A method for predicting the residual life of a kilowatt-class solid oxide fuel cell stack

Abstract

The application discloses a kind of kilowatt solid oxide fuel cell stack residual life prediction methods, steps are as follows: by the test of starting, loading and continuous running of electric pile, obtain voltage, current, power data;Using optimization algorithm, based on the experimental data obtained, the SOFC electrochemical model containing six key unknown parameters is parameter identification, to determine model parameters;Build and initialize a homogeneous solid oxide fuel cell multi-physical field coupling model considering multiple attenuation mechanisms to predict the attenuation curve of the voltage of the electric pile with time;The residual life of the electric pile is determined based on the predicted voltage attenuation curve.The application does not need complex electrochemical test and a large number of historical data, only needs limited experimental data to realize parameter fast identification, greatly reduces the calculation cost by homogenization modeling, provides efficient and accurate life prediction means for the engineering application of SOFC electric pile.

Description

Technical Field

[0001] This invention belongs to the field of battery stack lifetime prediction technology, specifically relating to a method for predicting the remaining lifetime of a kilowatt-level solid oxide fuel cell stack. Background Technology

[0002] As a clean energy source with immense commercial potential, solid oxide fuel cells (SOFCs) have become a focal point for researchers in the energy field, prompting them to continuously pursue cost-effective and accurate modeling techniques. However, due to the complex chemical and electrical processes involved in SOFC modeling, which result in highly nonlinear properties, it is difficult to accurately predict SOFC characteristics. Therefore, accurate mathematical models are crucial for evaluating SOFC performance and optimizing its design under various conditions. SOFC mathematical models are characterized by multivariate and multimodal complexity, containing several interdependent unknown parameters that significantly affect output performance; even small changes can have substantial impacts. Obtaining these parameters within the fuel cell stack is extremely difficult. Therefore, establishing a parameter optimization and identification method that can operate effectively under different operating conditions, along with an efficient SOFC lifetime prediction model built based on these parameters, is of great significance for advancing SOFC stack lifetime prediction technology. Summary of the Invention

[0003] To address the aforementioned problems in existing technologies, this invention proposes a method for predicting the remaining life of kilowatt-level solid oxide fuel cell stacks. This method is rationally designed, overcomes the shortcomings of existing technologies, and has good results.

[0004] To achieve the above objectives, the present invention adopts the following technical solution: A method for predicting the remaining lifetime of a kilowatt-class solid oxide fuel cell stack includes the following steps: Step 1: Obtain voltage, current, and power data through fuel cell stack startup, loading, and continuous operation tests; Step 2: Using optimization algorithms, based on the experimental data obtained in Step 1, perform parameter identification on the SOFC electrochemical model containing six key unknown parameters, and determine the model parameters. Step 3: Construct and initialize a multiphysics coupled model of a homogenized solid oxide fuel cell that considers multiple decay mechanisms to predict the decay curve of the stack voltage over time; Step 4: Determine the remaining lifetime of the fuel cell stack based on the predicted voltage decay curve.

[0005] Further, step 1 specifically involves: first, heating the fuel cell stack by passing nitrogen gas through the anode and air through the cathode, raising the temperature from room temperature to 700°C at a rate of 1°C / min, and holding it until the temperature stabilizes; then applying a stepped current load, starting from 0A, increasing the current by 1A each time and holding for 3 minutes, until the output power of the fuel cell stack exceeds the output power during normal operation; next, decreasing the current by 0.5A each time and holding for 1 minute, until the output power of the fuel cell stack reaches the output power during normal operation, recording the corresponding current, voltage, and power data throughout the process; then maintaining a constant output current to ensure continuous and stable operation of the fuel cell stack, and continuously recording the voltage, current, and power data generated during operation.

[0006] Furthermore, in step 2, the output voltage of the electrochemical model The expression is: (1); in, This indicates the number of batteries in the fuel cell stack. Indicates open-circuit voltage. Indicates the Tafel slope, and These represent the exchange current densities at the anode and cathode, respectively. This represents the resistivity per unit area, where B is the empirical coefficient for concentration loss. The limiting current density; This represents the load current at the k-th data point. Must meet: ; The six key location parameters that need to be identified constitute the decision vector. The objective of parameter identification is to minimize the difference between the model-calculated voltage and the actual measured voltage. The objective function is... Mean squared error: (2); in, The voltage at the k-th data point measured in the experiment is represented by , and n represents the total number of experimental data points.

