A method for optimizing the loading rate of a fuel cell

Abstract

The present invention discloses a method for optimizing the loading rate of a fuel cell, comprising the following steps: establishing an initial global path loading model of the fuel cell; determining candidate loading rates through a loading test according to the initial global path loading model, and determining a reference loading rate from the candidate loading rates by using a clustering method; constructing a multi-objective function based on a dynamic weight factor by using the candidate (decision) loading rates to determine a complete global path loading model; optimizing the complete global loading model by using the Dijkstra algorithm to obtain an optimized optimal loading power path; the beneficial effects of the present invention are: it can significantly improve the system response speed and has strong robustness.

Description

Technical Field

[0001] The present invention relates to the field of fuel cell testing, and particularly to a method for optimizing the loading rate of a fuel cell. Background Art

[0002] Hydrogen fuel cells provide an inherently clean energy source. Since the by-products are only heat and water, they do not have an adverse impact on the environment during operation. With the progress of technology, hydrogen fuel cells will be able to provide energy for a range of stationary and mobile applications. However, the service life of fuel cells hinders their commercial development. The dynamic performance of fuel cells has a significant impact on their life. Especially during the loading process, operating parameters such as gas supply parameters and thermodynamic parameters fluctuate violently or for too long with the change of load power, which accelerates the degradation rate of the membrane of the fuel cell stack, thereby reducing the remaining service life. In view of this, in order to avoid the excessive decline of the fuel cell stack caused by too fast loading, engineers have carried out a large number of tests to calibrate the optimal loading rate. However, the load conditions are complex and changeable, and calibrating these loading rates requires a large amount of time and hydrogen cost. Summary of the Invention

[0003] In order to address the above problems, the present invention provides a method for optimizing the loading rate of a fuel cell. This method is based on a global path loading model and can solve the optimal loading rate of the fuel cell while shortening the test consumption. The method includes the following steps:

[0004] S1. Establish an initial global path loading model for the fuel cell;

[0005] S2. According to the initial global path loading model, determine candidate loading rates through loading tests, and use a clustering method to determine reference loading rates from the candidate loading rates;

[0006] S3. Use the candidate loading rates to construct a multi-objective function based on dynamic weight factors to determine a complete global path loading model;

[0007] S4. Use Dijkstra's algorithm to optimize the complete global loading model to obtain an optimized optimal loading power path.

[0008] The beneficial effects provided by the present invention are: it can significantly improve the system response speed and has strong robustness. Brief Description of the Drawings

[0009] Figure 1 is a flowchart of the method of the present invention;

[0010] Figure 2 is a schematic diagram of the global path loading model;

[0011] Figure 3 is a comparison chart of the calibrated test quantities; Figure 3(a) is the theoretically required calibration test quantity before model simplification, and (b) is the calibration test quantity after model simplification.

[0012] Figure 4 It is the implementation process of the Dijkstra algorithm to solve the optimal path. Specific implementation manners

[0013] To make the objectives, technical solutions and advantages of the present invention clearer, the embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0014] Please refer to Figure 1 , Figure 1 which is the flowchart of the method of the present invention. The present invention provides a method for optimizing the loading rate of a fuel cell, including the following steps:

[0015] S1. Establish an initial global path loading model for the fuel cell;

[0016] The initial global path loading model is composed of a starting power node P1, power nodes P i during the loading process, and a target power node P n and the connections therebetween; wherein there are multiple power nodes during the loading process, i = 2, 3,..., n - 1; the dynamic response time measured by loading at the optimal rate is used as the weight on the path between adjacent power nodes, and the weight is the distance between the power nodes, and the path traversed by the shortest distance from the starting power node P1 to the power node P n is the optimal loading power path.

[0017] As an embodiment, the present invention takes a 90kW engine as the research object. For the loading process of power increase, the power points in Table 1 are used as the common power points.

[0018] Table 1 Common power points of 90kW fuel cell engine

[0019]

[0020]

[0021] The starting power of the fuel cell stack is 41.80kW, and the target power is 67.10kW. The specific steps for optimizing the power loading rate are as follows:

[0022] Establish a global path planning model for fuel cell loading to solve the path formed by the optimal power nodes traversed from the starting power node P1 to the target power node P5. Refer to Figure 2 as shown, Figure 2 which is the schematic diagram of the global path planning model.

