Real-time rainflow counting method for thermal fatigue analysis of new energy power generation power modules

Abstract

The present invention discloses a real-time rainflow counting method for thermal fatigue analysis of a new energy power generation power module. This invention is executed during the interval between every two junction temperature samplings, and the steps are as follows: First, the data preprocessing module is used to screen out the extreme points of the junction temperature of the power generation power module, different filter window widths are selected according to the junction-to-case thermal resistance of the power generation power module calculated regularly, and the initially screened extreme points of the junction temperature are filtered with a specific window width; when the number of valid extreme points of the junction temperature is not less than 3, the amplitude differences between the latest three values are calculated, and the judgment of full cycle and half cycle is carried out in combination with the number of valid extreme points of the junction temperature; according to the preset analysis range of the junction temperature swing and the average junction temperature and the division of the analysis intervals within the analysis range, the original counting result is subjected to a standardized conversion, and the cyclic counting two-dimensional table in the memory is updated. This invention realizes high-efficiency real-time rainflow cyclic counting.

Description

Technical Field

[0001] The present invention belongs to the technical field of new energy power generation, and particularly relates to a real-time rainflow counting method for thermal fatigue analysis of a new energy power generation power module. Background Art

[0002] The operating environment of new energy power generation equipment is complex, and the operating conditions are random and fluctuating. Under harsh working conditions, the power module is the most vulnerable subsystem in new energy power generation equipment. Therefore, it is necessary to conduct online real-time assessment of the reliability of the power module. The packaging structure of the power module contains a variety of heterogeneous materials with different coefficients of thermal expansion. During the long-term exposure to thermal loads, the module will undergo thermal fatigue degradation due to alternating thermo-mechanical stresses, specifically manifested as the appearance of voids and cracks in the solder layer and the detachment of bonding wires, which affects the reliability and service life of the power module.

[0003] According to the aging phenomena of the solder layer and bonding wires, the service life of the power module can be divided into the initial crack stage, crack propagation stage, and unstable stage. The same thermo-mechanical stress has different damage degrees to the power module in different stages. In other words, at different stages, the minimum thermo-mechanical stress value that causes significant damage to the power module due to the thermo-mechanical stress is different.

[0004] The degradation of the power module due to thermal fatigue often occurs after long-term use. At this time, the module has aged and the relevant parameters have also changed, making it difficult to predict the fatigue failure of the module. At the same time, the aging speed of the module will become faster and faster as the aging degree deepens, which also makes it difficult to predict the remaining life of the module. Therefore, it is necessary to conduct real-time thermal fatigue analysis on the power module, which is the premise for the reliability and life assessment of the power module.

[0005] In the field of fatigue analysis, it is more reasonable to count the stress-strain cycles actually endured by the material and conduct fatigue tests based on the counting results or calculate the damage according to the ε-N (or S-N) curve. Due to the randomness of the operating conditions of the power module for new energy power generation, the thermal load history of the power module is also very complex. In order to quantitatively analyze the damage degree of thermo-mechanical stress to the power module, it is necessary to extract complete stress cycles from the complex thermal load history, and then obtain the load distribution. The corresponding method for this process is called the stress cycle counting method. Among them, the load distribution refers to the amplitude of the stress cycle and the number of times corresponding to the amplitude of the stress cycle. For the thermal fatigue analysis of the power module in new energy power generation equipment, the amplitude and mean value of the stress cycle correspond to the amplitude and mean value of the junction temperature cycle. In the development of structural fatigue analysis, more than a dozen stress cycle counting methods have emerged, and those applied in engineering are: half-cycle counting method, maximum slope counting method, rising edge counting method, peak counting method, maximum-minimum counting method, and rainflow counting method. Among them, the most widely used is the rainflow counting method.

[0006] The rainflow counting method is a two-parameter counting method proposed by Matsuiski, Endo and others. The counting result is represented by a vector of stress amplitude and stress mean. This method takes into account the non-linear behavior between material stress and strain, and believes that the existence of plasticity is a necessary condition for fatigue damage. And its plastic property is manifested as a stress-strain hysteresis loop, as Figure 1-2 shown. This counting principle endows the rainflow counting method with physical meaning. After its counting result is used for fatigue analysis, a better prediction accuracy is obtained. Since then, it has been gradually widely promoted in the engineering field and has become the most widely used stress cycle counting method in fatigue analysis.

[0007] The traditional rainflow counting method for thermal fatigue analysis of power modules used in new energy power generation is an offline stress cycle counting method. It is necessary to export load data to execute the program after the operation of new energy power generation equipment ends, which cannot meet the requirements of real-time thermal fatigue analysis of power modules.

[0008] The new energy power generation system is developing towards the direction of intelligence and Internet of Things, and various supporting technologies have also been integrated into new energy power generation equipment. Among them, due to the upgrade of sampling technology and communication technology, the state information such as temperature parameters and electrical parameters of power modules can be collected and uploaded in real time; due to the development of microprocessor technology, the computing power of microprocessors has been greatly improved, which makes it possible to calculate the load distribution in real time by applying the stress cycle counting method during the sampling period. It can be seen that in order to meet the requirements of on-site application of power modules used in new energy power generation, it is necessary to improve the traditional rainflow counting method to obtain a real-time rainflow counting method with high accuracy and strong real-time performance.

[0009] Most of the existing real-time rainflow counting methods are used for fatigue analysis of mechanical structures, and there are few optimization schemes for power modules used in new energy power generation. In the field of structural fatigue analysis, there are mainly two implementation approaches for the real-time rainflow counting method: The first type of method is to perform the traditional offline rainflow counting method on the sampled load history at regular intervals during the operation of the object to be evaluated, so as to count the stress cycles in the load history and then obtain the load distribution. The second type of method is to screen the extreme points in the load history in real time and classify the maximum and minimum values. The new minimum value is compared with the previous minimum value in the minimum value buffer, and the new maximum value is compared with the previous maximum value in the maximum value buffer to identify the full cycles and half cycles in the load distribution. Specifically, after screening out a new load extreme point, first determine whether the extreme point is a maximum or a minimum value and store it in the corresponding maximum or minimum value buffer. Taking the minimum value as an example, if the new minimum value is greater than or equal to the previous minimum value in the minimum value buffer, read in the new data; if the new minimum value is less than the previous minimum value, count the number of data in the maximum value buffer. If the number of data in the maximum value buffer is 1 at this time, count a half cycle for the maximum value and the previous minimum value and discard the previous minimum value; if the number of data points in the maximum value buffer is greater than 1 at this time, count a full cycle for the latest maximum value and the previous minimum value and discard the previous minimum value and the latest maximum value; if the number of data points in the maximum value buffer is 0 at this time, read in the new data, and its specific process is as Figure 3 shown.