[0007] Furthermore, an optimization algorithm is used to optimize the objective function, specifically including: Step 2.1: Randomly generate the potential solution set during algorithm initialization. , that is, the initial population, in which the first The first of the individuals Parameters It is generated by the following formula: (3); in and Indicates the lower and upper limits of the parameter. A vector representing random values ​​uniformly distributed between 0 and 1; Step 2.2: For each iteration t, calculate the population for each individual. fitness value Select the individual with the best fitness. ; Step 2.3: Establish a reward and punishment mechanism. The punishment mechanism is shown in formulas (4)-(7), and the reward mechanism is shown in formula (8). (4); (5); (6); (7); (8); in, and These represent the penalty and reward factors, respectively, with C and D representing the penalty coefficients. Indicates a decreasing control parameter. Indicates the number of iterations. Indicates the maximum number of iterations. Represents a random value that is uniformly distributed between 0 and 1; Step 2.4: In the initial stage of optimization, the parameters are randomly explored across all possible value ranges. When the penalty factor is ≥1, the parameters are forced to update their positions. This stage is the migration stage, in which position updates are performed using formulas (9)-(11). When the penalty factor is less than 1, the parameters are explored in a more refined manner in the region where they perform well. This stage is the development stage, in which the parameters are developed using formulas (12)-(15). (9); (10); (11); in, This indicates the new location after the migration phase. It is the first The parameter along the first The current coordinates of the dimension, and step represents the iteration step size of the parameters. , To randomly select the boundary between the maximum and minimum values ​​of a new region, A random number in the range 0 to 1; (12); (13); (14); (15); in, This indicates the new location after the development phase update. This represents the globally optimal parameter combination that minimizes the objective function value in the t-th iteration. This represents the second-best parameter combination that ranks second in objective function value in the t-th iteration. Indicates the migration step length. An angular parameter representing aggregation behavior. Represents a random value that is uniformly distributed between 0 and 1; Step 2.5: After the iteration is completed, the parameters represented by the globally optimal individual output in the last iteration are taken as the final identification result.

[0008] Further, in step 3, the construction of the multiphysics coupling model of the homogenized solid oxide fuel cell includes: In COMSOL software, the fuel cell stack is geometrically modeled and homogenized to obtain a homogenized fuel cell stack geometric model. The equivalent material parameters of each homogenized region in the model are calculated and input into the model as material properties. Based on the geometric model of the homogenized fuel cell stack, a set of control equations describing fluid flow, mass transfer, heat transfer, charge transfer and electrochemical reaction is set. The six key parameters identified in step 2 are used as initial parameter values ​​and input into the set of control equations to form the multiphysics coupling model of the homogenized solid oxide fuel cell. Three attenuation sub-models are coupled in the multiphysics coupling model: the anode nickel particle coarsening attenuation model, the cathode chromium deposition attenuation model, and the connector oxidation attenuation model. The anode nickel particle coarsening attenuation model is used to update the anode conductivity parameter in real time. The cathode chromium deposition attenuation model is used to update the effective three-phase interface length parameter of the cathode in real time. The connector oxidation attenuation model is used to update the areal resistivity parameter of the connector region in real time.

[0009] Furthermore, the homogenization process specifically includes: The SOFC anode and cathode channels, manifold, and PEN unit are homogenized to be equivalent to a porous medium with anisotropic material properties. The equivalent material parameters of a uniform PEN element are calculated using the equivalent volume method: (13); in, For equivalent material parameters, For dense material parameters, For volume; The equivalent thermal conductivity of a uniform PEN element is calculated using the equivalent thermal resistance method: (14); in, This represents the equivalent thermal conductivity of a uniform PEN element in the x, y, and z directions. This represents the cross-sectional area of ​​a uniform PEN cell in which heat is transferred along the x, y, and z directions. This represents the distance that heat is transferred in the x, y, and z directions within a uniform PEN cell. For type number, =1 indicates the anode. =2 indicates an electrolyte. =3 indicates the cathode; Total number of types; These represent the thermal conductivity of the anode, cathode, and electrolyte in the x, y, and z directions, respectively. These represent the cross-sectional areas of the anode, cathode, and electrolyte, respectively, in the x, y, and z directions. These represent the distances in the x, y, and z directions from which heat is transferred between the anode, cathode, or electrolyte; Calculate the permeability of a uniform PEN cell using Darcy's law: (15); in, The pressure drop of the fluid along the flow direction. The fluid pressure drop along the flow direction. Let be the geometric length of the flow channel. Darcy's coefficient of friction. For fluid density, For fluid velocity, The hydraulic diameter, For penetration rate, This represents the fluid viscosity.

