A durability evaluation method for a fuel cell system for vehicles of a step stress type

Abstract

The application is a kind of durability evaluation method of vehicle fuel cell system of step stress type. It includes: 1, obtaining the basic parameters of electric-electric hybrid power target vehicle and whole vehicle composed of fuel cell and power battery; 2, selecting battery capacity parameter matching and whole vehicle electric accessory power range; 3, determining fuel cell parameters and obtaining fuel cell theoretical life decline model; 4, calculating the optimal power distribution result under the target working condition; 5, under different combination configuration, calculating the proportion of each decline factor of fuel cell system and the cumulative value of decline rate; 6, constructing accelerated aging working condition; 7, carrying out equivalent accelerated durability test; 8, carrying out durability test on step stress type fuel cell system; 9, carrying out system durability evaluation after each stress test. The application can evaluate the stability and durability of vehicle fuel cell system in a short time, and solve the problems of time-consuming, labor-consuming and inaccurate prediction results in the prior art.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of batteries, and particularly relates to a step stress type fuel cell system durability evaluation method for vehicles. BACKGROUND

[0002] Fuel cell hybrid electric vehicles have the advantages of zero emission and high efficiency, have become an important branch of new energy vehicles, and have a broad development prospect in the future. However, due to the high initial cost and poor durability, it is necessary to further study the parameter matching and optimal control of the electric-electric hybrid power assembly composed of the fuel cell and the power battery, so as to ensure that the fuel cell system can avoid the dynamic operation conditions such as repeated start-stop and rapid load change which seriously affect the service life, so as to ensure that the actual operation time of the fuel cell can reach the commercial application target of 5000 hours. The national standard GB / T 38914-2020 “Vehicle Proton Exchange Membrane Fuel Cell Stack Service Life Test and Evaluation Method” has formulated the fuel cell stack stability test and single-factor life degradation test method under idle, rated, variable load and start-stop conditions.

[0003] How to test and evaluate the relative service life of the fuel cell in a short time, and make the test results equivalent to the actual service life, has become a research hotspot and technical problem to be solved in the current fuel cell durability test.

[0004] The existing durability performance prediction and accelerated aging condition establishment are mostly based on the statistical data of the actual working conditions of the vehicle, the data acquisition workload is large, and the durability prediction problem cannot be adapted to the change of the parameter matching and control conditions of the power assembly, and the working point of the fuel cell changes accordingly. At the same time, the performance degradation mechanism of the fuel cell system is complex, and there are many influencing factors, so that the actual service life prediction through the performance aging model has great modeling difficulty and the precision is difficult to guarantee. SUMMARY

[0005] The application provides a step stress type fuel cell system durability evaluation method for vehicles, which can evaluate the stability and durability of the fuel cell system for vehicles in a short time, and solves the problems of time-consuming and labor-consuming durability test, inaccurate prediction results, and inability to adaptively analyze the matching and use conditions of the electric-electric hybrid power target vehicle composed of the fuel cell and the power battery in the prior art.

[0006] The technical scheme of the application is described below in combination with the drawings:

[0007] A step stress type fuel cell system durability evaluation method for vehicles, comprising the following steps:

[0008] Step one, obtaining the basic parameters of the electric-electric hybrid target vehicle composed of fuel cell and power battery and the whole vehicle;

[0009] Step two, selecting battery capacity parameter matching and whole vehicle electric accessory power range;

[0010] Step three, determining fuel cell parameters and obtaining fuel cell theoretical life degradation model;

[0011] Step four, calculating the optimal power distribution result under the target working condition;

[0012] Step five, calculating the proportion of each degradation factor of the fuel cell system and the cumulative value of the degradation rate under different combination configurations;

[0013] Step six, constructing an accelerated aging working condition;

[0014] Step seven, performing equivalent accelerated durability test;

[0015] Step eight, performing durability test on the step stress fuel cell system;

[0016] Step nine, performing system durability evaluation after each stress test.

[0017] Further, in the step one, the basic parameters of the target vehicle and the whole vehicle include: the whole vehicle kerb mass, the motor power, the battery capacity configuration, the whole vehicle electric accessory power consumption range, and the typical driving working condition of the target vehicle, i.e. the target working condition;

[0018] The target working condition is divided into urban driving working condition segment and suburban driving working condition segment according to the speed characteristics, and is labeled as urban driving working condition and suburban driving working condition.

[0019] Further, the specific method of the step two is as follows:

[0020] The whole vehicle electric accessory power consumption and the power battery pack capacity matched with the measured system are divided into parameter ranges: low battery capacity / high electric accessory power consumption, medium battery capacity / medium electric accessory power consumption, and large battery capacity / low electric accessory power consumption.

[0021] Further, the specific method of the step three is as follows:

[0022] 31) determining fuel cell parameters; the fuel cell parameters include fuel cell system rated output power, maximum output power, efficiency distribution curve, fuel cell system efficiency, and single factor performance degradation rate;

[0023] Among them, the fuel cell system efficiency refers to the curve of the fuel cell efficiency changing with the fuel cell output power, the horizontal coordinate is the fuel cell output power, and the vertical coordinate is the fuel cell efficiency;

[0024] The fuel cell system degradation rate under a single factor refers to the fuel cell voltage attenuation rate of a fuel cell obtained through a bench test under various single degradation factors; the single degradation factors include start-stop operating condition degradation factors, idle operating condition degradation factors, variable load operating condition degradation factors, rated operating condition degradation factors, overload operating condition degradation factors;

[0025] 32) Obtain a fuel cell theoretical life degradation model through the fuel cell degradation rate under a single factor, specifically as follows:

[0026] A=k1n1+k2n2ΔP+k3t1+k 43 t2+k5t3

[0027] In the formula, A is the fuel cell output voltage degradation amount under the rated operating condition; n1 is the start-stop frequency; n2 is the variable load frequency; ΔP is the power variable load amplitude; t1 is the idle time; t2 is the overload operating condition duration; t3 is the rated operating condition duration; k1 is the voltage degradation rate of each start-stop; k2 is the voltage attenuation rate of each variable load; k3 is the fuel cell voltage attenuation rate caused by the idle operating condition; k4 is the fuel cell voltage attenuation rate caused by the overload operating condition; and k5 is the fuel cell voltage attenuation rate caused by the rated operating condition.

