A method for optimizing the rate of a fuel cell stack during loading

Abstract

The present invention provides a rate optimization method for a fuel cell stack during the loading process. A case analysis is performed with 14.96kW as the initial power and 48.29kW as the target power as the power boundary conditions, and the four control points of this loading condition are calculated. The relative positions of the control points determine the shape of the designed power-time curve. The power-time trajectory points are calculated based on the quasi-uniform cubic B-spline method. The least squares method is then used to fit the trajectory points to a cubic polynomial function, and the corresponding loading rate is calculated based on the reference power point. The curve shape is changed and the loading rate is corrected by changing the empirical parameters of the intermediate power control point through the single-cell consistency index. The beneficial effects of the present invention are: no large amount of loading test calibration is required, the dynamic response speed of the system is improved, and the consistency of the single cell is not significantly deteriorated.

Description

Technical Field

[0001] The present invention relates to the technical field of vehicle fuel cell loading, and in particular to a method for optimizing the rate of a fuel cell stack during a loading process. Background Art

[0002] The service life of automotive fuel cells mainly depends on their dynamic performance. The loading rate of the fuel cell stack has a significant impact on its dynamic performance. At present, in engineering practice, the loading rate is only optimized for a single goal (the fastest system dynamic response speed or the best single-cell voltage consistency). In theory, these two indicators cannot be taken into account at the same time. The increase in dynamic response speed will inevitably lead to a deterioration in the consistency of single cells. Domestic and foreign scholars have studied that a slow rate at the beginning and end of loading and a faster loading rate in the middle time period can improve the reliability of single cells. Based on this research conclusion, when the loading conditions are fixed, a rate optimization method for the fuel cell stack in the loading process is proposed to improve the dynamic response speed of the system, and the reliability of single cells will not be significantly deteriorated. Summary of the Invention

[0003] To address the above issues, the present invention provides a method for optimizing the rate of a fuel cell stack during loading, which is applied to vehicle fuel cell loading and ultimately improves system output performance. A local path optimization power-time trajectory algorithm is used to optimize the loading rate at a reference power point to enhance engine dynamic performance. This can improve the engine's dynamic response speed. A method for optimizing the rate of a fuel cell stack during loading, comprising:

[0004] S1: Obtain a loading process of an actual fuel cell stack, set four control points according to the loading process, and calculate the coordinates of the four control points;

[0005] S2: Calculate the cubic quasi-uniform B-spline power time trajectory points based on the obtained coordinates of the four control points;

[0006] S3: Fitting the B-spline power-time trajectory points based on the least squares method to obtain the cubic power-time function;

[0007] S4: Calculate the optimized rate (loading rate of the reference power point) based on the reference power point and the cubic power-time function;

[0008] S5: According to the single cell variance coefficient during the loading process, the longitudinal relative distance of the intermediate power control points is qualitatively adjusted to correct and adjust the loading rate to obtain an optimized rate.

[0009] Furthermore, the coordinates of the four control points are: the abscissa t1 of the first control point is the loading start time, t1=0, and its ordinate is the loading initial power P1; the abscissa t4 of the fourth control point is the theoretical loading dynamic response time, t4=2.85s, and its ordinate is the loading target power P4; the abscissas of the two middle control points are both half of the theoretical loading dynamic response time, that is, t2=t3=0.5t4. The calculation formulas for the power ordinates of the two middle control points are as follows:

[0010]

[0011] P3=P2+(P4-P1)·P f

[0012] Among them, P f It represents the ratio of the power difference between the two control points in the middle position to the loading amplitude, P2 represents the power on the ordinate of the second control point, and P3 represents the power on the ordinate of the third control point.

[0013] Furthermore, the theoretical loading dynamic response time t4 is calculated as follows:

[0014]

[0015] Among them, t4 represents the theoretical loading dynamic response time, P re,j represents the jth reference power, k re,j represents the reference rate corresponding to the jth reference power, E t The ratio of the fuel cell system loading dynamic response time that represents the actual hysteresis theory.