[0010] Furthermore, the anode nickel coarsening attenuation model characterizes the average radius of nickel particles using the following formula. Growth trend: (16); in, Indicates temperature. Indicates runtime. Indicates the volume fraction of nickel. Indicates the volume fraction of the ceramic phase. This represents the initial average radius of the nickel particles. This represents the average radius of the initial ceramic phase particles. The average particle coordination number is expressed as: (17); in, Represents the coordination number between ceramic phase particles; Will and Substituting into formula (18), the permeation threshold of Ni particles in the anode is solved. ; (18); in, The average diameter of ceramic phase particles; Anode conductivity : (19); In the formula, Indicates the intrinsic conductivity of the anode material. This represents the volume fraction of the porous anode material. The penetration threshold of Ni particles at the anode; The cathode chromium deposition attenuation model characterizes the reduction in the three-phase interface length using the following equation: (20); in, Indicates the effective three-phase interface length. Denotes Faraday's constant. Indicates the maximum height of the three-phase interface. The chromium deposition reaction rate is expressed as: (twenty one); In the formula, This represents the exchange current density of chromium oxidation. Indicating the cathode electrode mole fraction, This indicates the mole fraction of water vapor in the cathode electrode. Represents the universal gas constant. Indicates the cathode concentration overpotential; The linker oxidation attenuation model calculates the chromium oxide layer thickness growth using the following formula: (twenty two); in, This represents the rate constant of weight gain of the oxide scale. Indicates the activation energy of the oxide layer. Indicates the thickness of the chromium oxide layer; Oxide surface conductivity for: (twenty three); in, This represents the conductivity constant of the oxide scale. Indicates the activation energy of chromium oxide; The area resistivity of oxide scale : (twenty four).

[0011] Furthermore, in step 4, the voltage decay rate is calculated based on the predicted voltage decay curve and the initial stack voltage. : (25); in, The initial voltage of the fuel cell stack. For prediction The constant voltage of the fuel cell stack; The predicted time when the voltage decay rate of the fuel cell stack first reaches 30% is defined as the total lifetime of the fuel cell stack. Based on the time the fuel cell stack has been in operation, the remaining lifetime of the fuel cell stack is determined.

[0012] The beneficial technical effects of this invention are as follows: Compared with existing SOFC parameter identification methods, this invention does not rely on complex electrochemical tests or large amounts of historical operating data. It only requires limited voltage-current experimental data to accurately identify six key unknown parameters in the established SOFC electrochemical model using an efficient optimization algorithm. This method is simple to operate, has high identification accuracy, superior computational efficiency, and strong engineering applicability, making it an effective means for rapid identification of SOFC parameters under actual operating conditions. Traditional methods typically require repeated data collection under different operating conditions, which is cumbersome and costly, making it difficult to meet the needs of rapid on-site modeling and control. The parameter identification strategy based on optimization algorithms proposed in this invention provides a reliable and efficient solution for high-precision modeling and real-time performance evaluation of SOFC systems. Furthermore, lifetime prediction of kilowatt-level stacks requires significant computational investment and extremely high time costs, while homogenized modeling methods can greatly save on computational and time costs. This invention also uses a microscopic decay model of the anode, cathode, and connectors to accurately predict the lifetime of SOFC stacks, and the prediction conclusions have been experimentally verified to have good effectiveness. Attached Figure Description

[0013] Figure 1 This is a flowchart of the remaining lifetime prediction process in this invention; Figure 2 This is a schematic diagram of the homogenization principle in this invention; Figure 3 This is a polarization curve diagram of the 60-layer SOFC stack in an embodiment of the present invention; Figure 4 This is a Vt curve diagram of the 60-layer SOFC stack in an embodiment of the present invention; Figure 5 This is a voltage decay prediction curve for a 60-layer fuel cell stack in an embodiment of the present invention. Figure 6 This is a voltage decay prediction curve including the end-of-life point in an embodiment of the present invention; Detailed Implementation

