A method for durability testing of fuel cells for construction machines
By developing a fuel cell durability testing method based on actual operating data of engineering machinery, the problem that existing testing methods cannot meet the operating conditions of engineering machinery has been solved, and more accurate life assessment and durability testing have been achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- JIANGSU XCMG CONSTRUCTION MACHINERY RESEARCH INSTITUTE LTD
- Filing Date
- 2022-12-09
- Publication Date
- 2026-07-31
AI Technical Summary
Existing fuel cell durability testing methods cannot meet the requirements of engineering machinery during driving and operation, resulting in inaccurate life assessments.
A durability testing method based on actual operating data of engineering machinery is designed. By acquiring data under characteristic working conditions such as start-up, stop, travel, and operation, the output power and current of the fuel cell are calculated, a durability testing protocol is set, and the real working conditions of the engineering machinery are simulated for testing.
This improves the accuracy and scientific rigor of fuel cell durability testing, enabling it to better reflect the actual usage conditions of engineering machinery and enhance the lifespan prediction and assessment of fuel cells in engineering machinery application scenarios.
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Figure CN115963410B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a method for durability testing of fuel cells in engineering machinery, belonging to the field of fuel cell technology. Background Technology
[0002] Fuel cells, with their high power density and short refueling (hydrogen) time, are considered a clean energy alternative. In construction machinery, fuel cells have numerous potential applications, such as excavators, loaders, sanitation vehicles, dry and wet road vehicles, dump trucks, tractors, forklifts, dump trucks, and concrete mixers. However, current domestic development and application of fuel cells primarily targets automobiles. Unlike automobiles, which only have transportation functions, construction machinery is used in engineering construction and needs to meet operational requirements in specific scenarios, such as construction, water conservancy, power, roads, mining, ports, and national defense.
[0003] Currently, fuel cell durability and lifespan testing primarily focuses on automotive driving conditions, such as the commonly used New European Driving Cycle (NEDC) test protocol. However, this is not applicable to the application scenarios of construction machinery and does not reflect the real-world driving and operating conditions of such machinery. Although there are many methods for fuel cell durability testing, a fuel cell durability testing protocol based on the driving and operating conditions of construction machinery is lacking.
[0004] Different operating cycles lead to varying fuel cell degradation behaviors, resulting in different lifespan data and degradation models. Appropriate fuel cell durability testing protocols are fundamental to developing lifespan assessment methods. Fuel cell lifespan testing and evaluation methods are a key factor in its technological development. With the increasing demand for fuel cell power system engineering machinery, the need for durability lifespan testing and evaluation of fuel cells in this application scenario is becoming increasingly urgent. Therefore, it is necessary to develop durability testing protocols for fuel cells in engineering machinery for testing purposes.
[0005] The first existing technology proposes a test protocol that combines start-stop conditions and load conditions. Although it takes into account actual usage conditions and interleaves the average number of start-stop cycles per day of the vehicle into the load conditions at certain time intervals to form the durability conditions of the fuel cell engine system, it is difficult to directly meet the driving and operating conditions of construction machinery.
[0006] The second existing technology proposes to follow the actual pressure conditions under the current-variable load conditions in order to improve the reliability of the durability test of the fuel cell, but it does not propose a durability test protocol that can be directly used in the fuel cell test platform.
[0007] The third existing technology provides a fuel cell stack durability testing method based on actual operating data, and has been implemented in the actual operation of urban buses to assess the vehicle's lifespan during operation. However, this testing protocol only obtains operating condition data during vehicle startup, driving, and shutdown, which cannot meet the operating condition requirements of construction machinery.
[0008] Therefore, this invention will design an efficient and accurate fuel cell durability testing method for engineering machinery to solve the above problems. Summary of the Invention
[0009] Objective: To overcome the problem that existing durability testing methods have only one characteristic working condition and cannot meet the dual requirements of the walking and working conditions of construction machinery, this invention provides a method for durability testing of fuel cells in construction machinery.
[0010] Technical solution: To solve the above technical problems, the technical solution adopted by the present invention is as follows:
[0011] A method for durability testing of fuel cells in engineering machinery includes the following steps:
[0012] Step 1: Obtain actual operating data of the construction machinery. Classify the actual operating data according to the different working conditions of the construction machinery, such as starting, stopping, traveling, and working, to obtain the starting characteristic working condition, stopping characteristic working condition, traveling characteristic working condition, and working characteristic working condition of the construction machinery.