[0023] The dynamic response time measured by loading at the optimal rate on the path between adjacent power nodes is used as the weight. For example, represents the dynamic response time measured by loading from P1 to P2 at the optimal linear loading rate, which is also called the weight between P1 and P2. If these weights have been determined in advance, the power nodes are likened to position nodes and the weights are likened to the optimal distance between two position nodes. Then, the position nodes traversed by the shortest distance from the starting position P1 to the target position P5 form the optimal path.

[0024] Given the weights between all power nodes and adjacent nodes, the optimal power path and dynamic response time from P1 to P5 can be obtained through the Dijkstra algorithm.

[0025] It should be noted that in order to solve the optimal path, the global path loading model needs to make three assumptions.

[0026] Assumption Ⅰ: The loading rate between two adjacent power nodes is constant (linear loading).

[0027] Assumption Ⅱ: The loading amplitude between adjacent power nodes does not exceed three power intervals (there is no weight between P i and P i+n , n >= 4).

[0028] Assumption Ⅲ: The dynamic response time from P i to P i+m is equal to the response time from P i to P i+r plus the response time from P i+r to P i+m (Equation 1).

[0029] t(P i →P i+m ) = t(P i →P i+r ) + t(P i+r →P i+m ), m > r (1).

[0030] S2. According to the initial global path loading model, determine the candidate loading rates through loading tests, and use the clustering method to determine the reference loading rate from the candidate loading rates;

[0031] The specific loading test is as follows: taking a certain power node as the initial power P z , and taking a certain power node other than the initial power as the target power P t, different trial rates are set for the loading test to obtain the system dynamic response time and the variance of the single-cell voltage at different trial rates; when the trial rate decreases, but the system dynamic response time does not increase or the increase amplitude is less than the preset value, and the variance of the single-cell voltage still decreases, the minimum trial rate is obtained at this time; when the trial rate increases, the system dynamic response time does not decrease or the decrease amplitude is less than the preset value, and the increase amplitude of the variance of the single-cell voltage is greater than the preset value, the rate before the trial rate increase is used as the maximum trial rate; the minimum trial rate, the maximum trial rate, and the average value between the two are used as the candidate loading rates.

[0032] As an embodiment, since the loading amplitude at a linear rate cannot exceed three power intervals,

[0033] Taking P2 as the initial power and P5 as the target power, loading tests are carried out at different trial rates. And the response time of the fuel cell system power is statistically analyzed to characterize the dynamic response speed of the system.

[0034] The reliability of the stack loading is characterized by the maximum coefficient of variance of the single-cell voltage during the loading process. The calculation process of the coefficient of variance of the single-cell voltage of the fuel cell stack is shown in Equation 2. Where, C v represents the coefficient of variance of the single-cell voltage, V i represents the voltage of the i-th cell, represents the average single-cell voltage, and n represents the number of cells in the fuel cell stack.

[0035]

[0036] Table 2 shows the statistical results of the loading test.

[0037] The response time decreases monotonically with the increase of the decision rate, while the coefficient of variance of the single-cell voltage is opposite.

[0038] When the decision rate (trial rate) is 7 kW / s, it is considered that the loading rate is small enough, because when the decision rate continues to decrease, the system response time does not continue to increase and remains almost unchanged. When the decision rate decreases from 7 kW / s to 6 kW / s, the maximum coefficient of voltage variance still decreases. Therefore, 6 kW / s is taken as the minimum linear loading rate from P2 to P5. Similarly, the response time of 11 kW / s only differs from the response time of 10 kW / s by 0.05 seconds, and 11 kW / s is considered fast enough. Since the coefficient of variance of the voltage at 12 kW / s is significantly greater than the coefficient of variance of the voltage at 11 kW / s, and the coefficient of variance of the voltage at 12 kW / s is greater than 2% (near the critical value of reliability), if the loading rate is greater than 12 kW / s, the reliability of the stack will be significantly reduced. Therefore, 12 kW / s is taken as the maximum rate for this loading condition. The minimum loading rate of 6 kW / s, the maximum loading rate of 12 kW / s, and the average rate of the previous two are used as between two adjacent power nodes (Figure 2 ) The loading rate to be optimized (candidate rate).

[0039] Table 2 Statistical results of loading tests

[0040]

[0041] In addition, the present invention determines the optimal reference loading rate through a clustering algorithm.

[0042] The idea of the clustering algorithm is to cluster objects with similar features into one class.

[0043] For fuel cell loading, the features are the system response time and the coefficient of variation of the maximum voltage, and the objects are the tentative loading rates. First, visually observing from the last two columns in Table 2, the decision-making loading rates can be divided into two or three categories. For the feature of response time, based on the principle that the difference within the group is the smallest and the difference between groups is the largest, 6 kW / s and 7 kW / s are clustered into one category, and 8 kW / s to 12 kW / s are clustered into another category.