[0016] Furthermore, the cubic quasi-uniform B-spline power-time two-dimensional trajectory points are calculated according to the coordinates of the four control points. The input parameters of the fourth-order B-spline power planning algorithm are the order of the B-spline curve function, the parameter n, and n is one less than the number of control points. The outer loop variable u is the independent variable of the B-spline basis function, and the inner loop variable i is the serial number of the control point or B-spline basis function, with an initial value of 0.

[0017] Furthermore, the calculation process of the cubic quasi-uniform B-spline power-time trajectory points includes: a node vector calculation module, a B-spline basis function calculation module and a cubic quasi-uniform B-spline planning point calculation module, and finally a planned path is obtained.

[0018] Furthermore, the time coefficient of the cubic power-time function is obtained by fitting according to the following formula:

[0019]

[0020] S=(t v θ-P r )T (t v θ-P r )

[0021]

[0022]

[0023] Among them, t v is a Vandermonde matrix, b is the number of B-spline curve planning points, θ is the coefficient vector consisting of the polynomial coefficients of the fitting function to be determined, P r It is the output vector composed of planned power points.

[0024] The beneficial effects brought about by the technical solution provided by the present invention are:

[0025] 1. A local path optimization method is used to plan the power-time loading curve of the fuel cell stack.

[0026] 2. The loading rate can be optimized by reference power, reference rate and planned power-time curve, without the need for a large number of loading test calibrations in advance.

[0027] 3. By controlling the adjustment parameters of the two middle power control points, their relative positions are changed to control the shape of the curve. Therefore, when the common operating conditions change greatly or the stack voltage degrades significantly, offline updates are easier.

[0028] 4. The optimization effect can be intuitively verified through two performance indicators: the system dynamic response speed and the single-cell variance coefficient. The consistency of the single cell has not deteriorated significantly. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which:

[0030] Figure 1 This is a flow chart of a method for optimizing the rate of a fuel cell stack during a loading process according to an embodiment of the present invention.

[0031] Figure 2 4 is a structural diagram of a cubic quasi-uniform B-spline power time trajectory planning algorithm in an embodiment of the present invention.

[0032] Figure 3 This is a power-time curve diagram planned based on the path planning algorithm in an embodiment of the present invention. DETAILED DESCRIPTION

[0033] In order to have a clearer understanding of the technical features, purposes and effects of the present invention, specific embodiments of the present invention are now described in detail with reference to the accompanying drawings.

[0034] For a 90kW automotive fuel cell engine, the present invention provides a method for optimizing the rate of a fuel cell stack during loading, which is used to optimize the system's dynamic response speed or the reliability of a single cell. The reference power and rate points of the 90kW fuel cell engine are shown in Table 1:

[0035] Serial number Stack power (kW) (reference power) System output power (kW) Loading rate (kW / s) 1 7.81 7 8 2 14.96 13.5 9 3 22 20 10 4 28.6 25.5 10 5 35.2 31.5 10 6 41.8 36.5 8 7 48.29 41.5 8

[0036] Please refer to Figure 1 , Figure 1 The following is a flow chart of a method for optimizing the rate of a fuel cell stack during loading, according to an embodiment of the present invention. Because low-power loading is frequent and has poor dynamic performance, this embodiment uses the first seven power points in Table 1 as examples for rate optimization. These first seven power points represent the engine's loading rates to be optimized, and the power-time points to be planned are B-spline curve points. A B-spline curve is composed of multiple spline points, and is a linear combination of four B-spline basis functions (the basis functions correspond to the control points). The number of B-spline curve points is varied by controlling the independent variable step size of the B-spline basis functions.

[0037] In order to improve the reliability of the fuel cell stack, the designed power-time curve should be as flat as possible, and the curvature of the power-time curve is used to measure the flatness of the curve. c It represents the power geometric curvature with power as the ordinate and time as the abscissa. From formula (1), it can be seen that if the curvature of the stack power (P) is required to change continuously, then at least the second-order derivative of power with respect to time (P") changes continuously and is not a constant. Therefore, the power is at least a cubic function of time, and at least four power control points are required to control the shape of the power curve. When the number of control points is large, the degree of the curve is higher, the degree of its derivative will also be higher, and the curve will have more peaks and valleys. However, the fuel cell stack power is not allowed to decrease during the loading process. Therefore, a cubic B-spline power curve is constructed to optimize the loading rate of the reference power point.