[0013] Step 2: Based on the actual operating data of the construction machinery under different characteristic working conditions, obtain the pressure and flow rate of the hydraulic pump outlet of the construction machinery, and calculate the instantaneous power output of the fuel cell under different characteristic working conditions.
[0014] Step 3: Calculate the operating current of a single cell based on the instantaneous power output of the fuel cell under different characteristic operating conditions.
[0015] Step 4: Set the fuel cell current under different characteristic operating conditions in the fuel cell durability test protocol according to the operating current of a single cell under different characteristic operating conditions.
[0016] Step 5: Based on the actual operating data of the start-up and stop conditions, obtain the average number of start-ups and stop-ups of the construction machinery per day, and set the start-up and stop conditions of the fuel cell in the durability test protocol according to the average number of start-ups and stop-ups of the construction machinery.
[0017] Step 6: Based on the actual operating data of the walking conditions, obtain the average daily walking dynamic load change cycle and number of times of the construction machinery, and set the walking conditions of the fuel cell in the durability test protocol according to the average walking dynamic load change cycle and number of times of the construction machinery.
[0018] Step 7: Based on the actual operating data of the working conditions, obtain the actual operating data of the construction machinery during operation, the average single operation time and the average number of operations between each start-up and shutdown of the construction machinery, and set the operating conditions, operating cycle and number of cycles of the fuel cell in the durability test protocol.
[0019] Step 8: After completing the durability test protocol settings, perform cyclic testing on the fuel cell under various engineering machinery characteristic working conditions according to the durability test protocol to obtain the polarization curve characteristics of the fuel cell after the durability test.
[0020] As a preferred option, it also includes:
[0021] Calculate the average power output of the fuel cell under different characteristic operating conditions, and based on the average power output and operating time of the fuel cell under different characteristic operating conditions, calculate the amount of hydrogen required for fuel cell durability testing.
[0022] As a preferred option, it also includes:
[0023] Based on the instantaneous power output of the fuel cell under different operating conditions, calculate the proportion of power required in the fuel cell durability test.
[0024] As a preferred option, the operating conditions include: optimal economic efficiency, operation at frequently used driver locations, and optimal power efficiency.
[0025] As a preferred option, the formulas for calculating the instantaneous power output of the fuel cell under different operating conditions are as follows:
[0026]
[0027] Among them, P pump η is the instantaneous net power at the hydraulic pump outlet. pump For the efficiency of the hydraulic pump, η output The efficiency of the fuel cell system controller.
[0028] As a preferred option, the formula for calculating the average power output of the fuel cell under different operating conditions is as follows:
[0029]
[0030] in, η is the average net power output of the hydraulic pump. pump For the efficiency of the hydraulic pump, η output The efficiency of the fuel cell system controller.
[0031] As the preferred option, P pump =p*Q
[0032] Where p is the pressure at the hydraulic pump outlet and Q is the flow rate at the hydraulic pump outlet.
[0033] As the preferred solution
[0034] Among them, P pump The instantaneous net power at the hydraulic pump outlet, t n t is the current sampling time point. n+1 The next sampling time point is T, and the total measurement time is T.
[0035] As a preferred option, the formula for calculating the power demand ratio is as follows:
[0036]
[0037] Among them, P output P is the instantaneous power output of the fuel cell. rated This refers to the rated power of the fuel cell.
[0038] As a preferred solution, the method for obtaining the operating current of a single battery cell includes:
[0039] P output Substituting k and N into formula P output =k*N*P single Find P single Among them, P output P represents the instantaneous power output of the fuel cell, k is the power loss coefficient, N is the number of individual cells in the fuel cell stack, and P is the instantaneous power output of the fuel cell. single That is the power of a single battery cell.
[0040] P single Substitute into formula P single = -1.419 * 10 -4 *I 2 +0.858*I+0.434, find I.