[0010] In the publicly disclosed patent, CN111782706A provides a de-jitter real-time rainflow counting method for structural fatigue analysis, and its basic idea is to adopt the above-mentioned second type of method. On this basis, it temporarily stores the data points and corresponding stress cycle values that may cause stress cycle counting jitter in the future by constructing a database, so as to correct the stress cycle counting results during data jitter.

[0011] The above first type of method is essentially still an offline rainflow counting algorithm, and it has two specific implementation forms: The first implementation form is to perform the rainflow counting method only on the load data sampled during the algorithm execution period (that is, the time interval between two adjacent executions of the real-time rainflow algorithm). The disadvantage of this method is that stress cycles spanning multiple execution periods will be lost; The second implementation form is to perform the rainflow counting algorithm on all the accumulated load histories each time. The disadvantage of this method is that a large storage capacity is required to store the load history, and since the accumulated data volume will become larger and larger, for a processor with a fixed computing power, the execution time of the algorithm will also become longer and longer. These disadvantages are contradictory to the requirements of real-time, accuracy, and algorithm simplicity for the thermal fatigue analysis of power modules used in new energy power generation. Therefore, the first type of real-time rainflow counting method is not applicable to the real-time analysis of the thermal fatigue of power modules used in new energy power generation.

[0012] The above second - type method is a real - time rain - flow counting method in the true sense. Its essence is an improvement based on the offline rain - flow counting method with 4 points. When executing, it uses the maximum value and the minimum value as marks and executes two branches with similar content. The algorithm complexity is increased by 1 times compared with the single - branch method, making the process relatively complex.

[0013] If the above two types of methods are applied to the thermal fatigue analysis of power modules, they do not consider that at different stages, the minimum thermo - mechanical stress value that causes significant damage to the power module due to the thermo - mechanical stress is different. The thermo - mechanical stress not exceeding this threshold can be ignored for the damage of the power module. In addition, there may be sampling jitter and other situations when obtaining temperature parameters, resulting in many small fluctuations in the load history. Therefore, if all the collected load histories during the entire service life of the power module are not screened and real - time rain - flow counting is performed, it will not only cause waste of hardware resources but also affect the accuracy of the counting results. Summary of the Invention

[0014] Aiming at the problems that the existing conventional technologies cannot achieve real - time stress cycle counting and the existing real - time rain - flow counting methods have high complexity and are not suitable for on - site application of power modules for new - energy power generation, the present invention provides a real - time rain - flow counting method for thermal fatigue analysis of power modules for new - energy power generation. It improves the traditional rain - flow counting method and can accurately and real - time perform stress cycle counting on the thermal load borne by the power module on a converter controller with limited hardware resources, and convert it into a load distribution including cycle amplitude, cycle mean value, and cycle number.

[0015] To achieve the above object, the present invention adopts the following technical solutions: The real - time rain - flow counting method for thermal fatigue analysis of power modules for new - energy power generation includes:

[0016] Using an initialization module to set the following parameters: the junction - temperature sampling frequency, the upper bound of the discrete standardized junction - temperature swing range B u1 , the lower bound B l1 and the first interval division number n 1, the upper bound of the discrete standardized junction - temperature mean range B u2 , the lower bound B l2 and the second interval division number n 2, and initializing the storage and cache (including the real - time junction - temperature cache and the junction - temperature extreme - point cache);

[0017] The junction-to-case thermal resistance calculation module is used to calculate the junction-to-case thermal resistance between the power device chip and the module housing in the power generation module. The input data of the junction-to-case thermal resistance calculation module are the junction temperature, the case temperature, the conduction voltage, and the conduction current;

[0018] According to the fact that the power generation module has different junction-to-case thermal resistances at different stages of its service life, the appropriate rainflow filter window width is selected through the rainflow filter window width selection module. ;

[0019] Data preprocessing: It is processed by the data preprocessing module, which includes an extreme point filter and a rainflow filter. The input data are the real-time junction temperature data T j and the rainflow filter window width . The output data are the effective junction temperature extreme point data; when the real-time junction temperature data are input, they first pass through the extreme point filter to screen out the extreme points in the real-time junction temperature data, and then the screened extreme points are input into the rainflow filter to filter out the junction temperature extreme points that have negligible damage to the power generation module or the junction temperature extreme points with fluctuations less than 1°C caused by sampling jitter;

[0020] The real-time rainflow cycle counting module performs real-time stress cycle counting on the effective junction temperature extreme points to obtain the original counting result of the stress cycle, that is, the stress cycle amplitude, the stress cycle mean value, and the corresponding number of times;

[0021] Discrete standardization: The range of the junction temperature swing to be analyzed ( B u1 , B l1 ) is evenly divided into standard n 1 equal part, and the range of the junction temperature mean value to be analyzed ( B l2 , B u2 ) is evenly divided into standard n 2 equal parts, and the original counting result of the stress cycle obtained by the real-time rainflow cycle counting module is matched with these intervals, recorded as the upper bound value of the interval, and the standardized stress cycle corresponding to these intervals is updated;

[0022] The standardized stress cycle output by the discrete standardization module is stored in a two-dimensional table in the memory through the memory storage module.

[0023] Furthermore, in the real-time rainflow cycle counting module, when the number of effective junction temperature extreme points is not less than 3, the amplitude differences between the latest three values are calculated, and the full cycle and half cycle are judged in combination with the number of effective junction temperature extreme points.

