Hierarchical and domain-divided energy management method for hybrid power system of hydrogen energy high-speed train

By adopting a three-layer design architecture layered domain energy management method in the multi-source hybrid system of hydrogen-energy high-speed train, the system's response problems and high operating costs are solved under high power demand conditions, and the system's economy and stability are improved.

CN119975107APending Publication Date: 2025-05-13SOUTHWEST JIAOTONG UNIV +1
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Patent Information

Application Number
CN202510355099.5
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-03-25
Publication Date
2025-05-13

AI Technical Summary

Technical Problem

The multi-source hybrid system of hydrogen-energy high-speed trains is difficult to respond quickly under high power demand conditions, resulting in power oscillation and over-limit compensation of power batteries; at the same time, the system's operating costs are high, the energy management is complex, and the power source consistency is poor, which affects the economic and stability of the system.

Method used

A hierarchical domain energy management method using a three-layer design architecture includes a system-level dynamic power distribution layer, a domain-level power optimization layer and a module-level cost control layer. Through the construction of bargaining game algorithms, self-organized mapping neural networks and convex optimization problems, we can achieve layer-by-layer refined management of different types of power sources and performance conditions.

Benefits of technology

It effectively reduces the operating cost of the multi-source hybrid system, extends the service life of the power source, ensures the stability of the coordinated operation of the multi-power source, avoids power oscillation and power battery over-limit compensation, and improves the economic and durability of the system.

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Abstract

The invention discloses a hierarchical and domain-divided energy management method for a hybrid power system of a hydrogen energy high-speed train, and the method comprises the steps: constructing an operation cost game model between a fuel cell aggregation system and a power cell aggregation system through a system-level dynamic power distribution layer, adopting a bargaining game algorithm to obtain an aggregation system power distribution scheme by solving sub-game Nash equilibrium; the domain-level power optimization layer is used for dividing logic control domains according to operation characteristics and performance degradation conditions of power sources by adopting a self-organizing mapping neural network and an improved clustering structure identification algorithm which is determined by self-classification and is based on point sorting, and optimizing output reference power of different domains according to the overall performance of the domains; and the module-level cost control layer is used for constructing a convex optimization problem of optimal power among the modules by taking reduction of the operation cost as a target, so that optimal control of the module cost is realized. Economical and stable operation of the multi-source hybrid power system is effectively guaranteed, the service life of a power source is prolonged, and layer-by-layer fine management is achieved.
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Description

Technical Field

[0001] The present invention belongs to the technical field of hybrid power high-speed trains, and in particular relates to a hierarchical and domain-based energy management method for a hybrid power system of a hydrogen energy high-speed train. Background Art

[0002] As global rail transit develops towards cleaner and more efficient directions, hydrogen energy, as a clean, zero-carbon, pollution-free renewable energy source, has broad development prospects in the field of rail transit. Hydrogen-powered high-speed trains are a new type of green transportation tool. Compared with traditional catenary-powered trains, their operation does not rely on external power grids, reducing infrastructure construction and maintenance costs. At the same time, hydrogen-powered high-speed trains have strong adaptability and can be used on a variety of lines, especially in non-electrified line sections. As its core power architecture, the multi-source hybrid power system integrates multiple types of power sources such as fuel cell systems and power battery systems to achieve efficient energy utilization and dynamic distribution. At present, the multi-source hybrid power system of hydrogen-powered high-speed trains still has the following problems in practical applications that need to be optimized:

[0003] The control of large-scale fuel cells and power batteries is complex: Due to the high operating speed and high power demand of high-speed trains, multi-source hybrid power systems need to integrate a large number of fuel cell modules and power battery modules. Large-scale power source group control may cause the fuel cell to be unable to respond quickly to dynamic changes in power, resulting in over-limit compensation of the power battery and power oscillation. However, there is still little research on large-scale multi-source hybrid power systems.

[0004] Difficulty in optimizing operating costs: Multi-source hybrid power systems integrate a large number of power sources. Since the performance of the power sources is affected by many factors such as factory status, operating process, and environmental conditions, the output characteristics and performance status of each power source are different, resulting in a high-dimensional state space for energy management of the multi-source hybrid power system and complex solutions, which limits the system's operating economy and durability.

[0005] Poor consistency of multi-source hybrid power systems: fuel cell consistency mainly focuses on the consistency of performance degradation, and power battery consistency mainly focuses on the consistency of SOC. Excessive use of any sub-module in the fuel cell and power battery system or premature degradation of its life to the end will destroy the balance of the entire system, leading to system instability and affecting the safe operation of the system. Summary of the invention

[0006] In order to solve the above problems, the present invention proposes a layered and domained energy management method for a hybrid power system of a hydrogen-powered high-speed train, which can effectively ensure the economical operation of the multi-source hybrid power system, extend the service life of the power source, ensure the stability of the coordinated operation of multiple power sources, and realize layer-by-layer refined management of different types of power sources and different performance conditions.

[0007] To achieve the above-mentioned purpose, the technical solution adopted by the present invention is: a hierarchical and domain-based energy management method for a hybrid power system of a hydrogen-powered high-speed train, which adopts a three-layer design architecture including a system-level dynamic power allocation layer, a domain-level power optimization layer, and a module-level cost control layer, including the steps of:

[0008] S1, by means of the system-level dynamic power allocation layer, an operation cost game model between the fuel cell aggregation system and the power battery aggregation system is constructed, and a bargaining game algorithm is used to obtain the power allocation scheme of the aggregation system by solving the sub-game Nash equilibrium;

[0009] S2, after passing through the domain-level power optimization layer, the fuel cell system and the power battery system are divided into logical control domains according to their respective operating characteristics and performance degradation using a self-organizing map neural network combined with an improved self-classification-based point sorting clustering structure identification algorithm, and the output reference power of different domains is optimized according to the overall performance of the domains;

[0010] S3, finally, using the module-level cost control layer, a convex optimization problem of the optimal power between modules is constructed with the goal of reducing the operating cost, thus achieving optimal control of module cost.