[0028] Further, the specific method of step four is as follows:

[0029] 41) Obtain the optimal power distribution curve of the fuel cell system under the target operating condition through a dynamic programming algorithm under multiple parameter matching and electric accessory power consumption, specifically as follows:

[0030] Select the battery SOC as the fuel cell system state quantity, and the fuel cell output power as the control quantity, and then the state equation of the system is expressed as:

[0031]

[0032] In the formula, I is the battery current, calculated by the following formula:

[0033]

[0034] In the formula, U oc is the open circuit voltage; R0 is the battery internal resistance; Cap bat is the battery capacity; P bat is the battery power; Δt is the time interval; T bat is the battery temperature;

[0035] 42) Provide vehicle driving power P tr_req and electric accessory power consumption P acc_req , specifically realized by the following formula:

[0036] P fc +P bat =P tr_req +P acc_req

[0037] where P tr_req is the driving power of the vehicle, and P

[0038]

[0039] where m is the mass of the vehicle, g is the acceleration of gravity, θ is the road slope, δ is the rotational mass conversion coefficient, C D is the wind resistance coefficient, A is the windward area of the vehicle, ρ is the air density, v(k) and a(k) are the speed and acceleration of the vehicle at this time, respectively;

[0040] 43) determining the cost function of the dynamic programming algorithm, specifically including hydrogen consumption, fuel cell degradation, and battery degradation;

[0041] 44) solving the global optimization of the dynamic programming algorithm, specifically as follows:

[0042] 441) calculating the cost function of each SOC point in the terminal state space;

[0043]

[0044] 442) calculating the cost function of each SOC point in the kth stage state space;

[0045]

[0046] where P is the instantaneous cost generated by the kth stage SOC and the fuel cell output power ; is the optimal cost function value of the k+1th stage SOC point to the terminal, that is:

[0047]

[0048] 443) solving the corresponding optimal fuel cell output power according to the optimal cost function

[0049]

[0050] 444)Repeat steps 441)-443) until the initial state, complete the reverse optimization process of dynamic programming algorithm, and then sequentially solve the optimal SOC and optimal fuel cell output power sequence in each stage by the system state equation, so as to obtain the global optimal solution of the system.

[0051] Further, the specific method of step five is as follows:

[0052] 51) In the time domain, the number / amplitude / duration of each degradation factor in the optimal power allocation curve obtained in step four under a single target operating condition is counted;

[0053] 52) The cumulative degradation amount of the fuel cell voltage under a single target operating condition, the time distribution of each single degradation factor and the voltage degradation amount caused by each single degradation factor are obtained by the fuel cell theoretical life degradation model in step three;

[0054] 53) The voltage degradation amounts caused by each degradation factor under the urban driving condition and the suburban driving condition are summed up respectively, so as to obtain the cumulative voltage degradation amounts of the urban driving condition and the suburban driving condition under a single target operating condition.

[0055] Further, the specific method of step six is as follows:

[0056] The specific numerical value and fluctuation of the fuel cell power calculation result obtained by the dynamic programming algorithm under the target operating condition specifically presents three types of data characteristics, which are stable power, small amplitude / high frequency fluctuation based on stable power and large amplitude / low frequency fluctuation based on stable power; based on the life degradation rate equivalent principle, the following data segment processing is performed;

[0057] 61) Power feature clustering;

[0058] The power and time history curve data under the target operating condition are traversed, the power and the amplitude and frequency of power change are taken as characteristic parameters, the k-means clustering method is used to cluster the optimal power curve obtained in step four, and three types of data characteristics are obtained, one type is the basic stable power during urban driving, small amplitude / high frequency variable load under the basic stable power and large amplitude / low frequency variable load under the basic stable power; the second type of data characteristic is the medium stable power during suburban driving, small amplitude / high frequency variable load under the medium stable power and large amplitude / low frequency variable load under the medium stable power; the third type of data characteristic is the high stable power during suburban driving, small amplitude / high frequency variable load under the high stable power and large amplitude / low frequency variable load under the high stable power;

[0059] 62) Equivalent of basic stable power variable load amplitude;

[0060] The small amplitude / high frequency variable load power amplitudes under each stable power are accumulated as the first type of loading data under the basic stable power;

[0061] The large amplitude / low frequency variable load power amplitude under the basic stable power is accumulated as the second type of loading data.

[0062] 63) The power variable load amplitude under the medium-high stable power is equivalent.

[0063] The large amplitude / low frequency variable load power amplitude under the medium stable power is accumulated as the third type of loading data.

[0064] The large amplitude / low frequency variable load power amplitude under the high stable power is accumulated as the fourth type of loading data.

[0065] In combination with the four types of loading data formulated, the fuel cell aging degradation amount caused by variable load at different power levels under each stress level of the fuel cell system configured with large battery capacity / low electrical accessory power consumption, the fuel cell system configured with medium battery capacity / medium electrical accessory power consumption, and the fuel cell system configured with low battery capacity / high electrical accessory power consumption is completely retained, and the life degradation accumulation value caused by power and variable load is equivalent to the cumulative voltage degradation amount counted out in step five.

[0066] 64) Accelerated aging condition construction;

[0067] For the fuel cell system configured with large battery capacity / low electrical accessory power consumption, the fuel cell system configured with medium battery capacity / medium electrical accessory power consumption, and the fuel cell system configured with low battery capacity / high electrical accessory power consumption, the accelerated aging conditions corresponding to the stress are constructed, so that the fuel cell voltage degradation amount under a single accelerated aging condition and the fuel cell voltage degradation amount under a single target condition are equal during accelerated testing.

[0068] The accelerated aging condition adopts a square wave form with a duty cycle of 50% for amplitude loading, each square wave cycle is 10s, and the four types of loading data correspond to four square waves, the starting power of each square wave rising edge corresponds to the stable power of the four types of loading data, respectively, and the amplitude of each square wave corresponds to the variable load power amplitude accumulation value under the four types of loading data.

[0069] Each group of accelerated aging conditions starts and ends with a basic stable power of 5s, and the total running time of a group of accelerated aging conditions is 50s, denoted by T'.

[0070] Further, the specific method of step seven is as follows:

[0071] Start the fuel cell system, continuously run the accelerated aging condition, the running time is the actual working time per day, then use the voltage at the rated power point to characterize the durability degradation, and finally stop the machine.

