CN116879781A - Life prediction method for electrochemical performance of solid oxide fuel cell stack - Google Patents

Abstract

The invention belongs to the technical field of solid oxide fuel cells, and specifically relates to a method for predicting the life of the electrochemical performance of solid oxide fuel cell stacks. It includes the following steps: define the failure threshold of electrochemical performance, and obtain the index requirements for the corresponding voltage attenuation rate and internal resistance growth rate; obtain the data of changes in voltage and current with operating time required for the electrochemical performance attenuation prediction model; according to the stack According to the operating parameters of the stack, a polarization curve model is established; an empirical attenuation model of the stack is established; based on the early operating status of the stack, the decay rate and attenuation acceleration of the stack are calculated; and the future of the stack is predicted based on the total attenuation amplitude defined by the stack failure threshold. decay trend and remaining life. The invention can effectively analyze the impact of four working conditions of stable operation, start-stop, load change and sudden failure on the SOFC stack voltage attenuation rate, obtain the electrochemical performance attenuation law and remaining life of the stack, and has high prediction accuracy and The advantage of wide applicability.

Description

Lifetime Prediction Method for Electrochemical Performance of Solid Oxide Fuel Cell Stacks

Technical field

The invention belongs to the technical field of solid oxide fuel cells, and specifically relates to a method for predicting the life of the electrochemical performance of solid oxide fuel cell stacks.

Background technique

The Solid Oxide Fuel Cell (SOFC) stack is an efficient and environmentally friendly energy conversion device. It has the characteristics of high efficiency, low pollution, and flexible fuel, so it has broad application prospects in the energy field. However, the electrochemical performance of SOFC gradually declines over time, which seriously restricts the promotion of its application. Due to the long life requirements of commercial applications, SOFCs need to be able to meet long-term continuous operation and multiple start-stop conditions under harsh operating conditions. However, the actual life of SOFC can usually reach thousands to tens of thousands of hours, and it requires a lot of manpower and material resources. Corresponding results cannot be obtained in a short time, which seriously hinders the progress of SOFC research and development. Therefore, it is of great significance to study the life prediction method of SOFC.

At present, many scholars have studied the life prediction method of SOFC. Among them, the method based on electrochemical performance monitoring is the most commonly used one. This method monitors the electrochemical performance of SOFC and analyzes its change patterns to predict the life of SOFC. However, the current prediction methods have many problems, such as low prediction accuracy and long test period.

Therefore, it is necessary to establish a life prediction method for the electrochemical performance of solid oxide fuel cell stacks, analyze the attenuation law and remaining life of the stack, guide the operation and maintenance of the stack, and accelerate the research and development of SOFC stacks.

Contents of the invention

The purpose of the present invention is to overcome the above-mentioned shortcomings of the prior art and provide a method for predicting the life of the electrochemical performance of a solid oxide fuel cell stack.

In order to achieve the above objects, the technical solution adopted by the present invention is:

A life prediction method for the electrochemical performance of solid oxide fuel cell stacks, including the following steps:

S0. Choose an appropriate SOFC stack life failure prediction method.

Failure prediction methods for SOFC stacks are generally divided into three categories: data-based methods (model-free methods), model-based methods and hybrid methods.

S1. Define the failure threshold of electrochemical performance attenuation according to the expected life index, and further decompose the attenuation rate under continuous operating conditions and hot and cold cycle conditions according to the failure threshold of the stack to obtain the corresponding voltage attenuation rate and internal resistance growth rate. index requirements.

The failure threshold of the SOFC stack is defined as 50% to 80%. Taking the voltage that is easiest to measure as an example, the life of the SOFC stack is considered to be terminated when the voltage of the SOFC stack decays to 50% to 80% of the initial voltage.

The attenuation rate decomposition is mainly used to monitor the attenuation state of the SOFC stack during operation. When the attenuation rate of the SOFC stack at a certain moment during operation is much higher than the above attenuation rate index, you can choose to optimize the process parameters. Reduce the attenuation rate of the stack and increase the operating life of the stack.

S2. Select appropriate SOFC stack health indicators to reflect the attenuation state of the stack during operation.

Commonly used health indicators include measuring voltage, power, electrochemical reaction area, model parameters, etc.

The SOFC stack will be affected by operating parameters such as current density during actual service. Therefore, the rated voltage operating under rated current density and rated working condition parameters is selected as the health indicator to eliminate the impact of changes in operating condition parameters on the output voltage. This reflects the true attenuation state of the stack.

S3. Use the stack to conduct continuous operation and hot and cold cycle durability tests to obtain data on changes in voltage and current with operating time required for the electrochemical performance attenuation prediction model.

Test and record the change curves of temperature, voltage and current over time, and regularly collect polarization curves and electrochemical impedance spectra during the operation of the stack, and perform data analysis.