[0024] Further, in the rainflow filter window width selection module, the rainflow filter window width is the first rainflow filter window width , the second rainflow filter window width or the third rainflow filter window width . In the initial stage of crack growth in the power generation module, stress cycles with a junction temperature swing exceeding the first rainflow filter window width are considered; in the crack propagation stage, stress cycles with a junction temperature swing exceeding the second rainflow filter window width are considered; in the unstable stage of the power generation module, stress cycles with a temperature swing exceeding the third rainflow filter window width are considered, where ; ω 1 ranges from (10~15 °C]; ω 2 ranges from [6~10 °C]; ω 3 ranges from 3~5 °C;

[0025] Judging which stage of the service life the power generation module is in is based on the junction-to-case thermal resistance Z th(j-c) . When the junction-to-case thermal resistance is lower than the threshold Z1, it corresponds to the initial stage of crack growth in the power generation module, and the first rainflow filter window width is selected. When the junction-to-case thermal resistance exceeds Z1 but is less than Z2, it corresponds to the crack propagation stage of the power generation module, and the second rainflow filter window width is selected; when the junction-to-case thermal resistance exceeds Z2, it corresponds to the unstable stage of the power generation module, and the third rainflow filter window width is selected; let the initial junction-to-case thermal resistance of the power generation module be Z0, then Z1 = 1.05Z0 and Z2 = 1.15Z0.

[0026] Furthermore, in the junction-to-case thermal resistance calculation module, the junction-to-case thermal resistance is calculated by formula (1), where T j ( t ) is the temperature of the power device chip, T c ( t ) is the module case temperature, P IGBT ( t ) is the instantaneous power loss of the power device chip:

[0027] (4).

[0028] Further, in the data preprocessing module,

[0029] The real-time junction temperature data is input into the real-time junction temperature buffer one by one, and for the latest three adjacent junction temperature data , substitute it into formula (2) to judge the data point in the middle whether it is an extreme point. If formula (2) holds, then judge it is an extreme point; if formula (2) does not hold, then judge it is not an extreme point, and shift forward to the position of , and read in the new real-time junction temperature data as the new value of, and re-execute the extreme point judgment;

[0030] When is judged to be an extreme point, then judge the difference between and the window width of the rainflow filter : If , then delete , read in the next real-time junction temperature data as the new value of, and re-execute the size judgment; if , then retain , store into the junction temperature extreme point buffer PV, remove and move forward to the position of , read in the next real-time junction temperature data as the new value of, and this process is as formula (3);

[0031] (5)

[0032] (6).

[0033] Furthermore, the real-time rainflow cycle counting module processes the effective junction temperature extreme point data output by the data preprocessing module in real time. After each new effective junction temperature extreme point is screened out, the real-time rainflow cycle counting module is executed to identify the full cycles and half cycles in the effective junction temperature extreme point data in real time, and when the number of junction temperature extreme points is not less than 3, it is executed in a loop until all the junction temperature stress cycles in the junction temperature extreme point buffer PV are identified;

[0034] The object of action of the real-time rainflow cycle counting module each time it is executed is only the latest three points in the junction temperature extreme point buffer, and the execution content is simple addition, subtraction and conditional judgment.

[0035] Even further, the execution steps of the real-time rainflow cycle counting module are as follows:

[0036] 1) Store the effective junction temperature extreme points screened out by the data preprocessing module into the junction temperature extreme point buffer PV point by point. If there is no new value, wait for the new value to arrive;

[0037] 2) Check whether the number of data in the junction temperature extreme point buffer is greater than or equal to 3. If not, continue to wait for the input of a new value. If so, extract the latest three values in the junction temperature extreme point buffer and mark them in the order of writing as , that is, the third new value from the end is marked as , the second new value from the end is marked as , and the first new value from the end is marked as ;

[0038] 3) Calculate the amplitude difference between two adjacent values in : , ;

[0039] 4) Compare the magnitude relationship between and ; if , continue to wait for the input of a new valid junction temperature extreme point and re-extract the latest three values in the junction temperature extreme point buffer; if , enter the next process;

[0040] 5) Judge whether the number of data in the junction temperature extreme point buffer PV is 3 at this time. If it is 3, enter the semi-cycle counting process; if it is not 3, enter the full-cycle counting process;

[0041] 6) Input the original counting result of the full cycle or semi-cycle into the discrete normalization module to obtain the normalized stress cycle;

[0042] 7) Write the normalized stress cycle into the full-cycle two-dimensional table or semi-cycle two-dimensional table in the memory. This two-dimensional table is the stress cycle amplitude, stress cycle mean value, and the corresponding number of times;

[0043] 8) Judge whether the new energy power generation module has stopped running: if the new energy power generation module has stopped running, end the execution of the real-time rainflow cycle counting module; if the new energy power generation module continues to run, return to the data preprocessing module to wait for the input of a new junction temperature sampling value.

[0044] Furthermore, in step 5), the semi-cycle counting process is as follows:

[0045] Use to mark the semi-cycle and record the stress cycle amplitude as , the stress cycle mean value as , and then remove from the junction temperature extreme point buffer PV.

[0046] Furthermore, in step 5), the full-cycle counting process is as follows:

[0047] Use Mark the full cycle and record the stress cycle amplitude as , the stress cycle mean value is , then remove it in the PV of the buffer at the extreme point of the junction temperature .

[0048] Furthermore, the discrete normalization module pre-determines the ranges of the stress cycle amplitudes (also known as the junction temperature swing) to be analyzed ( B l1 , B u1 ) and the stress cycle mean values (also known as the average junction temperature) ( B l2 , B u2 ), and divides the ranges into n 1, n 2 intervals respectively; matches the stress cycle amplitude and the mean value output by the real-time rainflow cycle counting module with the divided intervals, and updates the cycle counts of the corresponding intervals; taking the stress cycle amplitude as an example, if the set range of the stress cycle amplitude is ( B l1 , B u1 ), and it is divided into n 1 interval, then the width of each interval is , convert to the standard value: , if the calculation result exceeds the upper bound B u1 of the discrete normalization, then take it as the upper bound value B u1 ; perform the same operation on the stress cycle mean value to obtain the standard value of the stress cycle mean value, and finally add the stress cycle count once at the ( position in the full cycle two-dimensional table.

[0049] The beneficial effects of the present invention are as follows:

[0050] 1. The real-time rainflow counting method proposed by the present invention can perform real-time identification of full cycles and half cycles in cooperation with the previous two effective junction temperature extreme points after each effective junction temperature extreme point is screened out.

[0051] 2. The present invention adopts a point-by-point calculation form, that is, it can calculate between every two sampled real-time junction temperature data, without missing any junction temperature data points, making the counting result of the load distribution more accurate.

[0052] 3. The real-time rainflow counting method proposed by the present invention does not require reordering the load history. While reducing the process complexity, it can also make the counting process closer to the actual operating conditions of the power generation module.