[0041] As a preferred option, the formula for calculating the hydrogen mass in a fuel cell is as follows:
[0042]
[0043] Where, m H Let η be the mass of hydrogen in the fuel cell, Q be the amount of electricity output by the fuel cell, and η be the mass of hydrogen in the fuel cell. fuel Let q represent the efficiency of the fuel cell, and q represent the calorific value of the hydrogen in the fuel cell.
[0044] As the preferred solution
[0045] in, The average power output of the fuel cell is T, where α is the capacity reserve factor, and T is the average power output of the fuel cell. workThis refers to the total operating time of the entire machine.
[0046] Beneficial effects: The method for durability testing of fuel cells in engineering machinery provided by this invention has the following advantages compared with the prior art:
[0047] (1) The fuel cell durability test method provided by the present invention is based on the real operating data of engineering machinery, and extracts typical working conditions for driving and operation respectively. The method is simple in logic, easy to operate, and convenient for engineering application.
[0048] (2) The fuel cell durability testing method provided by the present invention combines the driving conditions and working conditions of engineering machinery, fills the gap in the working conditions of engineering machinery in the existing fuel cell durability testing protocol, and helps to make the durability testing protocol more efficient and accurate in reflecting the actual use of fuel cells in engineering machinery, thereby improving the accuracy of fuel cell durability testing evaluation in engineering machinery.
[0049] (3) When designing the combination of driving and working conditions, the cycle and number of cycles of each working condition are determined according to the ratio of start-stop, driving and working time and the ratio of number of times in the actual application of the construction machinery. This is conducive to improving the scientificity and accuracy of predicting and evaluating the life of the fuel cell of construction machinery based on the data obtained from the above durability test protocol.
[0050] (4) The fuel cell durability testing method provided in this invention can conduct independent and mixed testing and evaluation of the working conditions and driving conditions of engineering machinery. The fuel cell durability evaluation results under driving conditions and working conditions can be used to analyze the degradation behavior, thereby enabling the targeted development of fuel cells suitable for engineering machinery application scenarios, thereby improving the overall durability, reliability and economy of the machine. Attached Figure Description
[0051] Figure 1 This is a flowchart of the method for durability testing of fuel cells in engineering machinery according to the present invention.
[0052] Figure 2 This is a schematic diagram of a fuel cell durability testing protocol commonly used in existing technologies.
[0053] Figure 3 This is a schematic diagram illustrating a fuel cell application scenario according to one embodiment of the present invention. An excavator is used as an example.
[0054] Figure 4 This is a graph showing the flow and pressure data of a hydraulic pump collected under various operating conditions of construction machinery, as provided in one embodiment of the present invention. It includes three operating condition points: optimal power performance, optimal economy, and points frequently used by the driver.
[0055] Figure 5 A power demand data diagram for various operating conditions of construction machinery is provided as an embodiment of the present invention.
[0056] Figure 6 A diagram showing the flow rate, pressure, and power of a hydraulic pump during the walking operation of engineering machinery, provided as an embodiment of the present invention.
[0057] Figure 7 The image shows the polarization curve and power density curve data of a single cell of a fuel cell in one embodiment.
[0058] Figure 8 This is a diagram showing the required operating current under start-stop and travel conditions of engineering machinery, provided as an embodiment of the present invention.
[0059] Figure 9 This is a diagram showing the required operating current data for various working conditions of engineering machinery, provided as an embodiment of the present invention.
[0060] Figure 10 This is a diagram showing the working current data for the basic working cycle of construction machinery, provided as an embodiment of the present invention. It includes start-up, dynamic load driving, work cycles at different operating conditions, and shutdown. Detailed Implementation
[0061] The present invention will be further described below with reference to specific embodiments.
[0062] like Figure 1 As shown, a method for durability testing of fuel cells in engineering machinery includes the following steps:
[0063] Step 1: Based on the actual operating data of the construction machinery during driving and operation, obtain the actual operating data of the construction machinery in the characteristic working conditions of starting, walking, working and stopping, and obtain the power distribution demand data for each characteristic working condition.