[0072] Further, the specific method of step eight is as follows:

[0073] 81) Run the accelerated aging conditions in three stages in sequence, and the stress conditions are from low to high, and the running time of each stage is 100 h. The three stages respectively correspond to the fuel cell system durability test under the conditions of a fuel cell system with large battery capacity / low electrical accessory power consumption, a fuel cell system with medium battery capacity / medium electrical accessory power consumption, and a fuel cell system with low battery capacity / high electrical accessory power consumption. The same fuel cell is used in the three durability test stages, and different accelerated aging conditions are loaded in different stages;

[0074] 82) In each stage of the durability test, the durability test is arranged according to the working time to ensure that the cumulative accelerated aging condition time reaches 100 h of test requirements, but the integrity of the accelerated aging condition needs to be ensured. At the beginning and end of the single-day test, the start-stop operation of the fuel cell system needs to be recorded.

[0075] Further, the specific method of step nine is as follows:

[0076] 91) Use the durability test data of the three stages to correct the fuel cell theoretical life degradation model in step three by a fitting method to obtain the actual life degradation model of the fuel cell system with large battery capacity / low electrical accessory power consumption, the fuel cell system with medium battery capacity / medium electrical accessory power consumption, and the fuel cell system with low battery capacity / high electrical accessory power consumption. The corrected actual life degradation model of the fuel cell is as follows:

[0077] A' = aA + b

[0078] In the formula, A' is the actual performance degradation of the fuel cell in the fuel cell system, A is the theoretical performance degradation of the fuel cell, a is the environmental acceleration coefficient, and b is the degradation offset.

[0079] 92) Draw the output voltage data of the fuel cell under the rated working condition at the end of each basic accelerated durability test condition in the rectangular coordinate system with time as the horizontal coordinate and the output voltage of the fuel cell as the vertical coordinate to obtain the voltage change trajectory of the fuel cell under the three-stage durability condition test;

[0080] 93) Set the output voltage of the fuel cell in the initial state of life as U0, and the output voltage of the fuel cell when it degrades to the specified minimum extent, i.e., the output voltage degrades by 10%, as U end; using the data of fuel cell output voltage decay curve in fuel cell system with large battery capacity / low power consumption of electrical accessories, the actual life decay model of fuel cell in fuel cell system with large battery capacity / low power consumption of electrical accessories at initial output voltage U0 is obtained by fitting method, the expected full life cycle working time t1 of fuel cell in fuel cell system with large battery capacity / low power consumption of electrical accessories under accelerated aging condition is obtained by using fuel cell actual decay model when fuel cell decays to U end ;

[0081] 94) using the data of fuel cell output voltage decay curve in fuel cell system with medium battery capacity / medium power consumption of electrical accessories, the actual decay model of fuel cell at initial voltage U1 is obtained, the horizontal coordinate of intersection point of decay model curve and voltage U end is t2, t2-100 is the expected use time of fuel cell in fuel cell system with medium battery capacity / medium power consumption of electrical accessories under accelerated aging condition, the fuel cell actual decay model curve is translated so that the intersection point of curve and vertical axis is U0, that is, the equivalent full life cycle actual decay model of fuel cell in fuel cell system with medium battery capacity / medium power consumption of electrical accessories at initial output voltage U0 is obtained, the horizontal coordinate of intersection point of equivalent full life cycle actual decay model and voltage U end is t'2, which is the expected full life cycle working time of fuel cell system in fuel cell system with medium battery capacity / medium power consumption of electrical accessories under accelerated aging condition;

[0082] 95) using the data of fuel cell output voltage decay curve in fuel cell system with low battery capacity / high power consumption of electrical accessories, the actual decay model of fuel cell at initial voltage U2 is obtained, the horizontal coordinate of intersection point of decay model curve and voltage U end is t3, t3-200 is the expected use time of fuel cell in fuel cell system with low battery capacity / high power consumption of electrical accessories under accelerated aging condition, the fuel cell actual decay model curve is translated so that the intersection point of curve and vertical axis is U0, that is, the equivalent full life cycle actual decay model of fuel cell in fuel cell system with low battery capacity / high power consumption of electrical accessories at initial output voltage U0 is obtained, the horizontal coordinate of intersection point of equivalent full life cycle actual decay model and voltage U end is t'3, which is the expected full life cycle working time of fuel cell system in fuel cell system with low battery capacity / high power consumption of electrical accessories under accelerated aging condition;

[0083] 96) Use symbol T to represent the time of single target working condition, T' to represent the time of single accelerated aging working condition, and define the accelerated aging factor as follows:

[0084]

[0085] By obtaining the single accelerated aging working condition time T' and the expected full life cycle working time t, the accelerated aging factor β, and the single target working condition driving mileage s, the estimated life and the estimated total driving mileage of the fuel cell system under the target working condition are calculated when the vehicle is used;

[0086] 97) Compare the vehicle use estimated life T of the fuel cell system with large battery capacity / low electric accessory power consumption, the vehicle use estimated life T of the fuel cell system with medium battery capacity / medium electric accessory power consumption, and the vehicle use estimated life T of the fuel cell system with low battery capacity / high electric accessory power consumption with the design life index of the fuel cell system, and then realize the evaluation of the selection and matching of the fuel cell hybrid power system. 1,总 、T 2,总 、T 3,总

[0087] The beneficial effects of the present application are:

[0088] 1) The accelerated aging test working condition construction method proposed in the present application does not need real vehicle running data as input, and can complete the construction of the test working condition and the analysis of the vehicle adaptability before the real vehicle is built;

[0089] 2) The step stress accelerated durability test and analysis method proposed in the present application is suitable for various fuel cell hybrid vehicles and different parameter matching conditions, and can also obtain the parameter matching and control requirements for making the actual measured fuel cell have better durability according to the test results;

[0090] 3) The global optimization calculation of the dynamic specification algorithm applied in the present application only needs to input the fuel cell engine system efficiency curve and the life decline influence factor under a single factor and other external performance, and the required data can be provided by the supplier, which is easy to connect the work between upstream and downstream enterprises;

[0091] 4) In the process of working condition construction and result analysis of the present application, the research on the internal aging mechanism of the fuel cell and the construction of the aging model are not needed, which avoids the problems of numerous parameter requirements and poor calculation result precision in modeling and simulation calculation;

[0092] 5) The stress conversion and working condition equivalent method proposed in the present application has comprehensive construction elements and wide application range, can evaluate the system durability in a short test time, and obtain the vehicle adaptability analysis results combined with the parameter matching and control of the fuel cell hybrid power system;

[0093] ​6) The power of the electrical accessories in the application represents the power consumption in the case of intelligent equipment application and the need for refrigeration in the passenger compartment, etc. When compiling the acceleration durability test conditions, it can be considered together to further clarify the adaptability of the target vehicle.