[0044] Similarly, for the feature of the coefficient of variation of the maximum voltage, 6 kW / s and 7 kW / s are clustered into one category, 8 kW / s to 11 kW / s are clustered into the second category, and 12 kW / s is a separate category.

[0045] Regardless of which feature is used for clustering, 8 kW / s to 11 kW / s are clustered into one category.

[0046] Moreover, it can be seen from Table 2 that the response times of 8 kW / s and 9 kW / s only differ from the maximum rate of 12 kW / s by 0.1 second and 0.2 second respectively, indicating that the system response speeds of these two loading rates are already fast enough. In addition, the response time of 7 kW / s loading is much slower than that of 8 kW / s (0.95 seconds slower). Also, the coefficients of variation of the maximum voltage for 8 kW / s and 9 kW / s loadings are both less than 2%. Therefore, 8 kW / s and 9 kW / s are used as the common test rates. In the foregoing, the minimum loading rate of 6 kW / s, the maximum loading rate of 12 kW / s, and the average rate of the former two of 9 kW / s are candidate loading rates; the intersection of the common test rate and the candidate loading rates is 9 kW / s.

[0047] S3. Using the reference loading rate, construct a multi-objective function based on the dynamic weight factor to determine the complete global path loading model;

[0048] It should be noted that in the above embodiments, with P2 as the initial power and P5 as the target power, in order to obtain a complete loading path, multiple tests need to be carried out with different initial powers and different target powers. For example, with P1 as the initial power and P2 as the target power, obtain their corresponding weights, which will not be elaborated here. Below, calibration loading tests are formulated according to the initial global path loading model established in the first step.

[0049] A loading test is carried out between every two adjacent power nodes. The power node with a smaller serial number is used as the starting power, and the power node with a larger serial number is used as the target power.

[0050] In Figure 2 , there are a total of 9 weights, and each decision rate corresponds to 9 groups of loading tests.

[0051] Therefore, 27 groups of loading tests are required for three decision rates (here corresponding to the minimum loading rate of 6 kW / s, the maximum loading rate of 12 kW / s, and the average rate of the former two mentioned above). The specific calibration test conditions are shown in Formula 3. Among them, k d,i represents the i-th decision loading rate.

[0052] It can be seen from Formula 3 that there are a total of 12 elements in the matrix, and each element corresponds to a loading condition corresponding to the weight in Figure 2 .

[0053]

[0054] Compared with the traditional calibration method (theoretically), the number of calibration tests determined based on the initial model of global path planning is reduced by at least 65.38%. 81 tests are required before the simplification of the global path loading model ( Figure 3 -a) to obtain the optimal rate solution. After the model is simplified, 78 calibration tests are still required.

[0055] However, the number of calibration tests determined by the initial global path loading model is only 27 times. Moreover, while solving the optimal solution of the global path model, the optimal solutions from P1 to P i (1 < i < 5) are saved, and no additional calibration tests are required. However, when the target power becomes P i , theoretically, 3 i-1 more calibration tests are still required to obtain the optimal solution. Therefore, establishing a global path loading model can reduce a large number of tests, and this calibration test scheme is easy to implement.

[0056] In this embodiment, the multi-objective function constructed based on the dynamic weight coefficient adjustment method can not only calculate the weights in Figure 2 , but also allocate different weight coefficients to the evaluation indexes of the loading effect when the loading conditions change.

[0057] To construct a complete global path loading model, it is necessary to determine the optimal loading rate between adjacent power nodes.

[0058] This optimal loading rate is calculated by constructing a multi-objective cost function.

[0059] The specific calculation process is shown in Formulas 4 and 5. Among them, P z represents the initial power (P1 in this case), P t represents the target power (P5 in this case), k d,i represents the i-th decision rate; t d,i represents the system response time measured by loading at the decision rate k d,i ; C vmaxd,i represents the maximum coefficient of variance of the single-cell voltage calculated during the loading process at the decision rate k d,i ; t d,i * and C vmaxd,i * respectively represent the normalized response time and the maximum voltage variance coefficient; w t and w c respectively represent the weight coefficients of the time cost and the voltage variance cost; m represents the number of reference loading rates (3 in this case); select one as the optimal loading rate between adjacent power nodes according to the principle of the minimum cost value.