S4. Based on the operating parameters of the stack, establish a polarization curve model to fit the test data at different times and reveal the parameters that undergo significant attenuation during the operation of the SOFC stack.

S5. Establish an empirical attenuation model of the stack, obtain the calculation formula of the voltage attenuation rate by fitting, analyze the changing trends of the voltage and internal resistance of the SOFC stack during different operating conditions, and obtain the attenuation rate and attenuation acceleration at different times.

S6. Based on the early operating status of the stack, calculate the decay rate and decay acceleration of the stack. Through continuous iteration of the equation, obtain the future rated voltage, and predict the future decay trend and remaining life of the stack based on the total attenuation amplitude defined by the failure threshold.

Further, in step S4, the polarization curve model is:

U＝E _Nernst -ηo _hm -η _act -η _c o _n (1)

In formula (1), U refers to the output voltage of the SOFC stack;

eta _hm is the ohmic loss, eta _act is the activation loss, and eta _c o _n is the concentration loss;

E _Nernst is the Nernst voltage, which refers to the highest voltage that the SOFC can output under ideal conditions with no current and no overpotential.

Further, ohmic polarization is caused by ion conduction resistance in the electrolyte and electron conduction resistance (resistance) in the electrodes. When calculating ohmic loss, it is necessary to consider the ohmic loss of four parts, namely anode, electrolyte, cathode and metal connector. The ohmic loss of each part, etao _hm, is calculated by the following formula:

ηo _hm = j·ASR (2)

In equation (2), j is the current density and ASR is the area specific resistance.

Further, the ohmic loss includes anode ohmic loss, electrolyte ohmic loss, cathode ohmic loss and metal connector ohmic loss. The calculation formula of the ohmic loss is:

η _ohm =j(ASR _anode +ASR _cathode +ASR _electrolyte +ASR _interconnect ) (3)

In formula (3), j is the current density, and ASR _anode , ASR _cathode , ASR _electrolyte and ASR _interconnect respectively represent the area specific resistance of the anode, cathode, electrolyte and metal connector.

Furthermore, the electrochemical reaction must also overcome the activation energy barrier, which is the reaction resistance. The polarization caused by this reaction resistance is called activation polarization or activation loss eta _act .

The Butler-Volmer equation is used to express the relationship between current density and activation loss, and equation (4) is used to express the activation loss eta _act :

In formula (4), j ₀ is the exchange current density of the SOFC stack in the equilibrium state; R is the gas constant in J/(mol·K), generally 8.314J/(mol·K); T is Temperature, the unit is K; n is the number of electrons transferred when a molecule of fuel undergoes an electrochemical reaction; F is Faraday's constant, the unit is C/mol, the general value is 96485C/mol;

sinh ^-1 (x) is the expression of the inverse hyperbolic sine function,

Furthermore, the electrochemical reaction of the SOFC stack occurs in the active layer of the cathode and anode, and the concentration of the reaction components in the flow channel is different from the concentration of the active layer, which will reduce the battery output, mainly reflecting its impact on E _Nernst and the reaction rate, which Part of the voltage loss is called concentration loss eta _con :

In formula (5), j _L is the limiting current density, that is, the current density when the concentration of reactants in the active layer is equal to the concentration of reactants in the flow channel; It represents the decrease in E _Nernst caused by diffusion, /> It represents the reduction in reaction rate caused by the concentration difference of the reaction components in the flow channel and the activation layer; α represents the transfer coefficient.

Further, in step S5, the operating conditions include stable operating conditions, start-stop conditions, variable load conditions and sudden failure conditions, by monitoring the polarization curve and electrochemical impedance spectrum of the SOFC stack. Analyze the impact of different operating conditions on voltage attenuation rate;

During the SOFC stack durability test, the voltage attenuation v _k is expressed as:

v _k ＝v _D +v _T ·n _T +v _V ·n _V +v _S ·n _S (6)

In equation (6), v _k is the voltage attenuation of the SOFC stack per thousand hours within k time;

Voltage attenuation under stable operating conditions: v _D represents the voltage attenuation under stable operating conditions per thousand hours, the unit is V/kh;

Voltage attenuation under start-stop conditions: v _T represents the average voltage attenuation rate caused by each start-stop condition, the unit is V/time; n _T represents the number of start-stop conditions per thousand hours, the unit is times/kh;

Voltage attenuation under variable load conditions: v _V represents the average voltage attenuation rate caused by each variable load condition, the unit is V/time; n _V represents the number of variable load conditions per thousand hours, the unit is times/kh;

Voltage attenuation under sudden fault conditions (delamination, cracking, etc.): v _S represents the average voltage attenuation rate caused by each sudden fault condition, in V/time; n _S represents bursts per thousand hours The number of critical fault conditions, unit is times/kh;

Calculate the proportion of attenuation caused by the four operating conditions based on the actual test results, and thereby calculate the expected target attenuation rate under various corresponding operating conditions.

