Fuel cell working condition generation method based on state transition probability

Abstract

The invention relates to the technical field of fuel cells, in particular to a fuel cell working condition generation method based on a state transition probability. A state transition frequency matrix F is constructed according to the power output of the fuel cell system and the residence time of each power, the state transition frequency matrix F is normalized into a state transition probability matrix P, the state transition probability matrix P and a residence time probability distribution function adopt a random sampling mode, and a working condition spectrum is automatically generated by means of a programming tool. The method is a working condition spectrum dynamic modeling based on state transition probability, modeling and optimization are carried out on power point residence time based on Gamma distribution, a random working condition spectrum generation method combining state transition and residence time distribution is adopted, and the residence time is dynamically optimized by adopting a compression strategy. Therefore, the working condition spectrum which accords with actual dynamic characteristics and can be flexibly adjusted according to requirements is generated.

Description

Technical Field

[0001] The present invention relates to the technical field of fuel cells, and particularly to a method for generating fuel cell operating conditions based on state transition probability. Background Art

[0002] With the rapid development of the global new energy vehicle industry, fuel cell vehicles, as an efficient and clean power system, have received extensive attention. The fuel cell system is the core component of a fuel cell vehicle, and its main function is to convert the chemical energy of hydrogen into electrical energy to provide driving force for the vehicle. Due to limitations in materials and control levels, most of the fuel cell vehicles currently operating in China adopt a relatively simple energy management strategy for steady-state power generation. However, when each manufacturer formulates this strategy, it will also refer to various relevant factors such as vehicle speed, SOC, slope, load, etc. to varying degrees for power point jump logic determination. Therefore, during actual operation, the power output of the fuel cell system often shows a complex jump pattern in a short period of time, and the jump pattern is more unpredictable for strategies with a higher correlation with instantaneous change variables such as vehicle speed. The operating condition spectrum is a time series that describes the power output of the fuel cell system changing with time, that is, the power jump pattern, and is used to simulate the real operating conditions during vehicle operation. Through the operating condition spectrum, the following research and tests can be carried out: 1. Performance evaluation: Evaluate performance indicators such as the efficiency and response time of the fuel cell system through specific operating conditions. 2. Durability test: Analyze the durability and life characteristics of the fuel cell system under frequent start-stop or different load conditions. 3. Control strategy optimization: Optimize the energy management strategy of the fuel cell system based on dynamic operating conditions to reduce energy consumption or extend the life of the fuel cell stack. Therefore, to ensure the accuracy and authenticity of research and test results, the development and testing of fuel cell systems will deeply rely on the operating condition spectrum that can truthfully reflect actual operating conditions.

[0003] The current methods for generating the operating condition spectrum of fuel cell vehicles mainly rely on the following two methods:

[0004] 1. Directly generated based on actual operation data. By collecting a section of vehicle operation data, instead of modeling or extracting characteristics from the operation data, the operating condition spectrum is directly generated based on the original power point sequence. This method can provide operating condition inputs that conform to the actual operating state of the vehicle in the early stage of fuel cell system research and development, but there are many deficiencies. For example, 1), lack of flexibility: This method directly reflects the operation data and cannot adjust the characteristics of the operating condition spectrum according to specific test requirements. For example, if it is necessary to control the start-stop times and adjust the power point distribution, it is difficult to achieve with the method based on the original data. 2), limited by data integrity: When the collected data quality is poor (such as some operating conditions are missing or the sampling is insufficient), the generated operating condition spectrum may be incomplete, affecting the accuracy of fuel cell system performance testing. 3), unable to predict dynamic characteristics: Without establishing a mathematical model, it can only statically reflect the operation data and is difficult to simulate the dynamic behavior of the fuel cell system under unknown conditions.

[0005] 3. Standardized operating condition generation. It is to generate the fuel cell operating condition spectrum using fixed operating condition curves (such as NEDC or WLTP standards). For example, the NEDC operating condition curve describes the speed-time relationship under urban and suburban driving conditions, and converts the speed-time curve into a fuel cell power point curve. However, the disadvantages are obvious: 1), lack of real dynamic characteristics: Standard operating conditions are usually based on typical vehicle usage scenarios, but cannot fully reflect the dynamic behavior of the fuel cell system. For example, the fuel cell system may frequently switch power points during actual operation, while the change of the standard operating condition curve is relatively gentle. 2), limited to specific scenarios: Standard operating conditions are applicable to standardized test scenarios with high consistency. However, it is not applicable to the performance evaluation of fuel cell vehicle models in special states that do not conform to the conventional, such as some high-frequency switching, dynamic load, and extreme operation.