[0014] The specific embodiments of the present invention will be further described below with reference to specific examples: A method for predicting the remaining lifetime of a kilowatt-class solid oxide fuel cell stack, such as Figure 1 As shown, it includes the following steps: Step 1: Obtain limited but critical experimental data on voltage, current, and power through fuel cell stack startup, loading, and continuous operation tests; specifically: First, the fuel cell stack was heated by passing nitrogen gas through the anode and air through the cathode, from room temperature to 700°C at a rate of 1°C / min, and held until the temperature stabilized. Then, a stepped current loading was applied, starting from 0A, increasing the current by 1A each time and holding for 3 minutes, until the output power of the fuel cell stack exceeded the output power of the fuel cell stack during normal operation. Next, the current was decreased by 0.5A each time and held for 1 minute, until the output power of the fuel cell stack reached the output power of normal operation, and the corresponding current, voltage, and power data were recorded throughout the process. After that, the output current was kept constant to allow the fuel cell stack to operate continuously and stably, and the voltage, current, and power data generated by the fuel cell stack during operation were continuously recorded.

[0015] Step 2: Using an optimization algorithm, based on the experimental data obtained in Step 1, perform parameter identification on the SOFC electrochemical model containing six key unknown parameters, and determine the model parameters; specifically: Output voltage of the electrochemical model The expression is: (1); in, This indicates the number of batteries in the fuel cell stack. Indicates open-circuit voltage. Indicates the Tafel slope, and These represent the exchange current densities at the anode and cathode, respectively. This represents the resistivity per unit area, where B is the empirical coefficient for concentration loss. For limiting current density, This represents the load current at the k-th data point; The current density at each data point adopted by the model must be kept below the specified limit current density, therefore Must meet: (2); The six key location parameters that need to be identified constitute the decision vector. The objective of parameter identification is to minimize the difference between the model-calculated voltage and the actual measured voltage. The objective function is... Mean squared error: (3); in, This represents the voltage at the k-th data point measured in the experiment, and n represents the total number of experimental data points. The objective function is optimized using optimization algorithms, specifically including: Step 2.1: Randomly generate the potential solution set during algorithm initialization. , i.e., the initial population, is used as the starting point for optimization, where the _i_th The first of the individuals Parameters It is generated by the following formula: (4); in and This represents the lower and upper limits of the parameter, i.e., the lower and upper limits of the parameter to be identified. A vector representing random values ​​uniformly distributed between 0 and 1; Step 2.2: During the iteration process, the position of the parameters is continuously adjusted, as shown in formula (5): (5); Where n is the number of individuals in the population, i.e. the total number of potential solutions, and d represents the number of dimensions or parameters in the problem; For each iteration t, calculate the value of each individual in the population. fitness value Select the individual with the best fitness. ; Step 2.3: To motivate the parameters to iterate toward the optimal value, a reward and penalty mechanism is established. The penalty mechanism is shown in formulas (7)-(10), and the reward mechanism is shown in formula (11). (6); (7); (8); (9); (10); in, and These represent the penalty and reward factors, respectively, with C and D representing the penalty coefficients. Indicates a decreasing control parameter. Indicates the number of iterations. Indicates the maximum number of iterations. Represents a random value that is uniformly distributed between 0 and 1; Step 2.4: In the initial stage of optimization, the parameters are randomly explored across all possible value ranges. When the penalty factor is ≥1, the parameter is forced to update its position. This stage is the migration stage, in which position updates are performed using formulas (11)-(13). When the penalty factor is less than 1, the parameters are explored in a more refined manner in the region where they perform well. This stage is the development stage, in which the parameters are developed using formulas (14)-(17). (11); (12); (13); in, This indicates the new location after the migration phase. It is the first The parameter along the first The current coordinates of the dimension, and step represents the iteration step size of the parameters. , To randomly select the boundary between the maximum and minimum values ​​of a new region, A random number in the range 0 to 1; (14); (15); (16); (17); in, This indicates the new location after the development phase update. This represents the globally optimal parameter combination that minimizes the objective function value in the t-th iteration. This represents the second-best parameter combination that ranks second in objective function value in the t-th iteration. Indicates the migration step length. An angular parameter representing aggregation behavior. This represents a random value that is uniformly distributed between 0 and 1.

[0016] Step 2.5: After the iteration is completed, the parameters represented by the globally optimal individual output in the last iteration are taken as the final identification result.