Further, the calculation formula of voltage attenuation rate v _D′ under stable operating conditions:

In formula (7), v _D′ represents the voltage attenuation rate of the SOFC stack per thousand hours of stable operation, in %/kh; U _f represents the fuel utilization rate under stable operating conditions, in %; T represents the stack The average internal temperature, the unit is K; j represents the current density under stable operating conditions, the unit is A·cm ^-2 .

Furthermore, the attenuation changes in voltage and internal resistance in the polarization curve test results of SOFC are consistent with the trend of quadratic functions. Therefore, the stack empirical attenuation model calculation formula is established:

In equation (8), α ₀ is the change amount at the initial moment, v is the decay rate, t is the running time, and a is the decay acceleration.

Further, in step S6, the health status of the SOFC stack at different times is N = [av α] ^T , the current time is defined as k, and the future decay trend of the SOFC stack is predicted based on the information at time k and before time k. , the health state at time k is expressed as N _k =[ _ak v _k α _k ] ^T .

When evaluating the state of the SOFC stack, the decay state α _k , decay rate v _k and decay acceleration a _k at time k are calculated by calculating the information at time k and before time k.

When predicting the attenuation trend of the SOFC stack, through the iterative stack empirical attenuation model calculation formula (8), the attenuation state α _k at time k can be obtained from the attenuation state α k at time k _{+ t} , and further k+ Rated voltage at time t Finally, the remaining service life of the SOFC stack is obtained.

In step S6, if the SOFC stack has been in stable operating conditions during operation, the operating conditions of the SOFC stack and its auxiliary systems will not fluctuate, and the voltage value of the SOFC stack will attenuate by v _k over a long period of time. If the amount is reduced, the predicted life T _f of the SOFC stack can be calculated through equation (9):

In equation (9), T _f is the predicted life of the SOFC stack, ΔU is the attenuation amplitude, v _k is the voltage attenuation of the SOFC stack per thousand hours at time k, and K _p is the actual operating life of the SOFC stack and Scale factor for laboratory simulation test life.

Furthermore, the remaining service life prediction process of the SOFC stack is:

① Obtain the rated voltage of the SOFC stack at the initial moment The failure threshold coefficient m of SOFC stack attenuation is defined according to the expected life index, which is generally 0.5 to 0.8.

② Conduct a durability test on the SOFC stack to obtain polarization curves and electrochemical impedance spectrum data at different times. When the average open circuit voltage of the chip is lower than 1.10V, detect whether the SOFC stack is cracked or leaking. When the average open circuit voltage of the chip is When it is not less than 1.10V, establish a polarization curve model and extract the attenuation state characteristic parameters.

③ Determine the attenuation state α _k and obtain the attenuation rate v _k and attenuation acceleration a _k . If the attenuation acceleration a _k is less than or equal to 0, then the remaining service life of the SOFC stack RUL = unknown; if the attenuation acceleration a _k is greater than 0, continue Next step.

④According to the polarization curve model (1) and voltage empirical attenuation model calculation formula (8), obtain the rated voltage at k+t time

⑤If Less than or equal to m, then the remaining service life of the SOFC stack RUL=k+t; if/> is greater than m, then according to t=t+1,/> Repeat step ④.

Compared with the prior art, the beneficial technical effects of the present invention are:

This invention analyzes the impact of the SOFC stack on the voltage attenuation rate under four working conditions: stable operating conditions, start-stop conditions, variable load conditions and sudden failure conditions, and obtains the performance of the SOFC stack under different working conditions. The decay rate and decay acceleration under different conditions can be used to predict the decay trend and degree of the SOFC stack under different operating conditions.

(1) High prediction accuracy: The present invention uses polarization curves, electrochemical impedance spectroscopy and other electrochemical performance parameters for comprehensive analysis, and can obtain high-precision electrochemical data of the SOFC stack. Establish a polarization curve model based on the operating parameters of the stack to predict the trend and degree of electrochemical performance degradation of the SOFC stack, and accurately predict the decay trend and remaining life.

(2) Short test cycle: The present invention adopts online monitoring technology to monitor the electrochemical performance of the SOFC stack in real time, thereby improving the prediction accuracy and test efficiency, and reducing test costs and time costs.

(3) Wide applicability: The present invention is suitable for various types and specifications of SOFC stacks, can predict SOFC stacks with different electrochemical performance attenuation laws, and has broad application prospects.

