two methods used for matching (the variance of the design code is "σ 2 Dcode ”, and the variance of the alternative matching method is σ 2 RAlt Therefore, the standard deviation (σ) of the comparison is:

number

[0043] Since matching is based on the 95 / 95 statistic, the matching criteria is calculated from the following formula:

number

[0044] The final matching criteria were: 1) the calculated 95 / 95 two-sided tolerance (K * σRecon) (where "k" is the critical tolerance for the number of data samples) and 2) the safety analysis (k95 / 95σ) uncertainty.

[0045] There are some important notes regarding the values ​​used in this calculation. In one embodiment, the variance used in the design code is the variance from the set of benchmarks used to verify the uncertainty used in the safety analysis. The set of benchmarks may include benchmarks from other plants if poolability is demonstrated. A rigorous calculation of SRecon takes into account the variance of the verification code. However, if only the design code variance is considered, and SRecon is greater than the uncertainty of the safety analysis, the final verification criterion will remain the same, regardless of the uncertainty of the verification method. In one embodiment, if the verification code benchmark does not fit the range of the design code benchmark or if the uncertainty of the verification method is unknown / unavailable (e.g., when using a non-design method as the verification method), the verification code variance should be conservatively set to zero when determining the verification criterion.

[0046] Note that some STAR implementation procedures define a cross-check review criterion that, if exceeded, prompts a review of both the design cycle-specific and the cross-check cycle-specific calculations. This value is calculated in the same way as the cross-check acceptance criterion, except that the variance used is based solely on the current plant benchmark. Exceeding the cross-check review criterion initially (before a follow-up) does not necessarily mean that a current cycle control rod worth measurement needs to be performed.

[0047] As an example, based on the above, the matching criteria for △TRW, △RBW, and △MTC in BOC HZP are as follows:

number

[0048] It should be noted that the other matching approaches described by this disclosure assume that the rodless flux predicted by the design code has an uncertainty comparable to that used in the benchmark case used to establish the power distribution uncertainty. However, this assumption is borne out during power-rise physical testing at the 70% and 100% plateaus, which required that the root mean square (RMS) difference between the measured and predicted radial RPD for each fuel assembly be 5% or less.

[0049] For STAR verification purposes, RMS may be calculated based on a non-tilted quadrant-symmetric power distribution because core tilt does not affect MTC, total, and total control bank worth. Also, for STAR verification purposes, passing the test at near-BOC conditions is sufficient regardless of power level. In some embodiments, it is conservative to use current test results using RMS comparisons as a basis for measured power distributions that include measured tilt. Overview of the Example

[0050] Based on the above, the disclosed STAR matching procedure requires the use of a design code to generate two sets of cycle-specific best estimate predictions for HZP MTC, HZP total control rod worth, and HZP total control bank worth, and the use of alternative empirical formulas for both the current cycle and the reference measurement cycle. The assembly flux values ​​used in the formulas are obtained from the HZP ARO calculations by the design code.

[0051] The match is performed by comparing the control rod worth and ITC differences between the current cycle and the reference measurement cycle calculated by the two methods. The STAR match requires that the two predictions agree within the uncertainty range used in the safety analysis calculations.

[0052] Another verification procedure requires that the design code's power distribution meet a power-up criterion that the root mean square (RMS) difference between the quadrant-symmetric measured and predicted assembly powers for each fuel assembly is less than or equal to 5% at any power and burnup before reaching high-temperature full-power (HFP) equilibrium. Note that this is automatically verified by meeting the power-up test criteria for the rms assembly MP required during power-up start-up testing.

[0053] This approach complies with the matching requirements of the STAR Topical (WCAP-16011-PA) because all factors described in the STAR Topical for the estimation method were explicitly considered in the development of the rodless design model on which the assembly fluxes used in the method are based, the method is referenced to plant measurements, uncertainties are identified, and matching criteria have been developed that are within the combined uncertainties of the two matching methods but no larger than the uncertainties used in the safety analysis.