[0064] like Figure 2-3 As shown, taking an excavator as an example, the power and energy consumption of the hydraulic pump during actual operation are collected to provide a basis for calculating the power demand and allocation when a fuel cell is used as a power source. In this excavator example, the flow rate and pressure of the excavation test hydraulic pump are collected under various working conditions, such as... Figure 4 As shown. Based on the collected hydraulic pump flow rate and pressure, the fuel cell output power at the corresponding operating point is calculated using mathematical model M1. The resulting fuel cell output power curves under various operating conditions are shown in the figure. Figure 5 As shown in the figure. In the embodiment described, the hydraulic pump flow rate and pressure were tested under walking conditions using the excavator, and the fuel cell output power at the corresponding working point was calculated using the power mathematical model M1. The resulting curves of hydraulic pump flow rate, pressure, and fuel cell output power during the walking test are shown in the figure. Figure 6 As shown.
[0065] The power mathematical model M1 includes:
[0066] P pump =p*Q
[0067]
[0068]
[0069]
[0070] Among them, P pump Let be the instantaneous net power at the hydraulic pump outlet, p be the pressure at the hydraulic pump outlet, and Q be the flow rate at the hydraulic pump outlet. The average net power output of the hydraulic pump is t. n t is the current sampling time point. n+1 The next sampling time point is T, the total measurement time is P. output η is the instantaneous power output of the fuel cell. pump For the efficiency of the hydraulic pump, η output For the efficiency of the fuel cell system controller, The average power output of the fuel cell. The average power of the hydraulic pump is obtained by integrating the instantaneous power. The efficiency η of the hydraulic pump. pump The efficiency η of the fuel cell system controller ranges from 70% to 90%. output The value ranges from 80% to 99%. In the example excavator, η pump =0.83, η output =0.9.
[0071] Data on working conditions and walking conditions collected according to the embodiment (see...) Figure 4-6 The peak and average net power output of the hydraulic pump and the peak and average output power of the fuel cell under different operating conditions were calculated using the mathematical model M1, as shown in Table 1. These include the optimal operating conditions for power performance, the optimal operating conditions for economy, the operating conditions commonly used by the driver, and the driving operating conditions.
[0072] Table 1. Power calculation of engineering machinery under different operating conditions in one embodiment.
[0073]
[0074] Step 2: The rated power of the fuel cell must not be lower than the peak power at each operating point of the construction machinery during startup, travel, operation, and shutdown. Based on the actual operating data of the construction machinery, the instantaneous power P output by the fuel cell is calculated using mathematical model M1. outputThe feedback to the fuel cell control module allows us to obtain the power demand ratio of the fuel cell at each operating point. Based on the polarization curve characteristics and power-current relationship characteristics of the fuel cell, the output current of the fuel cell at each operating point is obtained.
[0075] The polarization curve and power density curve of a single cell of a fuel cell in one embodiment are shown below. Figure 7 As shown. Based on the power demand ratio and the power density-current density curve of a single cell, the mathematical model M2 of the fuel cell under different operating conditions, including power distribution, output current, and power, is obtained:
[0076]
[0077] P output =k*N*P single
[0078] P single = -1.419 * 10 -4 *I 2 +0.858*I+0.434
[0079] Where ω is the power demand ratio at each operating point, P output It is the instantaneous output power of the fuel cell, P. rated P is the rated power of the fuel cell, k is the power loss factor, N is the number of individual cells in the fuel cell stack, and P is the rated power of the fuel cell. single I represents the power of a single cell, and I represents the operating current of a single cell. The mathematical model for the power and current of a single cell is obtained by fitting the polarization curve and power density curve of the fuel cell in the embodiment, with the regression coefficient R. 2 It is 0.9999.
[0080] like Figure 8-10 As shown, based on the obtained characteristic working conditions of the above-mentioned engineering machinery, the current load demand data of the corresponding fuel cell power system for start-up, shutdown, travel, and operation are calculated.
[0081] The actual operating data of the construction machinery is used to obtain the output power of the fuel cell by analyzing the flow and pressure data of the hydraulic pump that can be collected during the operation of the construction machinery through mathematical model M1. Based on the required output power of the fuel cell, the operating current of the fuel cell is obtained through mathematical model M2. The operating current of the fuel cell under different operating conditions of the construction machinery is then added to the fuel cell durability test.
[0082] Step 3: The collection of actual operating data of construction machinery can also produce the following beneficial effect: obtain the hydrogen consumption under different operating conditions, and thus obtain the hydrogen capacity required for construction machinery.