[0038]

[0039] In the above formula, P' represents the first-order derivative of power with respect to time.

[0040] The specific steps of this embodiment are as follows:

[0041] (1) Obtain a loading process of an actual fuel cell stack, set four control points according to the loading process, and calculate the coordinates of the four control points;

[0042] For the loading process with an initial load power of 14.96kW and a target load power of 48.29kW, the normalized standard deviation of the fuel cell stack loading rate influencing the dynamic response time and the single-cell variance coefficient is first calculated as the influencing factor. Then, the reference rate is determined based on the dynamic performance indicator with the largest influencing factor (dynamic response time or single-cell variance coefficient). The calculation process of the influencing factor is as follows:

[0043]

[0044] Among them, C v Represents the single cell variance coefficient of the fuel cell stack, V j represents the voltage of the jth single cell, is the average single cell voltage; l is the number of batteries.

[0045]

[0046] Among them, k d,i represents the i-th decision rate; k d,3 =10kW / s (larger loading rate, generally close to the limit rate, but less than the limit value, the limit rate is subjectively set according to the inherent characteristics of the fuel cell), k d,1 =6kW / s (This value should be set to ensure that k d,1 The dynamic response time during loading is faster than that of k d,3 Loading time is slow by 1-2 seconds), k d,2 =8kW / s (the average of the first two). n is the number of decision rates (n is 3). d,i and C vmax,i They represent when the decision rate is k d,i The fuel cell system power dynamic response time (the loading dynamic response time measured by the experiment) and the maximum single cell variance coefficient (single cell reliability evaluation index) during the loading process, t d,i * and C vmax,i * Indicates that t d,i and C vmax,i Perform normalization.

[0047] Among them, IF t and IF Cv They represent the factors affecting loading rate on loading dynamic response time and single cell variance coefficient respectively. and Respectively represent t d * and C vmax * The average value of .

[0048] Results show that rate has a greater impact on dynamic response time, so the reference rate is 10 kW / s, the maximum decision rate. To avoid excessive variance in the individual cell loading process, loading is generally performed in a pattern of starting slow, then increasing in speed, and then decreasing in speed. Therefore, fine-tuning the rate values ​​at both ends is performed. The rate values ​​in the fourth column of Table 1 are the final reference rate values.

[0049] (2) Determine the time horizontal coordinate t of the control point of each power interval. The shape of each planned power curve depends on the relative positions of the four control points. The horizontal coordinate of the first control point is the loading start time t1, t1 = 0, and its vertical coordinate is the loading initial power P1. The 14.96kW in the second row of Table 1 is the loading initial power. The horizontal coordinate of the fourth control point is the theoretical dynamic response time t4, t4 = 2.85s, and its vertical coordinate is the loading target power P4. The 48.29kW in the seventh row of Table 1 is the loading target power. This setting is to adjust the difference between the rate in the middle position of the curve and the rate at the two ends, so as to avoid the rate at the two ends being too large and the stack decaying too quickly. Considering that there is a certain error between the actual and theoretical dynamic response time of the stack. Assuming that the reference time calculated by the reference rate is used as the actual time, the theoretical loading dynamic response time is shortened by 20% compared with the actual time, and the theoretical loading time is about 2.85 seconds; the power range of the two control points in the middle position accounts for P f Setting the percentage to 10% and empirically adjusting the parameters shows that a larger percentage increases the rate at the middle power position and decreases the rate at the beginning and end. When the percentage is 0, the loading rate at all positions is equal, and the power-time curve is linear. For the two middle control points, theoretically, a larger difference in their horizontal or vertical coordinates indicates a slower loading process in the middle, while faster loading rates at the beginning and end indicate faster fuel cell degradation. To simplify the calculations, the horizontal coordinates of the two middle control points are set to half the reference loading time.

[0050]

[0051] Among them, t4 represents the theoretical loading dynamic response time, P re,j represents the jth reference power, k re Indicates the corresponding reference rate (as shown in Table 1). t The ratio of the fuel cell system load dynamic response time to the actual hysteresis theory is 20% in this case. The abscissas of the first and last control points are 0 and t4, respectively, and the abscissas of the two middle control points are 0.5t4.

