Hydrogen fuel hybrid system coordination energy management method for city area train

Abstract

The application discloses a kind of hydrogen fuel hybrid power system coordination energy management method for city area train, it is related to energy management method technical field.The method includes the following steps: by bayesian optimization algorithm, in combination with road condition, the initial value of coordination variable is optimized offline globally, and high-quality coordination variable initial value is obtained;Using Markov power prediction model, according to the real-time state of train and historical driving data, the future short-time power demand is predicted rolling;The optimized initial value of coordination variable is input into PMP online solver together with the predicted power demand information, to realize the real-time optimal control of power distribution of fuel cell and lithium battery in city area train hydrogen fuel hybrid power system.The method has the advantages of fast calculation speed, good robustness, strong instantaneous optimization capability and the like.

Description

Technical Field

[0001] This invention relates to the field of energy management methods, and in particular to a collaborative energy management method for a hydrogen fuel hybrid power system for urban rail transit. Background Technology

[0002] Traditional electric suburban trains require overhead contact lines for power supply, resulting in high maintenance and construction costs. Hydrogen fuel cell suburban trains, with their high efficiency, zero emissions, and flexible construction capabilities, are considered a significant development direction for new energy public transportation. Proton exchange membrane fuel cells, with their low operating temperature and high energy density, have already demonstrated enormous application potential in rail transit and other scenarios.

[0003] However, fuel cells suffer from slow dynamic response and low power density. In practical applications, they are often paired with lithium batteries / supercapacitors, which offer faster response and higher power density, to form a hybrid power system for trains. When multiple energy sources power the train, the energy flow becomes complex, necessitating the development of a reasonable Energy Management System (EMS) to ensure the rational allocation of energy during train operation. The main purpose of EMS research is to rationally allocate the instantaneous power of fuel cells and lithium batteries while meeting the train's power requirements, thereby simultaneously reducing hydrogen consumption and the lifespan degradation of critical components. Existing EMS systems can be categorized into three main types: rule-based, optimization-based, and learning-based.

[0004] Rule-based EMS achieves control through pre-defined condition judgments and execution strategies. Commonly used methods include wavelet transform, power follower algorithms, and fuzzy control algorithms. For example, Mazouzi, A. et al. proposed a comprehensive optimization method for EMS based on fuzzy control. Simulations show that this method can effectively improve the efficiency of fuel cells. The above methods are essentially heuristic algorithms, making it difficult to achieve global optimization under complex operating conditions. Learning-based EMS relies on historical data for model training and strategy generalization, such as EMS based on reinforcement learning, deep reinforcement learning (DRL), or neural networks. Reference [Park, Geunyoung, et al. "Development of a real-timelink-based predictive energy management strategy for extending FCEV lifespan using an experiment-driven degradation model." Applied Energy 397 (2025):126246] proposes a method integrating the advantages of model predictive control and deep reinforcement learning, reducing the operating cost of hybrid power systems by 2.13% compared to DRL alone. However, this type of method has high requirements for data quality and training stability, and its interpretability and online adaptability are often insufficient, which makes it difficult to promote in practical engineering applications.