[0053] 4. The real-time rainflow cycle counting module in the present invention only involves simple conditional judgments and addition and subtraction calculations, and there is only one loop. Only one buffer is involved in the loop. Therefore, the requirements of this module for computing power and storage are also relatively low, providing a solution for the real-time online calculation of the load distribution of new energy power generation modules and the field application of thermal fatigue analysis.

[0054] 5. The present invention adopts a rainflow filter design with variable window width. By using the junction-to-case thermal resistance of the power module as the basis for selecting the window width of the rainflow filter, different filter window widths are adopted at different stages of the service life of the power module. It can not only filter out stress cycles that have negligible damage to the power module during this period, but also filter out the junction temperature fluctuation points caused by sampling fluctuations. Specifically, in the early stage of the power module's use, the present invention only focuses on the larger amplitude of the junction temperature swing. Then, the aging state of the power module is judged according to the junction-to-case thermal resistance, and the window width of the rainflow filter is changed to include the smaller amplitude of the junction temperature swing in the scope of real-time rainflow counting; this can reduce the calculation pressure on the calculation unit and the access pressure on the buffer unit and the storage unit, and save the expenditure of hardware resources without sacrificing accuracy. Description of the Drawings

[0055] Figure 1 is a load data diagram of a full cycle;

[0056] Figure 2 is a stress-strain hysteresis loop diagram corresponding to the load data of a full cycle, where is a full cycle;

[0057] Figure 3 is a flowchart of an example of the second type of method in the existing real-time rainflow counting method;

[0058] Figure 4 is a brief flowchart of the method of the present invention;

[0059] Figure 5 is a program flowchart of the junction-to-case thermal resistance calculation and rainflow filter window width selection module of the present invention;

[0060] Figure 6 is a program flowchart of the data preprocessing module of the present invention;

[0061] Figure 7 、 Figure 8 and Figure 9 are all schematic diagrams of data preprocessing and rainflow filter screening extreme points of the present invention, where Figure 7 represents x2 is not an extreme point, Figure 8 indicating x 2 is an extreme point but x 2 and x 3 are within the window width of the rain - flow filter, Figure 9 indicating x 2 is an extreme point and x 1 and x 3 are outside the window width of the rain - flow filter;

[0062] Figure 10 is the program flow chart of the real - time rain - flow counting, discrete normalization, and memory storage module of the present invention;

[0063] Figure 11 is the overall flow chart of the method of the present invention;

[0064] Figure 12 is the load - history waveform diagram of Embodiment 2;

[0065] Figure 13 is the distribution diagram of load extreme points screened by the data pre - processing module in Embodiment 2, that is, the distribution diagram of extreme points of junction - temperature data;

[0066] Figure 14 is the three - dimensional diagram of the full - cycle load distribution of Embodiment 2. Detailed implementation manners

[0067] To make the objectives and technical solutions of the present invention clearer and more understandable, the present invention will be further described below in conjunction with the specification drawings and specific implementation manners.

[0068] The present invention is a real - time rain - flow counting method for thermal fatigue analysis of new - energy power - generation power modules. The input of this method is the thermal - load data of the power - generation power module, that is, junction - temperature data, and the output is the load distribution of the power - generation power module. It includes the following steps, as Figure 4 shown:

[0069] Use the initialization module to set the junction - temperature sampling frequency, initialize the buffers (including the real - time junction - temperature buffer and the junction - temperature extreme - point buffer), the upper bound B u1 , lower bound B l1 and the number of interval divisions n 1 of the discrete - normalized junction - temperature swing range, the upper bound B u2 , lower bound B l2 and the number of interval divisions n 2 of the discrete - normalized junction - temperature mean range, and initialize the storage;

[0070] The junction-to-case thermal resistance calculation module is used to calculate the thermal resistance between the power device chip and the module housing in the power generation power module; the input data of the junction-to-case thermal resistance calculation module are the junction temperature, the case temperature, the on-voltage and the on-current, and the output data is the junction-to-case thermal resistance; the case temperature can be measured by a temperature sensor, and the on-voltage and on-current can be measured by the module's own sensor;

[0071] According to the different junction-to-case thermal resistances of the power generation module at different stages of its service life, a suitable rainflow filter window width is selected through the rainflow filter window width selection module; the input data of the rainflow filter window width selection module is the junction-to-case thermal resistance, and the output data is the rainflow filter window width ;

[0072] Data preprocessing: The data preprocessing module is used for processing. This module includes two parts: extreme point filter and rain flow filter. The input data is real-time junction temperature data. T j and rain flow filter window width , the output data is the effective junction temperature extreme point data; when the real-time junction temperature data is input, it first passes through the extreme point filter to filter out the extreme points in the real-time junction temperature data, and then the filtered extreme points are input into the rain flow filter to filter out the junction temperature extreme points that can be ignored for damage to the power module or the extreme points with fluctuations less than 1°C due to sampling jitter.

[0073] The damage magnitude of different power modules is different and also depends on the required accuracy.

[0074] The junction temperature data can be obtained from methods such as thermal sensitive electrical parameters, such as the on-state voltage drop proposed in patent CN113376497A. The measurement circuit and gate drive circuit are integrated to extract the on-state voltage drop in real time online and load current I , a method for online extraction of IGBT junction temperature information is realized.

[0075] The real-time rain flow cycle counting module is used to count the effective junction temperature extreme points in real time to obtain the original counting results of the stress cycle, namely, the stress cycle amplitude, the stress cycle mean and the corresponding number of times; the input data of the real-time rain flow cycle counting module is the effective junction temperature extreme point data screened by the data preprocessing module, and the output data is the original counting results of the stress cycle;

[0076] Discrete standardization: The junction temperature swing range to be analyzed ( B u1 , B l1 ) is divided equally into standard n 1, divide the junction temperature mean range to be analyzed ( Bl2 , B u2 ) is evenly divided into standard n 2 equal parts, and the original count result of the stress cycle obtained by the real-time rainflow cycle counting module is matched with these intervals, recorded as the upper bound value of the interval, and the standardized stress cycle corresponding to these intervals is updated; the input data is the original count result of the stress cycle, and the output is the standardized stress cycle;

[0077] The standardized stress cycle output by the discrete standardization module is stored in a two-dimensional table in the memory through the memory storage module.