[0006] To sum up, the above two main technical paths have the following obvious deficiencies:

[0007] 1. Direct generation based on actual operation data lacks flexibility: The generated operating condition spectrum is fixed and cannot flexibly adjust characteristics such as start-stop times and power point distribution according to test requirements.

[0008] 2), relying on complete data: When some operating condition points are missing, the generated operating condition spectrum may not be able to fully reflect the actual characteristics.

[0009] 3), static characteristics: The directly generated operating condition spectrum lacks dynamic modeling and is difficult to meet the test requirements of new scenarios.

[0010] 2. Disadvantages of standardized operating condition generation:

[0011] 1), strong limitations: It is difficult to reflect the actual operating conditions and cannot describe the dynamic power point switching and start-stop behavior.

[0012] 2) Inadaptable to actual working condition test requirements: For example, for the operating behaviors under high-frequency switching or extreme conditions, the standard working condition curve is insufficiently described.

[0013] Therefore, there is an urgent need for a working condition generation method that can adapt to the actual working condition test requirements for generating the fuel cell working condition spectrum. Summary of the Invention

[0014] The problem to be solved by the present invention is to provide a working condition generation method that can adapt to the actual working condition test requirements for generating the fuel cell working condition spectrum.

[0015] In view of the deficiencies of the prior art, the technical solution adopted by the present invention to solve its technical problems is: A fuel cell working condition generation method based on state transition probability, including the following steps.

[0016] Step 1: Collect vehicle operation data. The collected data includes the power output of the fuel cell system and the residence time of each power. The power output and the residence time of each power are used as the basic data for generating the working condition spectrum.

[0017] Step 2: Discretize the fuel cell power output and residence time into multiple intervals and define the corresponding power states and residence times. The multiple intervals are S = {S 1 , S 2 , S 3 , S 4 ,... S i ,... S j ,......}; Judge and count the power output curve in the original data, count the switching frequency between each interval, and construct a state transition frequency matrix F.

[0018] Step 3: Normalize the state transition frequency matrix F into a state transition probability matrix P. The state transition probability matrix P describes the switching rule between power points; count the residence time of each power point and statistically fit the residence time to obtain a residence time probability distribution function.

[0019] Step 4: Use the state transition probability matrix P and the residence time probability distribution function in a random sampling manner, and automatically generate a working condition spectrum with the help of programming tools.

[0020] Preferably, in Step 3, the Gamma distribution is used to fit the residence time.

[0021]

[0022] where t represents the residence time of the fuel cell system at the power point Si.

[0023] α > 0: Shape parameter, used to control the shape of the distribution.

[0024] ββ > 0: Scale parameter, used to control the range of the distribution;

[0025] Γ(α): Gamma function, which plays a role in normalization to ensure that the Gamma distribution is a valid probability distribution function, defined as:

[0026]

[0027] Preferably, when S = {S 1 , S 2 , S 3 , S 4 , S 5 , S 6} in step two, the state transition frequency matrix F is:

[0028]

[0029] where f ij represents the number of times of transitioning from state S i to state S j .

[0030] Preferably, the state transition frequency matrix F is normalized to obtain the state transition probability matrix P as:

[0031]

[0032] where:

[0033]

[0034] Preferably, step four specifically includes the following process,

[0035] ① Set the initial state: Set the initial state of the fuel cell system to S 1 , that is, 0 kW power, set the total simulation time to T 工况谱时间 , and the simulated time t 累计 = 0;

[0036] ② State transition: Randomly generate the next power point S t+1 based on the state transition probability matrix P:

[0037] P(S(t + 1) = S j |S(t + 1) = S i ) = p ij

[0038] ③ Generation of residence time: In the current state S i , randomly generate the residence time of the next power point based on the residence time distribution rule and add the currently accumulated duration; generate the residence time T i by fitting or adjusted power point residence time distribution.

[0039]

[0040] Updated simulated time:

[0041] t 累计 = t 累计 + T i

[0042] ④ Repeat the above steps ② and ③ to determine whether the cumulative duration is greater than the total duration of the duty cycle spectrum until t 累计 >T 工况谱时间 Implement state transition, i.e., generate the stay step;

[0043] ⑤ End, and the duty cycle spectrum generation is completed.

[0044] The beneficial effects of the present invention are as follows:

[0045] 1. Significantly improved flexibility. In the prior art, the method for generating a duty cycle spectrum based on actual operation data lacks flexibility and cannot flexibly adjust the start-stop times and power point distributions according to test requirements. However, the present invention can adjust the state transition frequency and the characteristics of the residence time distribution according to different test objectives by introducing the state transition probability matrix and the residence time distribution modeling, so as to generate a duty cycle spectrum adapted to different test requirements, and this flexibility significantly improves the pertinence of the fuel cell system test.

