A parameter correction method for a solid oxide fuel cell stack model

Abstract

The application discloses a parameter correction method of a solid oxide fuel cell stack model. The method comprises the following steps: building an output voltage model and an anode and cathode outlet component model; testing output voltages of the fuel cell stack under different output currents respectively to obtain corresponding I-V discharge curves; performing division processing on each I-V discharge curve; performing filtering on steady-state data in each I-V discharge curve to obtain useful data of each I-V discharge curve; substituting current data in the useful data of each I-V discharge curve into a steady-state model to obtain molar fractions of hydrogen, oxygen and water corresponding to each I-V discharge curve, and calculating corresponding partial pressure ratio values, substituting the partial pressure ratio values into the output voltage model, and calculating and correcting correction values of each parameter in the output voltage model. The application can accurately correct parameters of the solid oxide fuel cell stack model, and more truly reflect current characteristics and dynamic information of the solid oxide fuel cell stack.

Description

Technical Field

[0001] This invention relates to the field of fuel cell technology, and in particular to a method for parameter correction of a solid oxide fuel cell stack model. Background Technology

[0002] Solid oxide fuel cells (SOFCs) are currently the most efficient fuel cell technology, characterized by wide fuel applicability, high waste heat quality, low maintenance costs, and reversible operation, making them highly promising for current power generation systems. With the increasing prevalence of SOFCs, the importance of designing, simulating, analyzing, and developing high-efficiency fuel cell systems is becoming increasingly prominent, and the accurate modeling of the fuel cell stack, a core component of the fuel cell system, is gradually gaining attention.

[0003] Currently, the construction of solid oxide fuel cell stack models mainly relies on two categories: mechanistic analysis and testing methods. However, the diverse process structures and complex thermal, gas, and electrical mechanisms of SOFCs are difficult to describe accurately, posing challenges to the establishment of mechanistic models. Testing methods, on the other hand, require a large amount of experimental data, and due to the constraints of the hardware and operating conditions of actual systems, achieving comprehensive data acquisition presents significant difficulties. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a parameter correction method for a solid oxide fuel cell stack model. This method achieves accurate correction of the solid oxide fuel cell stack model parameters using limited experimental test data, thereby more realistically reflecting the current characteristics and dynamic information of the solid oxide fuel cell stack.

[0005] To solve the above problems, the present invention adopts the following technical solution:

[0006] The present invention provides a parameter correction method for a solid oxide fuel cell stack model, comprising the following steps:

[0007] S1: Construct a solid oxide fuel cell stack model, which includes an output voltage model and an anode / cathode outlet component model;

[0008] S2: Adjust the anode inlet flow rate and cathode inlet flow rate of the solid oxide fuel cell stack to the set values, test the output voltage of the solid oxide fuel cell stack under different output currents, and plot the IV discharge curve for each output current;

[0009] S3: Divide and process each IV discharge curve as follows:

[0010] Data in each IV discharge curve with voltage fluctuation amplitude less than or equal to ±2% are classified as steady-state data, and data in the IV discharge curve with voltage fluctuation amplitude greater than ±2% are classified as dynamic data.

[0011] S4: The Kalman filter algorithm is used to filter the steady-state data in each IV discharge curve to obtain the useful data of each IV discharge curve;

[0012] S5: Convert the anode and cathode outlet component model into a steady-state model, substitute the current data from the useful data of each IV discharge curve into the steady-state model, obtain the mole fractions of hydrogen, oxygen and water corresponding to each IV discharge curve, and calculate the corresponding partial pressure ratio.

[0013] S6: Substitute the useful data and voltage division ratio corresponding to each IV discharge curve into the output voltage model, calculate the correction value of each parameter in the output voltage model, and assign each parameter the corresponding correction value.

[0014] In this scheme, a solid oxide fuel cell stack model is first constructed. Then, the output voltage of the solid oxide fuel cell stack is tested under multiple different output currents. The IV discharge curves under each output current are collected. The IV discharge curves under each output current are processed to obtain useful stable data. Then, the useful stable data are substituted into the steady-state model to calculate the mole fractions of hydrogen, oxygen, and water corresponding to each IV discharge curve, and the corresponding partial voltage ratios are calculated. Finally, the data are substituted into the output voltage model to calculate the correction values ​​of each parameter in the output voltage model, and each parameter is assigned the corresponding correction value. This allows the solid oxide fuel cell stack model to reflect the current characteristics and dynamic information of the real solid oxide fuel cell stack.