[0078] The flowcharts of the above-mentioned crust thermal resistance calculation module and rainflow filter window width selection module are as Figure 5 shown. Considering that at different stages of the service life of the power module, the minimum thermomechanical stress value that causes significant damage to the power module due to the thermomechanical stress it bears is different, the thermomechanical stress not exceeding this threshold can be ignored for the damage of the power module. At the initial stage of solder crack, consider the stress cycle with the junction temperature swing exceeding ; at the solder crack propagation stage, consider the stress cycle with the junction temperature swing exceeding ; at the unstable stage of the power module, consider the stress cycle with the temperature swing exceeding , where . Judging which stage of the service life the power module is in is based on the junction-to-case thermal resistance . When the junction-to-case thermal resistance is lower than the threshold , corresponding to the initial stage of solder crack, select the window width of the rainflow filter as , when the junction-to-case thermal resistance exceeds , but is less than , corresponding to the solder crack propagation stage, select the window width of the rainflow filter as ; when the junction-to-case thermal resistance exceeds , corresponding to the unstable stage of the power module, select the window width of the rainflow filter as . The junction-to-case thermal resistance is calculated by formula (1). In the formula T j ( t ) is the chip temperature, T c ( t ) is the module case temperature, P IGBT ( t ) is the instantaneous power loss of the chip.

[0079] (7)

[0080] The flowchart of the above data preprocessing module is as Figure 6As shown, it inputs the real-time junction temperature data into the real-time junction temperature buffer one by one, and for the latest three adjacent junction temperature data , substitutes them into formula (2) to judge the data point in the middle whether it is an extreme point. If equation (2) holds, then judge it is an extreme point; if equation (2) does not hold, then judge it is not an extreme point. As Figure 7 shown, shift forward to the position of , and read in the new real-time junction temperature data as 's new value, and re-execute the data preprocessing module. When is judged to be an extreme point, then judge the difference between and the window width of the rainflow filter : If , as Figure 8 shown, then delete , read in the next junction temperature value as 's new value, and re-execute the data preprocessing module; if , as Figure 9 shown, then retain , store into the extreme point buffer PV, remove and shift forward to the position of , read in the next junction temperature value as 's new value, and this process is as formula (3).

[0081] (8)

[0082] (9)

[0083] The flowcharts of the above real-time rainflow cycle counting module, discrete normalization module, and storage in memory module are as Figure 10 shown. The real-time rainflow cycle counting module processes the effective junction temperature extreme point data output by the data preprocessing module in real time. The program of this module can be executed after each new effective junction temperature extreme point is screened out. It can identify full cycles and half cycles in the effective junction temperature extreme point data in real time, and when the number of extreme points is not less than 3, it loops to execute this algorithm until all stress cycles up to that moment are identified. The object of action of the real-time rainflow cycle counting module each time it is executed is only the latest three points in the extreme point buffer, and the execution content is simple addition, subtraction, and conditional judgment, which has a relatively low requirement for the computing power of the processor. The execution process of the real-time rainflow cycle counting module is as follows:

[0084] 1) The real-time rainflow cycle counting module stores the effective junction temperature extreme points screened by the data preprocessing module into the junction temperature extreme point buffer PV point by point. If there is no new value, it waits for the arrival of a new value.

[0085] 2) Check whether the number of data in the extreme point buffer is greater than or equal to 3. If not, continue to wait for the input of a new value; if so, extract the latest three values in the extreme point buffer and mark them in the order of writing as That is, the third-to-last new value is marked as The second-to-last new value is marked as The last new value is marked as .

[0086] 3) Calculate the range (amplitude difference) between two adjacent values in : , .

[0087] 4) Compare the magnitude relationship between and . If , continue to wait for the input of a new effective junction temperature extreme point and re-extract the latest three values in the extreme point buffer; if , enter the next process.

[0088] 5) Determine whether the number of data in the extreme point buffer PV at this time is 3. If it is 3, enter the semi-cycle counting process; if it is not 3, enter the full-cycle counting process.

[0089] a) Semi-cycle counting process: Mark the semi-cycle with and record the stress cycle amplitude as , the stress cycle mean value as , and then remove from the extreme point buffer PV.

[0090] b) Full-cycle counting process: Mark the full-cycle with and record the stress cycle amplitude as , the stress cycle mean value as , and then remove from the junction temperature extreme point buffer PV.

[0091] 6) Input the original counting results of the full cycle or semi-cycle into the discrete normalization module to obtain the normalized stress cycle.

[0092] 7) Write the normalized stress cycle into the full-cycle two-dimensional table or semi-cycle two-dimensional table in the memory. This two-dimensional table is the stress cycle amplitude, the stress cycle mean value, and the corresponding number of times.

[0093] 8) Determine whether the device has stopped running: If the device has stopped running, end the real-time rainflow counting program; if the device continues to run, return to step 2.

[0094] The above-mentioned discrete normalization module pre-determines the range of the stress cycle amplitude (junction temperature swing) to be analyzed ( B l1 , B u1 ) and the range of the stress cycle mean value (average junction temperature) ( B l2 , B u2 ), and divides the ranges into n 1, n 2 intervals respectively. Match the stress cycle amplitude and mean value output by the real-time rainflow cycle counting module , with the divided intervals, and update the cycle count of the corresponding intervals. Taking the stress cycle amplitude (full cycle) as an example, if the set range of the stress cycle amplitude is ( B l1 , B u1 ), and it is divided into n 1 interval, then the width of each interval is , and convert to the standard value: , if the calculation result exceeds the upper bound of the discrete normalization B u1 , then take it as the upper bound value B u1 . Do the same operation for the average junction temperature to obtain the standard value of the average junction temperature , and finally add the stress cycle count once at the ( position in the full cycle two-dimensional table.

[0095] The above-mentioned write to memory module stores the normalized stress cycle in the form of a two-dimensional table. The two-dimensional table uses the stress cycle amplitude and mean value as the horizontal and vertical axes, and stores the corresponding stress cycle count at . In addition, to distinguish between full cycles and half cycles, the two-dimensional table in the memory is marked with cycle, and is divided into a half cycle two-dimensional table and a full cycle two-dimensional table, where cycle = 1 corresponds to the full cycle two-dimensional table, and cycle = 0.5 corresponds to the half cycle two-dimensional table.

[0096] Example 1 (the load data in this example is junction temperature data)

[0097] Table 1 Load data of Example 1 (assuming a load is generated every 0.1 second)

[0098]

[0099] In the present invention, the calculation of the case thermal resistance and the selection of the filter window width are implemented using a timer interrupt, which is executed once every fixed time, and the window width of the filter is updated. The flowchart is as Figure 5 shown. Assume that the window width of the rainflow filter selected according to the case thermal resistance is 3.