[0054] The correlations determined according to the above method are applicable to all cycles that have characteristics relative to the reference cycle in the method defined in items 3 and 4 of the STAR Applicability Criteria (Tables 3-4 of WCAP-16011-PA).

[0055] While the above disclosure has been described with respect to the elimination of LPPT using the STAR method, it should be understood that the disclosure is also applicable to the checks required by applying the Alternative Control Rod Worth Verification (ARWV) method to eliminate control rod worth testing in W-NSSS plants. Thus, the present disclosure provides a basis for the elimination of LPPT testing in both the CE-NSSS and W-NSSS, and provides a method for reducing the risks associated with conducting the testing under non-standard plant operating conditions.

[0056] 1, a method 100 for transitioning a nuclear reactor to a power generating state during initial cycle start-up is illustrated in accordance with at least one aspect of the present disclosure. In various embodiments, the method 100 includes placing the nuclear reactor in a zero power state, such as an HZP state (102).

[0057] In various embodiments, the method 100 further includes eliminating (104) a low-power physical test (LPPT) for the current cycle of the reactor based on a predetermined set of criteria. In various embodiments, the set of criteria may be the criteria established by the STAR Act and the ARWV Act, as described elsewhere herein. In various embodiments, the set of criteria may be the criteria established by WCAP-16011-PA, as described elsewhere herein.

[0058] In various embodiments, eliminating 104 a low-power physical test (LPPT) may include a first prediction using a first design code to predict a first set of values ​​for elements of the LPPT. In various embodiments, the elements of the LPPT may be, for example, an MTC, a total RBW, or a TRW. In various embodiments, the first design code may be any code approved for making design code predictions for elements of the LPPT.

[0059] In various embodiments, eliminating low-power physical testing (LPPT) (104) further includes developing empirical equations for the LPPT elements using data from past reactor cycles. As described elsewhere herein, empirical equations for MTC, total RBW, and TRW may be established based on data from past reactor cycles. In various embodiments, the data from past cycles includes rodless cycle-specific data. In various embodiments, developing the empirical equations includes applying a regression fit to data from past reactor cycles to determine a reasonable fit for the LPPT elements, as described elsewhere herein.

[0060] In various embodiments, eliminating 104 the low-power physical test (LPPT) may further include predicting a second set of values ​​for elements of the LPPT using empirical equations. As described elsewhere herein, the second prediction may be performed using the developed empirical equations, thus providing an independent alternative prediction to justify eliminating the LPPT.

[0061] In various embodiments, eliminating the low-power physical test (LPPT) (104) may further include checking the first value against a second value. In various embodiments, checking the first value against the second value includes calculating a difference between the first value for the current reactor cycle and a first reference value from a reference cycle, and calculating a difference between the second value for the current reactor cycle and a second reference value from the reference cycle. As described elsewhere herein, this checking may require that the two predictions agree within the uncertainty range used in the assessment calculation.

[0062] In various embodiments, the method 100 further includes transitioning the reactor 106 to a power-producing state without performing LPPT based on the match (106). As described elsewhere herein, if the two predictions match, the STAR and ARWV methods can eliminate LPPT, thereby reducing the start-up testing time required before placing the reactor in a power-producing state.

[0063] In various embodiments, the present disclosure provides a control system, such as a computer, tablet, smartphone, or the like, that includes a processor and memory storing computer-readable instructions that, when executed by the processor, cause the processor to perform various functions provided by the present disclosure. The control system may receive data, such as data from past reactor cycles, to create the empirical formula. The memory may store any amount of data, such as data from past cycles and data from a reference cycle used for matching.