[0094] 7) The content and method described in the application can be combined with the operating conditions at the power point of the fuel cell. The fuel cell system level durability test and evaluation can also be decomposed into gas path and cooling subsystems, and durability test conditions for components such as the stack, air compressor, and hydrogen circulating pump, and vehicle adaptability evaluation methods. BRIEF DESCRIPTION OF DRAWINGS

[0095] In order to more clearly illustrate the technical solutions of the embodiments of the application, the drawings needed in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the application, and therefore should not be considered as a limitation on the scope. For those skilled in the art, other related drawings can also be obtained without creative labor.

[0096] Figure 1 The flowchart of the application is shown in the figure.

[0097] Figure 2 The accelerated aging condition diagram is shown in the figure.

[0098] Figure 3 The fuel cell voltage decay trajectory diagram under step stress durability test is shown in the figure. DETAILED DESCRIPTION

[0099] The technical solutions in the embodiments of the application will be described clearly and completely below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are only some of the embodiments of the application, not all. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of the application.

[0100] Referring to Figure 1 A step stress type vehicle fuel cell system durability evaluation method, comprising the following steps:

[0101] Step 1, obtain the basic parameters of the electric-electric hybrid power target vehicle composed of fuel cell and power battery and the whole vehicle;

[0102] The basic parameters of the target vehicle and the whole vehicle include: the whole vehicle kerb mass, the motor power, the battery capacity configuration, the whole vehicle electrical accessory power consumption range and the typical driving conditions of the target vehicle, i.e. the target conditions;

[0103] The target working condition is divided into city driving working condition segment and suburb driving working condition segment according to the speed characteristics, and is labeled as city driving working condition and suburb driving working condition.

[0104] Step two, select the battery capacity parameter matching and the whole vehicle electric accessory power range;

[0105] The specific method is as follows:

[0106] The power consumption of the whole vehicle electric accessory and the capacity of the power battery group matched with the measured system are divided into parameter ranges, which are low battery capacity / high electric accessory power consumption, medium battery capacity / medium electric accessory power consumption, and large battery capacity / low electric accessory power consumption. Hereinafter, the fuel cell system configured with large battery capacity / low electric accessory power consumption is referred to as configuration 1 fuel cell system; the fuel cell system configured with medium battery capacity / medium electric accessory power consumption is referred to as configuration 2 fuel cell system; and the fuel cell system configured with low battery capacity / high electric accessory power consumption is referred to as configuration 3 fuel cell system.

[0107] Step three, determine the fuel cell parameters and obtain the fuel cell theoretical life degradation model;

[0108] The specific method is as follows:

[0109] 31) Determine the fuel cell parameters; the fuel cell parameters include fuel cell system rated output power, maximum output power, efficiency distribution curve, fuel cell system efficiency, and single factor performance degradation rate;

[0110] The fuel cell system efficiency refers to the curve of the fuel cell efficiency changing with the fuel cell output power, the horizontal coordinate is the fuel cell output power, and the vertical coordinate is the fuel cell efficiency;

[0111] The degradation rate of the fuel cell system under a single factor refers to the fuel cell voltage attenuation rate of the fuel cell under various single degradation factors obtained by building a bench test according to the "National Standard GB / T 38914-200 Vehicle Proton Exchange Membrane Fuel Cell Stack Service Life Test and Evaluation Method"; the single degradation factor includes start-stop working condition degradation factor, idle working condition degradation factor, variable load working condition degradation factor, rated working condition degradation factor, and overload working condition degradation factor; the fuel cell voltage attenuation rate directly reflects the life attenuation of the fuel cell.

[0112] 32) Obtain the fuel cell theoretical life degradation model through the fuel cell voltage attenuation rate of the fuel cell under a single degradation factor, which is as follows:

[0113] A=k1n1+k2n2ΔP+k3t1+k 43 t2+k5t3

[0114] In the formula, A is the theoretical performance attenuation of fuel cell, which describes the amount of fuel cell output voltage decline under rated operating conditions, and the unit is volt (V); n1 is the number of start-stop times; n2 is the number of variable load times; ΔP is the power variable load amplitude, and the unit is kilowatt (kW); t1 is the idling time, and the unit is minute (min); t2 is the duration of overload operating conditions, and the unit is minute (min); t3 is the duration of rated operating conditions, and the unit is minute (min); k1 is the voltage decline rate of each start-stop, and the unit is volt per time (V / time); k2 is the voltage attenuation rate of each variable load, and the unit is volt per time per kilowatt (V / (time·kW)); k3 is the fuel cell voltage attenuation rate caused by idling operating conditions, and the unit is volt per minute (V / min); k4 is the fuel cell voltage attenuation rate caused by overload operating conditions, and the unit is volt per minute (V / min); k5 is the fuel cell voltage attenuation rate caused by rated operating conditions, and the unit is volt per minute (V / min).

[0115] Step four, calculating the optimal power distribution result under the target operating conditions;

[0116] The specific method is as follows:

[0117] 41) Obtain the optimal power distribution curve of the fuel cell system under the target operating conditions by a dynamic programming algorithm (DP, Dynamic Programming), and the specific steps of the DP algorithm are as follows:

[0118] Select the battery SOC as the state quantity of the fuel cell system, and the fuel cell output power as the control quantity, and then the state equation of the system is expressed as:

[0119]

[0120] In the formula, I is the battery current, which is calculated by the following formula:

[0121]

[0122] In the formula, U oc is the open circuit voltage; R0 is the battery internal resistance; Cap bat is the battery capacity; P bat is the battery power; Δt is the time interval; T bat is the battery temperature;

[0123] 42) The fuel cell power source includes an engine P fc and a battery P bat , which are used to provide vehicle driving power P tr_req and electrical accessory power consumption P acc_req , and are specifically implemented by the following formula:

[0124] P fc +Pbat = P tr_req + P acc_req

[0125] wherein the driving power P of the vehicle tr_req is expressed as:

[0126]