[0060] J i * represents the cost value from the starting power P z loaded to P d,i at the decision rate k t . For each loading condition, assuming that the weight coefficients have been determined, select one decision rate from the three decision rates as the optimal loading rate between adjacent power nodes according to the principle of the minimum cost value.

[0061] J i * (P z ,P t ,k d,i ) = w t t d,i * + w c C vmaxd,i * , i = 1, 2,..., m (4)

[0062]

[0063] The specific calculation process of the weight coefficients of the time cost and the voltage variance cost is as shown in Formulas 6 - 10.

[0064] It can be seen from Formula 4 that the cost function value of the loading effect depends on the loading condition and the decision rate. When the loading condition is determined, the cost function is only related to the decision rate. Therefore, the contribution degrees of the time cost and the voltage variance cost to reducing the cost function J (w t0 and w c0 ) are positively correlated with the influence degree of the decision rate on the cost (represented by the differential of the cost with respect to the decision rate).

[0065] Therefore, the 6-8 formula can be written. Among them, the two variables on the right side of the 6 formula respectively represent the average absolute differential of the time cost and the voltage variance cost with respect to the decision loading rate.

[0066]

[0067]

[0068] w t0 + w c0 = 1 (8)

[0069]

[0070] h f + h c = 1 (10)

[0071] w t0 and w c0 represent the weight coefficients of the time cost and the voltage variance from the perspective of numerical calculation.

[0072] However, for the working conditions with a small loading amplitude (P i to P n , n < i + 4, i and n are positive integers), if the difference in the dynamic response time when loaded at different decision rates exceeds 1 second (for example, the time difference between 6 kW / s and 9 kW / s in Table 2), it indicates that the response time makes a significant contribution to reducing the cost function value, and a greater weight should be assigned to the time cost.

[0073] Therefore, for such cases, the subjective weight coefficients of the time cost and the voltage variance coefficient are set to h t (0.8) and h c (0.2) respectively. The contribution degrees of the time cost and the voltage variance to the cost function (w t0 and w c0 ) are corrected through Formula 9 and Formula 10.

[0074] w t and w c represent the contribution degrees (weight coefficients) of the corrected time cost and voltage cost to the cost function respectively.

[0075] S4. Optimize the complete global loading model using Dijkstra's algorithm to obtain the optimized optimal loading power path.

[0076] Statistically calibrate the results in the form of Table 3.

[0077] As can be seen from Table 3, the optimal loading rate when loading from P2 to P5 is 9 kW / s, and the corresponding dynamic response time is 2.55 seconds. Take this time asFigure 1 The weight value between power node P2 and power node P5. Similarly, the weight values of other adjacent power nodes are counted in the same way to construct a complete global path loading model.

[0078] Table 3 Calibration results of P2 loaded to P5 (t c and C vmaxc : The system dynamic response time and the maximum voltage variance coefficient measured by the calibration loading test, J(w0) and J(w): The cost function values corresponding before and after the weight coefficient correction, k opt (w0) and k opt (w): The optimal linear loading rates corresponding before and after the weight coefficient correction)

[0079]

[0080] Let Figure 2 All power nodes in it form a set V and are divided into two groups. The first group is the set S of nodes for which the shortest path has been found. The second group is the set U of nodes for which the shortest path is uncertain.

[0081] Each power node corresponds to a dynamic response time. The time of the nodes in set S is the response time of the shortest path from the starting power s to this power node. The time of the power nodes in set U is the current shortest path response time from the starting point s to this node, which only includes the nodes in S as intermediate nodes.

[0082] The specific implementation process is as Figure 4 shown. Power node N is an adjacent node in the forward traversing direction of node k. Matrix (Formula 11) shows the optimal path from P1 loaded to P5, and the dynamic response time calculated by the model is 3.65 seconds.

[0083]

[0084] To verify the optimization effect and stability of the inventive method, loading verification tests are carried out at the reference rate and the optimal rate respectively. And the system dynamic response time measured by the verification test and the maximum voltage variance coefficient during the loading process are compared. At the same time, to verify the robustness of the model, the loading condition is changed from the original P1 loaded to P5 to P0 loaded to P4, but the optimal rate solution remains unchanged to see if the optimization effect is stable.