[0005] Compared to the two methods mentioned above, optimization-based EMS, with its clear logical structure and ease of engineering deployment, has significant engineering application value in the field of hybrid power system energy management. Optimization-based EMS can be further subdivided into global optimization algorithms and instantaneous optimization algorithms. Classical global optimization algorithms include dynamic programming, particle swarm optimization, and genetic algorithms. For example, Lin et al. proposed a battery state of charge (SOC) trajectory optimization strategy based on dynamic programming. As a global optimization scheme, it aims to improve the economic performance of fuel cell hybrid electric vehicles under various driving conditions. Experimental results show that this strategy improves fuel economy by 7.39% compared to ECMS (Equivalent Hydrogen Consumption Strategy). Furthermore, it reduces fuel cell lifespan loss costs by 32.09%. While global optimization algorithms can obtain theoretically optimal solutions, they heavily rely on complete and accurate prior information, resulting in high computational complexity and making online application impossible. In contrast, instantaneous optimization algorithms have the advantage of not requiring prior knowledge of the entire process, enabling real-time online responses to changing road conditions and vehicle states, reducing computational load, and facilitating implementation in onboard controllers. The instantaneous optimization algorithm based on Pontryagin is one of the most classic instantaneous optimization algorithms. The literature [Song, Ke, et al. "Pontryagin's minimum principle-based real-time energy management strategy for fuel cell hybrid electric vehicle considering both fuel economy and power source durability." Energy 205 (2020): 118064] proposes a real-time and near-optimal EMS based on Pontryagin's Maximum Principle (PMP) to optimize the fuel economy and power source durability of the system. The results show a significant reduction in daily operating costs and a slight improvement in durability for fuel cells. Huangfu et al. proposed a real-time EMS based on an improved PMP to find a balance between fuel economy and durability in fuel cell hybrid systems. Comparison of this strategy with a finite state machine strategy revealed a 10.1% reduction in hydrogen consumption and stable battery SOC. All of the above schemes, based on optimal control theory, achieve synergistic optimization of multiple objectives, including fuel economy and power source durability, while ensuring real-time performance. However, the effectiveness of the PMP algorithm in engineering practice is limited by its inherent theoretical characteristics.On the one hand, the convergence speed and optimization accuracy of the algorithm are extremely sensitive to the initial values ​​of the costate variables, which are often difficult to set accurately in real-time applications, easily leading to slow convergence or getting trapped in local optima, thus restricting the real-time performance of the algorithm. On the other hand, PMP (Power Management Platform) is highly dependent on accurate knowledge of future operating conditions. If there is a lack of effective prediction or the prediction is biased, the decisions made based on the current moment will be difficult to truly coordinate the balance between hydrogen consumption and the state of charge (SOC) of the power battery throughout the entire operating cycle, resulting in an imbalance between the two, that is, the inability to achieve efficient and sustainable energy distribution between the hydrogen fuel cell and the power battery. Summary of the Invention

[0006] The technical problem to be solved by this invention is how to provide a collaborative energy management method for hydrogen fuel hybrid power systems for urban trains that has fast calculation speed, good robustness and strong instantaneous optimization capability.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a collaborative energy management method for a hydrogen fuel cell hybrid power system for urban rail transit, comprising the following steps:

[0008] Offline parameter optimization: Using the Bayesian optimization algorithm and road conditions, the initial values ​​of the costate variables are optimized offline globally to obtain the optimized initial values ​​of the costate variables;

[0009] Online short-term power forecasting: Using a Markov power forecasting model, rolling forecasts of future short-term power demand are made based on real-time train status and historical travel data.

[0010] Online real-time power allocation: The optimized initial values ​​of the costate variables and the predicted power demand information are input together into the PMP online solver to achieve real-time optimal control of the power allocation between the fuel cell and lithium battery in the urban train hydrogen fuel hybrid power system.

[0011] The beneficial effects of adopting the above technical solution are as follows: 1) The method combines the actual line information of train operation to realize offline adaptive tuning of key parameters of PMP algorithm, effectively overcomes the limitation of traditional initial value setting relying on experience, significantly shortens the online optimization time, and improves the real-time performance of the overall EMS.

[0012] 2) A power prediction model based on Markov chains was constructed. This model can predict the short-term power demand in the future based on the train operating conditions and historical train operating data, thereby providing a data basis for the optimization decision of PMP and improving the robustness of EMS in dealing with actual changing operating conditions.