[0011] Furthermore, in step S1, the system-level dynamic power allocation layer adopts a bargaining game to determine the power allocation between the fuel cell aggregation system and the power battery aggregation system, including the steps of:

[0012] S11, in an offline state before the system is operated, respectively establishing aggregation models of the fuel cell system and the power battery system according to the output characteristics and performance attenuation characteristics of the fuel cell and the power battery to characterize the overall performance of the system;

[0013] S12, taking the fuel cell aggregation system and the power battery aggregation system as the two parties in the bargaining game, the ultimate game goal of the two is to minimize the operating cost of their respective aggregation systems, and construct a system-level bargaining game model;

[0014] S13, initialize the cost increasing factors of different aggregation systems, take the current high-speed train demand power as the input of the bargaining game model, and the fuel cell and power battery aggregation systems obtain the optimal solutions of their respective games based on the principle of sub-game Nash equilibrium optimal solution on the basis of satisfying the power constraints, thereby realizing system-level power allocation.

[0015] Furthermore, in step S11, the fuel cell and power battery aggregation system model regards multiple internal modules as a whole to characterize the overall performance of the system;

[0016] For the fuel cell aggregation system, the efficiency and performance attenuation of the fuel cell aggregation system are the average values ​​of the internal modules, which is an average value model, and the expression formula is:

[0017]

[0018] Where n fc is the number of fuel cell modules in the fuel cell aggregation system; η fcs is the efficiency of the fuel cell aggregation system, and the output power P of the aggregation system fcs Size is related, satisfying P fcs =n fc ×P fci ; i is the fuel cell serial number; P fci is the output power of the i-th fuel cell module; D fcs is the performance attenuation degree of the fuel cell polymerization system, and the attenuation degree of each module in the polymerization system at a certain time t fci related;;

[0019] The output power and maximum and minimum power limits of the fuel cell aggregation system are sum value models, which are the sum of the corresponding values ​​of each internal module, and the expression formula is:

[0020]

[0021] Where P fcs,max and P fcs,min The maximum and minimum output power of the fuel cell aggregation system respectively; P fci,max and P fci,min are the maximum and minimum output powers of the i-th fuel cell module, respectively;

[0022] The efficiency, performance degradation, output power and maximum and minimum power limits of the power battery aggregation system are the same as those of the fuel cell; the SOC of the power battery aggregation system is an average value model, and the expression formula is:

[0023]

[0024] Where n bat SOC is the number of fuel cell modules in the power battery aggregation system; bats SOC for the power battery aggregation system; SOC bati is the SOC of the i-th power battery in the aggregation system.

[0025] Furthermore, in step S13, the two parties involved in the system-level bargaining game model are the fuel cell aggregation system and the power battery aggregation system. The game goal of each party is to reduce its own operating costs. The operating costs of the fuel cell and power battery aggregation systems are C fcs and Cbats , the cost increasing factors are δ fc and δ bat The game process between the fuel cell aggregation system and the power battery aggregation system is carried out using a three-stage bargaining model game, including:

[0026] Phase 1: The fuel cell aggregation system first proposes its own output power P fcs,1 According to the power demand constraint of the high-speed train, the power battery aggregation system can obtain its own output power P under this scheme. bats,1 , the operating costs of both parties in the game are [C fcs,1 C bats,1 ] indicates that the power battery aggregation system chooses to accept or reject the proposal. If it accepts, then the P fcs,1 and P bats,1 The output reference power of the fuel cell aggregation system and the power battery aggregation system; if rejected, enter the next stage;

[0027] Phase 2: Having rejected the previous proposal, the power battery aggregation system proposes its own solution P bats,2 , since the two parties have not reached an agreement, the game process will continue. In order to complete the game process, the cost of both parties will increase in this stage. At this time, the operating cost of both parties is [δ fc C fcs,2 δ bat C bats,2 ]; Similarly, the fuel cell aggregation system chooses to accept or reject the proposal. If it accepts, then P fcs,2 and P bats,2 The output reference power of the fuel cell aggregation system and the power battery aggregation system; if rejected, enter the next stage;

[0028] Phase 3: The fuel cell aggregation system continues to propose its own solution. Under this solution, the operating cost of both parties is [δ 2 fc C fcs,3 δ 2 bat C bats,3 ], if the power battery aggregation system continues to reject the proposal, the negotiation breaks down and the cost of both parties is set to [+∞+∞];

[0029] The backward induction method is used to find the subgame Nash equilibrium, and finally the reference power of the fuel cell and power battery aggregation system is obtained.

[0030] Furthermore, in step S2, the domain-level power optimization layer first divides the fuel cell system and the power battery aggregation system into logical control domains according to their respective operating characteristics and performance attenuation, and uses a self-organizing map neural network to learn the nonlinear characteristics of each power source to generate a low-dimensional, discrete mapping; the self-organizing map neural network is an unsupervised artificial neural network that uses a competitive learning strategy to achieve gradual optimization by relying on competition between neurons, and uses a neighbor relationship function to maintain the topological structure of the input space. A two-layer self-organizing map neural network consists of an input layer and a competition layer;

[0031] The fuel cell realizes nonlinear feature parameter extraction through a self-organizing map neural network, including the following steps:

[0032] S21, select the characteristic value of the fuel cell module, which consists of its efficiency, performance degradation, operating cost, output power and output power increment, expressed as x i =[ζ fci θ fci C fci P fci ΔP fci ]; The self-organizing map neural network model is recommended. Since the eigenvalue is a five-dimensional variable, the input layer of the fuel cell self-organizing map neural network is set to 5 neurons. The competition layer neurons are connected in a hexagonal plane structure, and the number is set to 5√N, where N is the number of training samples. Each neuron in the competition layer has a five-dimensional weight initialized to a very small random number, and w ij,k Represents, where ij represents the position of the neuron in the competition layer, and k represents the weight dimension of the neuron; determines the neighborhood radius function σ(t), and the neuron learning rate change function ρ(t);

[0033] S22, randomly select an input sample x from the training set i , the competition layer neurons calculate x according to their respective weights i The Euclidean distance between the nodes. The neuron with the smallest Euclidean distance has the highest similarity with the input sample and is the winning node;

[0034] S23, determining other neurons included in the winning neighborhood according to the neighborhood radius σ(t) at this time, and updating the weights of the neurons in the winning neighborhood according to the neuron learning rate function ρ(t) and the distance between the neuron and the winning node;

[0035] S24, repeating steps S22 and S23 until the learning rate of the neuron is less than the threshold value, and the self-organizing map neural network learning ends;

[0036] The training process of the power battery SOM neural network is the same as that of the fuel cell SOM neural network, but the characteristic value of the power battery is composed of its efficiency, performance degradation, SOC, operating cost and output power, which is expressed as x i =[ζ fci θ fci τ bati C bati P bati ].