[0052] (3) Calculate the power ordinate P of the control point c. By adjusting the relative positions of the vertical coordinates of the two middle control points, the shape of the planned power curve is controlled to control the loading rates at the start, middle and end positions. The power change rate during the fuel cell loading process changes from slow to fast and then to slow, which can improve the consistency and dynamic response speed of the single cell. The slow loading at the beginning and the end is to avoid the single cell variance coefficient being too large, and the fast loading in the middle is to improve the dynamic response speed. The power range proportions of the two control points in the middle are set to 10% respectively (empirical adjustment parameters). The calculation formula for the power vertical coordinates of the two middle control points is as shown in Formula 3:

[0053]

[0054] P3=P2+(P4-P1)·P f (3)

[0055] Among them, P f This represents the ratio of the power difference between the two control points in the middle to the loading amplitude (target power - starting power), set to 10% in this case. P1 represents the power on the ordinate of the first control point (i.e., the loading starting power), P2 represents the power on the ordinate of the second control point, P3 represents the power on the ordinate of the third control point, and P4 represents the power on the ordinate of the fourth control point (i.e., the loading target power).

[0056] The ordinates of the first and last control points of each loading condition are the loading start target and loading target power, respectively.

[0057] The cubic quasi-uniform B-spline power-time two-dimensional trajectory points are calculated based on the obtained control points. The input parameters of the fourth-order (k=4) B-spline power planning algorithm are the order of the B-spline curve function (k-1), the parameter n (one less than the number of control points), the outer loop variable u (the independent variable of the B-spline basis function), and the inner loop variable i (the serial number of the control point or B-spline basis function, the initial value is 0). The algorithm output is a vector composed of power-time points, which is path. The process of implementing this algorithm is as follows: Figure 2 The specific process is as follows:

[0058] Ⅰ Node vector calculation module

[0059] The range of the knot vector is the domain of the B-spline basis function. The knot vector of the B-spline basis function can be calculated according to the power time curve order (k-1=3) and n=3. First, determine the number of segments of the spline curve (n-k+2=1), and then calculate the knot vector from the zeroth spline basis function B 0,k (u) to the nth basis function B n,k(u) involves a total of (n+k+1=8)8 nodes. Since the number of nodes in the middle is 0 (number of segments - 1=0), the variables of the (k-1+2=5)th through the (n+k-1+2=8)th nodes are set to 1, and the variables of the remaining nodes are set to 0.

[0060] IIB spline basis function calculation module

[0061] The basis function has the following recursive formula: From formula 4, it can be seen that the i-th basis function depends on the order k, the basis function sequence number i, and the independent variable u. When the order k is not less than 2, each time the basis function is recursively iterated, a basis function of order (k-1) is derived, and the sequence number i of the second basis function is assigned the value i+1. To calculate the newly derived basis function, the basis function calculation module needs to be called again ( Figure 2 ) to the next iteration. When the iteration reaches k = 1, calculate the first-order basis functions and calculate B by reverse recursion. i,k (u m After calculating the i-th k-order basis function, save it, then update the inner loop interface variable i (let i = i + 1) and continue to call the basis function calculation module to calculate the (i + 1)-th k-order basis function and save it. After calculating the n-th k-order basis function, the saving module will output B in the form of a column vector. k (u m ).

[0062]

[0063] Ⅲ Cubic quasi-uniform B-spline planning point calculation module

[0064] The planning trajectory is composed of planning points, each of which corresponds to the basis function independent variable u. According to the control point vectors calculated in the second and third steps and the fourth-order basis function vector calculated in the previous step, it can be calculated that when u is u m The specific calculation process is as follows:

[0065]

[0066] In the above formula, the first line of the control point matrix C (the first 4*2-dimensional matrix on the right side of the second equal sign) is the time horizontal coordinate obtained in the second step, and the second line is the power vertical coordinate obtained in the third step. m )(the rightmost 4-dimensional column vector in Equation 5) performs matrix multiplication. D m represents the coordinates of the mth (m=1,2,…,200) power time planning point. The basis function independent variable u is u m The time and power point obtained is t m and P mFinally, save the power time point coordinates, update the outer loop independent variable u (u = u + 0.005), and re-call the B-spline basis function calculation module ( Figure 2 ). Calculate and save the next power-time coordinate point in the same way until the last planning point is calculated in a loop, and output the accumulated saved path.