[0064] The foregoing method and disclosure provide many advantages. The method provides a highly accurate method for predicting control rod worth based solely on data from a design model. The method uses insights from fundamental reactor physics, coupled with power rise test results, to determine whether control rod worth measurements are necessary. The method provides several tests to determine whether power rise test results provide evidence to discontinue control rod worth testing, regardless of whether the normal power rise test fails. The method does not require technical specification changes or license submissions. The method is not dependent on any particular neutronics design code or methodology. Additionally, the method can be easily implemented using neural net machine learning.

[0065] Various aspects of the subject matter described herein are illustrated in the following examples.

[0066] Example 1 - A method for transitioning a nuclear reactor to a power generating state during initial cycle start-up, the method including placing the reactor in a zero power state, negating a low power physical test (LPPT) for the current cycle of the reactor based on a predetermined set of criteria, and transitioning the reactor to a power generating state without conducting an LPPT based on a check. Current LPPTs require the reactor to transition from a zero power state to a power generating state. The check includes predicting a first set of values ​​for elements of the LPPT using a first design code, developing empirical equations for the elements of the LPPT using data from past cycles of the reactor, predicting a second set of values ​​for the elements of the LPPT using the empirical equations, and checking the first values ​​against the second values.

[0067] Example 2 - The method of example 1, wherein the data from past cycles includes data specific to a control rodless cycle.

[0068] Example 3 - The method of Example 1 or Example 2, wherein developing the empirical equation includes applying a regression fit to data from past cycles of the reactor.

[0069] Example 4 - The method of any one of Examples 1-3, wherein eliminating LPPT further comprises determining an uncertainty associated with each empirical formula.

[0070] Example 5 - The method of any one of Examples 1-4, wherein the element comprises a moderator temperature coefficient.

[0071] Example 6 - The empirical formula for the moderator temperature coefficient is defined as follows, as described in Example 5:

number

number

[0072] Example 7 - The method of any one of Examples 1-6, wherein the element comprises total control rod worth.

[0073] Example 8 - The empirical formula for total control rod worth is defined as follows, as described in Example 7:

number

[0074] Example 9 - The method of any one of Examples 1-8, wherein the element includes a total control bank value.

[0075] Example 10 - The method of Example 9, where the empirical formula for total control bank value is defined as follows:

number

number

number

[0076] Example 11 - The method of any one of Examples 1-10, wherein matching the first value with the second value includes calculating a difference between the first value for the current cycle of the reactor and a first reference value from the reference cycle, and calculating a difference between the second value for the current cycle of the reactor and a second reference value from the reference cycle.

[0077] Example 12 - A method for transitioning a nuclear reactor to a power generation state, the method including placing the reactor in a zero power state, eliminating a low power physical test (LPPT) for a current cycle of the reactor based on a predetermined set of criteria, and transitioning the reactor to a power generation state without conducting the LPPT based on a calculation. A current LPPT requires the reactor to transition from a zero power state to a power generation state. The elimination includes predicting a first set of values ​​for elements of the LPPT using a first design code, the elements including at least one of a moderator temperature coefficient, a total control rod worth, and a total control bank worth, developing empirical equations for the elements of the LPPT using data from past cycles of the reactor, predicting a second set of values ​​for the elements of the LPPT using the empirical equations, calculating a difference between the first values ​​for the current cycle of the reactor and the first reference value from a reference cycle, and calculating a difference between a second value for the current cycle of the reactor and the second reference value from the reference cycle.

[0078] Example 13 - The method of example 12, wherein the data from past cycles includes data specific to a control rodless cycle.

[0079] Example 14 - The method of Example 12 or Example 13, wherein generating the empirical equation includes applying a regression fit to data from past cycles of the reactor.

[0080] Example 15 - The method of any one of Examples 12-14, wherein eliminating LPPT further comprises determining an uncertainty associated with each empirical formula.