[0037] Furthermore, in step S2, an improved self-classification-based point-sorting clustering structure identification algorithm is used to divide the trained self-organizing map neural network competition layer into category areas, including the steps of:

[0038] S25, extract the weights w of all neurons in the competition layer ij,k , establish the set D{11,12,13,…,ij}, Represent the remaining unchecked neurons, checked neurons, and the set of currently reachable neurons respectively. Randomly select a neuron and put it into O;

[0039] S26, select the first neuron in O, add it to R, and delete it from D and O; calculate the reachable distances from all neurons in D to this neuron, and sort the neurons in ascending order according to the reachable distances and add them to O;

[0040] S27, if there are still unchecked neurons in D at this time, repeat step S26 until D is an empty set, then go to step S28;

[0041] S28, using the silhouette coefficient as the evaluation criterion for the quality of the domain division results of the competition layer of the self-organizing map neural network, selecting an appropriate number of domain divisions μ to maximize the silhouette coefficient, then μ at this time is the optimal number of domain divisions for the competition layer neurons, at this time, the domain division network of the self-organizing map combined with the improved self-classification determined clustering structure identification algorithm based on point sorting is completed, and the real-time fuel cell data during operation is input into the fuel cell domain division network to realize the classification of fuel cells;

[0042] The process of determining the power battery domain network is the same as that of the fuel cell.

[0043] Furthermore, in step S2, after determining the domains of the fuel cell and the power battery, the domain-level power optimization layer optimizes the output reference power of different logic domains according to the overall performance of the domains;

[0044] For fuel cells, the cost optimization Lagrangian function between fuel cell domains is constructed:

[0045]

[0046] Where n fc is the number of fuel cells; f i (P fcsi ) is the output power of the i-th fuel cell, P fcsi The average power cost when fcs is the output reference power of the fuel cell system; λ is the Lagrange multiplier;

[0047] After solving, the reference power between each sub-domain of the fuel cell is obtained according to the following formula:

[0048]

[0049] The process of solving the reference power between the various domains of the power battery is the same as that of the fuel cell.

[0050] Furthermore, the module-level cost control layer aims to reduce operating costs, constructs a convex optimization problem for the optimal power between modules, and achieves optimal control of module costs. The cost of a single fuel cell module includes its hydrogen consumption cost and the performance attenuation cost of the fuel cell, which can be expressed as follows:

[0051]

[0052] In the formula, C fci,H2 is the hydrogen consumption cost of the fuel cell; C fci,loss The performance degradation cost of the fuel cell;

[0053] The hydrogen consumption of the fuel cell is obtained through data fitting. The performance degradation of the fuel cell is related to its four states: high power operation, low power operation, variable load operation and start-stop, which can be expressed as:

[0054]

[0055] In the formula, p H2 and p fc are the unit prices of hydrogen and fuel cells, respectively; s(P) is the hydrogen consumption function of the fuel cell, which is related to its output power; g(P,N,t) is the performance loss function of the fuel cell, which is related to its output power P, the number of starts and stops N, and the sampling time t of the control system;

[0056] The cost of a single power battery module includes its equivalent hydrogen consumption cost, the performance degradation cost of the power battery, and the SOC offset cost of the power battery. The expression formula is:

[0057]

[0058] In the formula, C bati,H2 is the equivalent hydrogen consumption cost of the power battery; C bati,loss is the performance degradation cost of the power battery; C bati,socThe SOC offset cost of the power battery;

[0059] The three costs of the above power batteries are expressed as:

[0060]

[0061] In the formula, p bat and p soc They represent the unit price of the power battery and the SOC loss coefficient respectively; α(P) is the hydrogen consumption function of the power battery, which is related to its output power; β(P) is the performance loss function of the power battery, which is related to its output power P. The greater the output power of the power battery, the greater the performance degradation, and P bati is the output power of the ith power battery module; γ(SOC) is the SOC loss function of the power battery. The purpose of this cost is to ensure that the SOC of the power battery does not deviate too much from the reference value to ensure that it can cope with the increased load power demand at any time. bati is the SOC of the i-th power battery module.

[0062] Furthermore, the operating cost of the fuel cell aggregation system, the power battery aggregation system and the sub-domain is the sum of the internal costs, which is expressed as follows:

[0063]

[0064] In the formula, C fcsk and C batsk are the operating costs of the fuel cell and power battery in the kth sub-domain, C fci and C bati are the operating costs of the i-th fuel cell and power battery module respectively; n fck is the number of fuel cell modules contained in the kth fuel cell sub-domain; n batk is the number of power battery modules contained in the kth power battery sub-domain; μ fc is the number of fuel cell domains, μ bat The number of power battery domains.

[0065] Furthermore, fuel cells and power batteries are subject to the following limitations during operation:

[0066]

[0067] Among them, P fci and P bati Represent the output power of the i-th fuel cell and power battery module respectively; P fci,min and P fci,max Respectively represent the minimum and maximum output power of the i-th fuel cell module; P bati,min and P bati,maxRespectively represent the minimum and maximum output power of the i-th power battery module; SOC bati represents the SOC of the i-th power battery module, SOC bati,min and SOC bati,max Respectively represent the minimum and maximum values ​​of the SOC range of the i-th power battery module; P load Indicates the required power of the system; n fc and n bat Represent the number of fuel cell modules and power battery modules respectively.

[0068] The beneficial effects of adopting this technical solution are:

[0069] The present invention discloses a hierarchical and domain-based energy management method for a multi-source hybrid power system for a hydrogen-powered high-speed train. The method has a three-layer design architecture. The system-level dynamic power allocation layer distinguishes between a fuel cell system and a power battery system in consideration of the operating characteristics of different types of power sources, so as to achieve differentiated management of different power sources. In the domain-level power optimization layer, a self-organizing map neural network is combined with an improved point-sorting-based clustering structure identification algorithm determined by self-classification to dynamically divide the logic control domains according to the real-time operating data of different types of power sources, so as to ensure that the characteristics of the modules in the domains are similar, and to allocate power with reference to the overall performance of different domains, which is conducive to avoiding the "short board effect" of the multi-source hybrid power system (such as premature failure of a module due to overload) and prolonging the overall life of the fuel cell and power battery system. In the module-level cost control layer, a convex optimization problem of the optimal power between modules is constructed with the goal of reducing the operating cost, which can effectively reduce the operating cost of each module during operation and improve the economy of the system operation.