[0127] wherein m is the mass of the vehicle; g is the acceleration of gravity; θ is the road slope; δ is the rotational mass conversion coefficient; C D is the wind resistance coefficient; A is the windward area of the vehicle; ρ is the air density; v(k) and a(k) are respectively the speed and acceleration of the vehicle at this time;

[0128] 43) The cost function in the DP algorithm is determined, specifically including three parts of hydrogen consumption, fuel cell attenuation, and battery attenuation;

[0129] 44) The specific solution process of the global optimization of the DP algorithm is as follows:

[0130] 441) The cost function of each SOC point in the terminal state space is calculated

[0131]

[0132] 442) The cost function of each SOC point in the kth stage state space is calculated

[0133]

[0134] wherein is the instantaneous cost generated by the kth stage SOC and the fuel cell output power ; and is the optimal cost function value of the k+1th stage SOC point to the terminal, that is:

[0135]

[0136] 443) The optimal fuel cell output power corresponding to the optimal cost function

[0137]

[0138] 444)Repeat steps 441)-step 443) until the initial state, complete the inverse optimization process of DP algorithm, and then sequentially solve the optimal SOC and optimal fuel cell output power sequence by the system state equation, so as to obtain the global optimal solution of the system.

[0139] Step five, statistics of the proportion of each degradation factor and the cumulative value of degradation rate of the fuel cell system under different combination configurations;

[0140] The specific method is as follows:

[0141] 51) In the time domain, the number / amplitude / duration of each degradation factor under a single target working condition in the optimal power distribution curve obtained in step four is counted;

[0142] 52) Through the fuel cell theoretical life degradation model in step three, the cumulative degradation amount of fuel cell voltage under a single target working condition, the time distribution of each single degradation factor and the voltage degradation amount caused by each single degradation factor are obtained;

[0143] 53) The voltage degradation amount caused by each degradation factor under the urban driving condition and the suburban driving condition is summed up, so as to obtain the cumulative voltage degradation amount of the urban driving condition and the suburban driving condition under a single target working condition.

[0144] Step six, constructing an accelerated aging condition;

[0145] The specific method is as follows:

[0146] Based on the change of the optimal power of the fuel cell extracted in step four, the calculated results of the fuel cell power of the DP algorithm under the target working condition of the three configurations, and the specific values and fluctuation of the three configurations, three types of data characteristics are presented, which are stable power, small amplitude / high frequency fluctuation based on stable power and large amplitude / low frequency fluctuation based on stable power; Based on the equivalent principle of life degradation rate, the following data segment processing is carried out;

[0147] 61) Power feature clustering;

[0148] The power and time history curve data under the target working condition are traversed, the power and the amplitude and frequency of power change are taken as the characteristic parameters, the k-means clustering method is used to cluster the optimal power curve obtained in step four, and three types of data characteristics are obtained, one type is the basic stable power during urban driving, small amplitude / high frequency variable load under the basic stable power, and large amplitude / low frequency variable load under the basic stable power; The second type of data characteristic is the medium stable power during suburban driving, small amplitude / high frequency variable load under the medium stable power, and large amplitude / low frequency variable load under the medium stable power; The third type of data characteristic is the high stable power during suburban driving, small amplitude / high frequency variable load under the high stable power, and large amplitude / low frequency variable load under the high stable power;

[0149] 62) Equivalent of power amplitude of basic steady power variation;

[0150] The voltage decay of fuel cell has little effect on the steady power other than initial idle speed and overload. The small amplitude / high frequency power amplitude of power variation under each steady power is accumulated as the first type of loading data under basic steady power;

[0151] The large amplitude / low frequency power amplitude of power variation under basic steady power is accumulated as the second type of loading data;

[0152] 63) Equivalent of power amplitude of medium-high steady power variation;

[0153] The large amplitude / low frequency power amplitude of power variation under medium steady power is accumulated as the third type of loading data;

[0154] The large amplitude / low frequency power amplitude of power variation under high steady power is accumulated as the fourth type of loading data;

[0155] The voltage decay of fuel cell under each stress level of configurations 1, 2 and 3 under different power levels due to power variation is completely reserved by combining the four types of loading data, and the accumulated life decay value caused by power and its variation factors is equivalent to the cumulative voltage decay value counted in step 5;

[0156] 64) Construction of accelerated aging conditions;

[0157] For fuel cell systems with different configurations, accelerated aging conditions under corresponding stresses are constructed so that the fuel cell voltage decay under a single accelerated aging condition and the fuel cell voltage decay under a single target condition are equal during accelerated testing;

[0158] In order to facilitate testing, the accelerated aging conditions are loaded in the form of square wave with a duty cycle of 50%, each square wave cycle is 10s, and the above four types of loading data correspond to four square waves, the starting power of each square wave rising edge corresponds to the steady power of the four types of loading data respectively, and the amplitude of each square wave corresponds to the accumulated value of the variation power amplitude under the four types of loading data respectively;

[0159] Each group of accelerated aging conditions starts and ends with a basic steady power of 5s, and the total running time of a group of accelerated aging conditions is 50s, denoted by T'. The schematic diagram of accelerated aging conditions is shown in FIG. 1. Figure 2

[0160] Step seven, equivalent accelerated durability test;

[0161] The specific method is as follows: ​

[0162] The equivalent accelerated durability test of the fuel cell system under different stress conditions is carried out, and the operation method is as follows: starting the fuel cell system, circulating the continuous operation accelerated aging condition, the operation time is the actual working time per day, then using the voltage at the rated power point to characterize the durability degradation, and finally stopping.

[0163] Step eight, carrying out durability test on the step stress fuel cell system;

[0164] The specific method is as follows:

[0165] 81) The accelerated aging conditions under three stress conditions are sequentially operated in three stages (the stress conditions are from low to high), and the operation time of each stage is 100h, and the three stages correspond to the durability test of the fuel cell system under three kinds of combined configurations respectively. The same fuel cell is used in the three durability test stages, and different accelerated aging conditions are loaded in different stages.

[0166] 82) In each stage of the durability test, the durability test is arranged according to the working time, so as to ensure that the cumulative accelerated aging condition time reaches 100h of the test requirement, but the integrity of the accelerated aging condition needs to be ensured; at the beginning and end of the single day test, the start and stop operation of the fuel cell system needs to be recorded.

[0167] Step nine, carrying out system durability evaluation after each stress test is completed.