[0067] (4) Based on the least squares method, the B-spline power-time path points obtained in the previous step are fitted into a cubic power-time function. The time coefficient calculation process of the cubic fitting function is as shown in Equations 6 and 7. v is a Vandermonde matrix, b (b = 200) is the number of B-spline curve planning points (the number of discrete points of the basis function independent variable u). θ is the coefficient vector consisting of the polynomial coefficients of the fitting function to be determined, P r The output vector is composed of the planned power points. When the error function S reaches its minimum value, its partial derivative with respect to each coefficient is zero. The specific derivation process is shown in Equation 7. The fitting result is as follows: Figure 3 As shown, the determination coefficient is 0.99, indicating that the fitting effect is very good. The fitting effect is generally expressed by the determination coefficient R 2 The closer its value is to 1, the stronger the ability of time to explain power is. The specific expression of the determination coefficient is shown in formula 8, P m Indicates the mth planned power point, P p It represents the corresponding fitting prediction point. The denominator is understood as the discreteness of the planned power point, and the numerator is the error between the fitting prediction power and the planned power. Dividing the two can eliminate the influence of the discreteness of the planned power point.

[0068]

[0069] S=(t v θ-P r ) T (t v θ-P r )

[0070]

[0071]

[0072]

[0073] (5) Calculate the loading rate of the reference power point. Calculate the optimized reference power rate based on the reference power points in Table 1 and the cubic power-time curve fitted in the previous step. First, let the power-time function obtained in the previous step be equal to the i-th (i=2,3,…,7) reference power point (P re,i ), and solve for t re,iThe zero point of the cubic function is the loading time t corresponding to the reference power point re,i Then, based on the power-time curve obtained in step 5, the time derivative is taken to obtain the rate-time expression and the corresponding coefficients (the vector on the right side of Equation 10). Finally, the optimized loading rate is obtained by performing matrix multiplication using Equation 10 based on the matrix (5*3 dimensions) of the loading time corresponding to the reference power point and the coefficients of each order term of the rate-time function expression. The rate optimization results are shown in Table 2.

[0074] P re,i =θ3t re,i 3 +θ2t re,i 2 +θ1t re,i +θ0 (9)

[0075]

[0076] Table 2 Calculation results of reference power point loading slope based on local path planning method

[0077] Reference power (kW) Reference rate (kW / s) Optimized rate (kW / s) 14.96 9 9.57 22 10 11.73 28.6 10 12.55 35.2 10 12.51 41.80 8 11.61 48.29 8 9.65

[0078] (6) Correct the loading rate corresponding to the reference power point. From the calculation results in Table 2, when the stack power is loaded from 14.96kW to 48.29kW, its power rate shows a decrease-increase-decrease trend, which is consistent with the basic theory. However, the loading rate of the middle point may be too high, or even exceed its limit rate. In order to avoid the middle power point rate being too fast, the difference in rate between the middle power point and the initial and final power points can be controlled by adjusting the relative position of the middle control power point. From the theoretical analysis of the third step, it can be seen that the greater the horizontal or vertical relative position distance between the two middle control points, the greater the power rate planned at the middle position relative to the rate at the two sides. Therefore, reduce P in Formula 2. f (The ratio of the power of the two middle power control points to the loading amplitude) can reduce the loading rate at the middle position and increase the rate near the start and end positions. When the two middle control points completely overlap, the planned power time curve is just a linear curve, that is, the rate at the middle position is equal to the rate on both sides. The control point parameter P f The adjustment method and the proportional gain coefficient K in the PID controller p The adjustment method is similar: increase P f , the power rate increases in the middle position and decreases on both sides, which improves the reliability of the stack (in most cases), but P f Too large a value will cause a large variance coefficient at the intermediate power point, reducing the reliability of the single battery. For the PID controller, increasing K p , the speed at which the control quantity approaches the target value increases, but K pToo large will cause overshoot of the control amount. The specific adjustment amount of these two parameters can only be adjusted qualitatively according to the performance indicators of the research object.