[0013] 3) The above-mentioned offline hyperparameter optimization algorithm is deeply coupled with the online power prediction and allocation algorithm, which not only ensures the rapid convergence of the power allocation solution, but also enhances the system's adaptability to changing operating conditions, and finally realizes the optimal control of the hydrogen fuel cell urban train hybrid power system. Attached Figure Description

[0014] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0015] Figure 1 This is an overall flowchart of the method described in the embodiments of the present invention;

[0016] Figure 2 This is a train circuit topology diagram of hydrogen fuel cell hybrid power in this embodiment of the invention;

[0017] Figure 3 This is a fitting curve diagram of the traction and braking characteristics of urban trains in an embodiment of the present invention;

[0018] Figure 4 This is a diagram of the equivalent circuit model of the fuel cell in an embodiment of the present invention;

[0019] Figure 5 This is a comparison chart of fuel cell modeling and measured data in an embodiment of the present invention;

[0020] Figure 6 This is the equivalent circuit model of the lithium battery in the embodiments of the present invention;

[0021] Figure 7 This is a fitted surface plot of the equivalent hydrogen consumption rate of the lithium battery in an embodiment of the present invention;

[0022] Figure 8 This is a detailed flowchart of the method described in the embodiments of the present invention;

[0023] Figure 9 This is a flowchart of the initial value optimization process for costate variables based on BO in the method described in this embodiment of the invention;

[0024] Figure 10 This is a flowchart of the train power prediction process in the method described in the embodiments of the present invention. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0026] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0027] like Figure 1 As shown, this invention discloses a collaborative energy management method for a hydrogen fuel cell hybrid power system for urban rail transit, comprising the following steps:

[0028] Offline parameter optimization: Using the Bayesian optimization algorithm and road conditions, the initial values ​​of the costate variables are optimized offline globally to obtain the optimized initial values ​​of the costate variables;

[0029] Online short-term power forecasting: Using a Markov power forecasting model, rolling forecasts of future short-term power demand are made based on real-time train status and historical travel data.

[0030] Online real-time power allocation: The optimized initial values ​​of the costate variables and the predicted power demand information are input together into the PMP online solver to achieve real-time optimal control of the power allocation between the fuel cell and lithium battery in the urban train hydrogen fuel hybrid power system.

[0031] The above steps will be explained in detail below with specific methods.

[0032] Model of a hydrogen fuel cell hybrid power system for urban trains:

[0033] The topology of the hydrogen fuel cell hybrid urban rail transit circuit is as follows: Figure 2 As shown, it mainly includes a hybrid power system and a traction drive system.

[0034] The hydrogen fuel cell serves as the main power source, connected to the DC bus via a single-phase DC / DC boost converter. This converter adjusts its output current to meet the main power demand of the bus. To compensate for the poor dynamic response of the hydrogen fuel cell, a lithium battery is used as an auxiliary power source. It is connected to the DC bus via a bidirectional DC / DC converter. During sudden changes in power demand from urban trains, the high power density of the lithium battery allows for rapid charging and discharging to maintain the system's power balance.

[0035] 1) Urban Rail Traction Power Model

[0036] The method is based on the analysis of actual operation data of a certain type A urban rail train. It uses a fitting function to characterize the mathematical relationship between traction / braking force and speed, as shown in equation (1):

[0037] (1)

[0038] In the formula, The traction force of the train is expressed in kN. The braking force of the train is expressed in kN. Let be the train's speed, in km / h; a, b, c, d, and e are fitting coefficients, with values ​​of 169.4, 6788.5, 22.2, 177.2, and 13360.8 respectively. The traction and braking curves corresponding to this model are shown below. Figure 3 As shown.

[0039] Train running resistance mainly includes basic resistance and additional resistance. Additional resistance mainly includes gradient additional resistance and curve additional resistance. The formula for calculating the basic resistance of a train is shown in formula (2).

[0040] (2)

[0041] In the formula, f, h and k are the basic drag coefficients, which are taken as 5.6, 0.156 and 0.0028 respectively; M is the total mass of the EMU; and g is the acceleration due to gravity.

[0042] The total resistance experienced by the train during operation is shown in equation (3).

[0043] (3)

[0044] In the formula, i is the slope of the ramp in thousands of degrees, A is the experimental constant, which is taken as 700 in this application; and R is the radius of the curve.

[0045] According to Newton's second theorem, the dynamic balance equation of the train set during the train's operation is shown in equation (4), where the three equations correspond to the train's traction, inertia and braking conditions, respectively.