Description of the drawings

The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

Figure 1 is a schematic flow diagram of the present invention;

Figure 2 is a schematic diagram of the change curve of the actual voltage and the rated voltage of the SOFC stack in the present invention during continuous operation;

Figure 3 is a flow chart for predicting the remaining service life of the SOFC stack of the present invention;

Figure 4 is a voltage change curve diagram of the constant current discharge of the SOFC stack in Example 1 during 6 hot and cold cycles;

Figure 5 is a polarization curve diagram of the SOFC stack in Example 1 during 6 hot and cold cycles;

Figure 6 is a diagram showing changes in the internal resistance of the SOFC stack in Example 1 during six hot and cold cycles.

Detailed ways

The expected life index requirements of a certain project for SOFC stacks are expected life ≥ 80,000 hours, and expected number of hot and cold cycles ≥ 100 times (5 cold starts from 750°C to room temperature, 95 hot starts from 750°C to room temperature).

Therefore, a life prediction method for the electrochemical performance of a solid oxide fuel cell stack provided by the present invention is used to analyze its voltage decay rate and expected life. Referring to Figure 1, the specific steps are as follows:

Step S0: Select a data-based and model-based hybrid method to predict the life of the SOFC stack. The hybrid method is mainly established based on the SOFC decay mechanism and combines experimental data to determine the parameters in the model.

Step S1: Define the failure threshold of voltage attenuation as 50% based on the expected life indicators "predicted value of stack life ≥ 80000h" and "predicted value of stack hot and cold cycles ≥ 100 times", and determine continuous operation based on the failure threshold of the stack The attenuation rate under working conditions and hot and cold cycle conditions is further decomposed, and the corresponding index requirements for voltage attenuation rate and internal resistance growth rate are obtained.

Continuous and stable operating conditions: Under operating conditions of 750°C and current density 0.3A·cm ^-2 , the average attenuation rate per 1,000 hours is ≤18mΩ·cm ² and the attenuation rate deviation is ≤3mΩ·cm ² ; that is, the average chip voltage Attenuation rate ≤5.3mV/kh or average voltage attenuation rate ≤0.62%/kh;

Hot and cold cycle service conditions: (1) 95 hot starts (200~750℃): At a current density of 0.3A·cm ^-2 , the average attenuation rate of each hot and cold cycle is ≤13mΩ·cm ² and the attenuation rate deviation is ≤ 3mΩ·cm ² ; that is, the average voltage attenuation rate of the chip is ≤ 4mV/time or the average voltage attenuation rate is ≤ 0.47%/time; (2) 5 hot starts (room temperature ~ 750℃): at a current density of 0.3A·cm ^-2 , The average attenuation rate of each hot and cold cycle is ≤30mΩ·cm ² and the attenuation rate deviation is ≤3mΩ·cm ² ; that is, the average voltage attenuation rate of the chip is ≤9.0mV/time or the average voltage attenuation rate is ≤1%/time.

In step S1, the attenuation rate decomposition is mainly used to monitor the attenuation state of the SOFC stack during operation. When the attenuation rate of the SOFC stack at a certain moment during operation is much higher than the above attenuation rate index, you can choose to The process parameters are optimized to reduce the attenuation rate of the stack and improve the operating life of the stack.

Step S2: Select the rated voltage operating under rated current density and working condition parameters as the health indicator of the SOFC stack to eliminate the impact of changes in current density and working condition parameters on the output voltage, thereby reflecting the true attenuation state of the stack. The change curve of the actual voltage and the rated voltage of the SOFC stack during continuous operation is shown in Figure 2.

Step S3: Use a SOFC short stack composed of 4 ^cells with an electrode area of 10×10cm2 to conduct continuous operation and hot and cold cycle durability tests to obtain the data of voltage and current running over time required by the electrochemical performance attenuation prediction model. .

In step S3, the temperature, voltage and current change curves with time are tested and recorded, and the polarization curve and electrochemical impedance spectrum during the operation of the stack are collected every 100 hours or after each hot and cold cycle, and data analysis is performed.

Step S4: Based on the operating parameters of the stack, establish a polarization curve model to fit the test data at different times and reveal the parameter with the largest attenuation rate among the two parameters of voltage and internal resistance during the operation of the SOFC stack;

Step S5: Establish the empirical attenuation model of the stack, obtain the calculation formula of the voltage attenuation rate by fitting, and analyze the voltage and internal resistance of the SOFC stack under different operating conditions (stable operating conditions, start-stop conditions, and variable load conditions) and sudden fault conditions) to obtain the attenuation rate and attenuation acceleration at different times.

Step S6: Calculate the decay rate and decay acceleration of the stack based on the early operating status of the stack, obtain the future rated voltage through continuous iteration of the equation, and predict the future decay trend and remaining life of the stack based on the total attenuation amplitude defined by the failure threshold. .

During the SOFC durability test, polarization curves were collected at different times, and the following polarization curve model was used to fit the test data at different times:

U＝E _Nernst -η _ohm -η _act -η _con (10)

In equation (10), U refers to the output voltage of the SOFC stack;

eta _ohm is the ohmic loss, eta _act is the activation loss, and eta _con is the concentration loss; E _Nernst is the Nernst voltage, which refers to the direction of the SOFC under ideal conditions with no current and no overpotential. The highest voltage that can be output externally.