[0100] The present invention provides a real-time rainflow counting method for thermal fatigue analysis of new energy power generation modules. The overall flowchart is as Figure 11 shown, and the specific steps are as follows:

[0101] 1) When the power module starts to work, this method also synchronously starts to execute the initialization program: set an appropriate junction temperature sampling frequency; clear the real-time junction temperature buffer and the extreme point buffer; assume that the discrete normalization module evenly divides the junction temperature swing range to be analyzed ( B l1 , B u1 ) into n 1 standard intervals, and evenly divides the junction temperature mean range ( B l2 , B u2 ) into n 2 standard intervals; configure the memory to be in a state waiting for writing.

[0102] In this embodiment, the junction temperature sampling frequency is set to 10 Hz, that is, a new real-time junction temperature is obtained every 0.1 second, the real-time junction temperature buffer and the extreme point buffer are cleared, and the upper bound B u1 = 40 and the lower bound B l1 = 4 of the discrete normalization of the stress cycle amplitude are set, the number of partitions is n 1 = 9, the upper bound B u2 = 100 and the lower bound B l2 = 60 of the discrete normalization of the stress cycle mean are set, the number of partitions is n 2 = 10; configure the memory to be in a state waiting for writing.

[0103] 2) Receive the real-time junction temperature data and write the real-time junction temperature data to the end of the real-time junction temperature buffer.

[0104] In this embodiment, when the first data 68 is received, it is written to the end of the real-time junction temperature buffer, which is also the first position.

[0105] 3) Count the number of data in the real-time junction temperature buffer and execute the following branches:

[0106] a) If the number of data in the real-time junction temperature buffer is not 3, return to step 2 and wait for new real-time junction temperature data to be transmitted.

[0107] b) If the number of data in the real-time junction temperature buffer is equal to 3, execute step 4.

[0108] In this embodiment, when only the first junction temperature data 68 is received, the number of data in the real-time junction temperature buffer is 1, and the judgment in step 3 is not established. Then return to step 2 to receive the second junction temperature data 74 and write it into the real-time junction temperature buffer. At this time, the judgment in step 3 is still not established, so return to step 2 to receive the third junction temperature data 84 and write it into the real-time junction temperature buffer. At this time, the data in the real-time junction temperature buffer is .

[0109] 4) Label the data in the real-time junction temperature buffer in the writing order as , and substitute into for preliminary screening of local extreme points, and execute the following branches:

[0110] a) If the calculation result of is less than or equal to 0, remove from the real-time junction temperature buffer, and return to step 2 to wait for new real-time junction temperature data to be transmitted;

[0111] b) If the calculation result of is greater than 0, enter step 5.

[0112] In this embodiment, the values in the real-time junction temperature buffer at this moment are , corresponding to respectively. Substitute into to get , then remove 68, return to step 2 to read the fourth real-time junction temperature data 82, and write it to the end of the real-time junction temperature buffer. At this time, the data in the real-time junction temperature buffer is , and execute step 3 and step 4 again. When executing step 4, since , enter step 5.

[0113] 5) Query and obtain the window width of the rainflow filter . If it is updated, it means that the power module has entered a new life stage, and the filter uses the new window width; if it is not updated, continue to use the original window width.

[0114] In this embodiment, the window width of the rainflow filter obtained by query is .

[0115] 6) Calculate the value of , and execute the following branches:

[0116] a) If holds, it is proved that the range of the junction temperature change from to is not within the consideration range of this stage, and needs to be removed from the real-time junction temperature buffer, and return to step 2 to read new real-time junction temperature data;

[0117] b) If it does not hold, it is proved that the range of the junction temperature change from to is within the consideration range of this stage, and needs to be removed from the real-time junction temperature buffer, and is stored at the end of the extreme point buffer.

[0118] In this embodiment, when entering step 6 for the first time, the data in the real-time junction temperature buffer is . Since , 82 is removed, and return to step 2 to read the 5th data 71. Then execute steps 3, 4, and 5 again. When entering step 6 for the second time, the data in the real-time junction temperature buffer is [74, 84, 71]. Since , it shows that the range of the junction temperature change from to is within the consideration range of this period, and 74 needs to be removed from the real-time junction temperature buffer, and 84 is stored at the end of the extreme point buffer.

[0119] 7) Count the number of data in the extreme point buffer PV, and execute the following branches:

[0120] a) If the number of data in PV is less than 3, return to step 2 and continue to wait for new real-time junction temperature data to be transmitted;

[0121] b) If the number of data in PV is greater than or equal to 3, extract the latest three extreme point data in PV, and mark them in the writing order as .

[0122] In this embodiment, when executing step 7 for the first time, the number of data in the real-time junction temperature buffer is only 1, that is, 84. Therefore, steps 2 to 6 need to be repeatedly executed until the data in the extreme point buffer is [84, 71, 85], and then execute step 7 again. At this time, the number of data in the extreme point buffer is 3, and [84, 71, 85] is marked as .

[0123] 8) Calculate the range (amplitude difference) between adjacent two points in : , .

[0124] In this embodiment, when executing step 8 for the first time, , at this time , .

[0125] 9) Compare with and execute the following branches:

[0126] a) If , then return to step 2 and wait for new real-time junction temperature data to be incoming;

[0127] b) If , execute step 10.

[0128] In this embodiment, when step 9 is first executed, , , since , then enter step 10.

[0129] 10) Judge the number of data in the extreme point buffer PV and execute the following branches:

[0130] a) If the number of data is 3, then count a half cycle, mark the half cycle with and record the junction temperature swing as , and the average junction temperature as . Then remove the data point from the junction temperature extreme point buffer PV.

[0131] b) If the number of data is not 3, then count a full cycle, mark the full cycle with and record the junction temperature swing as , and the average junction temperature as , then remove from the junction temperature extreme point buffer PV.

[0132] In this embodiment, when step 10 is first executed, the data in the extreme point buffer PV is [84, 71, 85], and the number of data is 3, then count a half cycle, record the stress cycle amplitude , the stress cycle average value , and mark this cycle as a half cycle with the flag bit cycle = 0.5, and at the same time remove 84 from the extreme point buffer PV.