[0046] (4)

[0047] In the formula, The inertial mass coefficient of the train; This refers to the train's acceleration.

[0048] Ignoring system losses, the power calculation formula during train operation is shown in equation (5).

[0049] (5)

[0050] In the formula: The power of the following vehicles under traction conditions; The power of the following vehicles under coasting conditions; The following figures represent the power of the vehicle under braking conditions.

[0051] 2) Fuel cell model:

[0052] Based on the output characteristics of the fuel cell, the method establishes an equivalent circuit model of the fuel cell, such as... Figure 4 As shown.

[0053] in accordance with Figure 4 The circuit model can be represented by equation (6):

[0054] (6)

[0055] In the formula Open circuit voltage (V); This represents the number of cells connected in series in the fuel cell. denoted as Nernst potential under standard conditions; T is the operating temperature of the fuel cell; z is the number of electrons transferred per mole of reaction; F is the Faraday constant; R is the ideal gas constant. This refers to the hydrogen inlet pressure (bar). This refers to the oxygen intake pressure (bar). The activation overvoltage (V) of the fuel cell; The delay unit is used to simulate the response delay characteristics in the actual physical process of a fuel cell; N is the number of fuel cells; A is the Tafel slope; This represents the actual operating current (A) of the fuel cell; The current is the exchange current (A). The ohmic overvoltage (V) of the fuel cell; The internal resistance (Ω) of the fuel cell; This refers to the output voltage (V) of the fuel cell. and , , There is a relationship (7) among the three:

[0056] (7)

[0057] The functional relationship between the hydrogen consumption rate and the output power of a fuel cell is shown in equation (8):

[0058] (8)

[0059] In the formula, The hydrogen consumption rate of the fuel cell is expressed in g / s. This is the output voltage of the fuel cell, measured in volts (V). is the Faraday constant, taken as 96485 C / mol; For the transfer efficiency of the DC / DC converter; The molar mass of hydrogen is 2.02 g / mol. The output power of the fuel cell is expressed in kW. A simplified model of the hydrogen consumption rate of the fuel cell system was obtained by polynomial fitting of the measured hydrogen consumption data, as shown in equation (9):

[0060] (9)

[0061] In the formula, , and These are the polynomial fitting coefficients.

[0062] To verify the correctness of the established model, the actual data and the fitted curve were compared, and the specific results are as follows: Figure 5 As shown.

[0063] 3) Lithium battery model:

[0064] This application uses the RINT model of lithium battery for analysis, and the mathematical relationship between its current, internal resistance and output voltage is shown in Equation (10).

[0065] The method uses the RINT model of a lithium battery as the simulation model for the lithium battery, and its equivalent circuit diagram is as follows: Figure 6 As shown.

[0066] according to Figure 6 The mathematical relationships between the lithium battery current, internal resistance and output voltage are listed, as shown in equation (10).

[0067] (10)

[0068] In the formula, This refers to the current of the lithium battery. This is the open-circuit voltage of the lithium battery; This represents the internal resistance of the lithium battery. This refers to the output power of the lithium battery. This indicates the current state of charge of the lithium battery; This indicates the initial state of charge of the lithium battery; This is the maximum capacity of the lithium battery.

[0069] The expression for the charge and discharge efficiency of a lithium battery is shown in equation (11).

[0070] (11)

[0071] In the formula, This indicates the discharge efficiency of the lithium battery; This indicates the charging efficiency of the lithium battery.

[0072] The equivalent hydrogen consumption rate of lithium batteries is shown in equation (12).

[0073] (12)

[0074] In the formula, This represents the equivalent hydrogen consumption rate of a lithium battery. The average hydrogen consumption rate of the fuel cell; The average charging efficiency of lithium batteries; This represents the average discharge efficiency of the lithium battery. The average output power of the lithium battery is represented by the corresponding three-dimensional surface plot of this model, as shown below. Figure 7 As shown.