[0015] Preferably, the formula for the output voltage model in step S1 is as follows:

[0016]

[0017] Where V is the output voltage of the solid oxide fuel cell stack, and N cell T represents the number of cells in the solid oxide fuel cell stack, I represents the output current of the solid oxide fuel cell stack, and T represents the total current. s R is the temperature of the fuel cell stack, R is the gas constant, and F is the Faraday constant. These represent the partial pressures of hydrogen, oxygen, and water inside the solid oxide fuel cell stack (related to the molar composition of the corresponding gases), T0 is room temperature, z is the number of moles of electrons in the reaction, and C... re The concentrations of hydrogen gas are E0 and k. EK is the empirical constant of Nernst electromotive force, δ and γ are the empirical constants of Ohmic impedance of solid oxide fuel cell stack, k1 and k2 are the empirical constants of exchange current, and k3 is the empirical constant of limiting current.

[0018] Preferably, the formula for the anode and cathode outlet component model in step S1 is as follows:

[0019]

[0020]

[0021]

[0022]

[0023]

[0024]

[0025] i∈{CO, CO2, H2, H2O, O2, N2},

[0026] Where N is the molar amount of the mixed fluid composed of all reactants, and C 10，i C represents the mole fraction of reactant i at the anode outlet of a solid oxide fuel cell stack. 12，i Fi is the mole fraction of reactant at the cathode outlet of the solid oxide fuel cell stack, and F9 is the anode inlet flow rate of the solid oxide fuel cell stack. 11 C represents the cathode inlet flow rate of the solid oxide fuel cell stack. 9，i C represents the mole fraction of reactant i at the anode inlet of a solid oxide fuel cell stack. 11，i F represents the mole fraction of reactant i at the cathode inlet of a solid oxide fuel cell stack. 10 F represents the anode outlet flow rate of a solid oxide fuel cell stack. 12 This refers to the cathode outlet flow rate of a solid oxide fuel cell stack. Let i be the stoichiometric coefficient of reactant i in reaction j1. Let i be the stoichiometric coefficient of reactant i in reaction j2. The reaction rate of the anodic electrochemical reaction in a solid oxide fuel cell stack. R represents the reaction rate of the cathode electrochemical reaction in a solid oxide fuel cell stack, OR represents the oxidation reaction, and the chemical equation for OR is H₂ + O₂. 2- →H₂O + 2e - RR is a reduction reaction, and the chemical equation for RR is: F is the Faraday constant, N cellWhere is the number of cells in the solid oxide fuel cell stack, and I is the output current of the solid oxide fuel cell stack.

[0027] Preferably, in step S2, the test time for testing the output voltage of the solid oxide fuel cell stack under each output current is not less than t1 minutes, and the interval between adjacent tests is not less than t2 minutes. t1 ≥ 30, t2 ≥ 15.

[0028] Preferably, the method for converting the anode and cathode outlet component model into a steady-state model is as follows:

[0029] The anode and cathode outlet component model Setting all values ​​to 0 yields the steady-state model, whose formula is as follows:

[0030]

[0031]

[0032]

[0033]

[0034]

[0035]

[0036] i∈{CO, CO2, H2, H2O, O2, N2}.

[0037] Preferably, the formula for calculating the corresponding partial pressure ratio based on the mole fractions of hydrogen, oxygen, and water corresponding to a certain IV discharge curve in step S5 is as follows:

[0038]

[0039] in, These are the hydrogen partial pressure, oxygen partial pressure, and water partial pressure inside the solid oxide fuel cell stack, respectively. This represents the mole fraction of hydrogen at the anode outlet of the solid oxide fuel cell stack. This represents the mole fraction of water at the anode outlet of a solid oxide fuel cell stack. This represents the mole fraction of oxygen at the cathode outlet of a solid oxide fuel cell stack.