[0168] The specific method is as follows:

[0169] 91) Using the durability test data of the three stages, the fuel cell theoretical life degradation model in step three is modified by fitting method, and the fuel cell actual life degradation model of the fuel cell system under three kinds of combined configurations is obtained. The modified fuel cell actual life degradation model is as follows:

[0170] A' = aA + b

[0171] In the formula, A' is the actual performance attenuation (fuel cell output voltage attenuation) of the fuel cell in the fuel cell system; A is the theoretical performance attenuation (fuel cell output voltage attenuation) of the fuel cell in step three; a is the environmental acceleration coefficient; b is the degradation offset.

[0172] 92) The output voltage data of the fuel cell under the rated condition at the end of each basic accelerated durability test condition is plotted in the rectangular coordinate system with time as the horizontal coordinate and fuel cell output voltage as the vertical coordinate, and the fuel cell voltage change trajectory under the three stages of durability condition test is obtained as shown in the following figure: Figure 3As shown, segment ab is the fuel cell output voltage decay curve in configuration 1 fuel cell system; segment bc is the fuel cell output voltage decay curve in configuration 2 fuel cell system; and segment cd is the fuel cell output voltage decay curve in configuration 3 fuel cell system.

[0173] 93) Set the output voltage of the fuel cell at the initial stage of its lifespan to U0, and the output voltage when the fuel cell degrades to the specified minimum level (output voltage degradation of 10%) to U. end Using the data from curve ab, a fitting method can be used to obtain the actual lifespan degradation model of the fuel cell in configuration 1 fuel cell system when the initial output voltage is U0. This actual degradation model can then be used to calculate the degradation rate of the fuel cell to U0. end The expected full life cycle working time t1 under accelerated aging chemical conditions.

[0174] 94) For curve bc, the output voltage of the fuel cell has decayed from U0 to U1. Using the data from curve bc, the actual decay model of the fuel cell at the initial voltage of U1 can be obtained. The decay model curve is related to the voltage U. end The x-coordinate of the intersection point is t2, and (t2-100) represents the expected service life of the fuel cell in the configuration 2 fuel cell system under accelerated aging conditions. Furthermore, the actual degradation model curve of the fuel cell in segment bc is shifted so that the intersection point with the vertical axis is U0. This yields the equivalent full-lifecycle actual degradation model of the fuel cell in the configuration 2 fuel cell system when the initial output voltage is U0. The equivalent full-lifecycle actual degradation model and the voltage U... end The x-coordinate t′2 of the intersection of the curves represents the expected full lifecycle operating time of the fuel cell system in configuration 2 under accelerated aging conditions.

[0175] 95) For curve cd, the output voltage of the fuel cell has decayed from U0 to U2. Using the data from curve cd, the actual decay model of the fuel cell at the initial voltage of U2 can be obtained. The decay model curve is related to the voltage U. end The x-coordinate of the intersection point is t3, and (t3-200) represents the expected service life of the fuel cell in the configuration 3 fuel cell system under accelerated aging conditions. Furthermore, the actual degradation model curve of the fuel cell in segment cd is shifted so that the intersection point of the curve and the y-axis is U0. This yields the equivalent full-lifecycle actual degradation model of the fuel cell in the configuration 3 fuel cell system when the initial output voltage is U0. The equivalent full-lifecycle actual degradation model and the voltage U... end The x-coordinate t′3 of the intersection of the curves represents the expected full lifecycle operating time of the fuel cell system in configuration 3 under accelerated aging conditions.

[0176] 96) Use symbol T to represent the time of single target working condition, T' to represent the time of single accelerated aging condition, and define the accelerated aging factor as follows:

[0177]

[0178] The single accelerated aging time T' obtained through step five, the expected full life cycle working time t, and the accelerated aging factor β are used to calculate the estimated life and the estimated total driving distance of the fuel cell system in the target working condition when used in the vehicle.

[0179] The single accelerated aging time of the fuel cell system of configuration 1 is T' (unit: h), the accelerated aging factor is β, the expected full life cycle in the accelerated aging condition is t1 (unit: h) obtained by using the actual degradation model of the fuel cell, the time of single target working condition is T (unit: h), the distance of single target working condition is s (unit: km), the estimated life T 1,总 and the estimated total driving distance S 1,总 of the fuel cell system in the vehicle can be obtained through the following formula:

[0180] T 1,总 = β × t1

[0181]

[0182] Similarly, the estimated life T 2,总 , T 3,总 and the estimated total driving distance S 2,总 , S 3,总 of the fuel cell systems of configurations 2 and 3 in the vehicle can be calculated.

[0183] 97) Compare the estimated life T 1,总 , T 2,总 , T 3,总 of the fuel cell systems of different configurations in the vehicle with the design life index of the fuel cell system, and then evaluate the selection and matching of the fuel cell hybrid power system.

[0184] In summary, the present application can evaluate the stability and durability of the fuel cell system for vehicles in a short time, and the evaluation accuracy is high.

[0185] In addition, it should be noted that each specific technical feature described in the above specific embodiments can be combined in any appropriate manner without contradiction, and in order to avoid unnecessary repetition, the present application will not describe various possible combinations again.

[0186] Furthermore, the various embodiments of the present application can be combined with each other, as long as it does not violate the spirit of the present application, and it should be considered as disclosed in the present application.