[0133] 11) Discretely standardize the counting results of the full cycle and the half cycle. The range of the stress cycle amplitude (junction temperature swing) to be analyzed is ( B l1 , B u1 ) and the range of the stress cycle average value (average junction temperature) is ( B l2 , Bu2 ), and divide the ranges into n 1, n 2 intervals respectively. Match the temperature swing output by the real-time rainflow cycle counting module , with the divided intervals, and update the cycle times of the corresponding intervals.

[0134] In this embodiment, when step 11 is executed for the first time, what is extracted is , half cycle. For the stress cycle amplitude, the set upper bound of discrete standardization B u1 = 40, the lower bound B l1 = 4, the number of partitions is n 1 = 9, then the width of each partition is , and convert the stress cycle amplitude to the standard value: . For the stress cycle mean, the set upper bound of discrete standardization of the stress cycle mean B u2 = 100, the lower bound B l2 = 60, the number of partitions is n 1 = 10, then the width of each partition is , and convert the stress cycle mean to the standard value: . So the obtained standardized stress cycle is , and the corresponding label is cycle = 0.5, which means half cycle.

[0135] 12) If cycle = 0.5, write the standardized stress cycle into the half cycle two-dimensional table in the memory; if cycle = 1, write the standardized stress cycle into the half cycle two-dimensional table in the memory.

[0136] In this embodiment, when step 12 is executed for the first time, the input standardized stress cycle is a half cycle: cycle = 0.5, , so add 1 to the number value at the position of the half cycle two-dimensional table.

[0137] 13) Detect the operating state of the new energy power generation equipment (i.e., the new energy power generation power module), and make the following judgments:

[0138] a) If the new energy power generation equipment has stopped running, end this program.

[0139] b) If the new energy power generation equipment is still running, return to step 7.

[0140] In this embodiment, when the execution reaches step 13 for the first time, assuming that the new energy power generation device is still operating, it returns to step 7 to check the number of data in the extreme point buffer. At this time, PV = [71, 85], which does not meet the requirements, so it returns to step 2 to wait for new real-time junction temperature data to be input, and then steps 2 to 13 are executed until the new energy power generation device stops operating. Table 2 shows the execution results of the embodiment in Table 1 at each junction temperature sampling point.

[0141] Table 2 Execution Results of Embodiment 1 at Each Junction Temperature Sampling Point

[0142]

[0143] The following specifically describes in combination with Embodiment 2, and the load data of this embodiment is junction temperature data. The waveform diagram of Embodiment 2 is as Figure 12 shown. In this embodiment, it is assumed that the window width selected by the rainflow filter is , the upper bound of the discrete standardization of the stress cycle amplitude is set as B u1 = 80, the lower bound B l1 = 5, the number of partitions is n 1 = 15, the upper bound of the discrete standardization of the stress cycle mean is B u2 = 110, the lower bound B l2 = 70, the number of partitions is n 2 = 10. Figure 13 is the distribution diagram of the effective junction temperature extreme points obtained after data preprocessing when . Figure 14 is the three-dimensional representation diagram of the standardized stress cycle two-dimensional table (full cycle) of Embodiment 2.

[0144] Table 3 Original Counting Results of Embodiment 2

[0145]

[0146] Table 4 Standardized Stress Cycle Two-Dimensional Table (Full Cycle) of Embodiment 2

[0147]

[0148] Table 5 Standardized Stress Cycle Two-Dimensional Table (Half Cycle) of Embodiment 2

[0149]

[0150] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the technical principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be regarded as the protection scope of the present invention.

Claims

1. A real-time rainflow counting method for thermal fatigue analysis of new energy power generation power modules, characterized in that, Including: Set the following parameters using the initialization module: the junction temperature sampling frequency, the upper bound of the discrete normalized junction temperature swing range B u1 , the lower bound B l1 and the number of divisions in the first interval n 1, the upper bound of the discrete normalized junction temperature mean range B u2 , the lower bound B l2 and the number of divisions in the second interval n 2, and initialize the storage and buffer; A case-to-case thermal resistance calculation module is used to calculate the case-to-case thermal resistance between the power device chip and the module housing in the power generation module. The input data of the case-to-case thermal resistance calculation module are the junction temperature, the case temperature, the conduction voltage, and the conduction current. According to the different junction-to-case thermal resistances of the power generation module at different stages of its service life, a suitable rainflow filter window width is selected through the rainflow filter window width selection module ; Data preprocessing: It is processed by a data preprocessing module, which includes an extreme point filter and a rainflow filter. The input data is real-time junction temperature data T j and the window width of the rainflow filter , and the output data is valid junction temperature extreme point data; When the real-time junction temperature data is input, it first passes through an extreme point filter to screen out the extreme points in the real-time junction temperature data, and then the screened extreme points are input into a rainflow filter to filter out the junction temperature extreme points with negligible damage to the power generation module or the junction temperature extreme points with fluctuations less than 1°C caused by sampling jitter. The real-time rainflow cycle counting module performs real-time stress cycle counting on the effective junction temperature extreme points to obtain the original counting result of the stress cycle, that is, the stress cycle amplitude, the stress cycle mean value, and the corresponding number of times. Discrete standardization: The range of the junction temperature swing to be analyzed ( B u1 , B l1 ) is evenly divided into n 1 equal parts, and the range of the mean junction temperature to be analyzed ( B l2 , B u2 ) is evenly divided into n 2 equal parts. Then, the original count result of the stress cycle obtained by the real-time rainflow cycle counting module is matched with these intervals, recorded as the upper bound value of the interval, and the standardized stress cycle corresponding to these intervals is updated; The standardized stress cycle output by the discrete normalization module is stored in a two-dimensional table in the memory through the memory storage module.

2. The real-time rainflow counting method for thermal fatigue analysis of new energy power generation power modules according to claim 1, characterized in that, In the real-time rainflow cycle counting module, when the number of effective junction temperature extreme points is not less than 3, the amplitude differences between the latest three values are calculated, and the full cycle and half cycle are judged in combination with the number of effective junction temperature extreme points.