[0040] Preferably, in step S6, the particle swarm optimization algorithm is used to calculate the correction values ​​of each parameter in the output voltage model.

[0041] The beneficial effects of this invention are: through limited experimental test data, it enables precise correction of the parameters of the solid oxide fuel cell stack model, and more realistically reflects the current characteristics and dynamic information of the solid oxide fuel cell stack. Attached Figure Description

[0042] Figure 1 This is a flowchart of this embodiment;

[0043] Figure 2 This is a comparison chart of the IV discharge curve of a solid oxide fuel cell stack model and the IV discharge curve of a real solid oxide fuel cell stack. Detailed Implementation

[0044] The technical solution of the present invention will be further described in detail below through embodiments and in conjunction with the accompanying drawings.

[0045] Example: This example describes a parameter correction method for a solid oxide fuel cell stack model, such as... Figure 1 As shown, it includes the following steps:

[0046] S1: Build a solid oxide fuel cell stack model, which includes an output voltage model and anode / cathode outlet component models.

[0047] The formula for the output voltage model is as follows:

[0048]

[0049] Where V is the output voltage of the solid oxide fuel cell stack, and N cell T represents the number of cells in the solid oxide fuel cell stack, I represents the output current of the solid oxide fuel cell stack, and T represents the total current. s R is the temperature of the fuel cell stack, R is the gas constant, and F is the Faraday constant. These represent the partial pressures of hydrogen, oxygen, and water inside the solid oxide fuel cell stack (related to the molar composition of the corresponding gases), T0 is room temperature, z is the number of moles of electrons in the reaction, and C... re The concentrations of hydrogen gas are E0 and k. E δ and γ are empirical constants of Nernst electromotive force, δ and γ are empirical constants of Ohmic impedance of solid oxide fuel cell stack, k1 and k2 are empirical constants of exchange current, and k3 is empirical constant of limiting current.

[0050] The formula for the anode and cathode outlet component model is as follows:

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057] i∈{CO, CO2, H2, H2O, O2, N2},

[0058] Where N is the molar amount of the mixed fluid composed of all reactants, and C 10，i C represents the mole fraction of reactant i at the anode outlet of a solid oxide fuel cell stack. 12，i Fi is the mole fraction of reactant at the cathode outlet of the solid oxide fuel cell stack, and F9 is the anode inlet flow rate of the solid oxide fuel cell stack. 11 C represents the cathode inlet flow rate of the solid oxide fuel cell stack. 9，i C represents the mole fraction of reactant i at the anode inlet of a solid oxide fuel cell stack. 11，i F represents the mole fraction of reactant i at the cathode inlet of a solid oxide fuel cell stack. 10 F represents the anode outlet flow rate of a solid oxide fuel cell stack. 12 This refers to the cathode outlet flow rate of the solid oxide fuel cell stack. Let i be the stoichiometric coefficient of reactant i in reaction j1. Let i be the stoichiometric coefficient of reactant i in reaction j2. The reaction rate of the anodic electrochemical reaction in a solid oxide fuel cell stack. OR represents the reaction rate of the cathode electrochemical reaction in a solid oxide fuel cell stack, where OR is the oxidation reaction and the chemical equation for OR is H₂ + O₂. 2- →H₂O + 2e - RR is a reduction reaction, and the chemical equation for RR is: F is the Faraday constant, N cell Where is the number of cells in the solid oxide fuel cell stack, and I is the output current of the solid oxide fuel cell stack;

[0059] S2: Adjust the anode inlet flow rate and cathode inlet flow rate of the solid oxide fuel cell stack to the set values, test the output voltage of the solid oxide fuel cell stack under different output currents, and plot the IV discharge curve for each output current;

[0060] The test time for testing the output voltage of a solid oxide fuel cell stack operating under a single output current shall be no less than 30 minutes, and the interval between adjacent tests shall be no less than 15 minutes.

[0061] S3: Divide and process each IV discharge curve as follows:

[0062] Data in each IV discharge curve with voltage fluctuation amplitude less than or equal to ±2% are classified as steady-state data, and data in the IV discharge curve with voltage fluctuation amplitude greater than ±2% are classified as dynamic data.