[0075] The method consists of three stages: offline parameter optimization, online short-term power prediction, and online real-time power allocation. The architecture diagrams for each stage are shown below. Figure 8 As shown. The offline parameter optimization stage is based on the Bayesian optimization algorithm and uses rolling solutions of costate variables by fusing line parameters; the online short-term power prediction stage establishes a Markov chain model using historical data to predict power demand at the second level online; the online real-time power allocation stage combines the outputs of the above two stages and allocates the power of fuel cells and lithium batteries in real time based on the Pontryagin minimum principle.

[0076] 1) Offline parameter optimization stage

[0077] When applying PMP to solve the power allocation of hybrid trains online, the initial values ​​of the costate variables have a significant impact on the solution efficiency and results. Traditional methods such as the shooting method rely on experience and are prone to getting trapped in local optima. Therefore, the proposed method uses Bayesian optimization (BO) to first optimize the initial values ​​of the costate variables offline and constructs the cost function shown in equation (13).

[0078] (13)

[0079] In the formula, Indicated by The total system cost obtained by solving the PMP with initial values ​​for the costate variables; L is the instantaneous cost function; For system state variables; For system control variables; For the terminal cost function; Let T be the value of the system state variable at the terminal time.

[0080] Initial values ​​of costate variables during the solution process Unknown, and the cost function J is related to The specific analytical expression is difficult to obtain, the evaluation cost is high, and it may also have complex characteristics such as multi-peak and non-convexity. Therefore, the problem form is optimized as shown in equation (14):

[0081] (14)

[0082] In the formula, This indicates that the objective function The initial value of the costate variable that achieves its minimum value on the constraint set x is the optimal solution to the optimization problem. Since... To evaluate costly black-box functions, Bayesian optimization is a suitable approach. Perform hyperparameter optimization.

[0083] The optimization process begins by constructing an initial set of observation points and employing a Gaussian Process (GP) as a probabilistic surrogate model. In Gaussian process modeling, the hypothesis function follows the prior distribution:

[0084] (15)

[0085] In the formula It is a mean function. Let be the covariance function.

[0086] Then, based on the GP, a posterior distribution is calculated. The next evaluation point is determined by maximizing the acquisition function, and the cost function value of that point is calculated. If it is better than the current optimal solution, an update is performed. The acquisition function used in this method is the expected improvement acquisition function, which is defined as shown in equation (16).

[0087] (16)

[0088] In the formula, Represents the initial value of the current optimal costate variable. The corresponding optimal objective function value.

[0089] Finally, using new data points ( , Update the surrogate model. Repeat the above process until the preset convergence condition is met. Finally, the initial values ​​of the costate variables that minimize the total cost of PMP online solution can be obtained. The specific process of this method is as follows: Figure 9 As shown.

[0090] 2) Online short-term power prediction stage

[0091] During actual vehicle operation, the changing operating conditions exhibit Markov characteristics, which can be used to predict the power output of urban rail trains. Power prediction provides forward-looking information for subsequent online power allocation by power management systems (PMPs), thereby improving the response speed and optimization effectiveness of real-time power allocation.

[0092] Therefore, the method divides the train operation into four typical conditions: acceleration traction, constant speed traction, constant speed coasting, and deceleration braking. When the train speed is within ±2 km / h of the target value, it can be considered as a constant speed operation. In this state, the train is actually alternating between traction and coasting. Therefore, the constant speed condition can be further divided into constant speed traction and constant speed coasting. The correspondence between each condition and parameters such as required power, speed, and acceleration is shown in Table 1.

[0093] Table 1: Classification of Operating Conditions for Power Prediction of Urban Trains

[0094]

[0095] Based on the above division and combined with historical driving data, a Markov prediction model corresponding to each operating condition is established. The specific process is as follows.

[0096] Assuming that under the given operating condition m, the train power demand at time k is... After l-step state transition, the power demand changes from Convert to The probability is Its mathematical definition is shown in equation (17).

[0097] (17)

[0098] To estimate the transition probability, power demand needs to be treated as a state variable, and statistics should be performed based on the transition frequency between states. The probability values ​​should be calculated using the maximum likelihood estimation method shown in equation (18).