[0085] Table 5 shows the performance verification results of the fuel cell system. The results indicate that the system response time measured when loading from P1 to P5 at the optimized loading rate is 23.19% shorter than that before optimization, and the maximum voltage variance coefficient only increases by 8.46% compared to that before optimization. This shows that after optimizing the rate, the dynamic response speed of the fuel cell system can be significantly improved. The results of the robust operating condition test (loading from P0 to P4) show that the response time after optimization is 27.78% shorter than that before optimization, while the maximum voltage variance coefficient only increases by 6.15% compared to that before optimization, and the optimization effect remains almost unchanged. Therefore, the global path planning loading model of the invention can significantly improve the system response speed by optimizing the loading rate, and the model has strong robustness.

[0086] Table 5 Performance Optimization Verification of the Fuel Cell System with the Optimal Loading Rate

[0087]

[0088]

[0089] Generally speaking, the beneficial effects of the present invention are as follows: it can significantly improve the system response speed and has strong robustness.

[0090] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for optimizing the loading rate of a fuel cell, characterized in that: Including the following steps: S1. Establish an initial global path loading model for the fuel cell; The initial global path loading model consists of a starting power node P1, power nodes P during the loading process i and a target power node P n and the connections between them; there are multiple power nodes during the loading process, where i = 2, 3,..., n - 1; the dynamic response time measured by loading at the optimal rate on the path between adjacent power nodes is used as the weight, and the weight is the distance between the power nodes. The shortest distance from the starting power node P1 to the power node P n is the optimal loading power path. Three assumptions need to be made for the global path loading model: Assumption Ⅰ: The loading rate between two adjacent power nodes is constant (linear loading); Hypothesis II: The loading amplitude between adjacent power nodes does not exceed three power intervals, where there is no weight value between P i and P i+n , n >= 4; Hypothesis III: Loading from P at the optimal rate i to P i+m has a dynamic response time equal to the response time from P i to P i+r plus the response time from P i+r to P i+m , as shown in Equation 1: t(P i →P i+m ) = t(P i →P i+r ) + t(P i+r →P i+m ), m > r (1); S2. According to the initial global path loading model, determine the candidate loading rates through loading tests, and use the clustering method to determine the reference loading rate from the candidate loading rates; S3. Use the decision-making loading rate to construct a multi-objective function based on the dynamic weight factor to determine the complete global path loading model; S4. Use Dijkstra's algorithm to optimize the complete global loading model to obtain the optimized optimal loading power path.

2. The method for optimizing the fuel cell loading rate according to claim 1, wherein: The loading test includes three different constraint conditions, specifically as follows: setting the loading between two adjacent power nodes in a linear manner; setting the loading amplitude between two adjacent power nodes not exceeding three power intervals; setting that the dynamic response time from the power node P i to P i+m is equal to the response time from P i to P i+r plus the response time from P i+r to P i+m .

3. The method for optimizing the fuel cell loading rate according to claim 1, characterized in that: The specific loading test is as follows: taking a certain power node as the initial power P z , taking a certain power node other than the initial power as the target power P t , setting different probing rates to conduct the loading test, and obtaining the system dynamic response time and the variance of the single-cell voltage at different probing rates; when the probing rate decreases, but the system dynamic response time does not increase or the increase amplitude is less than the preset value, and the variance of the single-cell voltage still decreases, the minimum probing rate is obtained at this time; when the probing rate increases, the system dynamic response time does not decrease or the decrease amplitude is less than the preset value, and the increase amplitude of the variance of the single-cell voltage is greater than the preset value, the rate before the probing rate does not decrease is taken as the maximum probing rate; taking the minimum probing rate, the maximum probing rate, and the average value between the two as the candidate loading rates.

4. The method for optimizing the fuel cell loading rate according to claim 3, characterized in that: Taking the system dynamic response time and the variance of the single-cell voltage as indicators, and following the principle of minimizing the within-group difference and maximizing the between-group difference, cluster the trial rates to obtain the system dynamic response time class and the single-cell voltage variance class; Select the common trial rates in the system dynamic response time class and the single-cell voltage variance class; select the intersection of the common trial rates and the candidate loading rates as the reference loading rate.

5. The method for optimizing the fuel cell loading rate according to claim 1, characterized in that: The multi-objective function is as follows: Among them, P z represents the initial power, P t represents the target power, k d,i represents the i-th decision rate; t d,i represents the measured system response time loaded at the decision rate k d,i ; C vmaxd,i represents the maximum single-cell voltage variance coefficient calculated during the loading process at the decision rate k d,i ; t d,i * and C vmaxd,i * respectively represent the normalized response time and the maximum voltage variance coefficient; w t and w c respectively represent the weight coefficients of the time cost and the voltage variance cost; m represents the number of decision loading rates; select one as the optimal loading rate between adjacent power nodes according to the principle of the minimum cost value.

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