3. The real-time rainflow counting method for thermal fatigue analysis of new energy power generation power modules according to claim 1, characterized in that, In the rainflow filter window width selection module described above, the rainflow filter window width is the first window width of the rainflow filter , the second window width of the rainflow filter or the third window width of the rainflow filter . In the initial stage of crack growth in the power generation module, stress cycles with a junction temperature swing exceeding the first window width of the rainflow filter are considered; in the crack propagation stage, stress cycles with a junction temperature swing exceeding the second window width of the rainflow filter are considered; in the unstable stage of the power generation module, stress cycles with a temperature swing exceeding the third window width of the rainflow filter are considered, where ; ω The value range of 1 is (10~15℃]; ω The value range of 2 is [6~10℃]; ω The value range of 3 is 3~5℃; Judging which stage of the service life the power generation module is in is based on the junction-to-case thermal resistance Z th(j-c) ; when the junction-to-case thermal resistance is lower than the threshold value Z1, it corresponds to the initial stage of crack growth of the power generation module, and the first window width of the rainflow filter is selected ; when the junction-to-case thermal resistance exceeds Z1 but is less than Z2, it corresponds to the crack propagation stage of the power generation module, and the second window width of the rainflow filter is selected ; when the junction-to-case thermal resistance exceeds Z2, it corresponds to the unstable stage of the power generation module, and the third window width of the rainflow filter is selected ; assuming that the initial junction-to-case thermal resistance of the power generation module is Z0, then Z1 = 1.05Z0 and Z2 = 1.15Z0.

4. The real-time rainflow counting method for thermal fatigue analysis of new energy power generation power modules according to claim 3, characterized in that, In the described junction-to-case thermal resistance calculation module, the junction-to-case thermal resistance is calculated by formula (1), where T j ( t ) is the temperature of the power device chip, T c ( t ) is the temperature of the module case, P IGBT ( t ) is the instantaneous power loss of the power device chip: (1)。 5. The real-time rainflow counting method for thermal fatigue analysis of new energy power generation power modules according to claim 1, characterized in that, In the data preprocessing module, Input the real-time junction temperature data into the real-time junction temperature buffer one by one, and for the latest three adjacent junction temperature data , substitute them into formula (2) to determine whether the data point in the middle is an extreme point. If equation (2) holds, then it is determined that it is an extreme point; if equation (2) does not hold, then it is determined that it is not an extreme point, and shift forward to the position of , and read in the new real-time junction temperature data as the new value, and re-perform the extreme point judgment; When is determined as an extreme point, then determine the difference between and the window width of the rainflow filter size relationship: If , then delete , read the next real-time junction temperature data as new value, and re-perform the size judgment; if , then retain , store in the junction temperature extreme point buffer PV, remove and move forward to position, read the next real-time junction temperature data as new value, this process is as shown in formula (3); (2) (3)。 6. The real-time rainflow counting method for thermal fatigue analysis of new energy power generation power modules according to claim 1, characterized in that, The real-time rainflow cycle counting module processes the effective junction temperature extreme point data output by the data preprocessing module in real time. After each new effective junction temperature extreme point is screened out, the real-time rainflow cycle counting module is executed to identify the full cycle and half cycle in the effective junction temperature extreme point data in real time, and it is executed cyclically when the number of junction temperature extreme points is not less than 3 until all the junction temperature stress cycles in the junction temperature extreme point buffer PV are identified. The object of action of the real-time rainflow cycle counting module each time it is executed is only the latest three points in the junction temperature extreme point buffer, and the execution content is simple addition, subtraction, and conditional judgment.

7. The real-time rainflow counting method for thermal fatigue analysis of new energy power generation power modules according to claim 6, characterized in that, The execution steps of the real-time rainflow cycle counting module are as follows: 1) The effective junction temperature extreme points screened out by the data preprocessing module are stored point by point in the junction temperature extreme point buffer PV. If there is no new value, wait for the arrival of a new value. 2) Check whether the number of data in the junction temperature extreme point buffer is greater than or equal to 3. If not, continue to wait for the input of a new value. If so, extract the latest three values in the junction temperature extreme point buffer and mark them respectively in the order of writing as , that is, the third new value from the bottom is marked as , the second new value from the bottom is marked as , and the last new value is marked as ; 3) Calculate the amplitude difference between two adjacent values in , ; 4) Compare with to determine their magnitude relationship; if , continue to wait for the input of a new valid junction temperature extreme point and re-extract the latest three values from the junction temperature extreme point buffer; if , proceed to the next process; 5) Judge whether the number of data in the junction temperature extreme point buffer PV at this time is 3. If it is 3, enter the half cycle counting process. If it is not 3, enter the full cycle counting process. 6) Input the original counting result of the full cycle or half cycle into the discrete normalization module to obtain the standardized stress cycle. 7) Write the standardized stress cycle into the full cycle two-dimensional table or half cycle two-dimensional table in the memory. This two-dimensional table is the stress cycle amplitude, the stress cycle mean value, and the corresponding number of times. 8) Judge whether the new energy power generation module stops running: If the new energy power generation module stops running, end the execution of the real-time rainflow cycle counting module; if the new energy power generation module continues to run, return to the data preprocessing module to wait for the input of new junction temperature sampling values.

8. The real-time rainflow counting method for thermal fatigue analysis of a new energy power generation power module according to claim 7, wherein, In step 5), the half cycle counting process is as follows: Use to mark the semi - cycle and record the stress cycle amplitude as , the stress cycle mean value as , and then remove it from the peak junction temperature buffer PV .

9. The real-time rainflow counting method for thermal fatigue analysis of a new energy power generation power module according to claim 7, wherein, In step 5), the full cycle counting process is as follows: Use to mark the full cycle and record the stress cycle amplitude as , the mean value of the stress cycle as , and then remove it from the buffer PV at the extreme point of the junction temperature .

10. The real-time rainflow counting method for thermal fatigue analysis of a new energy power generation power module according to claim 1, wherein, The discrete normalization module pre-determines the range of stress cycle amplitudes to be analyzed ( B l1 , B u1 ) and the range of stress cycle means ( B l2 , B u2 ), and divides each range into n 1, n 2 intervals; matches the stress cycle amplitudes and means output by the real-time rainflow cycle counting module with the divided intervals, and updates the cycle counts of the corresponding intervals; Taking the stress cycle amplitude as an example, if the set range of the stress cycle amplitude is ( B l1 , B u1 ), and it is divided into n 1 interval, then the width of each interval is , and is converted to the standard value: . If the calculation result exceeds the upper bound of the discrete standardization B u1 , then it is taken as the upper bound value B u1 ; the same operation is performed on the stress cycle mean value to obtain the standard value of the stress cycle mean value . Finally, the number of stress cycles is added once at the position of ( ) in the full-cycle two-dimensional table.

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