[0017] Step 3: Construct and initialize a multiphysics coupled model of a homogenized solid oxide fuel cell that considers multiple decay mechanisms to predict the decay curve of the stack voltage over time; Specifically, the construction of the multiphysics coupling model for homogenized solid oxide fuel cells includes: In COMSOL software, the fuel cell stack is geometrically modeled and homogenized to obtain a homogenized fuel cell stack geometric model. The equivalent material parameters of each homogenized region in the model are calculated and input into the model as material properties. Based on the geometric model of the homogenized fuel cell stack, a set of control equations describing fluid flow, mass transfer, heat transfer, charge transfer and electrochemical reaction is set. The six key parameters identified in step 2 are used as initial parameter values ​​and input into the set of control equations to form the multiphysics coupling model of the homogenized solid oxide fuel cell. Three attenuation sub-models are coupled in the multiphysics coupling model: the anode nickel particle coarsening attenuation model, the cathode chromium deposition attenuation model, and the connector oxidation attenuation model. The anode nickel particle coarsening attenuation model is used to update the anode conductivity parameter in real time; the cathode chromium deposition attenuation model is used to update the effective three-phase interface length parameter of the cathode in real time; and the connector oxidation attenuation model is used to update the areal resistivity parameter of the connector region in real time.

[0018] The homogenization process specifically involves: like Figure 2 As shown, the SOFC anode and cathode channels, current collectors, and PEN units are homogenized, which is equivalent to a porous medium with anisotropic material properties. The physical parameters in each direction are equivalently homogenized and converted. The anisotropy of the homogenized material properties is used to characterize the differences in the physical properties of the original material in each direction. The battery stack is homogenized to obtain a homogenized geometric model, and the material parameters of each part of the battery cell structure are equivalently processed, as follows: The equivalent material parameters of a uniform PEN element are calculated using the equivalent volume method: (18); in, For equivalent material parameters, For dense material parameters, For volume; The equivalent thermal conductivity of a uniform PEN element is calculated using the equivalent thermal resistance method: (19); in, This represents the equivalent thermal conductivity of a uniform PEN element in the x, y, and z directions. This represents the cross-sectional area of ​​a uniform PEN cell in which heat is transferred along the x, y, and z directions. This represents the distance that heat is transferred in the x, y, and z directions within a uniform PEN cell. For type number, =1 indicates the anode. =2 indicates an electrolyte. =3 indicates the cathode; Total number of types; These represent the thermal conductivity of the anode, cathode, and electrolyte in the x, y, and z directions, respectively. These represent the cross-sectional areas of the anode, cathode, and electrolyte, respectively, in the x, y, and z directions. These represent the distances in the x, y, and z directions from which heat is transferred between the anode, cathode, or electrolyte; Calculate the permeability of a uniform PEN cell using Darcy's law: (20); in, The pressure drop of the fluid along the flow direction. The fluid pressure drop along the flow direction. Let be the geometric length of the flow channel. Darcy's coefficient of friction. For fluid density, For fluid velocity, The hydraulic diameter, For penetration rate, This represents the fluid viscosity.

[0019] Specifically, the coarsening of nickel particles in the anode is due to the phenomenon of "small particles dissolving and large particles growing" caused by surface diffusion of nickel particles at high temperatures. Assuming that the average radius of ceramic phase particles remains constant, the anode nickel coarsening attenuation model characterizes the average radius of nickel particles using the following formula. Growth trend: (twenty one); in, Indicates temperature. Indicates runtime. Indicates the volume fraction of nickel. Indicates the volume fraction of the ceramic phase. This represents the initial average radius of the nickel particles. This represents the average radius of the initial ceramic phase particles. The average particle coordination number is expressed as: (twenty two); in, Represents the coordination number between ceramic phase particles; Will and Substituting into formula (23), the permeation threshold of Ni particles in the anode is solved. ; (twenty three); in, Represents the average diameter of YSZ particles; Anode conductivity : (twenty four); In the formula, Indicates the intrinsic conductivity of the anode material. This represents the volume fraction of the porous anode material. Cathode chromium poisoning occurs when chromium oxides adhere to reaction sites at the three-phase interface at high temperatures, leading to a reduction in the interface length and consequently a decrease in cathode electrode performance. The cathode chromium deposition degradation model characterizes this reduction in interface length using the following equation: (25); in, Indicates the effective three-phase interface length. Denotes Faraday's constant. Indicates the maximum height of the three-phase interface. The chromium deposition reaction rate is expressed as: (26); In the formula, This represents the exchange current density of chromium oxidation. Indicating the cathode electrode mole fraction, This indicates the mole fraction of water vapor in the cathode electrode. Represents the universal gas constant. Indicates the cathode concentration overpotential; Under prolonged high temperatures, chromium in the metal phase gradually transfers to the metal surface of the connector, eventually forming a chromium oxide layer. This oxide layer increases the area resistivity of the connector surface, weakening its conductivity. The connector oxidation decay model calculates the chromium oxide layer thickness growth using the following formula: (27); in, This represents the rate constant of weight gain of the oxide scale. Indicates the activation energy of the oxide layer. Indicates the thickness of the chromium oxide layer; Oxide surface conductivity for: (28); in, This represents the conductivity constant of the oxide scale. Indicates the activation energy of chromium oxide; The area resistivity of oxide scale : (29).