[0081] Example 16 - The method of any one of Examples 12-15, wherein the empirical formula for the moderator temperature coefficient is defined as follows:

number

number

[0082] Example 17 - The method of any one of Examples 12-16, wherein the empirical formula for total control rod worth is defined as follows:

number

[0083] Example 18 - The method of any one of Examples 12-17, wherein the empirical formula for total control bank value is defined as follows:

number

number

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[0084] While several embodiments have been illustrated and described, it is not the applicant's intention to restrict or limit the scope of the appended claims to such details. Numerous modifications, variations, changes, substitutions, combinations, and equivalents may be made to these embodiments, and those skilled in the art will recognize such modifications, variations, changes, substitutions, combinations, and equivalents without departing from the scope of the present disclosure. Furthermore, the structure of each element associated with the described embodiments can be alternatively described as a means for providing the function performed by that element. Also, where materials are disclosed for particular components, other materials may be used. It is therefore to be understood that the foregoing description and the appended claims are intended to cover all such modifications, combinations, and variations as fall within the scope of the disclosed embodiments. Furthermore, the appended claims are intended to cover all such modifications, variations, changes, substitutions, variations, and equivalents.

[0085] The foregoing detailed description has used block diagrams, flowcharts, and / or examples to illustrate various aspects of the devices and / or processes. To the extent that such block diagrams, flowcharts, and / or examples include one or more functions and / or operations, those skilled in the art will understand that each function and / or operation included in such block diagrams, flowcharts, and / or examples may be implemented, separately and / or collectively, by various hardware, software, firmware, or any combination thereof. Those skilled in the art will recognize that some aspects of the embodiments disclosed herein may be equivalently implemented, in whole or in part, in an integrated circuit, as one or more computer programs running on one or more computers (e.g., as one or more programs running on one or more computer systems), as one or more programs running on one or more processors (e.g., as one or more programs running on one or more microprocessors), as firmware, or substantially any combination thereof, and that designing circuitry and / or writing software and / or firmware code is within the skill of those skilled in the art in light of this disclosure. Additionally, those skilled in the art will appreciate that the mechanisms of the subject matter described herein may be distributed as one or more program products in a variety of forms, and that the exemplary forms of the subject matter described herein apply regardless of the particular type of signal-bearing medium used to actually effect the distribution.

[0086] The instructions used to program the logic to perform the various disclosed aspects may be stored in memory within the system, such as dynamic random access memory (DRAM), cache, flash memory, or other storage. Additionally, the instructions may be distributed over a network or using other computer-readable media. Thus, a machine-readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computer), including, but not limited to, a floppy disk, an optical disk, a compact disk, a read-only memory (CD-ROM), a magneto-optical disk, a read-only memory (ROM), a random access memory (RAM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), a magnetic or optical card, a flash memory, or any tangible, machine-readable storage device used to transmit information over the Internet using electrical, optical, acoustic, or other forms of propagated signals (e.g., carrier waves, infrared signals, digital signals, etc.). Accordingly, non-transitory computer-readable media includes any type of tangible machine-readable medium suitable for storing or transmitting electronic instructions or information in a form readable by a machine (e.g., a computer).

[0087] When the term "control circuitry" is used in any aspect of the specification, it may refer to, for example, hardwired circuitry, programmable circuitry (e.g., a computer processor including one or more individual instruction processing cores, a processing unit, a processor, a microcontroller, a microcontroller unit, a controller, a digital signal processor (DSP), a programmable logic device (PLD), a programmable logic array (PLA), or a field programmable gate array (FPGA)), a state machine circuit, firmware that stores instructions executed by the programmable circuitry, or any combination thereof. Control circuitry may collectively or individually be embodied as circuits that form part of a larger system, such as, for example, an integrated circuit (IC), an application specific integrated circuit (ASIC), a system on a chip (SoC), a desktop computer, a laptop computer, a tablet computer, a server, a smartphone, etc. Thus, a "control circuit" herein includes, but is not limited to, an electrical circuit having at least one discrete electrical circuit, an electrical circuit having at least one integrated circuit, an electrical circuit having at least one application-specific integrated circuit, an electrical circuit forming a general-purpose computing device configured by a computer program (e.g., a general-purpose computer configured by a computer program that at least partially executes the processes and / or devices described herein, or a microprocessor configured by a computer program that at least partially executes the processes and / or devices described herein), an electrical circuit forming a memory device (e.g., a form of random access memory), and / or an electrical circuit forming a communications device (e.g., a modem, a communications switch, or an optoelectronic appliance). Those skilled in the art will recognize that the subject matter described herein may be implemented in analog or digital form, or some combination thereof.