Claims

1. A step-stress-based durability evaluation method for automotive fuel cell systems, characterized in that, Includes the following steps: Step 1: Obtain the target electric-electric hybrid vehicle model and basic parameters of the whole vehicle, which consists of fuel cells and power batteries; Step 2: Select battery capacity parameters and power range for vehicle electrical accessories; Step 3: Determine the fuel cell parameters and obtain the theoretical lifespan degradation model of the fuel cell; Step 4: Calculate the optimal power allocation result under the target operating condition; Step 5: Calculate the percentage of each degradation factor and the cumulative degradation rate of the fuel cell system under different configuration combinations; Step Six: Construct accelerated aging conditions; Step 7: Conduct equivalent accelerated durability testing; Step 8: Conduct durability testing on the step stress fuel cell system; Step 9: After each stress test is completed, a system durability evaluation is performed; The specific method for step two is as follows: The power consumption of the vehicle's electrical accessories and the capacity of the power battery pack to be matched with the system under test are divided into parameter ranges: low battery capacity / high electrical accessory power consumption, medium battery capacity / medium electrical accessory power consumption, and large battery capacity / low electrical accessory power consumption. The specific method for step eight is as follows: 81) The fuel cell system was subjected to accelerated aging under three stress conditions in three stages, from low to high. Each stage lasted 100 hours. The three stages corresponded to the fuel cell system durability test under the following conditions: a fuel cell system with a large battery capacity and low power consumption of electrical accessories, a fuel cell system with a medium battery capacity and medium power consumption of electrical accessories, and a fuel cell system with a low battery capacity and high power consumption of electrical accessories. The same fuel cell was used in the three durability test stages, but different accelerated aging conditions were applied in different stages. 82) In the durability test at each stage, the durability test shall be arranged according to the working time, and the cumulative accelerated aging test time shall meet the test requirement of 100 hours, but the integrity of the accelerated aging test shall be guaranteed; at the beginning and end of the test each day, the start and stop operations of the fuel cell system shall be recorded. The specific method for step nine is as follows: 91) Using the durability test data from the three stages, the theoretical life degradation model of the fuel cell in step three is modified by fitting, resulting in actual life degradation models for fuel cell systems with large battery capacity / low power consumption of electrical accessories, medium battery capacity / medium power consumption of electrical accessories, and low battery capacity / high power consumption of electrical accessories. The modified actual life degradation models of the fuel cell are as follows: ； In the formula, This refers to the actual performance degradation of the fuel cell in the fuel cell system; This is for the theoretical performance degradation of fuel cells; This refers to the environmental acceleration factor. This is the decay offset; 92) Plot the output voltage data of the fuel cell under rated conditions at the end of each basic accelerated durability test condition on a rectangular coordinate system with time on the horizontal axis and fuel cell output voltage on the vertical axis to obtain the fuel cell voltage change trajectory under the three stages of durability test conditions. 93) Set the output voltage of the fuel cell at the initial stage of its lifespan to be... The output voltage of a fuel cell when it degrades to the specified minimum level, i.e., a 10% decrease in output voltage, is: ; Using data from the output voltage decay curves of fuel cells in a fuel cell system with large battery capacity and low accessory power consumption, a fitting method is used to obtain the initial output voltage of the fuel cell in the system at a given value. The actual lifespan degradation model of the fuel cell is used to obtain the degradation rate of the fuel cell to the point where it degrades. The time is accelerating the expected total life cycle working time under aging chemical conditions. ; 94) The voltage decay curve of the fuel cell output in a fuel cell system with medium battery capacity / medium power consumption is used to obtain the fuel cell's voltage at the initial voltage of [value missing]. The actual decay model at that time, the decay model curve and voltage The x-coordinate of the intersection point is , To assess the expected lifespan of a fuel cell in a fuel cell system with medium battery capacity and medium power consumption under accelerated aging conditions, the output voltage degradation curve of the fuel cell in this system is shifted relative to the actual degradation model curve, so that the intersection of the curve with the vertical axis is... That is, to obtain a fuel cell system with medium battery capacity / medium power consumption, the fuel cell has an initial output voltage of... The equivalent full life cycle actual degradation model at time, the equivalent full life cycle actual degradation model and voltage x-coordinate of the intersection of the curves For fuel cell systems configured with medium battery capacity / medium power consumption, the expected full life cycle operating time of the fuel cell system under accelerated aging conditions; 95) Using data from the fuel cell output voltage decay curve in a fuel cell system with low battery capacity and high accessory power consumption, determine the fuel cell's voltage at the initial voltage of... The actual decay model at that time, the decay model curve and voltage The x-coordinate of the intersection point is , To assess the expected lifespan of fuel cells in a fuel cell system with low battery capacity and high accessory power consumption under accelerated aging conditions, the output voltage degradation curve segment of the fuel cell in this system is shifted relative to the actual degradation model curve, so that the intersection point of the curve with the vertical axis is... That is, in a fuel cell system with low battery capacity / high power consumption of electrical accessories, the fuel cell has an initial output voltage of The equivalent full life cycle actual degradation model at time, the equivalent full life cycle actual degradation model and voltage x-coordinate of the intersection of the curves To optimize the expected full lifecycle operating time of fuel cell systems in accelerated aging conditions for configuration with low battery capacity / high electrical accessory power consumption; 96) Let the symbol T represent the time of a single target condition. The accelerated aging factor, representing the time of a single accelerated aging condition, is defined as follows: ； By obtaining a single accelerated aging process time and expected total lifecycle working time aging-accelerating factors Mileage in the form of a single target working condition The estimated lifespan and estimated total driving range of the fuel cell system under the target operating conditions were calculated. 97) Estimated vehicle lifespan for fuel cell systems with large battery capacity / low electric accessory power consumption, medium battery capacity / medium electric accessory power consumption, and low battery capacity / high electric accessory power consumption. By comparing the design life indicators with those of the fuel cell system, an evaluation of the selection and matching of the fuel cell hybrid power system can be achieved.

2. The step-stress type durability evaluation method for automotive fuel cell systems according to claim 1, characterized in that, In step one, the target vehicle model and basic parameters of the vehicle include: vehicle curb weight, motor power, battery capacity configuration, power consumption range of vehicle electrical accessories, and the typical driving conditions targeted by the target vehicle model, i.e., the target conditions. The target operating conditions are divided into urban driving condition segments and suburban driving condition segments according to vehicle speed characteristics, and are labeled accordingly, namely urban driving condition and suburban driving condition.

3. The step-stress type durability evaluation method for automotive fuel cell systems according to claim 1, characterized in that, The specific method for step three is as follows: 31) Determine the fuel cell parameters; the fuel cell parameters include the rated output power, maximum output power, efficiency distribution curve, fuel cell system efficiency, and single-factor performance degradation rate of the fuel cell system; Among them, fuel cell system efficiency refers to the curve of fuel cell efficiency as a function of fuel cell output power, with the horizontal axis representing fuel cell output power and the vertical axis representing fuel cell efficiency. The degradation rate of a fuel cell system under a single factor refers to the rate of voltage decay of the fuel cell under various single degradation factors obtained through bench testing; the single degradation factors include degradation factors under start-stop conditions, degradation factors under idling conditions, degradation factors under variable load conditions, degradation factors under rated conditions, and degradation factors under overload conditions. 32) The theoretical lifespan degradation model of the fuel cell is obtained by using the degradation rate of the fuel cell under a single factor, as follows: ； In the formula, This refers to the voltage decay of the fuel cell output under rated operating conditions. Number of starts and stops; For the number of load variations; For power load variation amplitude; Idle time; This refers to the duration of the overload condition. This refers to the rated operating duration. The voltage decay rate for each start-up and shutdown; This represents the voltage attenuation rate for each load change; The voltage decay rate of the fuel cell caused by idling conditions; The voltage decay rate of the fuel cell caused by overload conditions; This refers to the rate of voltage decay of the fuel cell under rated operating conditions.