In equation (10), the losses of each part are divided into ohmic loss eta _ohm , activation loss eta _act , and concentration loss eta _con according to the cause. Since ohmic polarization complies with Ohm's law and is easy to calculate and analyze during the operation of the SOFC stack , so in this embodiment, the ohmic loss is mainly analyzed in detail.

Ohmic losses are caused by the ion conduction resistance in the electrolyte and the electron conduction resistance (resistance) in the electrodes. When calculating ohmic loss, four parts of ohmic loss need to be considered, namely anode, electrolyte, cathode and metal connector. The ohmic loss of each part is calculated by the following formula:

_ηohm ＝j·ASR (11)

In equation (11), j is the current density, ASR is the area specific resistance, which is defined as L is the thickness, and σ is the conductivity. The ASR of each battery structure is the sum of the ASR of each part, then the ohmic loss of each battery structure is:

η _ohm =j(ASR _anode +ASR _cathode +ASR _electrolyte +ASR _interconnect ) (12)

In formula (12), ASR _anode , ASR _cathode , ASR _electrolyte and ASR _interconnect respectively represent the area specific resistance of the anode, cathode, electrolyte and metal connector.

The anode material is Ni/YSZ. The general relationship between the area specific resistance ASR _anode of the anode material and temperature is as follows:

The cathode material is LSC, and the general relationship between the area specific resistance ASR _cathode of the cathode material and temperature is:

The electrolyte material is YSZ. The general relationship between the area specific resistance ASR _electrolyte and temperature of the electrolyte is as follows:

The metal connector material is 430 ferritic stainless steel. The general relationship between the area specific resistance ASR _interc o _nnect of the metal connector material and temperature is as follows:

At 750°C, the area specific resistances of the anode, electrolyte, cathode and metal connector are 5.347E-08Ω·cm ² , 0.092Ω·cm ² , 0.002Ω·cm ² and 0.023Ω·cm ² respectively. The total area ratio The resistance is 0.118Ω·cm ² . The ohmic losses of the anode, electrolyte, cathode and metal connector at 0.3A·cm ^-2 are 1.604E-08V, 0.028V, 0.001V and 0.007V respectively, and the total ohmic loss is 0.036V.

In step S5, according to the polarization curve test results, it is found that the internal resistance R increased significantly during the durability test. Define α(t) as the attenuation change at time t, then R(t) can be written as:

R(t)＝R ₀ ·(1+α(t)) (17)

In equation (17), R ₀ is the value of the internal resistance R at the initial moment.

In the SOFC polarization curve test results, the attenuation change amount α(t) of voltage and internal resistance conforms to the trend of a quadratic function. Therefore, an empirical attenuation model of the SOFC stack is established:

In equation (18), α ₀ is the attenuation change amount at the initial moment, v is the attenuation rate, t is the running time, and a is the attenuation acceleration.

In step S6, the health status of the SOFC stack at different times is N = [aνα] ^T , the current time is defined as k, and the future decay trend of the SOFC stack is predicted based on the information at time k and before time k. The health state at time k is N _k = [ak _{ν k} α _k ] ^T to predict the future attenuation trend. The remaining service life prediction process of the SOFC stack is shown in Figure 3.

When evaluating the state of the SOFC stack, the decay state α _k , decay rate ν _k and decay acceleration a _k at time k are calculated by calculating the information at time k and before time k.

Subsequently, when predicting the attenuation trend of the SOFC stack, through the iterative stack empirical attenuation model calculation formula (18), the attenuation state α _k at time k can be obtained from the attenuation state α k at time k ₊ t, and further k + t can be obtained rated voltage at time Finally, the remaining service life of the SOFC stack is obtained.

Example 1

Six hot and cold cycle durability tests were conducted using a SOFC short stack composed of four cells with an electrode area of 10× ^10cm2 . During each hot and cold cycle test, when the stack is heated up and reduced, polarization curves and electrochemical impedance spectroscopy tests are performed. During the test of the polarization curve, the current density was set to gradually load from 0mA/cm ² to 450mA/cm ² , and then the electrochemical impedance spectrum was tested. After the test was completed, the SOFC stack was set to operate under a load of 300mA/cm ² Constant current 24h operation.

By monitoring the polarization curve and electrochemical impedance spectrum of SOFC, the impact of different operating conditions (stable operating conditions, start-up and stop conditions, variable load conditions and sudden fault conditions) on the voltage attenuation rate is analyzed. Calculate the proportion of attenuation caused by the four working conditions based on the actual test results, and thereby calculate the expected target attenuation rate under various corresponding working conditions.