[0083] The mathematical model M3 for the hydrogen capacity of engineering machinery includes:
[0084]
[0085]
[0086] Where Q represents the electrical output of the fuel cell. The average power output of the fuel cell is T, where α is the capacity reserve factor, and T is the average power output of the fuel cell. work The total working time of the machine is m H For the mass of hydrogen, η fuel Let η be the efficiency of the fuel cell, and q be the calorific value of the hydrogen in the fuel cell, q = 28667 kcal / kg. The capacity reserve factor α ranges from 0.005 to 0.5. The efficiency η of the fuel cell is... fuel The range is 20%-100%.
[0087] In this embodiment, the target is to operate continuously for 50 hours at the optimal power performance, with a capacity reserve factor α = 0.05 and a fuel cell efficiency η. fuel If the percentage is 60%, then the output power of the fuel cell in the embodiment is 462.5 kWh, and the amount of hydrogen carried by the engineering machinery in the embodiment cannot be less than 23.1 kg.
[0088] Step 4: In one embodiment, providing actual operating data of the construction machinery and obtaining operating condition data of the construction machinery during startup, travel, operation, and shutdown processes based on the actual operating data and the mathematical model includes the following steps:
[0089] The operation of the construction machinery is divided into multiple work cycles according to different working conditions. Based on the actual operating data of the construction machinery, mathematical models M1 and M2 are used to obtain the output power of the fuel cell at each working point, the operating time at each working point, and the total operating time of the fuel cell, thus obtaining the number of work cycles within each operating cycle. In the working conditions, the number of work cycles per unit time is called the operating efficiency η. 作业 .
[0090] In one embodiment of the excavator, the work efficiency η is obtained under different working conditions. 作业 As shown in Table 2.
[0091] Table 2 shows the operating efficiency of construction machinery at different operating conditions in one embodiment.
[0092]
[0093] Step 5: Based on the current load data of the fuel cell power system under start-up, driving, operation, and shutdown conditions obtained above, add it to the fuel cell testing process. According to the characteristics of the actual working cycle of the construction machinery, determine the cycle and number of cycles for different characteristic conditions such as start-up, driving, and operation, and add them to the construction machinery fuel cell durability test protocol.
[0094] In the fuel cell durability testing protocol, the number of start-stop cycles is set based on the average number of start-stop cycles per day for construction machinery.
[0095] In the fuel cell durability test protocol, the walking conditions are set according to the average daily walking dynamic load change cycle and number of times of the construction machinery.
[0096] In the fuel cell durability test protocol, the operating conditions are obtained based on the actual operating data of the construction machinery during operation. The operating condition cycle and the number of cycles are set according to the average single operation time and the average number of operations between each start-up and shutdown of the construction machinery.
[0097] According to the fuel cell testing protocol obtained above, the fuel cell is subjected to cyclic testing under the start-stop, driving and working conditions of the engineering machinery obtained above, and the polarization curve characteristics of the fuel cell after durability testing are obtained.
[0098] To address the need for durability and lifespan testing of fuel cell-powered engineering machinery under operating and driving conditions, a method for testing the durability of fuel cells in engineering machinery is designed. This method meets the requirements for testing fuel cell durability under different characteristic operating conditions during the driving and operation of engineering machinery. The operating condition points should include the optimal power performance, the optimal economic performance, and the points frequently used by the driver.
[0099] According to the aforementioned durability testing protocol, the purpose of performing load cycling on the fuel cell is to simulate the real operating conditions of the construction machinery and evaluate the durability of the fuel cell under the application scenarios of the construction machinery's driving and operation.
[0100] This invention develops a fuel cell durability testing protocol method based on the actual driving and operating conditions of construction machinery. The method, based on actual operating data, establishes a mathematical model to minimize the error between the operating time under various conditions during the test and actual statistical data, thereby evaluating the durability and lifespan of the fuel cell during the operation of construction machinery. This durability testing protocol can realistically reflect the actual operating conditions of construction machinery, and can more accurately and specifically evaluate the durability and lifespan of the fuel cell under the application scenarios of construction machinery driving and operating.