[0070] The present invention provides a way to solve the shortcomings of traditional methods in large-scale multi-source hybrid systems, such as many variables to be solved, complex state space, difficult control, and difficulty in balancing system durability and economy. The large-scale multi-source hybrid system structure is divided into system level, domain level and module level through hierarchical and domain control, and the control scope of each level is gradually narrowed, the dimension of the state space is reduced, and the control is simplified. The present invention divides the domains in real time according to the performance of the power source, and performs fine control on power sources with different performances, avoiding general unified power distribution, and can adjust the load power in real time according to the domain performance distribution, effectively control the consistency of the performance of the same type of power sources, and ensure the economical and stable operation of the multi-source hybrid system. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 It is a schematic flow chart of a hierarchical and domain-based energy management method for a hybrid power system of a hydrogen-powered high-speed train according to the present invention;

[0072] Figure 2 Schematic diagram of the bargaining game process in step S1 of the present invention;

[0073] Figure 3 This is the structure of the self-organizing map neural network in step S2 of the present invention. DETAILED DESCRIPTION

[0074] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention is further described below with reference to the accompanying drawings.

[0075] In this embodiment, see Figure 1 As shown, the present invention proposes a hierarchical and domain-based energy management method for a hybrid power system of a hydrogen-powered high-speed train, which adopts a three-layer design architecture including a system-level dynamic power allocation layer, a domain-level power optimization layer, and a module-level cost control layer, including the following steps:

[0076] S1, by means of the system-level dynamic power allocation layer, an operation cost game model between the fuel cell aggregation system and the power battery aggregation system is constructed, and a bargaining game algorithm is used to obtain the power allocation scheme of the aggregation system by solving the sub-game Nash equilibrium;

[0077] S2, after passing through the domain-level power optimization layer, the fuel cell system and the power battery system are divided into logical control domains according to their respective operating characteristics and performance degradation using a self-organizing map neural network combined with an improved self-classification-based point sorting clustering structure identification algorithm, and the output reference power of different domains is optimized according to the overall performance of the domains;

[0078] S3, finally, using the module-level cost control layer, a convex optimization problem of the optimal power between modules is constructed with the goal of reducing the operating cost, thus achieving optimal control of module cost.

[0079] (1) System-level dynamic power allocation layer:

[0080] In step S1, the system-level dynamic power allocation layer adopts a bargaining game to determine the power allocation between the fuel cell aggregation system and the power battery aggregation system, including the steps of:

[0081] S11, in an offline state before the system is operated, respectively establishing aggregation models of the fuel cell system and the power battery system according to the output characteristics and performance attenuation characteristics of the fuel cell and the power battery to characterize the overall performance of the system;

[0082] S12, taking the fuel cell aggregation system and the power battery aggregation system as the two parties in the bargaining game, the ultimate game goal of the two is to minimize the operating cost of their respective aggregation systems, and construct a system-level bargaining game model;

[0083] S13, initialize the cost increasing factors of different aggregation systems, take the current high-speed train demand power as the input of the bargaining game model, and the fuel cell and power battery aggregation systems obtain the optimal solutions of their respective games based on the principle of sub-game Nash equilibrium optimal solution on the basis of satisfying the power constraints, thereby realizing system-level power allocation.

[0084] In step S11, in order to reduce the computational pressure of the system, it is necessary to establish an aggregate model that characterizes the overall situation of the system. The fuel cell and power battery aggregate system model regards multiple internal modules as a whole to characterize the overall performance of the system.

[0085] For the fuel cell aggregation system, the efficiency and performance attenuation of the fuel cell aggregation system are the average values ​​of the internal modules, which is an average value model, and the expression formula is:

[0086]

[0087] Where n fc is the number of fuel cell modules in the fuel cell aggregation system; η fcs is the efficiency of the fuel cell aggregation system, and the output power P of the aggregation system fcs Size is related, satisfying P fcs =n fc ×P fci ; i is the fuel cell serial number; P fci is the output power of the i-th fuel cell module; D fcs is the performance attenuation degree of the fuel cell polymerization system, and the attenuation degree of each module in the polymerization system at a certain time t fci related;

[0088] The output power and the maximum and minimum power limits of the fuel cell aggregation system are sum value models, which are the sum of the corresponding values ​​of each internal module, and the expression formula is:

[0089]

[0090] Where P fcs,max and P fcs,min The maximum and minimum output power of the fuel cell aggregation system respectively; P fci,max and P fci,min are the maximum and minimum output powers of the i-th fuel cell module, respectively.

[0091] The efficiency, performance degradation, output power and maximum and minimum power limits of the power battery aggregation system are the same as those of the fuel cell; the SOC of the power battery aggregation system is an average value model, and the expression formula is:

[0092]

[0093] Where n bat SOC is the number of fuel cell modules in the power battery aggregation system; bats SOC for the power battery aggregation system; SOC bati is the SOC of the i-th power battery in the aggregation system.

[0094] In step S13, the two parties involved in the system-level bargaining game model are the fuel cell aggregation system and the power battery aggregation system. The game goal of each party is to reduce its own operating costs. The operating costs of the fuel cell and power battery aggregation systems are C fcs and C bats , the cost increasing factors are δ fc and δ bat , the game process between the fuel cell aggregation system and the power battery aggregation system is carried out with a three-stage bargaining model game, such as Figure 2 As shown, including:

[0095] Phase 1: The fuel cell aggregation system first proposes its own output power P fcs,1 According to the power demand constraint of the high-speed train, the power battery aggregation system can obtain its own output power P under this scheme. bats,1 , the operating costs of both parties in the game are [C fcs,1 C bats,1 ] indicates that the power battery aggregation system chooses to accept or reject the proposal. If it accepts, then the P fcs,1 and P bats,1 The output reference power of the fuel cell aggregation system and the power battery aggregation system; if rejected, enter the next stage;

[0096] Phase 2: Having rejected the previous proposal, the power battery aggregation system proposes its own solution P bats,2 , since the two parties have not reached an agreement, the game process will continue. In order to complete the game process, the cost of both parties will increase in this stage. At this time, the operating cost of both parties is [δ fc C fcs,2 δ bat C bats,2 ]; Similarly, the fuel cell aggregation system chooses to accept or reject the proposal. If it accepts, then P fcs,2 and P bats,2 The output reference power of the fuel cell aggregation system and the power battery aggregation system; if rejected, enter the next stage;

[0097] Phase 3: The fuel cell aggregation system continues to propose its own solution. Under this solution, the operating cost of both parties is [δ 2 fc C fcs,3 δ 2 batC bats,3 ], if the power battery aggregation system continues to reject the proposal, the negotiations will break down and the costs for both parties will be set to [+∞+∞].

