An online analytical method for a fuel cell stack model

Abstract

The application relates to an online analysis method of a fuel cell stack model, belonging to the technical field of fuel cell stack models. The method comprises the following steps: selecting a frequency f0 as the short-circuit frequency of the transmission part of the fuel cell stack model, selecting two frequencies f2 and f3 between a high frequency f1 and the frequency f0, obtaining the real and imaginary impedance values of the stack under the four disturbance currents, obtaining the element values of a model not containing the substance transmission part by using the impedance values, selecting a frequency f4 smaller than the frequency f0, obtaining the real and imaginary impedance values of the stack under the frequency f4, combining the obtained element values to obtain the element values of the transmission part circuit in the complete model; and bringing the frequency f0 into the complete model and the model lacking the transmission part respectively, comparing whether the impedance value difference of the two models is within an error range, adjusting the frequency f0, and obtaining the accurate circuit element impedance value. The application obtains the fuel cell model element impedance value method, avoids testing the complete impedance spectrum, and shortens the solution time for determining the model impedance value.

Description

Technical Field

[0001] This invention belongs to the field of fuel cell stack model technology, specifically relating to an online analytical method for fuel cell stack models. Background Technology

[0002] Fuel cells, with their high energy conversion efficiency, low operating temperature, and environmental friendliness, are a highly favored direction for new energy development. However, due to their complex structure, harsh working environment, and frequently changing operating conditions, various faults are inevitable in practical applications. If not addressed promptly, these faults can affect their durability and reliability. Using models to determine the type of fuel cell fault is a relatively effective method, but the accuracy of circuit component values ​​can introduce significant errors in fault diagnosis. Therefore, obtaining accurate model component values ​​is crucial for determining the precise type and severity of the fault.

[0003] Existing methods for obtaining model components use electrochemical impedance spectroscopy (EIS). The resistance values ​​of circuit components are obtained by fitting the EIS using a nonlinear least squares method. However, obtaining the EIS of a fuel cell is time-consuming, and since the fuel cell stack is dynamically changing, the obtained resistance values ​​do not reflect the true condition of the stack. Alternatively, PSO and differential evolution algorithms can be used, continuously changing the component values ​​and repeatedly judging the fit. While this yields good accuracy, it requires significant computational resources. Summary of the Invention

[0004] To address the aforementioned problems in the existing technology, the purpose of this invention is to provide an online analytical method for fuel cell stack models, which can rapidly obtain accurate resistance values ​​of fuel cell model elements online within the mid-to-high frequency range.

[0005] This invention provides the following technical solution: an online analytical method for fuel cell stack models, comprising the following specific steps:

[0006] S1. Select a frequency f0 within the range of the frequency of short circuit in the transmission part of the fuel cell model and the frequency of short circuit in the constant phase element of the model.

[0007] S2. Select a high frequency f1 within the frequency range that is higher than frequency f0 but lower than the frequency range of the constant phase element short circuit. Select two frequency points f2 and f3 with equal frequency intervals between frequencies f0 and f1. Apply AC current at frequency points f0, f1, f2, and f3 to the fuel cell to obtain the AC impedance value of the fuel cell at each frequency.

[0008] S3. Calculate the component values ​​of the fuel cell model excluding the transmission part using the obtained impedance values; calculate the real and virtual part resistance values ​​of the model omitting the transmission part based on the impedance values ​​obtained in step S2.

[0009] S4. Select a frequency f4 within the frequency range below frequency f0 where no short circuit occurs in the transmission section, and obtain the stack resistance value at frequency f4. Use the model component values ​​obtained above and the impedance value at frequency f4 to obtain the component values ​​of the material transport section of the complete model.

[0010] S5. Substitute the frequency f0 into the complete model to obtain the real and imaginary part resistance values;

[0011] S6. Determine whether the resistance value in S5 and the real and imaginary resistance values ​​of the model without the transmission part are within the set error range, adjust the frequency f0, and finally obtain the accurate component resistance value.

[0012] Furthermore, the upper limit of the frequency f0 is determined by the maximum frequency within a defined range that causes a short circuit in the constant phase element of the fuel cell equivalent circuit, denoted as f0max. The lower limit is determined based on the minimum frequency at which a short circuit occurs in the transmission section, denoted as f0min.