The output voltage variation curve of the constant current discharge during six hot and cold cycles of the SOFC stack in Example 1 is shown in Figure 4. In Example 1, the output voltage at the initial moment of constant current operation of the SOFC stack at a current density of 300 mA/cm ² is 3.628 V, and this output voltage is set as the first output voltage.

Voltage attenuation rate under stable operating conditions: As shown in Figure 4, the voltage attenuation rate under stable operating conditions mainly refers to the change rate of the output voltage before and after constant current operation for 24 hours at a current density of 300mA/ ^cm2 , that is, constant current operation. The rate of change of the voltage at the end moment and the voltage at the initial moment of constant current operation. In Example 1, the voltage attenuation after six times of constant current operation for 24 hours was 0.167V, 0.038V, 0.007V, 0.063V, 0.075V and 0.038V respectively. Compared with the first output voltage of 3.628V, the voltage each time The attenuation rates are 4.603%, 1.047%, 0.193%, 1.736%, 2.067% and 1.047% respectively. The total voltage attenuation rate caused by stable operating conditions is 9.647%, and the average voltage attenuation rate each time is 1.609%.

Voltage attenuation rate under start-stop conditions: The voltage attenuation rate under start-stop conditions mainly refers to the rate of change of the voltage at the initial moment of each constant current operation compared to the voltage at the end of the last constant current operation. Specifically analyzing Figure 4, it can be seen that the voltage attenuation caused by the six start-stop conditions in Example 1 is -0.075V, 0.178V, 0.089V, 0.045V and -0.080V respectively. The total voltage attenuation under six cycles is 0.157V. Compared with the first output voltage of 3.628V, the voltage attenuation rates each time are -2.067%, 4.906%, 2.453%, 1.240% and -2.205% respectively. The total voltage attenuation rate caused by start-stop conditions is 4.327%, and the average voltage attenuation rate caused by each start-stop condition is 0.865%.

Voltage attenuation rate under variable load conditions: During the polarization curve test of the hot and cold cycle durability test, the current density gradually increased from 0mA/cm ² to 450mA/cm ² , and the load of the SOFC stack continued to change. Therefore, the voltage change rate of the SOFC stack between the polarization curve test and the initial moment of constant current operation is the voltage attenuation rate caused by variable load conditions. The polarization curve of the SOFC stack in Example 1 during six hot and cold cycles is shown in Figure 5. Specific analysis can be obtained: During the six polarization curve tests, the SOFC stack was at a current density of 300 mA/cm ² The voltages are 3.632V, 3.604V, 3.360V, 3.300V, 3.224V and 3.188V respectively. At the initial moment of each constant current operation, the initial voltages of the SOFC stack are 3.628V, 3.536V, 3.320V, 3.224V, 3.116V and 3.121V respectively. The voltage attenuation caused by variable load conditions are 0.004V, 0.068V, 0.040V, 0.076V, 0.108V and 0.067V respectively. Compared with the first output voltage of 3.628V, the voltage attenuation rates caused by variable load conditions are respectively are 0.110%, 1.874%, 1.103%, 2.095%, 2.977% and 1.847%.

Voltage attenuation rate caused by sudden fault conditions: During the hot and cold cycle durability test, the SOFC short stack did not suffer from sudden faults such as cracking or air leakage, and it operated at a constant current at a current density of 300mA/ ^cm2 . There were no accidents such as gas outage or power outage. Therefore, in this embodiment, the voltage attenuation rate caused by sudden fault conditions can be ignored.

In addition, during the durability test of the SOFC stack for six hot and cold cycles, the internal resistance changes in the open circuit state are shown in Figure 6. The internal resistance change curve overall meets the trend of the quadratic function image, which also verifies the SOFC's The attenuation changes in voltage and internal resistance in the polarization curve test results are consistent with the trend of quadratic functions, so the SOFC stack empirical attenuation model in equation (18) is established.

Example 2

Based on literature research and preliminary testing, 7 sets of experimental data on continuous and stable operation of the stack under different test conditions were obtained, and the voltage attenuation rate of the SOFC stack under different operating conditions was analyzed.

The predicted value of the voltage attenuation rate is calculated using equation (7). Furthermore, the expected life T _f of the SOFC stack is calculated using equation (9). The failure threshold is defined as 50%. When the SOFC stack voltage decays to 50% of the initial voltage, Considered to be end of life. When the initial state voltage of a single cell is 0.85V at a current density of 0.3A/ ^cm2 , the total attenuation amplitude of the single cell voltage is 0.425V, and the average voltage attenuation rate of the single cell is 5.313mV/kh. K _p is the proportional factor between the actual operating life of the SOFC stack and the laboratory simulation test life, and the value is 1.260. The predicted voltage attenuation rate and expected life of the SOFC stack under seven different working conditions are shown in Table 1.