[0088] When the term "logic" is used in any aspect herein, it may refer to an app, software, firmware, and / or circuitry configured to perform any of the operations described above. Software may be embodied as a software package, code, instructions, instruction sets, and / or data recorded on a non-transitory computer-readable storage medium. Firmware may be embodied as hard-coded (e.g., non-volatile) code, instructions, instruction sets, and / or data in a memory device.

[0089] When terms such as "component," "system," "module," and the like are used in any aspect of this specification, they may refer to either control circuitry, computer-related entities, hardware, a combination of hardware and software, software, or software in execution.

[0090] The term "algorithm," when used in any aspect of this specification, refers to a self-consistent sequence of steps leading to a desired result, where the "steps" refer to manipulations of physical quantities and / or logical states which may, but do not necessarily, take the form of electrical or magnetic signals capable of being stored, transferred, combined, compared, and otherwise manipulated. These signals are commonly referred to as bits, values, elements, symbols, characters, terms, numbers, or the like. These and similar terms may be associated with the appropriate physical quantities and are merely convenient labels applied to these quantities and / or states.

[0091] The network may include a packet-switched network. The communication devices can communicate with each other using a selected packet-switched network communication protocol. An example of a communication protocol is an Ethernet communication protocol, which may allow communication using Transmission Control Protocol / Internet Protocol (TCP / IP). The Ethernet protocol conforms to or is compatible with the Ethernet standard entitled "IEEE 802.3 Standard," published by the Institute of Electrical and Electronics Engineers (IEEE) in December 2008, and / or newer versions of this standard. Alternatively or additionally, the communication devices can communicate with each other using an X.25 communication protocol. The X.25 communication protocol conforms to or is compatible with standards promulgated by the International Telecommunication Union Telecommunication Standardization Sector (ITU-T). Alternatively or additionally, the communication devices can communicate with each other using a frame relay communication protocol. The frame relay communication protocol conforms to or is compatible with standards promulgated by the Consultative Committee for International Telegraph and Telephone (CCITT) and / or the American National Standards Institute (ANSI). Alternatively or additionally, the transceivers can communicate with each other using an asynchronous transfer mode (ATM) communication protocol. The ATM communication protocol conforms to or is compatible with the ATM standard entitled "ATM-MPLS Network Interworking 2.0" published by the ATM Forum in August 2001, and / or a later version of this standard. Of course, other and / or later-developed connection-oriented network communication protocols are contemplated herein as well.

[0092] As is apparent from the foregoing disclosure, unless expressly stated otherwise, throughout the foregoing disclosure, descriptions using terms such as "processing," "calculating," "computing," "determining," "displaying," and the like refer to operations and processes of a computer system or similar electronic computing device that modify and transform data represented as physical (electronic) quantities in the computer system's registers or memory into other data similarly represented as physical quantities in the computer system's memory or registers or other information storage, transmission, or display devices.

[0093] One or more components may be referred to herein as being "configured to," "configurable to," "operable to," "adapted to," "capable to," "adaptable to," etc. Those skilled in the art will recognize that, unless the context requires otherwise, "configured to" may generally encompass active and / or inactive and / or standby components.