[0046] 2. More realistic dynamic characteristics. The standard duty cycle cannot accurately reflect the dynamic behavior in the actual operation of the fuel cell system (such as frequent power point switching). By using the state transition probability and the Gamma distribution to describe the power point switching and the residence time characteristics, the present invention mathematically ensures that the generated duty cycle spectrum can truly reproduce the dynamic power change law of the actual vehicle operation, thereby improving the credibility of the test and simulation results.

[0047] 3. Optimized test efficiency. The present invention designs a compression algorithm for the residence time (such as linear compression, non-linear compression, and distribution adjustment method), which solves the problems of distorted duty cycle spectrum distribution and insufficient dynamic characteristics caused by long-term residence in the prior art. Through the optimized residence time distribution, the generated duty cycle spectrum can more accurately simulate the complex operating environment, while improving the test efficiency and simulation accuracy of the fuel cell system. Description of the Drawings

[0048] Figure 1 is the algorithm flowchart involved in the present invention;

[0049] Figure 2 is the flowchart for generating a duty cycle spectrum in a software tool using the method of the present invention; Detailed Embodiments

[0050] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments. The embodiments of the present invention are given for purposes of illustration and description, and are not exhaustive or limit the present invention to the disclosed form. Many modifications and variations will be apparent to those of ordinary skill in the art. The embodiments are selected and described to better illustrate the principles of the present invention and its practical applications, and to enable those of ordinary skill in the art to understand the present invention and design various embodiments with various modifications suitable for specific purposes.

[0051] In view of the deficiencies of the existing operating condition spectrum generation methods, the present invention proposes a fuel cell operating condition generation method based on state transition probability. This method generates an operating condition spectrum that not only conforms to the actual dynamic characteristics but also can be flexibly adjusted according to requirements by statistically analyzing the power point distribution and switching rules in the actual vehicle operation data and constructing a mathematical model.

[0052] The specific steps are as follows:

[0053] 1. Collection of vehicle operation data: Select a target vehicle model according to the analysis requirements, and collect the power output of the fuel cell system and the residence time of each power through a remote monitoring system. To ensure that the power transfer probability and residence time distribution show objective laws, the collection time must be long enough. From the long-term operation of fuel cell vehicles, collect the power output and the residence time series of each power as the basic data for generating the operating condition spectrum.

[0054] 2. Discretize the fuel cell power output and residence time into multiple intervals and define the corresponding power states and residence times. Since the collected power output data of the original data belongs to a continuously changing curve, the power output can be discretized according to the characteristics of the strategy. The specific method is to discretize the fuel cell output power into fixed intervals, and each interval is defined as a steady-state interval / steady-state point S. The power interval division reflects the typical operating range of the fuel cell.

[0055] For example:

[0056] ① In the energy management strategy of the fuel cell system, 6 steady-state power generation points of 0kW, 15kW, 25kW, 35kW, 45kW, and 55kW are designed, and 6 steady-state states S can be designed. i：

[0057] S = {S 1 , S 2 , S 3 , S 4 , S 5 , S 6}

[0058] Where:

[0059] S 1= 0 kW

[0060] S 2 = [10 - 20) kW

[0061] S 3 = [20 - 30) kW

[0062] S 4 = [30 - 40) kW

[0063] S 5 = [40 - 50) kW

[0064] S 6 = [50 - 60] kW

[0065] ② Judge and count the power output curve in the original data, and count the switching between each state

[0066]

[0067] Frequency, construct the state transition frequency matrix F. Since staying at the same power point should not be regarded as "state transition" in essence, but the duration of the same state. Therefore, the diagonal elements should be taken as 0. After constructing the state transition frequency matrix F by counting the switching frequency between power points according to the operation data, normalize the state transition frequency matrix F to the state transition probability matrix P. The state transition probability matrix P describes the switching law between power points; count the residence time of each power point in the operation data and fit the probability distribution of the residence time. The probability distribution of the residence time describes the duration characteristics of the power point.

[0068] where f ij represents the number of times transferred from state S i to state S j .

[0069] ③ Normalize the state transition frequency matrix F to obtain the state transition probability matrix P, and P can reflect the switching law between power points.