By analyzing Table 1, it can be found that by comparing with the actual value of the voltage attenuation rate of the SOFC stack, it is verified that the calculation formula of the voltage attenuation rate v _D (t) under stable operating conditions in equation (7) can be better predicted Voltage decay rate of SOFC stack under different temperatures, different current densities and different fuel utilization rates.

Table 1 Voltage decay rate and life prediction for stable operation of SOFC stack under different operating conditions

Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by those skilled in the art within the essential scope of the present invention should also fall within the scope of the present invention. protection scope of the invention.

Claims (10)

1. A method for predicting the life of the electrochemical performance of a solid oxide fuel cell stack, comprising the steps of:

s0, selecting a SOFC stack life failure prediction method;

s1, defining an failure threshold value of electrochemical performance attenuation according to an expected life index, and further decomposing attenuation rates of a continuous operation working condition and a cold and hot circulation working condition according to the failure threshold value of a galvanic pile to obtain index requirements of corresponding voltage attenuation rates and internal resistance increase rates;

s2, selecting SOFC electric pile health indexes, and reflecting attenuation states in the electric pile operation process;

s3, performing continuous operation and cold and hot circulation durability test by using a galvanic pile, and obtaining the change data of voltage and current required by an electrochemical performance attenuation prediction model along with operation time;

s4, establishing a polarization curve model according to the operation parameters of the electric pile, and fitting test data at different moments to reveal the parameter with the maximum attenuation rate in the operation process of the SOFC electric pile;

s5, establishing an empirical attenuation model of the electric pile, fitting to obtain a calculation formula of a voltage attenuation rate, analyzing the variation trend of the voltage and the internal resistance of the SOFC electric pile in different operation working conditions, and obtaining attenuation rates and attenuation accelerations at different moments;

s6, according to the early-stage running state of the electric pile, calculating the attenuation rate and the attenuation acceleration of the electric pile, obtaining the future rated voltage through continuous iteration equations, and predicting the future attenuation trend and the residual life of the SOFC electric pile according to the total attenuation amplitude defined by the failure threshold.

2. The method for predicting the life of the electrochemical performance of a solid oxide fuel cell stack according to claim 1, wherein in step S4, the polarization curve model is: u=e _Nernst -η _ohm -η _act -η _con (1)

In formula (1), U refers to the output voltage of the SOFC stack;

η _ohm is ohmic loss, eta _act Is the activation loss, eta _con Is the concentration loss;

E _Nernst is the nernst voltage, which refers to the highest voltage that the SOFC can output outwards under ideal conditions without current, without overpotential.

3. The method for predicting the life of an electrochemical performance of a solid oxide fuel cell stack of claim 2, wherein the ohmic losses include an anode ohmic loss, an electrolyte ohmic loss, a cathode ohmic loss, and a metal-interconnect ohmic loss, the ohmic losses having a calculation formula:

η _ohm ＝j(ASR _anode +ASR _cathode +ASR _electrolyte +ASR _interconnect ) (3)

in formula (3), j is current density, ASR _anode 、ASR _cathode 、ASR _electrolyte And ASR _interconnect The area specific resistances of the anode, cathode, electrolyte and metal connection are shown, respectively.

4. The method for predicting the life of electrochemical performance of a solid oxide fuel cell stack according to claim 3, wherein the relation between the current density and the activation loss is expressed by using a Butler-Volmer equation, and the activation loss η is expressed by using the formula (4) _act ：

In formula (4), j ₀ The exchange current density of the SOFC stack in the balance state; r is a gas constant; t is the temperature; n is the number of electrons transferred when one molecule of fuel undergoes electrochemical reaction; f is Faraday constant;

sinh ^-1 (x) Is an expression of an anti-hyperbolic sine function,

5. the method for predicting electrochemical performance life of solid oxide fuel cell stack as recited in claim 4, wherein electrochemical reaction of the SOFC stack occurs in the active layers of the cathode and anode, and the difference in concentration of the reactant components and the active layer in the flow channels reduces the cell output, reflecting the difference in concentration to E _Nernst And the reaction rate, this portion of the voltage loss is called concentration loss eta _con ：

In formula (5), j _L Is the limiting current density, i.e. the current density at which the active layer reactant concentration is equal to the reactant concentration in the flow channels;indicating that diffusion results in E _Nernst Is decreased (1)>Indicating that the concentration difference of the reaction components in the flow channel and the activation layer leads to the reduction of the reaction rate; alpha is denoted as the transfer coefficient.