[0094] Those skilled in the art will recognize that the terms used herein, and in particular in the appended claims (e.g., the body of the appended claims), are "open" terms (e.g., the word "comprising" should be interpreted as "including, but not limited to," the word "having" should be interpreted as "having at least," the word "comprises" should be interpreted as "including, but not limited to," etc.). Those skilled in the art will further recognize that if a specific number of claimed elements is intended, such intention will be explicitly recited in the claim; otherwise, no such intention exists. For example, as an aid to understanding, the appended claims may introduce elements using the introductory phrases "at least one" and "one or more." However, the use of such phrases, by introducing a claim element with the indefinite article "a" or "an," should not be construed as limiting a particular claim that includes the claim element so introduced to claims that include only one such element, even if the same claim also includes "one or more" or "at least one" and an indefinite article such as "a" or "an" (e.g., "a" and / or "an" should ordinarily be construed to mean "at least one" or "one or more"). The same applies to definite articles used to introduce elements into claims.

[0095] Additionally, even when the number of elements in an introduced claim is explicitly recited, those skilled in the art will recognize that this generally translates to mean at least the recited number of elements (e.g., a phrase "two elements" without other modifiers generally translates to at least two elements, or more than two elements). Furthermore, when phrases similar to "at least one of A, B, and C, etc." are used, such phrases are generally intended to have the meaning that one skilled in the art would understand the phrase (e.g., "a system having at least one of A, B, and C" includes, but is not limited to, a system having only A, a system having only B, a system having only C, a system having A and B, a system having A and C, a system having B and C, and / or a system having A, B, and C, etc.). When phrases similar to "at least one of A, B, or C, etc." are used, such phrases are generally intended to have the meaning that one of ordinary skill in the art would understand the phrase (e.g., "a system having at least one of A, B, and C" includes, but is not limited to, a system having only A, a system having only B, a system having only C, a system having A and B, a system having A and C, a system having B and C, and / or a system having A, B, and C, etc.). Those of ordinary skill in the art will further understand that disjunctive words and / or disjunctive phrases presenting two or more alternative terms, whether in the specification, claims, or drawings, should generally be understood to contemplate the possibility of including one of the words, either of the words, or both words, unless the context dictates otherwise. For example, the phrase "A or B" is generally understood to include the possibilities of "A," or "B," or "A and B."

[0096] With respect to the appended claims, those skilled in the art will understand that the operations described therein may generally be performed in any order. Also, while various operational flow diagrams are shown in a sequence, it should be understood that various operations may be performed in an order other than that shown, or may be performed simultaneously. Examples of such alternative sequences include overlapping, interleaved, interrupted, reordered, incremental, and preparatory sequences. Furthermore, past tense adjectives such as "corresponding to" and "related to" are generally not intended to exclude such variations unless the context dictates otherwise.

[0097] It should be noted that references to "one embodiment," "an embodiment," "one example," "one example," etc. mean that a particular feature, structure, or characteristic described in connection with that embodiment is included in at least one embodiment. Thus, the appearances of the phrases "in one embodiment," "in an embodiment," "in one example," and "in one example" in various places throughout this specification do not necessarily all refer to the same embodiment. Furthermore, particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0098] Any patent applications, patents, non-patent publications, or other disclosure materials referred to herein and / or set forth in an Application Data Sheet are incorporated herein by reference to the extent that the incorporated material does not contradict this specification. Therefore, to the extent necessary, the disclosure expressly set forth herein supersedes any conflicting material incorporated herein by reference. Any material, or portion thereof, purportedly incorporated by reference that contradicts any existing definitions, statements, or other disclosure material set forth herein is incorporated only to the extent that no conflict arises between the incorporated material and the existing disclosure material.

[0099] "Comprises" (and any form of "comprises," such as "comprises" or "comprising"), "has" (and any form of "comprises," such as "had" or "having"), "include" (and any form of "includes," such as "included" or "comprising"), and "contains" (and any form of "contains," such as "contained" or "containing") are open-ended linking verbs. Thus, a system that "comprises," "has," "includes," or "contains" one or more elements has those one or more elements, but is not limited to having only those one or more elements. Similarly, a system, device, or apparatus element that "comprises," "has," "includes," or "contains" one or more features has those one or more features, but is not limited to having only those one or more features.