[0070]

[0071] Among them:

[0072]

[0073] 3. The dwell time is a non - negative random variable, which depends on the real - time operating conditions of the whole vehicle and its energy management strategy. The domain of the Gamma distribution is (0, +∞), so it is very suitable for describing the power - point dwell time of the fuel - cell system. At the same time, the power dwell time of the fuel - cell system has a certain central tendency. Even though there may be large fluctuations under specific operating conditions, the flexibility of the Gamma distribution (through the shape parameter α and the scale parameter β) can still well fit this characteristic. Therefore, after statistically analyzing the dwell time of each state Si, the Gamma distribution is used for fitting:

[0074]

[0075] where: t represents the dwell time of the fuel - cell system at the power point Si. Among them, for the dwell time of the power point S1 (i.e., 0 kW), it is necessary to decide whether to include it in the Gamma - distribution fitting according to the energy management strategy. If the strategy is relatively aggressive and the fuel - cell system always outputs closely following the demand of the whole vehicle, and the average value and peak value of the S1 dwell time are comparable to those of other power points, then it can be included in the fitting; if the strategy is relatively conservative, the average value and peak value of the S1 dwell time are large and quite different from those of other operating points, then it is not included in the fitting. At this time, the S1 dwell time can be set as an empirical value according to the target demand;

[0076] α > 0: shape parameter, used to control the shape of the distribution;

[0077] β > 0: scale parameter, used to control the range of the distribution;

[0078] Γ(α): Gamma function, which plays a role in normalization to ensure that the Gamma distribution is a valid probability - distribution function, and is defined as:

[0079]

[0080] Through Gamma fitting, we can also obtain the characteristics of the current operating state to quantitatively analyze the operating results of the current energy management strategy. For example, after fitting, if α = 1, the Gamma distribution degenerates into an exponential distribution, indicating that the power - point switching has no memory (i.e., the probability of each switch is independent of the past); when α > 1, the distribution is skewed to the right, indicating that the system power - point dwell time is longer and the distribution is concentrated; when α < 1, the distribution is skewed to the left, indicating that the system power - point dwell time is shorter. A larger β indicates a wider range of the dwell - time distribution, that is, the system may stay at the power point for a longer time. On the contrary, a smaller β indicates a narrower distribution range, and the dwell time is concentrated in a shorter interval. We can also directly calculate the average dwell time (expected value) E[T i and the variance of the dwell time Var(T i ).

[0081] E[Ti =α·β

[0082] Var(T i ) = α·β 2

[0083] Furthermore, due to the relatively conservative energy management strategies of some vehicle models, the working time at each steady state point is relatively long. When the duration continuously exceeds the time threshold T 停留阈值 such as 10 min, in the case of a fixed working condition spectrum time T 工况谱时间 such as 1 h, the long stay will occupy a relatively large proportion, thus compressing the distribution of other power points, resulting in the distortion of the working condition spectrum distribution and unable to fully reflect its dynamic characteristics. Therefore, it is necessary to perform a round of compression processing on the stay time to improve the dynamic characteristics of the working condition spectrum and optimize the test efficiency and simulation accuracy of the fuel cell system. The processing methods are as follows:

[0084] ① Quantitatively identify according to the above-mentioned operating state characteristic parameters α, β, E[T i , Var(T i ). For example, when E[T i >10 min, time compression needs to be prioritized.

[0085] ② After clarifying the characteristics of the processing object, the following three types of methods can be selected and are not limited to them for individual or combined processing according to the situation:

[0086] A. When the time distribution of all power points is relatively uniform, adopt the linear compression method:

[0087] Compress all stay times T i proportionally by a fixed ratio λ to obtain T i 压缩

[0088]

[0089] where

[0090] λ is the compression ratio, 0 < λ < 1

[0091] T 工况谱时间 is the target design duration of the working condition spectrum, such as 1 h.

[0092] T 原始时间 is the time selected for summarizing the operating conditions of the actual vehicle operation within a certain period of time in the target design of the working condition spectrum. For example, if the target design of the working condition spectrum is to fit and summarize the operating states of the fuel cell system of the vehicle model within a day (the actual operation is 8 h), then T 原始时间 = 8 h.

[0093] B. When the time distribution consistency of each power point is poor, such as the short duration of the high-power point and the long duration of the low-power point, the non-linear compression method is adopted, which retains the dynamics of the short-time stay points

[0094] and only adjusts the long-time stay points:

[0095]

[0096] C. Distribution adjustment method

[0097] The original residence time distribution is refitted into a compressed Gamma distribution, and time compression is achieved by adjusting the parameters of the Gamma distribution (such as the shape parameter α and the scale parameter β). This method has strong distribution continuity, and the characteristics of the compressed distribution are closer to the actual operating conditions.

[0098]

[0099] Ε[T i 压缩 = α'·β'

[0100] where

[0101] α′: The adjusted shape parameter, which controls the concentration degree of the distribution.