[0013] Furthermore, the frequency range of the short circuit of the constant phase element is determined by the resistance values ​​R1, R2, and C. PE The maximum and minimum values ​​of a component are determined by calculating its range of variation, and the formula is as follows:

[0014] ;

[0015] Where R1 is the ohmic resistance, R2 is the activation resistance, and C... PE The impedance of the constant phase element.

[0016] Furthermore, the frequency range of the short circuit in the transmission section is determined by the maximum and minimum values ​​obtained from the variation range of the resistance R3 and the C1 element, and the formula is as follows: Where R3 is the transmission resistance and C1 is the capacitance at the transmission point.

[0017] Furthermore, in step S2, the frequencies f2 and f3 are equal frequency intervals between f0 and f1, and are both multiples of 10.

[0018] Furthermore, in step S4, the frequency f4 is a frequency less than f0min, which is a multiple of 10.

[0019] Furthermore, in S6, when the resistance value result in S5 does not meet the set error range with respect to the real and imaginary parts of the model with the transmission part omitted, f0 is adjusted by increasing (f0max-f0min) / 10 each time.

[0020] By employing the above-described technology, the beneficial effects of the present invention compared to the prior art are as follows:

[0021] This invention enables the rapid online acquisition of accurate resistance values ​​for fuel cell model elements within the mid-to-high frequency range. This method avoids the problem of expensive impedance equipment caused by high excitation frequencies; it also avoids testing the complete impedance spectrum and shortens the solution time for determining the model resistance value, which is of great significance for subsequent fault diagnosis based on model parameters. Attached Figure Description

[0022] Figure 1 This is a schematic diagram illustrating the process of determining the short-circuit frequency in the transmission section of the model of this invention.

[0023] Figure 2 This is a schematic diagram of the complete fuel cell model of the present invention;

[0024] Figure 3 This is an equivalent circuit diagram of the present invention excluding the transmission circuit;

[0025] Figure 4 This is a graph showing the relationship between impedance and frequency of the RC parallel circuit of this invention;

[0026] Figure 5 This is a graph showing the relationship between impedance and frequency in the parallel R and RC circuit of this invention. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0028] Conversely, this invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of the invention as defined in the claims. Furthermore, to provide a better understanding of the invention, certain specific details are described in detail below. However, those skilled in the art will fully understand the invention even without these detailed descriptions.

[0029] Please see Figure 1-5 ,like Figure 1 As shown, this example provides an online analytical method for fuel cell stack models. Figure 2 In the fuel cell model shown, a suitable frequency f0 is selected within the range of the short circuit frequency of the transmission part and the short circuit frequency of the constant phase element in the model. For the range of f0, the upper limit of f0 is the frequency at which the constant phase element in the model will short circuit, which is denoted as f0max.

[0030] Figure 3 The frequency of short circuits:

[0031] f=f1= Among them, R1, R2, CPE The frequency range of the component varies with operating conditions and is also a range value. The frequency range of f1 is calculated by using historical values. The upper limit of the range is selected as the maximum value of f0, f0max.

[0032] The lower limit of f0 is solved by the formula f=1 / 2ΠR3C1 for short circuit of RC circuit. R3 and C1 are the material transfer resistance and material transfer capacitance, respectively, which vary with the working conditions of the fuel cell. The range of f is obtained by recording the range, and the minimum value is taken as the lower limit of f0, f0min.

[0033] Using the selected frequency f0 as a boundary, a high-frequency frequency f1 is chosen within the frequency range above f0 but below the short-circuit frequency of the constant-phase element. This ensures that the difference between the two frequencies is within a certain range, thereby guaranteeing more impedance information of the fuel cell stack and preventing the frequency interval from being too close, which would result in small differences in the stack impedance values ​​and affect the resistance accuracy of the circuit components. Two frequencies f2 and f3 with equal frequency intervals are selected between the two frequencies. Excitation currents at these four frequencies are applied to the fuel cell stack to obtain the stack response voltage. The real and imaginary parts of the stack impedance in the frequency domain are obtained using the Fast Fourier Transform method.

[0034] Substitute the obtained values ​​into the model that does not include the transmission part, such as... Figure 3 As shown, the ohmic resistance, activation resistance, and resistance of the constant phase element in the model are obtained by nonlinear least squares method, and a frequency f4 that is a multiple of 10 is found on the side where the frequency is less than the frequency f0.