[0100] As used in this disclosure, unless otherwise specified, the terms "substantially," "about," or "nearly" refer to an acceptable error for a particular value as determined by one of ordinary skill in the art, which depends in part on how the value is measured or determined. In certain embodiments, the terms "substantially," "about," or "nearly" mean within 1, 2, 3, or 4 standard deviations. In certain embodiments, the terms "substantially," "about," or "nearly" mean within 50%, 20%, 15%, 10%, 9%, 8%, 7%, 6%, 5%, 4%, 3%, 2%, 1%, 0.5%, or 0.05% of a value or range.

Claims

1. 1. A method for transitioning a nuclear reactor to a power generating state during initial cycle start-up, comprising: placing the reactor in a zero power state; Eliminating a low power physical test (LPPT) for the current cycle of the reactor based on a predetermined set of criteria, where the current LPPT is required to transition the reactor from the zero power state to the power generating state, said elimination comprising: predicting a first set of values ​​for elements of the LPPT using a first design code; developing empirical equations for the elements of the LPPT using data from past cycles of the reactor; predicting a second set of values ​​for the elements of the LPPT using the empirical formula; matching the first value with the second value; transitioning the reactor to the power-generating state without performing the LPPT based on the verification. method.

2. the data from the past cycles includes data specific to a control rodless cycle. The method of claim 1.

3. developing the empirical equation includes applying a regression fit to the data from the past cycles of the reactor; The method of claim 1.

4. and eliminating the LPPT further includes determining an uncertainty associated with each empirical formula. The method of claim 1.

5. the factor includes a moderator temperature coefficient; The method of claim 1.

6. 6. The method of claim 5, wherein the empirical formula for the moderator temperature coefficient is defined as follows: [Equation 25] Here, k ｍ０ , k ｍ１ , k ｍ２ , k ｍ３ , k ｍ４ is a constant derived from the plant-specific data set, ppm is the soluble boron concentration in the reactor coolant (parts per million), and φ １／２ is the mean high flux / heat flux ratio of the core, and L is the leakage of the core in Δk, defined as: [Equation 26] Here, Σ ｆｉ and Σ ａｉ are the fission cross sections and neutron absorption cross sections for neutron energy group i, and φ ｉ is the neutron flux of neutron energy group i, ν is the number of neutrons emitted per fission, and k ∞ and k ｅｆｆ are the infinite multiplication factor and effective multiplication factor of the core, and V is the volume of the operating core.

7. the factors include total control rod worth; The method of claim 1.

8. 8. The method of claim 7, wherein the empirical formula for total control rod worth is defined as follows: [Equation 26] Here, k ＴＲ０ , k ＴＲ１ , k ＴＲ２ , k ＴＲ３ is a constant derived from the plant-specific data set, ppm is the soluble boron concentration in the reactor coolant (parts per million), and φ ２／１ is the average heat flux / fast flux ratio of the core at BOC, HZP, and ARO, and φ ｉ is the neutron flux of neutron energy group i, and R ｉ is the number of CEA fingers inserted in assembly i.

9. the elements include a total control bank value; The method of claim 1.

10. 10. The method of claim 9, wherein the empirical formula for total control bank value is defined as: [0000] Here, k ＲＲ０ , k ＲＲ１ , k ＲＲ２ , k ＲＲ３ , k ＲＲ４ , k ＲＲ５ , k ＲＲ６ , k ＲＲ７ , k ＲＲ８ is a constant derived from the plant-specific data set, and k ｕｒ / k ｒ is the average rodless k ∞ and is defined as follows: [0000] Here, k ｉ is the number of control rods in assembly i ∞ and R ｉ is the number of control bank control rod fingers inserted in assembly i, and Δk ｒｆ is the value of one control rod finger. M is the total distance traveled by neutrons without the control rods, defined as: [0000] Here, D ｉ and Σ ａｉ is the diffusion constant and macroscopic absorption cross section of neutron energy group I, and Σ ｒ１ is the macro group 1 removal cross section.