[0098] The backward induction method is used to find the subgame Nash equilibrium, and finally the reference power of the fuel cell and power battery aggregation system is obtained.

[0099] 1) In stage 3, the proposal put forward by the fuel cell aggregation system is expected to be accepted by the power battery aggregation system. Therefore, the operating cost of the power battery aggregation system should be less than the cost at the negotiation breakdown point. The proposal of the fuel cell aggregation system is most beneficial to itself, making its own operating cost as small as possible. At this time, the game process satisfies the following formula:

[0100]

[0101] Since the operating costs of fuel cells and power batteries are positively correlated with their output power, the output power P of the fuel cell aggregation system is fcs Should be as small as possible, the output power P of the fuel cell polymerization system fcs,3 =P d -P bats,max , the output power P of the power battery aggregation system bats,max , at this time the operating costs of the two are [δ 2 fc C fcs (P d -P bats,max )δ 2 bat C bats (P bats,max )]. (To simplify the formula, C fcs (P) and C bats (P) represents the operating cost of the fuel cell and power battery aggregation system when the output power is P).

[0102] 2) Reverse induction to stage 2, stage 2 is the power battery aggregation system proposes its own solution, so the solution proposed by the power battery aggregation system is the most beneficial to itself, making its own operating cost the smallest, but at the same time the power battery aggregation system hopes that the fuel cell aggregation system can accept this proposal, so the operating cost of the fuel cell aggregation system at this time should be smaller than the operating cost in stage 3. At this time, the game process satisfies the following formula:

[0103]

[0104] The condition that satisfies the above formula is C fcs,2 =δ fc C fcs (P d -P bats,max ), at this time Pfcs,2 =φ(P fcs ,C fcs, δ fc C fcs (P d -P bats,max )), P bats,2 =P d -P fcs,2 , C bats,2 =C bats (P bats,2 ), the operating cost of both parties is [δ 2 fc C fcs (P d -P bats,max )δ bat C bats (P d -φ(P fcs ,C fcs ,δ fc C fcs (P d -P bats,max )))].

[0105] 3) Reverse induction to stage 1, stage 1 is the fuel cell aggregation system proposes its own solution, so the solution proposed by the fuel cell aggregation system is the most beneficial to itself, making its own operating cost the smallest, but at the same time the fuel cell aggregation system hopes that the power battery aggregation system can accept this proposal, so the operating cost of the power battery aggregation system at this time should be smaller than the operating cost in stage 2. At this time, the game process satisfies the following formula:

[0106]

[0107] The condition that satisfies the above formula is C bats,1 =δ bat C bats (P d -φ(P fcs ,C fcs ,δ fc C fcs (P d -P bats,max ))), at this time P bats,1 =φ(P bats ,C bats ,δ bat C bats (P d -φ(P fcs ,C fcs ,δ fc C fcs (P d -P bats,max), the output power and operating cost of the fuel cell polymerization system are P fcs,1 =P d -P bats,1 and C fcs,1 =C fcs (P fcs,1 ).

[0108] Finally, the optimal solution of the subgame Nash equilibrium of the fuel cell aggregation system and the power battery aggregation system is:

[0109]

[0110] (2) Domain-level power optimization layer:

[0111] In step S2, the domain-level power optimization layer first divides the fuel cell system and the power battery aggregation system into logical control domains according to their respective operating characteristics and performance attenuation, and uses a self-organizing map neural network to learn the nonlinear characteristics of each power source to generate a low-dimensional, discrete mapping; the self-organizing map neural network is an unsupervised artificial neural network that uses a competitive learning strategy to achieve gradual optimization through competition between neurons, and uses a neighbor relationship function to maintain the topological structure of the input space. A two-layer self-organizing map neural network consists of an input layer and a competition layer.

[0112] The fuel cell realizes nonlinear feature parameter extraction through a self-organizing map neural network, including the following steps:

[0113] S21, select the characteristic value of the fuel cell module, which consists of its efficiency, performance degradation, operating cost, output power and output power increment, expressed as x i =[ζ fci θ fci C fci P fci ΔP fci ]; self-organizing map neural network model (such as Figure 3 As shown in Figure 2, since the eigenvalue is a five-dimensional variable, the input layer of the fuel cell self-organizing map neural network is set to 5 neurons. The competition layer neurons are connected in a hexagonal plane structure, and the number is set to 5√N, where N is the number of training samples. Each neuron in the competition layer has a five-dimensional weight initialized to a very small random number, and w is used to represent the weight of the competition layer. ij,k Represents, where ij represents the position of the neuron in the competition layer, and k represents the weight dimension of the neuron; determines the neighborhood radius function σ(t), and the neuron learning rate change function ρ(t);

[0114] S22, randomly select an input sample x from the training set i , the competition layer neurons calculate x according to their respective weights iThe Euclidean distance between the nodes. The neuron with the smallest Euclidean distance has the highest similarity with the input sample and is the winning node;

[0115] S23, determining other neurons included in the winning neighborhood according to the neighborhood radius σ(t) at this time, and updating the weights of the neurons in the winning neighborhood according to the neuron learning rate function ρ(t) and the distance between the neuron and the winning node;

[0116] S24, repeating steps S22 and S23 until the learning rate of the neuron is less than the threshold value, and the self-organizing map neural network learning ends;

[0117] The training process of the power battery SOM neural network is the same as that of the fuel cell SOM neural network, but the characteristic value of the power battery is composed of its efficiency, performance degradation, SOC, operating cost and output power, which is expressed as x i =[ζ fci θ fci τ bati C bati P bati ].