[0101] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A method for durability testing of a fuel cell of a working machine, characterized by: Includes the following steps: Step 1: Obtain actual operating data of the construction machinery. Classify the actual operating data according to the different working conditions of the construction machinery, such as starting, stopping, traveling, and working, to obtain the starting characteristic working condition, stopping characteristic working condition, traveling characteristic working condition, and working characteristic working condition of the construction machinery. Step 2: Based on the actual operating data of the construction machinery under different characteristic working conditions, obtain the pressure and flow rate of the hydraulic pump outlet of the construction machinery, and calculate the instantaneous power output of the fuel cell under different characteristic working conditions; Step 3: Calculate the operating current of a single cell based on the instantaneous power output of the fuel cell under different characteristic operating conditions; Step 4: Set the fuel cell current under different characteristic operating conditions in the fuel cell durability test protocol according to the operating current of a single cell under different characteristic operating conditions; Step 5: Based on the actual operating data of the start-up and stop conditions, obtain the average number of start-ups and stop-ups of the construction machinery per day, and set the start-up and stop conditions of the fuel cell in the durability test protocol according to the average number of start-ups and stop-ups of the construction machinery; Step 6: Based on the actual operating data of the walking conditions, obtain the average daily walking dynamic load change cycle and number of times of the construction machinery, and set the walking conditions of the fuel cell in the durability test protocol according to the average walking dynamic load change cycle and number of times of the construction machinery. Step 7: Based on the actual operating data of the working conditions, obtain the actual operating data of the construction machinery during operation, the average single operation time and the average number of operations between each start-up and shutdown of the construction machinery, and set the operating conditions, operating cycle and number of cycles of the fuel cell in the durability test protocol. Step 8: After completing the durability test protocol settings, perform cyclic testing on the fuel cell under various characteristic working conditions of engineering machinery according to the durability test protocol, and obtain the polarization curve characteristics of the fuel cell after the durability test. The formulas for calculating the instantaneous power output of a fuel cell under different operating conditions are as follows: ; where P pump is the instantaneous net power at the outlet of the hydraulic pump, η pump is the efficiency of the hydraulic pump, η output is the efficiency of the fuel cell system controller.
2. A method for durability testing of a fuel cell for a working machine according to claim 1, characterized in that: Also includes: Calculate the average power output of the fuel cell under different characteristic operating conditions, and based on the average power output and operating time of the fuel cell under different characteristic operating conditions, calculate the amount of hydrogen required for fuel cell durability testing.
3. A method for durability testing of a fuel cell for a working machine according to claim 1, characterized in that: Also includes: Based on the instantaneous power output of the fuel cell under different operating conditions, calculate the proportion of power required in the fuel cell durability test.
4. A method for durability testing of fuel cells for working machines according to claim 1, characterized in that: The operational characteristics include: optimal economic operation, operation at frequently used driver locations, and optimal power operation.
5. A method for durability testing of a fuel cell for a working machine according to claim 2, characterized in that: The formulas for calculating the average power output of a fuel cell under different operating conditions are as follows: ; wherein, Pavg is the average net power at the hydraulic pump outlet, η pump η is the efficiency of the hydraulic pump output η is the efficiency of the fuel cell system controller.
6. A method for durability testing of a fuel cell for a working machine according to claim 1, characterized in that: ; Where p is the pressure at the hydraulic pump outlet and Q is the flow rate at the hydraulic pump outlet.
7. A method for durability testing of a fuel cell for a working machine according to claim 5, characterized in that: ; where P pump is the instantaneous net power of the hydraulic pump outlet, t n is the current sampling time point, is the next sampling time point, T is the total measurement time.
8. A method for durability testing of a fuel cell for a working machine according to claim 1, characterized in that: Methods for obtaining the operating current of a single battery cell include: Substitute , , N into the formula , solve for ; wherein, is the instantaneous power output by the fuel cell, k is a power loss coefficient, N is the number of cells in the fuel cell stack, P single is the power of a single cell. Substitute into the equation , and solve for . 9. A method for durability testing of a fuel cell for a working machine according to claim 2, characterized in that: The formula for calculating the hydrogen mass in a fuel cell is as follows: ; wherein, is the hydrogen mass for the fuel cell, is the electrical output of the fuel cell, η fuel is the efficiency of the fuel cell, q is the heat value of the hydrogen for the fuel cell; ; wherein, P is the average power output of the fuel cell, a is a capacity reservation factor, T work is the total machine operating time.