11. Matching the first value with the second value comprises: calculating a difference between the first value for the current cycle of the reactor and a first reference value from a reference cycle; calculating a difference between the second value for the current cycle of the reactor and a second reference value from the reference cycle; The method of claim 1.

12. 1. A method for transitioning a nuclear reactor to a power generating state, comprising: placing the reactor in a zero power state; Eliminating a low power physical test (LPPT) for a current cycle of the reactor based on a predetermined set of criteria, the current LPPT being required to transition the reactor from the zero power state to the power generating state, the elimination comprising: predicting a first set of values ​​for elements of the LPPT using a first design code, the elements including at least one of a moderator temperature coefficient, a total control rod worth, and a total control bank worth; developing empirical equations for the elements of the LPPT using data from past cycles of the reactor; predicting a second set of values ​​for the elements of the LPPT using the empirical formula; calculating a difference between the first value for the current cycle of the reactor and a first reference value from a reference cycle; calculating a difference between the second value for the current cycle of the reactor and a second reference value from the reference cycle; transitioning the reactor to the power-generating state without implementing the LPPT based on the calculation. method.

13. the data from the past cycles includes data specific to a control rodless cycle. The method of claim 12.

14. developing the empirical equation includes applying a regression fit to the data from the past cycles of the reactor; The method of claim 12.

15. and eliminating the LPPT further includes determining an uncertainty associated with each empirical formula. The method of claim 12.

16. 13. The method of claim 12, wherein the empirical formula for moderator temperature coefficient is defined as follows: [Equation 30] Here, k ｍ０ , k ｍ１ , k ｍ２ , k ｍ３ , k ｍ４ is a constant derived from the plant-specific data set, ppm is the soluble boron concentration in the reactor coolant (parts per million), and φ １／２ is the mean fast flux / heat flux ratio of the core, and L is the leakage of the core in Δk, defined as follows: [Equation 31] Here, Σ ｆｉ and Σ ａｉ is the fission cross section and neutron absorption cross section of neutron energy group i, φi is the neutron flux of neutron energy group i, ν is the number of neutrons emitted per fission, and k ∞ and k ｅｆｆ are the infinite multiplication factor and effective multiplication factor of the core, and V is the volume of the operating core.

17. 13. The method of claim 12, wherein the empirical formula for total control rod worth is defined as follows: [Equation 32] Here, k ＴＲ０ , k ＴＲ１ , k ＴＲ２ , k ＴＲ３ is a constant derived from the plant-specific data set, ppm is the soluble boron concentration in the reactor coolant (parts per million), and φ ２／１ is the average heat flux / fast flux ratio of the core at BOC, HZP, and ARO, and φ ｉ is the neutron flux of neutron energy group i, and R ｉ is the number of CEA fingers inserted in assembly i.

18. 13. The method of claim 12, wherein the empirical formula for total control bank value is defined as: [Equation 33] Here, k ＲＲ０ , k ＲＲ１ , k ＲＲ２ , k ＲＲ３ , k ＲＲ４ , k ＲＲ５ , k ＲＲ６ , k ＲＲ７ , k ＲＲ８ is a constant derived from the plant-specific data set, and k ｕｒ / k ｒ is the average rodless k ∞ and is defined as follows: [Equation 34] Here, k ｉ is the number of control rods in assembly i ∞ and R ｉ is the number of control bank control rod fingers inserted in assembly i, and Δk ｒｆ is the value of one control rod finger. M is the total distance traveled by neutrons without the control rods, defined as: [Equation 35] Here, D ｉ and Σ ａｉ is the diffusion constant and macroscopic absorption cross section of neutron energy group I, and Σ ｒ１ is the macro group 1 removal cross section.

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