[0118] In step S2, the improved self-classification-based point-sorting clustering structure identification algorithm is used to divide the trained self-organizing map neural network competition layer into category areas. The traditional point-sorting-based clustering structure identification algorithm needs to further determine the number of clusters and the neighborhood radius manually, and the clustering result is greatly affected by subjective factors. The improved self-classification-based point-sorting clustering structure identification algorithm can automatically determine the optimal number of clusters, including the steps of:

[0119] S25, extract the weights w of all neurons in the competition layer ij,k , establish the set D{11,12,13,…,ij}, Represent the remaining unchecked neurons, checked neurons, and the set of currently reachable neurons respectively. Randomly select a neuron and put it into O;

[0120] S26, select the first neuron in O, add it to R, and delete it from D and O; calculate the reachable distance (i.e., Euclidean distance) from all neurons in D to this neuron, and sort the neurons in ascending order according to the reachable distance and add them to O;

[0121] S27, if there are still unchecked neurons in D at this time, repeat step S26 until D is an empty set, then go to step S28;

[0122] S28, using the silhouette coefficient as the evaluation criterion for the quality of the domain segmentation results of the competition layer of the self-organizing map neural network, select the appropriate number of domains μ to maximize the silhouette coefficient. Then μ at this time is the optimal number of domains for the competition layer neurons. At this time, the self-organizing map is combined with the improved self-classification to determine the domain segmentation network based on the point sorting clustering structure identification algorithm to complete the real-time fuel cell data during operation. Input the fuel cell domain segmentation network to realize the classification of fuel cells.

[0123] The process of determining the power battery domain network is the same as that of the fuel cell.

[0124] After the sub-domains are determined, the output reference powers of different logic domains are further optimized according to the overall performance of the logic domains.

[0125] For fuel cells, the cost optimization Lagrangian function between fuel cell domains is constructed:

[0126]

[0127] Where n fc is the number of fuel cells; f i (P fcsi ) is the output power of the i-th fuel cell, P fcsi The average power cost when fcs is the output reference power of the fuel cell system; λ is the Lagrange multiplier;

[0128] After solving, the reference power between each sub-domain of the fuel cell is obtained according to the following formula:

[0129]

[0130] The process of solving the reference power between the various domains of the power battery is the same as that of the fuel cell.

[0131] (3) Module-level cost control layer:

[0132] The module-level cost control layer aims to reduce operating costs, constructs a convex optimization problem for the optimal power between modules, and achieves optimal control of module costs. The cost of a single fuel cell module includes its hydrogen consumption cost and the performance attenuation cost of the fuel cell, which can be expressed as:

[0133]

[0134] In the formula, C fci,H2 is the hydrogen consumption cost of the fuel cell; C fci,loss The performance degradation cost of the fuel cell.

[0135] The hydrogen consumption of the fuel cell is obtained through data fitting. The performance degradation of the fuel cell is related to its four states: high power operation, low power operation, variable load operation and start-stop, which can be expressed as:

[0136]

[0137] In the formula, p H2 and p fc are the unit prices of hydrogen and fuel cell respectively; s(P) is the hydrogen consumption function of the fuel cell, which is related to its output power; g(P,N,t) is the performance loss function of the fuel cell, which is related to its output power P, the number of starts and stops N, and the sampling time t of the control system.

[0138] The cost of a single power battery module includes its equivalent hydrogen consumption cost, the performance degradation cost of the power battery, and the SOC offset cost of the power battery. The expression formula is:

[0139]

[0140] In the formula, C bati,H2 is the equivalent hydrogen consumption cost of the power battery; C bati,loss is the performance degradation cost of the power battery; C bati,soc is the SOC offset cost of the power battery.

[0141] The three costs of the above power batteries are expressed as:

[0142]

[0143] In the formula, p bat and p soc They represent the unit price of the power battery and the SOC loss coefficient respectively; α(P) is the hydrogen consumption function of the power battery, which is related to its output power; β(P) is the performance loss function of the power battery, which is related to its output power P. The greater the output power of the power battery, the greater the performance degradation, and P bati is the output power of the ith power battery module; γ(SOC) is the SOC loss function of the power battery. The purpose of this cost is to ensure that the SOC of the power battery does not deviate too much from the reference value to ensure that it can cope with the increased load power demand at any time. bati is the SOC of the i-th power battery module.

[0144] The operating cost of the fuel cell aggregation system, power battery aggregation system and sub-domain is the sum of the internal costs, expressed as follows:

[0145]

[0146] In the formula, C fcsk and C batsk are the operating costs of the fuel cell and power battery in the kth sub-domain, C fci and C batiare the operating costs of the i-th fuel cell and power battery module respectively; n fck is the number of fuel cell modules contained in the kth fuel cell sub-domain; n batk is the number of power battery modules contained in the kth power battery sub-domain; μ fc is the number of fuel cell domains, μ bat The number of power battery domains.

[0147] Finally, during operation, fuel cells and power batteries are subject to the following limitations:

[0148]

[0149] Among them, P fci and P bati Represent the output power of the i-th fuel cell and power battery module respectively; P fci,min and P fci,max Respectively represent the minimum and maximum output power of the i-th fuel cell module; P bati,min and P bati,max Respectively represent the minimum and maximum output power of the i-th power battery module; SOC bati represents the SOC of the i-th power battery module, SOC bati,min and SOC bati,max Respectively represent the minimum and maximum values ​​of the SOC range of the i-th power battery module; P load Indicates the required power of the system; n fc and n bat Represent the number of fuel cell modules and power battery modules respectively.

[0150] The invented layered and domain-based energy management method for multi-source hybrid power systems for hydrogen-driven high-speed trains can effectively ensure the economical operation of the multi-source hybrid power system, extend the service life of the power source, ensure the stability of the coordinated operation of multiple power sources, and realize layer-by-layer refined management of different types of power sources and different performance conditions.

[0151] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A hierarchical and domain-based energy management method for a hybrid power system of a hydrogen-powered high-speed train, characterized in that: The three-layer design architecture includes a system-level dynamic power allocation layer, a domain-level power optimization layer, and a module-level cost control layer, including the following steps: S1, by means of the system-level dynamic power allocation layer, an operation cost game model between the fuel cell aggregation system and the power battery aggregation system is constructed, and a bargaining game algorithm is used to obtain the power allocation scheme of the aggregation system by solving the sub-game Nash equilibrium; S2, after passing through the domain-level power optimization layer, the fuel cell system and the power battery system are divided into logical control domains according to their respective operating characteristics and performance degradation using a self-organizing map neural network combined with an improved self-classification-based point sorting clustering structure identification algorithm, and the output reference power of different domains is optimized according to the overall performance of the domains; S3, finally, using the module-level cost control layer, a convex optimization problem of the optimal power between modules is constructed with the goal of reducing the operating cost, thus achieving optimal control of module cost.