[0020] Step 4: Determine the remaining lifetime of the fuel cell stack based on the predicted voltage decay curve.

[0021] Based on the predicted voltage decay curve and the initial stack voltage, the voltage decay rate is calculated. : (30); in, The initial voltage of the fuel cell stack. For prediction The constant voltage of the fuel cell stack; The predicted time when the voltage decay rate of the fuel cell stack first reaches 30% is defined as the total lifetime of the fuel cell stack. If the voltage decay rate is higher than this threshold, the fuel cell stack is considered to have lost its value for continued operation. The remaining lifetime of the fuel cell stack is determined based on the operating time of the fuel cell stack.

[0022] Furthermore, the original data for parameter optimization algorithms comes from actual running data. The parameters optimized by the parameter optimization algorithm need to be run in the coupled model and compared with the original data to confirm the correctness of this batch of parameters in order to make predictions over a longer period of time.

[0023] Example The present invention will be described using a stack of SOFC (100 mm × 100 mm) cells supported by 60 anodes as an example. The operating temperature is 750 °C, the fuel gas is methane with a flow rate of 2 L / min, and the cathode gas is air.

[0024] First, the fuel cell stack was heated. Nitrogen gas was introduced through the anode and air through the cathode. The stack was heated from room temperature to 700°C at a rate of 1°C / min, and the temperature was maintained at a stable level. The current was then gradually increased in steps, starting from 0A and increasing by 1A each time for 3 minutes, until the output power of the fuel cell stack slightly exceeded its normal operating output power. Then, the current was decreased by 0.5A each time for 1 minute, until the output power reached the normal operating output power. The corresponding current, voltage, and power were recorded. Afterward, the output current was kept constant to allow the fuel cell stack to operate continuously and stably, and the voltage, current, and power data generated during operation were continuously recorded. The results are as follows: Figure 3 and Figure 4 The polarization curve and Vt curve are shown.

[0025] The open-circuit voltage, the exchange current density at the anode and cathode, the area ratio resistance, the limiting current density, and the Tafel slope are selected as the decision vectors for the parameter optimization algorithm.

[0026] After parameter population iteration, the optimal parameter combinations were selected as shown in Table 1: Table 1 Optimal Parameter Combinations ; The obtained optimal parameters were substituted into the multiphysics coupling model of the homogenized solid oxide fuel cell, and Ni-YSZ was used as the anode material. , Substituting into formula (21), Substituting into formula (22), the voltage prediction curve for a 60-layer fuel cell stack is obtained by running the fuel cell stack lifetime prediction model, as shown below. Figure 5 As shown.

[0027] The maximum error between the voltage curve prediction by this model and the actual experimental data is 2.1%.

[0028] Define a failure threshold of 30% as the end-of-life value, such as... Figure 6 As shown, the voltage decay rate is calculated according to formula (30), where the initial voltage is 53.72V and the failure voltage is 37.60V.

[0029] The attenuation rate during the service phase was 6.9%, which did not exceed the failure threshold. The service time corresponding to the voltage attenuation failure threshold of 30% was taken as the total lifespan. The remaining lifespan was obtained by subtracting the service time from the total lifespan. The remaining lifespan was calculated to be 8938 hours.

[0030] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A method for predicting the remaining lifetime of a kilowatt-level solid oxide fuel cell stack, characterized in that, Includes the following steps: Step 1: Obtain voltage, current, and power data through fuel cell stack startup, loading, and continuous operation tests; Step 2: Using optimization algorithms, based on the experimental data obtained in Step 1, perform parameter identification on the SOFC electrochemical model containing six key unknown parameters, and determine the model parameters. Step 3: Construct and initialize a multiphysics coupled model of a homogenized solid oxide fuel cell that considers multiple decay mechanisms to predict the decay curve of the stack voltage over time; Step 4: Determine the remaining lifetime of the fuel cell stack based on the predicted voltage decay curve.