[0099] (18)

[0100] In the formula, This indicates that under operating condition m, the power demand is divided into N states. This indicates that the power output under this operating condition is from... arrive The transition probability, Indicates power from arrive Number of times, Representing state Total number of times generated.

[0101] By statistically analyzing the transition probabilities between all states, a complete transition probability matrix as shown in equation (19) can be constructed. .

[0102] (19)

[0103] In the formula, the matrix This characterizes the stochastic transfer process of power demand between different states under operating condition m.

[0104] Based on the transition probability matrix constructed above, a Markov chain power prediction model was established. The prediction process is as follows: Figure 10 As shown in Table 1, the operating condition type at time k is first determined, and then the corresponding transition probability matrix is ​​called to recursively generate the power demand state probability distribution sequence from time k+1 to k+lmax, where lmax is the preset maximum prediction step size. At each step, the power corresponding to the maximum probability value is used as the predicted value, and multi-step power prediction is achieved through progressive recursion.

[0105] 3) Online real-time power allocation stage

[0106] The method described above performs real-time power allocation to the system based on an equivalent hydrogen consumption minimization strategy. Traditional PMP (Power Management Platform) suffers from insufficient online dynamic adaptability due to the reliance on empirically set initial values ​​for costate variables and the lack of forward-looking analysis of operating conditions. To address this, this application constructs an adaptive PMP framework by offline determination of initial values ​​for costate variables through Bayesian optimization and online prediction of power demand using Markov chains, thereby significantly improving the decision-making response speed of the system under dynamic operating conditions.

[0107] The method first constructs the system's objective function J, which is to minimize the train's equivalent hydrogen consumption within a single control cycle. Its mathematical expression is:

[0108] (20)

[0109] In the formula, t is the time variable; state variable State of charge (SOC) of the lithium battery; control variables For the output power of the system's fuel cell and lithium battery, The instantaneous equivalent hydrogen consumption rate of the train is calculated using the method shown in equation (21).

[0110] (twenty one)

[0111] In the formula, This represents the equivalent hydrogen consumption rate of the fuel cell. The equivalent hydrogen consumption rate of the lithium battery is given by equations (9) and (12).

[0112] With the lithium battery SOC as the state variable, the system's state equation is:

[0113] (twenty two)

[0114] In the formula, The specific calculation method for the current flowing through the lithium battery is shown in equation (10). This refers to the rated capacity of the lithium battery.

[0115] According to the PMP solution principle, a Hamiltonian function needs to be constructed. In this system, the Hamiltonian function is:

[0116] (twenty three)

[0117] In the formula, Costate variables are also called Lagrange multipliers.

[0118] The dynamic process of costate variables can be described by canonical equations, which follow differential equations.

[0119] (25)

[0120] In practical applications, it operates within a discrete system; therefore, the iterative process of the costate variables follows the following rules:

[0121] (26)

[0122] In the formula, Indicates the step size of the algorithm execution; Let be the costate variable corresponding to the k-th step of the algorithm, and let be the costate variable corresponding to the 0th step. These are the initial values ​​for the costate variables.

[0123] The selection of directly affects the quality of the optimized control effect. The method takes the minimum hydrogen consumption under all operating conditions as the control objective, and determines the optimal value of the costate variable by optimizing the initial value of BO, as shown in equation (27):

[0124] (27)

[0125] The optimal power allocation of the system in each control cycle can be obtained by finding the minimum value of equation (23).

[0126] (28)

[0127] In the formula, R is the allowable set of the control variables, which is composed of the following constraint (29).

[0128] (29)

[0129] In the formula, This is the k-th step prediction value output during the power prediction stage. and This corresponds to the optimal power allocation values ​​for the fuel cell and lithium battery.

[0130] In summary, to verify the effectiveness of the proposed method and conduct in-depth experiments, a hydrogen fuel cell hybrid power system model for urban trains was first established, incorporating a traction power model, a fuel cell model, and a lithium battery model. Based on the established model, the strategy obtains the initial values ​​of the optimal costate variables offline through Bayesian optimization, and combines this with a Markov chain model to predict short-term power demand online. Subsequently, rapid power allocation is achieved based on PMP (Power Management Model), ultimately effectively improving the dynamic performance and adaptability of the system.