[0063] S4: The Kalman filter algorithm is used to filter the steady-state data in each IV discharge curve to obtain the useful data of each IV discharge curve;

[0064] S5: Convert the anode and cathode outlet component model into a steady-state model, substitute the current data from the useful data of each IV discharge curve into the steady-state model, obtain the mole fractions of hydrogen, oxygen and water corresponding to each IV discharge curve, and calculate the corresponding partial pressure ratio.

[0065] The method for converting the anode and cathode outlet component model into a steady-state model is as follows:

[0066] The anode and cathode outlet component model Setting all values ​​to 0 yields the steady-state model, whose formula is as follows:

[0067]

[0068]

[0069]

[0070]

[0071]

[0072]

[0073] i∈{CO, CO2, H2, H2O, O2, N2};

[0074] The formula for calculating the corresponding partial pressure ratio based on the mole fractions of hydrogen, oxygen, and water corresponding to a certain IV discharge curve is as follows:

[0075]

[0076] in, These are the hydrogen partial pressure, oxygen partial pressure, and water partial pressure inside the solid oxide fuel cell stack, respectively. This represents the mole fraction of hydrogen at the anode outlet of the solid oxide fuel cell stack. This represents the mole fraction of water at the anode outlet of a solid oxide fuel cell stack. This represents the mole fraction of oxygen at the cathode outlet of a solid oxide fuel cell stack.

[0077] S6: Substitute the useful data and voltage division ratio corresponding to each IV discharge curve into the output voltage model, use the particle swarm optimization algorithm to calculate the correction value of each parameter in the output voltage model, and assign each parameter the corresponding correction value.

[0078] In this scheme, a solid oxide fuel cell stack model is first constructed. Then, the output voltage of the solid oxide fuel cell stack is tested under multiple different output currents. IV discharge curves are collected under each output current. The IV discharge curves under each output current are processed to obtain useful stable data. This useful stable data is then substituted into the steady-state model to calculate the mole fractions of hydrogen, oxygen, and water corresponding to each IV discharge curve, and the corresponding partial voltage ratios are calculated. Finally, the data is substituted into the output voltage model to calculate the correction values ​​for each parameter in the output voltage model, and each parameter is assigned its corresponding correction value. The parameters that need correction in the output voltage model are E0 and k. E , δ, γ, k1, k2, k3.

[0079] Since this method only requires testing the output voltage of a solid oxide fuel cell stack operating at multiple different output currents, it does not require a large number of experiments. With limited experimental test data, it can accurately correct the parameters of the solid oxide fuel cell stack model and more realistically reflect the current characteristics and dynamic information of the solid oxide fuel cell stack.

[0080] This method is used to analyze the parameters E0 and k in the output voltage model. E A comparison of the IV discharge curves of the solid oxide fuel cell stack model obtained after correcting for δ, γ, k1, k2, and k3 with the IV discharge curves of the actual solid oxide fuel cell stack is shown in the figure. Figure 2 As shown.

Claims

1. A method for parameter correction of a solid oxide fuel cell stack model, characterized in that, Includes the following steps: S1: Construct a solid oxide fuel cell stack model, which includes an output voltage model and an anode / cathode outlet component model; S2: Adjust the anode inlet flow rate and cathode inlet flow rate of the solid oxide fuel cell stack to the set values, test the output voltage of the solid oxide fuel cell stack under different output currents, and plot the IV discharge curve for each output current; S3: Divide and process each IV discharge curve as follows: Data in each IV discharge curve with voltage fluctuation amplitude less than or equal to ±2% are classified as steady-state data, and data in the IV discharge curve with voltage fluctuation amplitude greater than ±2% are classified as dynamic data. S4: The Kalman filter algorithm is used to filter the steady-state data in each IV discharge curve to obtain the useful data of each IV discharge curve; S5: Convert the anode and cathode outlet component model into a steady-state model, substitute the current data from the useful data of each IV discharge curve into the steady-state model, obtain the mole fractions of hydrogen, oxygen and water corresponding to each IV discharge curve, and calculate the corresponding partial pressure ratio. S6: Substitute the useful data and voltage division ratio corresponding to each IV discharge curve into the output voltage model, calculate the correction value of each parameter in the output voltage model, and assign each parameter the corresponding correction value.