[0102] β′: The adjusted scale parameter, which controls the range of the distribution.

[0103] The adjustment of α′ and β′ can be carried out based on Ε[T i 压缩 .

[0104] 4. Through the above steps, when the ideal state transition probability matrix P and the residence time probability distribution function are obtained, the operating condition spectrum can be automatically generated based on this by adopting the random sampling method with the help of programming tools, reducing manual intervention and errors. The specific method is as follows:

[0105] ① Set the initial state: Set the initial state of the fuel cell system as S1, that is, 0 kW power, the total simulation time is T 工况谱时间 , the simulated time t 累计 = 0

[0106] ② State transition: Randomly generate the next power point S based on the state transition probability matrix P t+1 :

[0107] P(S(t + 1) = S j ∣S(t + 1) = S i ) = p ij

[0108] ③ Residence time generation: At the current state Si , randomly generate the residence time at the next power point based on the residence time distribution law and add the currently accumulated duration; generate the residence time T through the fitted or adjusted power point residence time distribution i

[0109]

[0110] Update the simulated time:

[0111] t 累计 = t 累计 + T i

[0112] ④ Loop the above steps ② and ③, and judge whether the accumulated duration is greater than the total duration of the working condition spectrum until t 累计 > T 工况谱时间 Realize state transition, that is, generate the residence step

[0113] ⑤ End, and the generation of the working condition spectrum is completed

[0114] The method of the present invention is a dynamic modeling of the working condition spectrum based on the state transition probability. The residence time at the power point is modeled and optimized based on the Gamma distribution. It is a random working condition spectrum generation method combining state transition and residence time distribution, and the residence time is dynamically optimized using a compression strategy, so as to generate a working condition spectrum that not only conforms to the actual dynamic characteristics but also can be flexibly adjusted according to requirements

Claims

1. A method for generating fuel cell operating conditions based on state transition probability, characterized in that: The following steps are included: Step 1: Collecting vehicle operation data, including the fuel cell system power output and the residence time of each power. The power output and the residence time of each power are used as the basic data for generating the operating spectrum; Step 2: Discretize the fuel cell power output and residence time into multiple intervals and define the corresponding power state and residence time. The multiple intervals are S = {S1, S2, S3, S4, ... S i ,...S j ,......}; Make judgment statistics on the power output curve in the original data, count the switching frequency between each interval, and construct the state transfer frequency matrix F; Step 3: normalize the state transfer frequency matrix F into the state transfer probability matrix P, which describes the switching rules between power points; statistically fit the residence time of each power point to obtain the residence time probability distribution function; Step 4: Use random sampling method to automatically generate the operating condition spectrum by programming tools using the state transition probability matrix P and the residence time probability distribution function.

2. The method for generating fuel cell operating conditions based on state transition probability as described in claim 1, characterized in that: In step 3, the fitting residence time is done using the Gamma distribution. Wherein, t represents the residence time of the fuel cell system at the power point Si; α>0: shape parameter, used to control the shape of the distribution; β>0: scale parameter, used to control the range of the distribution; Γ(α): Gamma function, which plays a normalization role to ensure that the Gamma distribution is a valid probability distribution function, defined as:

3. The method for generating fuel cell operating conditions based on state transition probability as described in claim 2, characterized in that: In step 2, when S = {S1, S2, S3, S4, S5, S6}, the state transition frequency matrix F is: where f ij Indicates that from state S i Transfer to state S j The number of times.

4. The method for generating fuel cell operating conditions based on state transition probability as described in claim 3, characterized in that: The state transition frequency matrix F is normalized to obtain the state transition probability matrix P: in:

5. The method for generating fuel cell operating conditions based on state transition probability as described in claim 4, characterized in that: Step 4 specifically includes the following processes: ① Set the initial state: Set the initial state of the fuel cell system to S1, i.e. 0kW power, and set the total simulation time to T 工况谱时间 , simulated time t 累计 =0; ②State transfer: Randomly generate the next power point S based on the state switching probability matrix P t+1 : P(S(t+1)=S j ∣S(t+1)=S i )=p ij ③Dwell time generation: In the current state S i , randomly generate the next power point residence time based on the residence time distribution law and add the current accumulated time; generate the residence time T through the fitted or adjusted power point residence time distribution i Update simulated time: t 累计 =t 累计 +T i ④ Loop through the above steps ②③ to determine whether the accumulated duration is greater than the total duration of the operating spectrum until t 累计 >T 工况谱时间 Realize state transfer, i.e., stop step generation; ⑤End, the operating condition spectrum is generated.

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