[0131] The proposed method was compared with other commonly used energy management strategies under different train operating conditions. Comparative experimental data revealed that the proposed algorithm has significant advantages in the following aspects: 1) The introduction of offline Bayesian optimization fundamentally ensures the real-time performance of the algorithm. Under typical operating conditions, the proposed strategy reduces the time taken by 19.6% and 64.8% compared to the Power Following (PF) strategy and the ECMS strategy, respectively. 2) The online power prediction model based on Markov chains effectively enhances the system's adaptability to different operating conditions. Comparative experiments under typical and atypical operating conditions show that the proposed algorithm outperforms PF and ECMS in terms of running time, DC bus voltage stability, and SOC maintenance, demonstrating stronger robustness. 3) The proposed strategy possesses good instantaneous optimization capabilities. Compared to ECMS, its equivalent hydrogen consumption is reduced by 2.06% and 4.02% under typical and atypical operating conditions, respectively.

[0132] Although the above embodiments have been described, those skilled in the art, once they understand the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the above descriptions are merely embodiments of the present invention and do not limit the scope of patent protection of the present invention. Any equivalent structural or procedural transformations made using the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of the present invention.

Claims

1. A method for collaborative energy management of a hydrogen fuel cell hybrid power system for urban rail transit, characterized in that... Includes the following steps: Offline parameter optimization: Using the Bayesian optimization algorithm and road conditions, the initial values ​​of the costate variables are optimized offline globally to obtain the optimized initial values ​​of the costate variables; Online short-term power forecasting: Using a Markov power forecasting model, rolling forecasts of future short-term power demand are made based on real-time train status and historical travel data. Online real-time power allocation: The optimized initial values ​​of the costate variables and the predicted power demand information are input together into the PMP online solver to achieve real-time optimal control of the power allocation between the fuel cell and lithium battery in the urban train hydrogen fuel hybrid power system.

2. The method for coordinated energy management of a hydrogen fuel cell hybrid power system for urban rail transit as described in claim 1, characterized in that: The road conditions include road curve radius, gradient, and speed limit.

3. The collaborative energy management method for a hydrogen fuel cell hybrid power system for urban rail transit as described in claim 1, characterized in that: Bayesian optimization is used to first perform offline optimization of the initial values ​​of the costate variables, and the cost function is constructed as shown in the following equation: ； In the formula, Represents the initial values ​​of costate variables The total system cost is obtained by solving the PMP; L is the instantaneous cost function; For system state variables; For system control variables; For the terminal cost function; The value of the system state variable at the terminal time T; The problem can be optimized as follows: ； In the formula, This indicates that the objective function The initial values ​​of the corresponding costate variables that achieve the minimum value on the constraint set x are used to apply Bayesian optimization. Perform hyperparameter optimization; During optimization, an initial set of observation points is first constructed, and a Gaussian process is used as the probabilistic surrogate model. In the Gaussian process modeling, the function is assumed to follow the following prior distribution: ； In the formula It is a mean function. It is the covariance function; Then, based on the GP, a posterior distribution is calculated. The next evaluation point is determined by maximizing the acquisition function, and the cost function value at that point is calculated. If it is better than the current optimal solution, an update is performed. The acquisition function is the expected improvement acquisition function, which is defined as follows: ； In the formula, Represents the initial value of the current optimal costate variable. The corresponding optimal objective function value; Finally, using new data points ( , Update the surrogate model and repeat the above process until the preset convergence condition is met, finally obtaining the initial values ​​of the costate variables that minimize the total cost of PMP online solution. .

4. The method for coordinated energy management of a hydrogen fuel cell hybrid power system for urban rail transit as described in claim 1, characterized in that: The real-time status of the train includes acceleration traction, constant speed traction, constant speed coasting, and deceleration braking.