6. The method for predicting the life of electrochemical performance of a solid oxide fuel cell stack according to claim 5, wherein in step S5, the operation conditions include a stable operation condition, a start-stop condition, a load-change condition and a sudden fault condition, and the influences of different operation conditions on the voltage decay rate are analyzed by monitoring the polarization curve and the electrochemical impedance spectrum of the SOFC stack;

voltage attenuation v during durability test of SOFC stack _k Expressed as:

v _k ＝v _D +v _T ·n _T +v _V ·n _V +v _S ·n _S (6)

in formula (6), v _k The voltage attenuation amount of the SOFC stack is equal to the voltage attenuation amount of the SOFC stack in every thousand hours within the k moment;

voltage attenuation for stable operation conditions: v _D Representing the voltage attenuation amount under the stable operation condition every thousand hours;

voltage attenuation of start-stop condition: v _T Represents the average voltage decay rate, n, caused by each start-up and shut-down condition _T The times of starting and stopping working conditions in thousands of hours are represented;

voltage attenuation of variable load condition: v _V Represents the average voltage decay rate, n, caused by each load-changing working condition _V The times of load changing working conditions in thousands of hours are represented;

voltage attenuation of sudden fault condition: v _S Represents the average voltage decay rate, n, caused by each sudden fault condition _S The number of sudden fault conditions per thousand hours is represented;

and calculating the proportion of the voltage attenuation caused by the four operating conditions according to the actual test result, thereby calculating the expected target attenuation rate under the corresponding various operating conditions.

7. The method for predicting electrochemical performance life of a solid oxide fuel cell stack of claim 6, wherein the voltage decay rate v under steady operation conditions _D， Is calculated according to the formula:

in formula (7), v _D′ The voltage attenuation rate of the SOFC stack is expressed as per thousand hours of stable operation, U _f The fuel utilization rate under the stable working condition is represented by T, the average temperature inside the electric pile is represented by T, and the current density under the stable working condition is represented by j.

8. The life prediction method of electrochemical performance of a solid oxide fuel cell stack according to claim 7, wherein the attenuation change amounts of voltage and internal resistance in the result of the polarization curve test of the SOFC stack conform to the trend of a quadratic function, so that a calculation formula of an empirical attenuation model of the stack is established:

in formula (8), α ₀ V is the decay rate, t is the run time, and a is the decay acceleration, which is the change in the initial time.

9. The method for predicting the life of electrochemical performance of a solid oxide fuel cell stack according to claim 8, wherein in step S6, the SOFC stack is in a health state n= [ aνα ] at different times] ^T Defining the current moment as k, predicting the future attenuation trend of the SOFC stack according to the k moment and the information before the k moment, wherein the health state at the k moment is expressed as N _k ＝[a _k ν _k α _k ] ^T ；

In evaluating the state of the SOFC stack, the decay state α at time k _k Rate of decay v _k And damping acceleration a _k The information at and before the k moment is calculated;

in predicting the attenuation trend of the SOFC electric pile, an empirical attenuation model calculation formula (8) of the electric pile is iterated, and the attenuation state alpha at the moment k is calculated _k Obtaining attenuation state alpha at k+t time _k+t Further obtain the rated voltage at the time of k+tFinally obtaining the residual service life of the SOFC stack;

in step S6, if the SOFC stack is always in a stable operation condition during operation, the SOFC stack and its auxiliary system conditions do not fluctuate, and the voltage value of the SOFC stack is v in a long time _k If the attenuation of (2) is reduced, calculating the predicted lifetime of the SOFC stack by the formula (9)Life T _f ：

In formula (9), T _f For the predicted lifetime of SOFC stacks, ΔU is the decay amplitude, v _k For the voltage attenuation quantity of the SOFC stack per thousand hours in the K moment, K _p The scale factor of the actual operation life of the SOFC stack and the laboratory simulation test life is used.

10. The method for predicting the life of the electrochemical performance of a solid oxide fuel cell stack according to claim 9, wherein the residual life prediction process of the SOFC stack is as follows:

(1) obtaining rated voltage of SOFC electric pile at initial timeDefining a failure threshold coefficient m of SOFC stack attenuation according to the life expectancy index;

(2) performing durability test on the SOFC stack to obtain polarization curve and electrochemical impedance spectrum data at different moments, detecting whether the SOFC stack is cracked or sealed and leaked when the average open-circuit voltage is lower than 1.10V, and establishing a polarization curve model when the average open-circuit voltage is not lower than 1.10V to extract attenuation state characteristic parameters;

(3) determining attenuation state alpha _k Obtaining the attenuation rate v _k And damping acceleration a _k If the acceleration a is attenuated _k If the service life is less than or equal to 0, the residual service life RUL of the SOFC stack is unknown; if the acceleration a is attenuated _k If the value is more than 0, continuing to carry out the next step;

(4) obtaining rated voltage at k+t time according to a polarization curve model (1) and a pile empirical attenuation model calculation formula (8)(5) If->M is smaller than or equal to m, and the residual service life RUL=k+t of the SOFC stack;

if it isGreater than m, then according to t=t+1, -/->And (5) repeating the step (4).