2. The hierarchical and domain-based energy management method for a hybrid power system of a hydrogen-powered high-speed train according to claim 1 is characterized in that: In step S1, the system-level dynamic power allocation layer adopts bargaining game to determine the power allocation between the fuel cell aggregation system and the power battery aggregation system, including the steps of: S11, in an offline state before the system is operated, respectively establishing aggregation models of the fuel cell system and the power battery system according to the output characteristics and performance attenuation characteristics of the fuel cell and the power battery to characterize the overall performance of the system; S12, taking the fuel cell aggregation system and the power battery aggregation system as the two parties in the bargaining game, the ultimate game goal of the two is to minimize the operating cost of their respective aggregation systems, and construct a system-level bargaining game model; S13, initialize the cost increasing factors of different aggregation systems, take the current high-speed train demand power as the input of the bargaining game model, and the fuel cell and power battery aggregation systems obtain the optimal solutions of their respective games based on the principle of sub-game Nash equilibrium optimal solution on the basis of satisfying the power constraints, thereby realizing system-level power allocation.

3. The hierarchical and domain-based energy management method for a hybrid power system of a hydrogen-powered high-speed train according to claim 2 is characterized in that: In the step S11, the fuel cell and power battery aggregation system model regards multiple internal modules as a whole to characterize the overall performance of the system; For the fuel cell aggregation system, the efficiency and performance attenuation of the fuel cell aggregation system are the average values ​​of the internal modules, which is an average value model, and the expression formula is: Where n fc is the number of fuel cell modules in the fuel cell aggregation system; η fcs is the efficiency of the fuel cell aggregation system, and the output power P of the aggregation system fcs Size is related, satisfying P fcs =n fc ×P fci ; i is the fuel cell serial number; P fci is the output power of the i-th fuel cell module; D fcs is the performance attenuation degree of the fuel cell polymerization system, and the attenuation degree of each module in the polymerization system at a certain time t fci related; The output power and the maximum and minimum power limits of the fuel cell aggregation system are sum value models, which are the sum of the corresponding values ​​of each internal module, and the expression formula is: Where P fcs,max and P fcs,min The maximum and minimum output power of the fuel cell aggregation system respectively; P fci,max and P fci,min are the maximum and minimum output powers of the i-th fuel cell module, respectively; The efficiency, performance degradation, output power and maximum and minimum power limits of the power battery aggregation system are the same as those of the fuel cell; the SOC of the power battery aggregation system is an average value model, and the expression formula is: Where n bat SOC is the number of fuel cell modules in the power battery aggregation system; bats SOC for the power battery aggregation system; SOC bati is the SOC of the i-th power battery in the aggregation system.

4. The method for hierarchical and domain-based energy management of a hybrid power system of a hydrogen-powered high-speed train according to claim 2 is characterized in that: In step S13, the two parties involved in the system-level bargaining game model are the fuel cell aggregation system and the power battery aggregation system. The game goal of each party is to reduce its own operating costs. The operating costs of the fuel cell and power battery aggregation systems are C fcs and C bats , the cost increasing factors are δ fc and δ bat The game process between the fuel cell aggregation system and the power battery aggregation system is carried out using a three-stage bargaining model game, including: Phase 1: The fuel cell aggregation system first proposes its own output power P fcs,1 According to the power demand constraint of the high-speed train, the power battery aggregation system can obtain its own output power P under this scheme. bats,1 , the operating costs of both parties in the game are [C fcs,1 C bats,1 ] indicates that the power battery aggregation system chooses to accept or reject the proposal. If it accepts, then the P fcs,1 and P bats,1 The output reference power of the fuel cell aggregation system and the power battery aggregation system; if rejected, enter the next stage; Phase 2: Having rejected the previous proposal, the power battery aggregation system proposes its own solution P bats,2 , since the two parties have not reached an agreement, the game process will continue. In order to complete the game process, the cost of both parties will increase in this stage. At this time, the operating cost of both parties is [δ fc C fcs,2 δ bat C bats,2 ]; Similarly, the fuel cell aggregation system chooses to accept or reject the proposal. If it accepts, then P fcs,2 and P bats,2 The output reference power of the fuel cell aggregation system and the power battery aggregation system; if rejected, enter the next stage; Phase 3: The fuel cell aggregation system continues to propose its own solution. Under this solution, the operating cost of both parties is [δ 2 fc C fcs,3 δ 2 bat C bats,3 ], if the power battery aggregation system continues to reject the proposal, the negotiation breaks down and the cost of both parties is set to [+∞+∞]; The backward induction method is used to find the subgame Nash equilibrium, and finally the reference power of the fuel cell and power battery aggregation system is obtained.

5. The hierarchical and domain-based energy management method for a hybrid power system of a hydrogen-powered high-speed train according to claim 1 is characterized in that: In step S2, the domain-level power optimization layer first divides the fuel cell system and the power battery aggregation system into logical control domains according to their respective operating characteristics and performance attenuation, and uses a self-organizing map neural network to learn the nonlinear characteristics of each power source to generate a low-dimensional, discrete mapping; the self-organizing map neural network is an unsupervised artificial neural network that uses a competitive learning strategy to achieve gradual optimization by relying on competition between neurons, and uses a neighbor relationship function to maintain the topological structure of the input space. A two-layer self-organizing map neural network consists of an input layer and a competition layer; The fuel cell realizes nonlinear feature parameter extraction through a self-organizing map neural network, including the following steps: S21, select the characteristic value of the fuel cell module, which consists of its efficiency, performance degradation, operating cost, output power and output power increment, expressed as x i =[ζ fci θ fci C fci P fci ΔP fci ]; The self-organizing map neural network model is recommended. Since the eigenvalue is a five-dimensional variable, the input layer of the fuel cell self-organizing map neural network is set to 5 neurons. The competition layer neurons are connected in a hexagonal plane structure, and the number is set to 5√N, where N is the number of training samples. Each neuron in the competition layer has a five-dimensional weight initialized to a very small random number, and w ij,k Represents, where ij represents the position of the neuron in the competition layer, and k represents the weight dimension of the neuron; determines the neighborhood radius function σ(t), and the neuron learning rate change function ρ(t); S22, randomly select an input sample x from the training set i , the competition layer neurons calculate x according to their respective weights i The Euclidean distance between the nodes. The neuron with the smallest Euclidean distance has the highest similarity with the input sample and is the winning node; S23, determining other neurons included in the winning neighborhood according to the neighborhood radius σ(t) at this time, and updating the weights of the neurons in the winning neighborhood according to the neuron learning rate function ρ(t) and the distance between the neuron and the winning node; S24, repeating steps S22 and S23 until the learning rate of the neuron is less than the threshold value, and the self-organizing map neural network learning ends; The training process of the power battery SOM neural network is the same as that of the fuel cell SOM neural network, but the characteristic value of the power battery is composed of its efficiency, performance degradation, SOC, operating cost and output power, which is expressed as x i =[ζ fci θ fci τ bati C bati P bati ].