5. The method for coordinated energy management of a hydrogen fuel cell hybrid power system for urban rail transit as described in claim 4, characterized in that, The construction method of Markov prediction models includes the following steps: Let P be the train power demand at time k under the given operating condition m. i After l-step state transition, the power demand changes from P i Convert to P j The probability is Its mathematical definition is shown in the following formula: ； In the formula, This represents the power demand at time k under the given operating condition m. This represents the power demand after l-step state transitions under the same operating condition m. Power demand is treated as a state variable, and statistics are performed based on the frequency of transitions between states. The probability values ​​are then calculated using the maximum likelihood estimation method shown in the following equation: ； In the formula, This indicates that under operating condition m, the power demand is divided into N states. This indicates that the power output under this operating condition is from... arrive The transition probability, Indicates power from arrive Number of times, Representing state Total number of times generated; By statistically analyzing the transition probabilities between all states, a complete transition probability matrix is ​​constructed. : ； In the formula, the matrix The stochastic transition process of power demand between different states under operating condition m is characterized, and a Markov chain power prediction model is established based on the transition probability matrix constructed above.

6. The method for coordinated energy management of a hydrogen fuel cell hybrid power system for urban rail transit as described in claim 5, characterized in that, The method for rolling forecasting of future short-term power demand includes the following steps: First, the operating condition type at time k is determined based on the set acceleration and velocity values. Then, the corresponding transition probability matrix is ​​called to recursively generate k+1 to k+l. max The sequence of power demand state probability distributions at time t, where l max The maximum prediction step size is preset, and the power corresponding to the maximum probability value is used as the prediction value for each step. Multi-step power prediction is achieved by iteratively calculating the power step size.

7. The method for coordinated energy management of a hydrogen fuel cell hybrid power system for urban rail transit as described in claim 5, characterized in that, The method for online real-time power allocation includes the following steps: First, we construct the objective function J of the system, which is to minimize the equivalent hydrogen consumption of the train within a single control cycle. Its mathematical expression is: ； In the formula, t is the time variable; state variable State of charge (SOC) of the lithium battery; control variables For the output power of the system's fuel cell and lithium battery, The instantaneous equivalent hydrogen consumption rate during train operation is calculated using the following formula: ； In the formula, This represents the equivalent hydrogen consumption rate of the fuel cell. This represents the equivalent hydrogen consumption rate of a lithium battery. With the lithium battery SOC as the state variable, the system's state equation is: ； In the formula, The current flowing through the lithium battery, This refers to the rated capacity of the lithium battery. According to the PMP solution principle, a Hamiltonian function needs to be constructed. In this system, the Hamiltonian function is: ； In the formula, x is the system state variable; u is the system control variable; Costate variables are also called Lagrange multipliers; t represents time; This represents the equivalent hydrogen consumption rate of a fuel cell. This indicates the equivalent hydrogen consumption rate of a lithium battery. The dynamic process of costate variables can be described by canonical equations, which follow differential equations: ； The iterative process of costate variables follows the following rules: ； In the formula, Indicates the step size of the algorithm execution; Let be the costate variable corresponding to the k-th step of the algorithm, and let be the costate variable corresponding to the 0th step. Initial values ​​for costate variables; With the goal of minimizing hydrogen consumption across all operating conditions, the optimal values ​​of the costate variables are determined by optimizing the initial values ​​of the BO variables. ； The optimal power allocation of the system in each control cycle is obtained by finding the minimum value of the Hamiltonian function; ； In the formula, R is the tolerance set of the control variables, which is composed of the following constraints: ； In the formula, This is the k-th step prediction value output during the power prediction stage. and This corresponds to the optimal power allocation values ​​for the fuel cell and lithium battery; This indicates the minimum power output allowed by the fuel cell; This indicates the maximum power that the fuel cell is allowed to output; This indicates the minimum power that a lithium battery is allowed to output. This indicates the maximum power that the lithium battery is allowed to output; and These represent the upper and lower limits of the state of charge (SOC) constraints for lithium batteries, respectively.

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