2. The method for predicting the remaining lifetime of a kilowatt-level solid oxide fuel cell stack according to claim 1, characterized in that, Step 1 is as follows: First, the fuel cell stack is heated by passing nitrogen gas through the anode and air through the cathode. The temperature is increased from room temperature to 700°C at a rate of 1°C / min, and held until the temperature stabilizes. Then, a stepped current loading is applied, starting from 0A and increasing by 1A each time while holding for 3 minutes, until the output power of the fuel cell stack exceeds the output power during normal operation. Next, the current is decreased by 0.5A each time while holding for 1 minute, until the output power of the fuel cell stack reaches the output power during normal operation. The corresponding current, voltage, and power data are recorded throughout the process. Afterward, the output current is kept constant to allow the fuel cell stack to operate continuously and stably, and the voltage, current, and power data generated during the operation of the fuel cell stack are continuously recorded.

3. The method for predicting the remaining lifetime of a kilowatt-level solid oxide fuel cell stack according to claim 1, characterized in that, In step 2, the output voltage of the electrochemical model The expression is: (1)； in, This indicates the number of batteries in the fuel cell stack. Indicates open-circuit voltage. Indicates the Tafel slope, and These represent the exchange current densities at the anode and cathode, respectively. This represents the resistivity per unit area, where B is the empirical coefficient for concentration loss. The limiting current density; This represents the load current at the k-th data point. Must meet: ; The six key location parameters that need to be identified constitute the decision vector. The objective of parameter identification is to minimize the difference between the model-calculated voltage and the actual measured voltage. The objective function is... Mean squared error: (2)； in, The voltage at the k-th data point measured in the experiment is represented by , and n represents the total number of experimental data points.

4. The method for predicting the remaining lifetime of a kilowatt-level solid oxide fuel cell stack according to claim 3, characterized in that, The objective function is optimized using optimization algorithms, specifically including: Step 2.1: Randomly generate the potential solution set during algorithm initialization. , that is, the initial population, in which the first The first of the individuals Parameters It is generated by the following formula: (3)； in and Indicates the lower and upper limits of the parameter. A vector representing random values ​​uniformly distributed between 0 and 1; Step 2.2: For each iteration t, calculate the population for each individual. fitness value Select the individual with the best fitness. ; Step 2.3: Establish a reward and punishment mechanism. The punishment mechanism is shown in formulas (4)-(7), and the reward mechanism is shown in formula (8). (4)； (5)； (6)； (7)； (8)； in, and These represent the penalty and reward factors, respectively, with C and D representing the penalty coefficients. Indicates a decreasing control parameter. Indicates the number of iterations. Indicates the maximum number of iterations. Represents a random value that is uniformly distributed between 0 and 1; Step 2.4: In the initial stage of optimization, the parameters are randomly explored across all possible value ranges. When the penalty factor is ≥1, the parameters are forced to update their positions. This stage is the migration stage, in which position updates are performed using formulas (9)-(11). When the penalty factor is less than 1, the parameters are explored in a more refined manner in the region where they perform well. This stage is the development stage, in which the parameters are developed using formulas (12)-(15). (9)； (10)； (11)； in, This indicates the new location after the migration phase. It is the first The parameter along the first The current coordinates of the dimension, and step represents the iteration step size of the parameters. , To randomly select the boundary between the maximum and minimum values ​​of a new region, A random number in the range 0 to 1; (12)； (13)； (14)； (15)； in, This indicates the new location after the development phase update. This represents the globally optimal parameter combination that minimizes the objective function value in the t-th iteration. This represents the second-best parameter combination that ranks second in objective function value in the t-th iteration. Indicates the migration step length. An angular parameter representing aggregation behavior. Represents a random value that is uniformly distributed between 0 and 1; Step 2.5: After the iteration is completed, the parameters represented by the globally optimal individual output in the last iteration are taken as the final identification result.

5. The method for predicting the remaining lifetime of a kilowatt-level solid oxide fuel cell stack according to claim 1, characterized in that, Step 3, the construction of the multiphysics coupling model for the homogenized solid oxide fuel cell includes: In COMSOL software, the fuel cell stack is geometrically modeled and homogenized to obtain a homogenized fuel cell stack geometric model. The equivalent material parameters of each homogenized region in the model are calculated and input into the model as material properties. Based on the homogenized fuel cell stack geometric model, a set of control equations describing fluid flow, mass transfer, heat transfer, charge transfer, and electrochemical reactions is established. The six key parameters identified in step 2 are input as initial parameter values ​​into the control equations, thus forming the multiphysics coupled model of the homogenized solid oxide fuel cell. Three attenuation sub-models are coupled within the multiphysics coupled model: the anode nickel particle coarsening attenuation model, the cathode chromium deposition attenuation model, and the connector oxidation attenuation model. The anode nickel particle coarsening attenuation model is used to update the anode conductivity parameter in real time; the cathode chromium deposition attenuation model is used to update the effective three-phase interface length parameter of the cathode in real time; and the connector oxidation attenuation model is used to update the areal resistivity parameter of the connector region in real time.