[0079] (7) Based on the loading rate results before optimization (reference rate) and after optimization in Table 3, a test condition was formulated for verification testing. The initial power of the test condition was 14.96kW and the target power was 48.29kW. The verification test results are shown in Table 3. The dynamic response time after optimization was shortened by 24.44% compared with the dynamic response time before optimization, and the maximum variance coefficient of the single cell increased by 1.09%. Therefore, the algorithm proposed in the present invention can significantly improve the dynamic response speed of the system under this loading condition, and the consistency of the single cell has not been significantly deteriorated.

[0080] Table 3 Optimization effect of path planning algorithm

[0081] Dynamic response time Maximum coefficient of variance Reference Rate 4.50s 2.76％ Optimized rate 3.40s 2.79％

[0082] pass Figure 3 It can be seen that after implementing the rate optimization method for the fuel cell stack in the loading process disclosed in the present invention, the fitting prediction points are almost consistent with the actual planning points.

[0083] The present invention has the following beneficial effects: it eliminates the need for extensive loading calibration tests, improves the system's dynamic response speed, and significantly reduces the reliability of individual cells. If the commonly used loading conditions vary significantly, the loading rates corresponding to each reference power point can be recalculated according to the technical approach of the present invention.

[0084] 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, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for optimizing the rate of a fuel cell stack during a loading process, characterized in that: include: S1: Obtain a loading process of an actual fuel cell stack, set four control points according to the loading process, and calculate the coordinates of the four control points; The coordinates of the four control points are: the horizontal coordinate of the first control point t 1 is the loading start time, t 1=0, the vertical axis is the initial power of loading P 1. The horizontal coordinate of the fourth control point t 4 is the theoretical loading dynamic response time, and its vertical axis is the loading target power P 4. The horizontal coordinates of the two middle control points are half of the theoretical loading dynamic response time, that is, t 2= t 3=0.5 t 4. The power ordinate calculation formula of the two middle control points is as follows: in, P f Indicates the ratio of the power difference between the two control points in the middle position to the loading amplitude, P 2 represents the power on the ordinate of the second control point, P 3 represents the power on the ordinate of the third control point; S2: Calculate the cubic quasi-uniform B-spline power time trajectory points based on the obtained coordinates of the four control points; Specifically: The three-dimensional trajectory points of the quasi-uniform B-spline power-time are calculated based on the coordinates of the four control points. The input parameters of the fourth-order B-spline power planning algorithm are the number of B-spline curve functions, parameter n, and outer loop variables. u , inner loop variables i , where n is one less than the number of control points, u is the independent variable of the B-spline basis function, i It is the serial number of the control point or B-spline basis function, and its initial value is 0; The calculation process of the cubic quasi-uniform B-spline power-time trajectory points includes: node vector calculation module, B-spline basis function calculation module and cubic quasi-uniform B-spline planning point calculation module, and finally the planned path is obtained; S3: Fitting the B-spline power-time trajectory points based on the least squares method to obtain the cubic power-time function; S4: Calculate the loading rate of the reference power point based on the reference power point and the cubic power-time function; S5: According to the single cell variance coefficient during the loading process, the longitudinal relative distance of the intermediate power control points is qualitatively adjusted to correct and adjust the loading rate to obtain an optimized rate.

2. The method for optimizing the rate of a fuel cell stack during a loading process according to claim 1, wherein: Theoretical loading dynamic response time t 4 The calculation formula is shown below: in, t 4 represents the theoretical loading dynamic response time, P re,j Indicates the j A reference power, k re,j Indicates the j The reference rate corresponding to the reference power is E t The ratio of the fuel cell system loading dynamic response time that represents the actual hysteresis theory.

3. The method for optimizing the rate of a fuel cell stack during a loading process according to claim 1, wherein: In step S3, the time coefficient of the cubic power-time function is obtained by fitting according to the following formula: Among them, t v is a Vandermonde matrix, b The number of points for the B-spline curve planning, θ is the coefficient vector consisting of the polynomial coefficients of the fitting function to be determined, P r It is the output vector composed of planned power points.

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