2. The parameter correction method for a solid oxide fuel cell stack model according to claim 1, characterized in that, The formula for the output voltage model in step S1 is as follows: Where V is the output voltage of the solid oxide fuel cell stack, and N cell T represents the number of cells in the solid oxide fuel cell stack, I represents the output current of the solid oxide fuel cell stack, and T represents the total current. s R is the temperature of the fuel cell stack, R is the gas constant, and F is the Faraday constant. These represent the partial pressures of hydrogen, oxygen, and water inside the solid oxide fuel cell stack, respectively. T0 is room temperature, z is the number of moles of electrons in the reaction, and C is the concentration of hydrogen. re The concentrations of hydrogen gas are E0 and k. E K is the empirical constant of Nernst electromotive force, δ and γ are the empirical constants of Ohmic impedance of solid oxide fuel cell stack, k1 and k2 are the empirical constants of exchange current, and k3 is the empirical constant of limiting current.

3. The parameter correction method for a solid oxide fuel cell stack model according to claim 1, characterized in that, The formula for the anode and cathode outlet component model in step S1 is as follows: i∈{CO, CO2, H2, H2O, O2, N2}, Where N is the molar amount of the mixed fluid composed of all reactants, and C 10，i C represents the mole fraction of reactant i at the anode outlet of a solid oxide fuel cell stack. 12，i Fi is the mole fraction of reactant at the cathode outlet of the solid oxide fuel cell stack, and F9 is the anode inlet flow rate of the solid oxide fuel cell stack. 11 C represents the cathode inlet flow rate of the solid oxide fuel cell stack. 9，i C represents the mole fraction of reactant i at the anode inlet of a solid oxide fuel cell stack. 11，i F represents the mole fraction of reactant i at the cathode inlet of a solid oxide fuel cell stack. 10 F represents the anode outlet flow rate of a solid oxide fuel cell stack. 12 This refers to the cathode outlet flow rate of a solid oxide fuel cell stack. Let i be the stoichiometric coefficient of reactant i in reaction j1. Let i be the stoichiometric coefficient of reactant i in reaction j2. The reaction rate of the anodic electrochemical reaction in a solid oxide fuel cell stack. R represents the reaction rate of the cathode electrochemical reaction in a solid oxide fuel cell stack, OR represents the oxidation reaction, RR represents the reduction reaction, F represents the Faraday constant, and N represents the oxidation reaction rate. cell Where is the number of cells in the solid oxide fuel cell stack, and I is the output current of the solid oxide fuel cell stack.

4. A parameter correction method for a solid oxide fuel cell stack model according to claim 1, 2, or 3, characterized in that, In step S2, the test time for testing the output voltage of the solid oxide fuel cell stack at each output current is not less than t1 minutes, and the interval between adjacent tests is not less than t2 minutes.

5. The parameter correction method for a solid oxide fuel cell stack model according to claim 3, characterized in that, The method for converting the anode and cathode outlet component model into a steady-state model is as follows: The anode and cathode outlet component model Setting all values ​​to 0 yields the steady-state model, whose formula is as follows: i∈{CO, CO2, H2, H2O, O2, N2}.

6. The parameter correction method for a solid oxide fuel cell stack model according to claim 5, characterized in that, In step S5, the formula for calculating the corresponding partial pressure ratio based on the mole fractions of hydrogen, oxygen, and water corresponding to a certain IV discharge curve is as follows: in, These are the hydrogen partial pressure, oxygen partial pressure, and water partial pressure inside the solid oxide fuel cell stack, respectively. This represents the mole fraction of hydrogen at the anode outlet of the solid oxide fuel cell stack. This represents the mole fraction of water at the anode outlet of a solid oxide fuel cell stack. This represents the mole fraction of oxygen at the cathode outlet of a solid oxide fuel cell stack.

7. A parameter correction method for a solid oxide fuel cell stack model according to claim 1, 2, or 3, characterized in that, In step S6, the particle swarm optimization algorithm is used to calculate the correction values ​​of each parameter in the output voltage model.

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