6. The method for predicting the remaining lifetime of a kilowatt-level solid oxide fuel cell stack according to claim 5, characterized in that, The homogenization process specifically involves: The SOFC anode and cathode channels, manifold, and PEN unit are homogenized to be equivalent to a porous medium with anisotropic material properties. The equivalent material parameters of a uniform PEN element are calculated using the equivalent volume method: (13)； in, For equivalent material parameters, For dense material parameters, For volume; The equivalent thermal conductivity of a uniform PEN element is calculated using the equivalent thermal resistance method: (14)； in, This represents the equivalent thermal conductivity of a uniform PEN element in the x, y, and z directions. This represents the cross-sectional area of ​​a uniform PEN cell in which heat is transferred along the x, y, and z directions. This represents the distance that heat is transferred in the x, y, and z directions within a uniform PEN cell. For type number, =1 indicates the anode. =2 indicates an electrolyte. =3 indicates the cathode; Total number of types; These represent the thermal conductivity of the anode, cathode, and electrolyte in the x, y, and z directions, respectively. These represent the cross-sectional areas of the anode, cathode, and electrolyte, respectively, in the x, y, and z directions. These represent the distances in the x, y, and z directions from which heat is transferred between the anode, cathode, or electrolyte; Calculate the permeability of a uniform PEN cell using Darcy's law: (15)； in, The pressure drop of the fluid along the flow direction. The fluid pressure drop along the flow direction. Let be the geometric length of the flow channel. Darcy's coefficient of friction. For fluid density, For fluid velocity, The hydraulic diameter, For penetration rate, This represents the fluid viscosity.

7. The method for predicting the remaining lifetime of a kilowatt-level solid oxide fuel cell stack according to claim 6, characterized in that, The anodic nickel coarsening attenuation model characterizes the average radius of nickel particles using the following formula. Growth trend: (16)； in, Indicates temperature. Indicates runtime. Indicates the volume fraction of nickel. Indicates the volume fraction of the ceramic phase. This represents the initial average radius of the nickel particles. This represents the average radius of the initial ceramic phase particles. The average particle coordination number is expressed as: (17)； in, Represents the coordination number between ceramic phase particles; Will and Substituting into formula (18), the permeation threshold of Ni particles in the anode is solved. ; (18)； in, The average diameter of ceramic phase particles; Anode conductivity : (19)； In the formula, Indicates the intrinsic conductivity of the anode material. This represents the volume fraction of the porous anode material. The penetration threshold of Ni particles at the anode; The cathode chromium deposition attenuation model characterizes the reduction in the three-phase interface length using the following equation: (20)； in, Indicates the effective three-phase interface length. Denotes Faraday's constant. Indicates the maximum height of the three-phase interface. The chromium deposition reaction rate is expressed as: (21)； In the formula, This represents the exchange current density of chromium oxidation. Indicating the cathode electrode mole fraction, This indicates the mole fraction of water vapor in the cathode electrode. Represents the universal gas constant. Indicates the cathode concentration overpotential; The linker oxidation attenuation model calculates the chromium oxide layer thickness growth using the following formula: (22)； in, This represents the rate constant of weight gain of the oxide scale. Indicates the activation energy of the oxide layer. Indicates the thickness of the chromium oxide layer; Oxide surface conductivity for: (23)； in, This represents the conductivity constant of the oxide scale. Indicates the activation energy of chromium oxide; The area resistivity of oxide scale : (24)。 8. The method for predicting the remaining lifetime of a kilowatt-level solid oxide fuel cell stack according to claim 7, characterized in that, In step 4, the voltage decay rate is calculated based on the predicted voltage decay curve and the initial stack voltage. : (25)； in, The initial voltage of the fuel cell stack. For prediction The constant voltage of the fuel cell stack; The predicted time when the voltage decay rate of the fuel cell stack first reaches 30% is defined as the total lifetime of the fuel cell stack. Based on the time the fuel cell stack has been in operation, the remaining lifetime of the fuel cell stack is determined.

Images