6. The hierarchical and domain-based energy management method for a hybrid power system of a hydrogen-powered high-speed train according to claim 1 or 5, characterized in that: In step S2, an improved self-classification-based point-sorting clustering structure identification algorithm is used to divide the trained self-organizing map neural network competition layer into category areas, including the steps of: S25, extract the weights w of all neurons in the competition layer ij,k , establish the set D{11,12,13,…,ij}, Represent the remaining unchecked neurons, checked neurons, and the set of currently reachable neurons respectively. Randomly select a neuron and put it into O; S26, select the first neuron in O, add it to R, and delete it from D and O; calculate the reachable distances from all neurons in D to this neuron, and sort the neurons in ascending order according to the reachable distances and add them to O; S27, if there are still unchecked neurons in D at this time, repeat step S26 until D is an empty set, then go to step S28; S28, using the silhouette coefficient as the evaluation criterion for the quality of the domain division results of the competition layer of the self-organizing map neural network, selecting an appropriate number of domain divisions μ to maximize the silhouette coefficient, then μ at this time is the optimal number of domain divisions for the competition layer neurons, at this time, the domain division network of the self-organizing map combined with the improved self-classification determined clustering structure identification algorithm based on point sorting is completed, and the real-time fuel cell data during operation is input into the fuel cell domain division network to realize the classification of fuel cells; The process of determining the power battery domain network is the same as that of the fuel cell.

7. The method for hierarchical and domain-based energy management of a hybrid power system of a hydrogen-powered high-speed train according to claim 1, characterized in that: In step S2, after determining the domains of the fuel cell and the power battery, the domain-level power optimization layer optimizes the output reference power of different logic domains according to the overall performance of the domains; For fuel cells, the cost optimization Lagrangian function between fuel cell domains is constructed: Where n fc is the number of fuel cells; f i (P fcsi ) is the output power of the i-th fuel cell, P fcsi The average power cost when fcs is the output reference power of the fuel cell system; λ is the Lagrange multiplier; After solving, the reference power between each sub-domain of the fuel cell is obtained according to the following formula: The process of solving the reference power between the various domains of the power battery is the same as that of the fuel cell.

8. The method for hierarchical and domain-based energy management of a hybrid power system of a hydrogen-powered high-speed train according to claim 1, characterized in that: The module-level cost control layer aims to reduce operating costs, constructs a convex optimization problem for the optimal power between modules, and achieves optimal control of module costs. The cost of a single fuel cell module includes its hydrogen consumption cost and the performance attenuation cost of the fuel cell, which can be expressed as: C fci =C fci,H2 +C fci,loss ; In the formula, C fci,H2 is the hydrogen consumption cost of the fuel cell; C fci,loss The performance degradation cost of the fuel cell; The hydrogen consumption of the fuel cell is obtained through data fitting. The performance degradation of the fuel cell is related to its four states: high power operation, low power operation, variable load operation and start-stop, which can be expressed as: In the formula, p H2 and p fc are the unit prices of hydrogen and fuel cells, respectively; s(P) is the hydrogen consumption function of the fuel cell, which is related to its output power; g(P,N,t) is the performance loss function of the fuel cell, which is related to its output power P, the number of starts and stops N, and the sampling time t of the control system; The cost of a single power battery module includes its equivalent hydrogen consumption cost, the performance degradation cost of the power battery, and the SOC offset cost of the power battery. The expression formula is: In the formula, C bati,H2 is the equivalent hydrogen consumption cost of the power battery; C bati,loss is the performance degradation cost of the power battery; C bati,soc The SOC offset cost of the power battery; The three costs of the above power batteries are expressed as: In the formula, p bat and p soc They represent the unit price of the power battery and the SOC loss coefficient respectively; α(P) is the hydrogen consumption function of the power battery, which is related to its output power; β(P) is the performance loss function of the power battery, which is related to its output power P. The greater the output power of the power battery, the greater the performance degradation, and P bati is the output power of the ith power battery module; γ(SOC) is the SOC loss function of the power battery. The purpose of this cost is to ensure that the SOC of the power battery does not deviate too much from the reference value to ensure that it can cope with the increased load power demand at any time. bati is the SOC of the i-th power battery module.

9. The hierarchical and domain-based energy management method for a hybrid power system of a hydrogen-powered high-speed train according to claim 8, characterized in that: The operating cost of the fuel cell aggregation system, power battery aggregation system and sub-domain is the sum of the internal costs, expressed as follows: In the formula, C fcsk and C batsk are the operating costs of the fuel cell and power battery in the kth sub-domain, C fci and C bati are the operating costs of the i-th fuel cell and power battery module respectively; n fck is the number of fuel cell modules contained in the kth fuel cell sub-domain; n batk is the number of power battery modules contained in the kth power battery sub-domain; μ fc is the number of fuel cell domains, μ bat The number of power battery domains.

10. The method for hierarchical and domain-based energy management of a hybrid power system of a hydrogen-powered high-speed train according to claim 1, characterized in that: Fuel cells and power batteries are subject to the following limitations during operation: Among them, P fci and P bati Represent the output power of the i-th fuel cell and power battery module respectively; P fci,min and P fci,max Respectively represent the minimum and maximum output power of the i-th fuel cell module; P bati,min and P bati,max Respectively represent the minimum and maximum output power of the i-th power battery module; SOC bati represents the SOC of the i-th power battery module, SOC bati,min and SOC bati,max Respectively represent the minimum and maximum values ​​of the SOC range of the i-th power battery module; P load Indicates the required power of the system; n fc and n bat Represent the number of fuel cell modules and power battery modules respectively.