[0035] The impedance value at this frequency is obtained by using the same method as above to obtain the real and imaginary impedances. Combined with the circuit component values ​​obtained above, the resistance and capacitance values ​​of the transmission section in the complete equivalent circuit model are fitted. The frequency f0 is then substituted into the complete model to calculate the resistance value. It is then determined whether the difference between f0 and the resistance value of the model excluding the transmission section is within a certain range. This determines whether f0 is a frequency that can guarantee the transmission section will not fail under this operating condition. If not, the frequency of f0 is increased to adjust it. The gain of f0 is (f0max - f0min) / 10, and then the evaluation continues.

[0036] like Figure 5 As shown, when the frequency is f0, the impedance of the fuel cell is the sum of the ohmic resistance, the activation resistance, and the mass transport resistance. When the frequency is greater than f0 but less than f1, the transport component in the model disappears, and the impedance at this point is only... Figure 3 The resistance of the circuit is shown. When it is greater than f2, the resistance of the electrode pile is reduced to only ohms.

[0037] Therefore, this invention simplifies the solution of the resistance values ​​of the fuel cell model components by selecting an appropriate frequency to short-circuit part of the transmission circuit, and the selected frequencies are all in the mid-to-high frequency range, so that the time required to obtain the response voltage by applying the excitation current to the fuel cell is shorter.

[0038] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An online analytical method for fuel cell stack models, characterized in that: The specific steps include the following: S1. Select a frequency f0 within the range of the frequency of short circuit in the transmission part of the fuel cell model and the frequency of short circuit in the constant phase element of the model. S2. Select a high frequency f1 within the frequency range that is higher than frequency f0 but lower than the frequency range of the constant phase element short circuit. Select two frequency points f2 and f3 with equal frequency intervals between frequencies f0 and f1. Apply AC current at frequency points f0, f1, f2, and f3 to the fuel cell to obtain the AC impedance value of the fuel cell at each frequency. S3. Calculate the component values ​​of the fuel cell model excluding the transmission part using the obtained impedance values; calculate the real and virtual part resistance values ​​of the model omitting the transmission part based on the impedance values ​​obtained in step S2. S4. Select a frequency f4 within the frequency range below frequency f0 where no short circuit occurs in the transmission section, and obtain the stack resistance value at frequency f4. Use the model component values ​​obtained above and the impedance value at frequency f4 to obtain the component values ​​of the material transport section of the complete model. S5. Substitute the frequency f0 into the complete model to obtain the real and imaginary part resistance values; S6. Determine whether the resistance value in S5 and the real and imaginary resistance values ​​of the model without the transmission part are within the set error range, adjust the frequency f0, and finally obtain the accurate component resistance value.

2. The online analytical method for a fuel cell stack model according to claim 1, characterized in that, The upper limit of the frequency f0 is determined by the maximum frequency within a certain range that causes a short circuit in the constant phase element of the fuel cell equivalent circuit, denoted as f0max. The lower limit is determined by the minimum frequency at which a short circuit occurs in the transmission section, denoted as f0min.

3. The online analytical method for a fuel cell stack model according to claim 2, characterized in that, The frequency range of the short circuit of the constant phase element is determined by the resistance values ​​R1, R2, and C. PE The maximum and minimum values ​​of a component are determined by calculating its range of variation, and the formula is as follows: ； Where R1 is the ohmic resistance, R2 is the activation resistance, and C... PE The impedance of the constant phase element.

4. The online analytical method for a fuel cell stack model according to claim 2, characterized in that, The frequency range of the short circuit in the transmission section is determined by the maximum and minimum values ​​obtained from the variation range of the resistance R3 and the component C1, and the formula is as follows: Where R3 is the transmission resistance and C1 is the capacitance at the transmission point.

5. The online analytical method for a fuel cell stack model according to claim 1, characterized in that, In step S2, frequencies f2 and f3 are equal frequency intervals between f0 and f1, and are both multiples of 10.

6. The online analytical method for a fuel cell stack model according to claim 5, characterized in that, In step S4, the frequency f4 is a frequency less than f0min, and it is a multiple of 10.

7. The online analytical method for a fuel cell stack model according to claim 6, characterized in that, In S6, when the resistance value result in S5 does not meet the set error range with respect to the real and imaginary parts of the model with the transmission part omitted, f0 is adjusted by increasing (f0max-f0min) / 10 each time.

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