4. The step-stress type durability evaluation method for automotive fuel cell systems according to claim 3, characterized in that, The specific method for step four is as follows: 41) The optimal power distribution curve of the fuel cell system under the target operating condition is obtained by using a dynamic programming algorithm under various parameter matching and electrical accessory power consumption conditions, as detailed below: Choosing the battery SOC as the state variable of the fuel cell system and the fuel cell output power as the control variable, the state equation of the system is expressed as: ； In the formula, The battery current is calculated using the following formula: ； In the formula, This is the open-circuit voltage; This refers to the battery's internal resistance. Battery capacity; Battery power; For time intervals; Battery temperature; 42) Provides vehicle driving power and power consumption of electrical accessories Specifically, it is achieved by the following formula: ； Among them, the vehicle's driving power Represented as: ； In the formula, For car quality; It is the acceleration due to gravity; Road slope; This is the rotational mass conversion factor; This refers to the drag coefficient; The frontal area of ​​the vehicle; air density; and These represent the car's speed and acceleration at this moment; 43) Determine the cost function of the dynamic programming algorithm, which specifically includes three parts: hydrogen consumption, fuel cell degradation, and battery degradation; 44) Solve the global optimization problem using the dynamic programming algorithm, as follows: 441) Calculate each SOC point in the terminal state space. Cost function : ； 442) Calculate each SOC point in the state space of the k-th stage. Cost function : ； In the formula, For the k-th stage, the SOC is The fuel cell output power is The resulting instantaneous costs; For the (k+1)th stage SOC point The optimal cost function value to the terminal, i.e.: ； 443) Based on the optimal cost function Solve for the corresponding optimal fuel cell output power. : ； 444) Repeat steps 441)-443) until the initial state is reached, completing the reverse optimization process of the dynamic programming algorithm. Then, through the system state equation, solve the optimal SOC and the optimal fuel cell output power sequence for each stage in the forward direction to obtain the global optimal solution of the system.

5. The step-stress type durability evaluation method for automotive fuel cell systems according to claim 4, characterized in that, The specific method for step five is as follows: 51) In the time domain, statistically analyze the number, amplitude, and duration of each decay factor in the optimal power distribution curve obtained in step four under a single target operating condition; 52) Using the fuel cell theoretical life degradation model in step three, we obtain the cumulative degradation of fuel cell voltage, the time distribution of each individual degradation factor, and the voltage degradation caused by each factor under a single target operating condition. 53) Sum the voltage decline caused by each degradation factor under urban driving conditions and suburban driving conditions respectively, so as to obtain the cumulative voltage decline under a single target condition for urban driving conditions and suburban driving conditions.

6. The step-stress type durability evaluation method for automotive fuel cell systems according to claim 1, characterized in that, The specific method for step six is ​​as follows: The specific magnitude and fluctuation of the fuel cell power calculation results obtained by the dynamic programming algorithm under the target operating condition exhibit three types of data characteristics: stable power, small-amplitude / high-frequency fluctuations based on stable power, and large-amplitude / low-frequency fluctuations based on stable power. Based on the equivalent principle of life degradation rate, the following data segment processing is performed. 61) Power feature clustering; The power and time history curves under the target operating conditions are traversed. Using power and the amplitude and frequency of power changes as feature parameters, the optimal power curves obtained in step four are clustered using the k-means clustering method. Three types of data features are obtained: the first type is the basic stable power during urban driving, small-amplitude / high-frequency load changes under basic stable power, and large-amplitude / low-frequency load changes under basic stable power; the second type is the medium stable power during suburban driving, small-amplitude / high-frequency load changes under medium stable power, and large-amplitude / low-frequency load changes under medium stable power; and the third type is the high stable power during suburban driving, small-amplitude / high-frequency load changes under high stable power, and large-amplitude / low-frequency load changes under high stable power. 2) Equivalent amplitude of basic stable power variable load; The amplitude values ​​of small / high-frequency load changes under each stable power are accumulated and used as the first type of loading data under the basic stable power. The amplitudes of large / low-frequency load change power under the basic stable power are accumulated and used as the second type of loading data; 3) Equivalent power load amplitude under medium to high stable power conditions; The amplitudes of large / low-frequency load change power under medium stable power are accumulated and used as the third type of loading data; The large / low frequency load power amplitudes under high stable power are accumulated and used as the fourth type of loading data; Based on the four types of load data, the aging degradation of fuel cells caused by load variation under different power levels at various stress levels under complete cycle conditions for fuel cell systems with large battery capacity / low power consumption, medium battery capacity / medium power consumption, and low battery capacity / high power consumption are fully preserved. Furthermore, the cumulative value of life degradation caused by power and load variation factors is equivalent to the cumulative voltage degradation calculated in step five. 4) Accelerate the construction of aging chemical conditions; For fuel cell systems with large battery capacity / low power consumption of electrical accessories, medium battery capacity / medium power consumption of electrical accessories, and low battery capacity / high power consumption of electrical accessories, accelerated aging conditions under corresponding stress are constructed so that the voltage degradation of fuel cells under a single accelerated aging condition is equal to that under a single target condition during accelerated testing. The accelerated aging process uses a square wave with a duty cycle of 50% for variable amplitude loading. Each square wave has a period of 10s. The four types of loading data correspond to four square waves. The starting power of each square wave rises corresponds to the stable power of the four types of loading data. The amplitude of each square wave corresponds to the cumulative value of the variable load power amplitude under the four types of loading data. Each acceleration aging cycle has a 5-second start and end phase, with a base stable power output. The total runtime of one acceleration aging cycle is 50 seconds, denoted by the symbol... express.

7. The step-stress type durability evaluation method for automotive fuel cell systems according to claim 1, characterized in that, The specific method for step seven is as follows: Start the fuel cell system and run it continuously in a cycle to accelerate the aging process. The running time is the actual working time per day. Then, the durability degradation is characterized by the voltage at the rated power point. Finally, the system is shut down.

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